Document [original]

Photoelectron Circular Dichroism of

Anionic Chiral Metal Complexes and

Deprotonated Molecules

vorgelegt von

M.Sc.

Jenny Triptow

ORCID:0000-0002-4048-3348

an der Fakult¨at II - Mathematik und Naturwissenschaften

der Technischen Universit¨at Berlin

zur Erlangung des akademischen Grades

Doktor*in der Naturwissenschaften

- Dr. rer. nat. -

genehmigte Dissertation

Promotionsausschuss:

Vorsitzender: Prof. Dr. Mario D¨ahne

Gutachter: Prof. Dr. Otto Dopfer

Gutachter: Prof. Dr. Melanie Schnell

Tag der wissenschaftlichen Aussprache: 20.11.2023

Berlin 2024

Contents

1. Introduction 1

1.1. Chirality.................................... 1

1.2. PECD in the Ionization of Neutral Molecules . . . . . . . . . . . . . . . . 2

1.3. PECD in Photodetachment or Anion PECD . . . . . . . . . . . . . . . . 8

1.4. Outlineofthisthesis ............................. 9

2. Scientific Background 11

2.1. MolecularStructures ............................. 11

2.2. Anion Photoelectron Spectroscopy . . . . . . . . . . . . . . . . . . . . . . 12

2.2.1. Selection Rules and Transition Probabilities in Photoelectron De-

tachment ............................... 13

2.2.2. Photoelectron Angular Distribution . . . . . . . . . . . . . . . . . 17

2.3. Enantiomers and Circular Polarized Light . . . . . . . . . . . . . . . . . 22

2.3.1. Nomenclature of Enantiomers . . . . . . . . . . . . . . . . . . . . 22

2.3.2. Light polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3. Experimental and Computational Methods 25

3.1. ChiralAnions................................. 25

3.1.1. Properties for Anions and Molecules . . . . . . . . . . . . . . . . 25

3.1.2. Creation of Anionic Chiral Systems . . . . . . . . . . . . . . . . . 28

3.2. Setup and Data Treatment . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.2.1. Production of Anionic Chiral Systems . . . . . . . . . . . . . . . . 34

3.2.2. Linear Time-of-Flight Mass Spectrometer (ToF-MS) . . . . . . . . 45

3.2.3. Velocity Map Imaging (VMI) . . . . . . . . . . . . . . . . . . . . 49

3.2.4. Laser System and Polarization Techniques . . . . . . . . . . . . . 72

3.2.5. Ascertaining a Single Photon Process and its Effectivness . . . . . 78

3.2.6. DataHandling ............................ 81

3.3. Density Functional Theory . . . . . . . . . . . . . . . . . . . . . . . . . . 97

3.3.1. Functionals .............................. 99

3.3.2. BasisSets ...............................100

3.3.3. Energies................................101

3.3.4. Choice of Functional and Basis Set . . . . . . . . . . . . . . . . . 103

4. Gold Complexes of Chiral Molecules 105

4.1. Introduction and Motivation . . . . . . . . . . . . . . . . . . . . . . . . . 105

4.2. MassSpectra .................................107

Contents

4.3. Photodetachment of Gold Complexes with Linear Polarized Light . . . . 109

4.3.1. Photoelectron Spectra . . . . . . . . . . . . . . . . . . . . . . . . 109

4.3.2. BetaParameter............................115

4.4. Computational Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

4.4.1. Calculated Structures of Gold Complexes . . . . . . . . . . . . . . 116

4.4.2. Calculated Energies of Gold Complexes . . . . . . . . . . . . . . . 132

4.4.3. BondCharacter............................140

4.5. Experiment vs Computational Results . . . . . . . . . . . . . . . . . . . 146

4.5.1. Peak X and Blue Shift . . . . . . . . . . . . . . . . . . . . . . . . 146

4.5.2. The Peak νXin Au−-3HTHF and Au−-Ala.............148

4.5.3. Peak A and Molecular Orbitals . . . . . . . . . . . . . . . . . . . 148

4.6. Photoelectron Circular Dichroism . . . . . . . . . . . . . . . . . . . . . . 152

4.7. Summary for Gold Complexes . . . . . . . . . . . . . . . . . . . . . . . . 159

5. Deprotonated Chiral Species 161

5.1. MassSpectra .................................162

5.2. Computational Considerations . . . . . . . . . . . . . . . . . . . . . . . . 164

5.2.1. Isomers ................................164

5.2.2. Tautomers...............................166

5.2.3. Orbitals ................................167

5.2.4. Calculated Detachment Energies . . . . . . . . . . . . . . . . . . . 169

5.3. Photoelectron Spectra with Linear Polarized Light . . . . . . . . . . . . . 173

5.3.1. Photoelectron Spectra of Deprotonated Alaninol . . . . . . . . . . 173

5.3.2. Photoelectron Spectra of Deprotonated 1-Indanol . . . . . . . . . 175

5.3.3. Anisotropy Parameter . . . . . . . . . . . . . . . . . . . . . . . . 177

5.4. PECD .....................................180

5.4.1. PECD of Deprotonated Alaninol . . . . . . . . . . . . . . . . . . 181

5.4.2. PECD of Deprotonated 1-Indanol . . . . . . . . . . . . . . . . . . 183

5.5. Summary ...................................192

6. Summary and Outlook 195

Appendices 199

Contents

List of Abbreviations

3HTHF 3-hydroxytetrahydrofuran

ADE adiabatic detachment energy

AIM (Bader’s quantum theory of) atom-in-molecule

Ala alaninol

Ala-H deprotonated alaninol

aug-cc-pVTZ augmented correlation-consistent polarized valence triple zeta

(basisset)

B3LYP-D3 Becke-3-parameters-Lee-Yang-Parr (hybrid functional) with Grimme’s

3. variant of dispersion correction

DFT density functional theory

FC Franck-Condon

Fen fenchone

FWHM full width at half maximum

HOMO highest occupied molecular orbital

Ind-H deprotonated 1-indanol

IUPAC International Union of Pure and Applied Chemistry

LCP left circular polarized

LIN linear polarized

MCP multichannel plate

Men menthone

MS mass spectrum/spectra

NBO natural bond orbitals

PAD photoelectron angular distribution

PECD photoelectron circular dichroism

PES photoelectron spectrum/spectra

PEM photoelastic modulator

III

Contents

POP polar onion peeling

QWP quarter waveplate

RCP right circular polarized

SE standard error

ToF-MS time of flight mass spectrometer

VDE vertical detachment energy

VMI velocity map imaging

ZPE zero-point energy

“If we knew what it was we were doing,

it would not be called research, would it?”

–Albert Einstein

Abstract

Photoelectron circular dichroism (PECD) emerges as an asymmetry in the spatial dis-

tribution (regarding the light direction) of electrons detached from chiral molecules with

left or right circular polarized light. In the past two decades PECD spectroscopy has

manifested as a potential method for enantiomeric discrimination, with a chiral sensi-

tivity that can surpass conventional methods, such as absorption circular dichroism.

Conventionally, photoemitted electrons from neutral chiral molecules are studied,

which can lead to PECD values of up to 20% [1]. Here, a modified version of PECD is

implemented where photodetached electrons from chiral anions are considered. It can

be called PECD in photodetachment or anion PECD.

This approach simplifies the experiment since photodetachment requires in general

less energy than ionization. Therefore, single photoelectron emission is achievable using

common table-top lasers. Furthermore, mass selection before photodetachment is possi-

ble such that electrons can clearly be assigned to a species of specific mass. Apart from

experimental advantages, the impact of short-range interactions (e.g. dipole moment,

scattering potential) between molecule and electron on the PECD will be revealed since

no cation but a neutral core is left behind after electron removal. Hence, this eliminates

the need for considering long-range Coulombic interactions. Furthermore, the idea of a

photodetached electron as a plane wave is challenged.

At the start of this work, no experimental or theoretical work had reported on anion

PECD. This effect in anions was even doubted to exist since photodetached electrons

are usually considered to be plane waves, which cannot carry an asymmetry. Only a

few years ago, the first successful experiments and calculations on anion PECD were

published [2–4].

The here investigated chiral anions are either chiral gold complexes, consisting of

a neutral chiral molecule (fenchone, menthone, 3-hydroxytetrahydrofuran or alaninol)

and an atomic gold anion, or deprotonated chiral molecules (alaninol, 1-indanol), which

are (in most cases) deprotonated at the hydroxyl group. These chiral systems are mass-

selected and subsequently photodetached by a tunable laser with either linear or circular

polarized light. Using velocity map imaging (VMI) photoelectron spectroscopy, the

kinetic energy of the detached electron and its spatial distribution are recorded, providing

insight into the energy-resolved PECD.

Unfortunately, gold complexes do not reveal any PECD but photoelectron spectra

measured with linear polarized light combined with density functional theory calcula-

tions yield intriguing results toward nonconventional hydrogen bonding. The photoelec-

tron spectra show that the hydrogen bonds are strong enough for an interaction between

gold and the chiral molecule. However, it does not lead to a measurable PECD effect.

Anion PECD is successfully measured for the deprotonated molecules from which the

deprotonated 1-indanol shows a particularly clear PECD. The strongest PECD is found

for detachment from HOMO-2 with around 11%, which is comparable to PECD values

of neutral molecules. Considering this asymmetry strength and the kinetic energy range

the PECD asymmetry is recorded, this work emphasizes the importance of short-range

interactions.

Zusammenfassung

Photoelektronen-Zirkulardichroismus (im Folgenden mit PECD abgek¨urzt nach der en-

glischen Bezeichnung) zeigt sich als Asymmetrie in der r¨aumlichen Verteilung von Elek-

tronen bez¨uglich der Ausbreitungsrichtung des Lichts, welche von ihrem chiralen Molek¨ul

durch links oder rechts zirkular polarisiertes Licht getrennt wurden. In den letzten bei-

den Jahrzehnten hat sich PECD Spektroskopie als potentielle Methode zur Enantiomere-

nunterscheidung behauptet und kann wegen der h¨oheren chiralen Sensitivit¨at etablierte

Methoden wie den Absorptions-Zirkulardichroismus ¨ubertreffen.

Konventionell werden Elektronen aus photoionisierten chiralen neutralen Molek¨ulen

untersucht. Dies kann zu PECD Werten von bis zu 20% f¨uhren [1]. Hier wird eine mod-

ifizierte Version des konventionellen PECD umgesetzt, welche die Untersuchung chiraler

Anionen zum Ziel hat. Diese Methode kann entweder PECD im Photodetachment oder

Anionen PECD genannt werden.

Dieser Ansatz vereinfacht das Experiment dahingehend, dass Photodetachment im

Allgemeinen weniger Energie ben¨otigt als Ionisation. Folglich werden Einphotonen-

prozesse mit kommerziell erh¨altlichen Tischlasern erm¨oglicht. Weiterhin k¨onnen Anio-

nen zuvor nach der Masse selektiert und dadurch eine bessere Zuordnung erreicht werden.

Neben den Vorteilen im experimentellen Aufbau k¨onnen auch der Einfluss von kurzre-

ichweitigen Wechselwirkungen (z.B. durch Dipolmoment und Streupotentialen) zwischen

Elektron und Molek¨ul auf das PECD Signal untersucht werden, da kein Kation sondern

ein neutrales Molek¨ul nach dem Photodetachment zur¨uckgelassen wird. Folglich k¨onnen

langreichweitige Coulombwechselwirkungen vernachl¨assigt werden. Außerdem wird die

Idee, das abgel¨oste Elektron als ebene Welle zu betrachten in Frage gestellt.

Zun¨achst waren weder experimentelle noch theoretische Arbeiten mit dieser Meth-

ode ver¨offentlicht worden. Es wurde sogar angezweifelt, ob Anionen-PECD ¨uberhaupt

detektierbar sei, da Photoelektronen aus Anionen ¨ublicherweise als ebene Welle betra-

chtet werden und daher keine Asymmetrie ¨ubermitteln k¨onnen. Erst k¨urzlich zeigten

experimentelle und theoretische Arbeiten einen Anion-PECD [2–4].

Bei den hier untersuchten chiralen Anionen handelt es sich entweder um chirale

Goldkomplexe, welche aus einem neutralen chiralen Molek¨ul (Fenchon, Menthon, 3-

Hydroxytetrahydrofuran oder Alaninol) und einem Goldanion bestehen, oder um ein

deprotoniertes Molek¨ul (Alaninol, 1-Indanol), was (meist) an der Hydroxyl-Gruppe de-

protoniert wird. Diese chiralen Systeme werden massenselektiert und anschließend mit-

tels eines durchstimmbaren Laser mit linearem oder zirkular polarisierten Licht pho-

todetached. Ein velocity-map-imaging (VMI) Spektrometer erm¨oglicht die Messung

der kinetischen Energie und r¨aumlichen Verteilung der abgel¨osten Elektronen, welches

schlussendlich die Messung eines energieaufgel¨osten PECDs erm¨oglicht.

Leider war es nicht m¨oglich, einen PECD f¨ur die Goldkomplexe zu messen.

Daf¨ur konnten aber Photoelektronenspektren (gemessen mit linear polarisierten Licht)

und density-functional-theory (DFT)-Rechnungen interessante Ergebnise bez¨uglich

un¨ublicher Wasserstoffbr¨uckenbindungen hervorbringen. Die Spektren zeigen, dass diese

Bindungen stark genug sind f¨ur eine Wechselwirkung zwischen Gold und chiralem

Molek¨ul, aber zu keinem messbaren PECD Effekt f¨uhren.

Ein Anionen-PECD wurde hingegen erfolgreich bestimmt f¨ur deprotonierte Molek¨ule,

insbesondere deprotoniertes 1-Indanol zeigt einen deutlichen PECD. Der st¨arkste PECD

wurde f¨ur Detachment aus dem HOMO-2 mit etwa 11% gemessen und ist in der St¨arke

vergleichbar mit PECD-Werten von neutralen Molek¨ulen. Wenn diese Signalst¨arke und

der Bereich der verwendeten kinetischen Energien, bei dem der PECD nachgewiesen

wurde, betrachtet werden, f¨allt auf, dass kurzreichweitige Wechselwirkungen in der Tat

eine wichtige Rolle spielen.

Eidesstattliche Erkl¨arung: Hiermit versichere ich, dass ich die vorliegende Arbeit selb-

stst¨andig verfasst und keine anderen als die angegebenen Quellen und Hilfsmittel be-

nutzt habe. Alle Ausf¨uhrungen, die anderen ver¨offentlichten oder nicht ver¨offentlichten

Schriften w¨ortlich oder sinngem¨aß entnommen wurden, habe ich kenntlich gemacht.

Die Arbeit hat in gleicher oder ¨ahnlicher Fassung noch keiner anderen Pr¨ufungs-

beh¨orde vorgelegen.

Statutory Declaration: I declare that I have authored this thesis independently, that

I have not used other than the declared sources/resources and that I have explicitly

marked all material which has been quoted either literally or by content from the used

sources.

This paper was not previously presented to another examination board and has not

been published.

Ort, Datum/Place, Date Jenny Triptow

1. Introduction

1.1. Chirality

Importance of Chirality in Daily Life

Fig. 1.1.1.: Carvone is a chiral molecule where the (R)-enantiomer can be found in mint

and the (S)-enantiomer is found in caraway. Despite the similar molecular structure, these

enantiomers lead to smell and taste that are quite different.

A familiar and famous beginner example of a chiral system is a pair of hands where

left and right hand can be seen as enantiomers of each other. Hence it is referred to

as “handedness” in the english language, which is the translation from the greek word

“chirality”. Although enantiomers are just mirror images of each other the effect in e.g.

biological systems can be quite different, even noxious.

On a benign scale, molecules like carvone exist in two different enantiomers, which

can be found in mint or caraway, respectively (figure 1.1.1). Regardless of the alike

structure both enantiomers lead to a different taste and smell, due to the different inter-

actions between the respective enantiomers and the taste/smell receptors. Unfortunately,

there are more harmful examples like methamphetamine or thalidomide. In the case of

1. Introduction

methamphetamine, the (R)-enantiomer (R from rectus, latin for right) is used in nasal

decongestant while the (S)-enantiomer (S from sinister, latin for left) is an addictive

stimulant, also known as crystal meth. Thalidomide, the active substance in Contergan,

was meant to be a sleep and sedatives medication but deformities of newborns were con-

nected with this medication in the 1960s. The malefactor is the (S)-enantiomer, which

was not properly separated from the sedative (R)-enantiomer.

Some Methods for Chiral Recognition

The methamphetamine and thalidomide examples show that the discrimination and

separation of enantiomers is of utter importance in medicine. Unfortunately, such sep-

aration is not easy since both enantiomers are “mirror-twins” of each other and hence

share almost the exact same properties like melting point, mass and dipole moment. A

lot of different methods for chiral recognition have been developed over time. They all

share the same general feature: to determine the type of enantiomer a chiral probe has

to be used. Going back to the example of the hand, the type of hand of person A can be

determined by a hand of person B (chiral probe) via a handshake (the experiment). As

always, person B offers the right hand for a greeting. If person A answers with a right

hand the handshake is successful and if A presents the left hand the handshake fails.

Some methods for chiral recognition are mentioned here: While Pasteur had to use

a simple microscope for chiral discrimination to separate the enantiomers of tartaric

acid crystals by hand [5] todays scientists can choose from a variety of chiral separation

and discrimination methods. Chemical techniques use diastereomer formation, which is

applied in chiral chromatography [6] and mass spectroscopy [7]. Conventional chiroptical

methods for chiral discrimination include polarimetry [8], Raman optical activity [9] and

circular dichroism [10]. However, the chiral response is strongly dependent on interaction

with the magnetic dipole moment, which leads in general to weak signals. Thus only

highly concentrated samples in solution are applicable for these techniques.

Meanwhile, a new class of chiroptical methods has emerged, which are solely dependent

on interactions with the electrical dipole moment of the chiral molecule and consequently

lead to a much bigger chiral response. Such techniques make chiral recognition in the gas

phase feasible. These methods include microwave three-wave mixing [11,12], Coulomb

explosion imaging [13,14] and photoelectron circular dichroism (PECD) techniques [15].

1.2. PECD in the Ionization of Neutral Molecules

In angle resolved photoelectron spectroscopy, the intensity in single photon ionization

can be described as

Ip= 1 + b1,pP1(cos(Θp)) + b2,pP2(cos(Θp)) (1.2.1)

with pbeing the light polarization and Pbeing Legendre polynominals. Θpis the

angle between the departing electron and the symmetry axis (for the PECD effect this

coincides with the propagation direction of light).

1. Introduction

Fig. 1.2.1.: PECD principle. A chiral molecule ((R)-(-)-1-indanol) is ionized by circular

polarized light. The electron is traveling either in for- or backward direction regarding the light

direction and depending on the type of circularly polarized light and the used enantiomer.

For an achiral system or linear polarized light, the b1,p term vanishes and the anisotropy

parameter b2,p (also known as β) is used to describe the intensity distribution for

molecules and atoms. Ritchie showed 1976 [16] that for the special case of chiral

molecules being photoionized by circularly polarized light, the b1,p term of equation

1.2.1 does not vanish and that an asymmetry, described by the dichroism parame-

ter b1,p, contributes to the intensity distribution. b1,p describes an asymmetry in the

forward-backward emission of emitted electrons regarding the propagation direction of

the ionizing light (figure 1.2.1) and changes sign if either the enantiomer or the circular

polarized light is changed (figure 1.2.2). Also, a clear dependency on the kinetic energy

of the emitted electron exists. This asymmetry is now known as the PECD effect and

is conventionally performed in the photoionization of neutral chiral molecules. In the

following it is referred to as neutral PECD or conventional PECD.

The PECD asymmetry is a pure electrical dipole effect and does not depend on weak

magnetic components, like it is the case with circular dichroism in absorption (CD). The

chiral sensitivity of the PECD effect is therefore expected to be superior to CD. The

first experimental confirmation was found in 2001 for the single photon ionization of 3-

bromocamphor with a strength in asymmetry of 3-4% and hence confirms the superiority

over CD, which typically has an effect on the order of 10−4- 10−5[17].

An analogous asymmetry can be found in the photoelectron angular distribution of

achiral molecules like CO and N2or even in an atom like He [18,19]. Such experiments

require either alignment of the achiral molecules or double photoionization, like in the

1. Introduction

Fig. 1.2.2.: PECD asymmetry dependencies. The electron flies either in forward (Fw) or

backward (Bw) direction, which defines the sign of the PECD asymmetry. The PECD asym-

metry reverses sign if either the other enantiomer or the other light polarization is taken.

case of He, to show Circular Dichroism in Angular Distribution (CDAD). Neither double

photoionization nor alignment of the molecules is needed in the case for chiral molecules

for CDAD (or PECD). However, alignment can have an enhancing effect on the PECD

asymmetry [20]. All PECD experiments presented here are performed on unoriented

molecules and still provide a significant PECD effect.

Further experiments show that the PECD effect is quite stable under changes in the

oscillator strength or electronic character of resonances in a multiphoton scheme. PECD

asymmetries occur always for a chiral molecule, that is, the ionization regime (tunneling

ionization regime, single or multiphoton) does not decide if a PECD is measured or

not: the PECD effect is a universal or general effect [21–23]. The PECD effect is of

pure quantum origin and can be depicted as the scattering of outgoing photoelectrons

or partial waves at the remaining chiral cation [15,20,21,23].

The picture of an electron probing the molecule by scattering is supported by the ob-

servation that PECD asymmetries are strongest for slow electrons and vanish completely

for too fast electrons, meaning electrons with a kinetic energy of more than about 10 or

20 eV [15,23–25]. Such electrons barely have any time to probe the chiral environment

and hence will not show a PECD effect.

Structural and Vibrational Sensitivity

An outstanding feature of the PECD asymmetry is the sensitivity to the structure

(isomerism, conformerism) and to even small structural changes (atomic and func-

tional group substitution), which neither the cross section for photoionization nor the

anisotropy parameter βin the case of ionization can deliver in such an extent [26]: In

the case of methyloxirane, the substitution from H to F in the CH3group at the chiral

center results in huge changes in the PECD signal of the highest occupied molecular

orbital (HOMO) at low electron kinetic energies (below 3 eV) while βstays quite un-

1. Introduction

changed [15,27]. Even if the substitution occurs not at a chiral center, like in the case of

camphor and 3-bromocamphor where an H is exchanged with Br, the PECD asymmetry

shows clear differences [23]. However, the substitution for an heavy element like Br does

not necessarily show an enhanced PECD effect [23].

Besides substitution, exchanging and moving groups within the molecule (isomerism)

leads to different PECD asymmetries: The isomerism of isopropanolamine and alaninol

can be described as the exchange of the NH2and the OH group. Fenchone and camphor

differ from each other by moving two methyl groups to another spot in the molecule.

While in the first example, the structural change happens at the chiral center, the

moving of methyl groups in fenchone/camphor occurs not at a chiral center and not at

the O-localized HOMO. Nevertheless, both examples show quite different PECD signals

for the isomers, confirming again that PECD asymmetries are sensitive to structural

changes even if the chiral center is not involved [28–31].

Even if no groups are moved or being substituted and only the orientation of groups is

changed in the molecule, the PECD effect is not alike as shown for isopropanolamine and

alaninol [30,31]. Another example is the rotation of the methyl group in methyloxirane,

which has shown to have a considerable influence on the PECD signal [15].

Due to the strong structural sensitivity, the amount of conformers and isomers has to

be controlled in PECD experiments by either using cooled molecules or molecules with a

low conformational space like fenchone [32]. If they are not accounted for, only a PECD

signal averaged over all conformers is measured. This could lead to a weakened overall

recorded PECD signal if the PECD signals of individual conformers compensate each

other, like in the case of alanine [15,33].

Besides structural differences, which are of static nature, dynamic processes like pop-

ulation in different vibrational levels can have noticeable influence on the PECD signal

as well. Responsible for this dependence is the “breakdown of the FC [Franck-Condon]

approximation” [34]: This approximation is based on the Born-Oppenheimer approx-

imation and it is assumed that electron-nuclear dynamics are completely decoupled,

meaning that the transition matrix elements, which govern the probability of an elec-

tronic transition are independent on the nuclear structure. Hence features of the electron

continuum should be independent from the vibrations of the cation and, except for shape

resonances, the PECD effect (and the βparameter) should not be sensitive to vibrational

modes [15,34]. Surprisingly, one of the first vibrationally resolved PECD experiments

from Garcia et al. [34] could find a clear dependence of PECD signals on vibrational

levels. The PECD signal can even change signs for adjacent vibrational modes. Neither

the Franck-Condon approximation nor simple kinetic energy effects could explain this

effect [15].

Similar to conformeric dependence, a PECD signal averaged over the vibrational levels

is measured if the molecule is vibrationally excited or the spectrum is not vibrationally

resolved. Especially for multiphoton experiments the vibrational excitation is important

since it can involve (specific) intermediate vibronic states.

1. Introduction

Influence of Ionized Molecular Orbital

The localization of the orbital the electron is coming from does not seem to determine the

strength of a PECD signal: While orbitals of molecules like 3-bromocamphor can show a

strong PECD effect for delocalized lone pairs and a weak PECD effect for localized lone

pairs (localized at bromine) [17] other molecules like fenchone or camphor can also give

strong PECD signals for localized lone pairs [29]. This seems counter-intuitive since an

electron in a delocalized orbital should “feel” more of the molecular structure. However,

there seems to be no simple correlation between the localization of orbitals and the

strength of the PECD signal [23].

Furthermore, the PECD asymmetry has been observed in detachment from both core

and valence orbitals. Most intriguing are the core orbitals since they are of scharacter

(symmetric) and hence should not contribute to an asymmetry. Consequently, PECD

asymmetries at core levels indicate that the PECD effect is a final state effect [1,20,23,

24,31]. On the other hand, PECD asymmetries are also dependent on the initial state

as seen from PECD effects arising in valence level ionization [23,29,31,33].

Some PECD Methods

PECD measurements can be performed with hemispherical analyzers like it is done

in the first PECD experiments and this method is still in use today [17,35–37]. In

hemispherical analyzers chiral probes can be used in gas [17,35], liquid phase (e.g.

fenchone) [37] and aqueous solution [36]. The liquid state is the “natural” state of many

chiral substances under environmental conditions and reflect conditions of biological

systems better than e.g. the gas phase. However, the hemispherical analyzer is restricted

in the angles it can cover. Mostly, the magic angle (around 54.7

) is used to avoid

anisotropy affecting the measured intensities. In contrast to the hemispherical analyzers,

a VMI spectrometer can not handle the liquid phase well (so far) [36]. On the other hand,

the combination of PECD experiments and velocity map imaging (VMI) spectroscopy

not only provides nice VMI-images but also allows to record the PECD signal over all

angles [15]. The experiments here are performed in gas phase and the combination of

PECD experiment and VMI spectroscopy is preferred to obtain the full-angle PECD

signals.

Since conventional PECD experiments are focused on the ionization of neutrals, ei-

ther synchrotron facilities or complex ionization schemes like multiphoton ionization

have to be employed. Synchrotron radiation can ionize the neutral molecules via sin-

gle photons and avoids the complex multiphoton processes but a special facility and

beam time are needed to perform the experiments. Such experiments include coinci-

dence techniques where photoelectrons and ions are detected coincidentally, like the

photoelectron-photoion coincidence (PEPICO) experiments [15,38].

Multiphoton processes on the other hand can be studied in the home laboratory

with fs- or ns lasers [21,39,40]. Experiments using the multiphoton technique involve

intermediate states, which influences the PECD signal since the strength in asymmetry

can change depending on the involved states. Theoretically, if certain intermediate

1. Introduction

states are carefully selected, a PECD signal of 68% could be possible, but this needs

good quantum control of the system and has so far not been shown experimentally [41].

Resonantly enhanced multiphoton ionization (REMPI) is one example for multiphoton

experiments. REMPI is molecule selective since the initial resonant photoabsorption has

to match a specific transition energy of the molecule. However, this scheme can be quite

complicated and the role of intermediate states in the PECD effect are not immediately

clear [21,39]. Further multiphoton experiments involve coincidence techniques, which

enables mass selective experiments [29,42,43] and even asymmetry measurements on

electrons and ions (PICD) [44]. It is important to mention that all ion detection and

hence the mass selections happens after ionization of the neutral molecules.

Further PECD experiments concentrate on enantiomeric excess measurements, which

can be facilitated by measuring forward and backward emitted electrons at the same

time [45] or by utilizing elliptical polarized light [46]. Also, clustering shows a noticeable

influence on the PECD signal like it is demonstrated for glycidol clusters [47].

PECD experiments with anions is a relatively new method, which emerged in the

recent years and involves mass selection before photodetachment, a relatively simple

laser system and a single photon process [2,3,48]. The ideas, challenges and advantages

of this experiment are described in more detail in section 1.3 but on a fundamental

perspective, it will be able to reveal the influence of short range interactions between

electron and molecule in contrast to long range interactions.

Summary

Conventional PECD on neutrals is an important technique to probe structures of chiral

molecules and to determine the enantiomer at hand. Many studies tried to reveal the

nature of the PECD effect by investigating its properties, which can be summarized as:

1. Universal effect: every chiral molecule should show a PECD asymmetry. The

PECD effect can be understand as scattering of the emitted electron in the poten-

tial of the chiral molecule. The ionization regime does not determine if a PECD

asymmetry exists or not.

2. Depends on the kinetic energy. Slow electrons (around Ekin <10 eV) are needed

to measure a PECD signal since the chiral molecule has to be probed.

3. Sensitive to the structure of the whole molecule (involvement of chiral center not

necessary)

4. Sensitive to vibrational level

5. Localization of electron does not correlate with PECD strength

6. Initial and final state effect (valence and core level)

7. Alignment not necessary but would enhance effect

8. No clear dependence on heavy elements like Br

1. Introduction

Considering the measurement of any PECD effect, the universality of the PECD asym-

metry gives a lot of freedom for theoretical and experimental designs. Experimental

setups can e.g. include single- or multiphoton setups and (apart from chirality) there

are no (strict) restrictions on molecular properties (in context of the PECD effect). A

PECD signal should always appear if the molecule is chiral and the electrons are slow

enough. The details about e.g. strength and kinetic energy dependency will be deter-

mined by the experimental method and choice of molecule.

The high sensitivity of the PECD asymmetry on structural differences makes this effect

an important tool to unambiguously identify the exact molecule at hand, if the molecule

can coexist as different conformers. Especially enantiomers can be differentiated. The

vibrational dependency can help to determine the internal energy of the molecule.

Unfortunately, there is a downside: A missing obvious correlation between the strength

of the PECD signal and molecular properties makes it difficult to “cherry-pick” chiral

molecules or systems. Even if a molecule is chosen in context of the PECD effect, the

conformeric space and vibrations need to be controlled since averaged PECD signals can

be weaker than individual ones. All these make conventional PECD experiments to a

complex problem, which requires proper control of the experiment. The same problems

could emerge for the PECD effect in photodetachment.

1.3. PECD in Photodetachment or Anion PECD

In this thesis, PECD spectroscopy is performed not on neutral molecules but on chiral

anions. The main difference is the detachment of an excess electron, which leaves behind

not a cation but a neutral core. The consequence is a missing long range Coulomb

potential from a monopole charge (cation core), leaving only short range potentials

originating from, for example, dipole interactions. Such a system would reveal the

importance of short range interactions on the PECD effect.

Furthermore, anionic systems enable mass selection before photodetachment and fa-

cilitate the removal of the electron since electron affinities are in general smaller than

ionization energies. This leads to the simplification of the used laser systems and pro-

cesses: Complex laser systems, like synchrotron radiation sources, can be replaced with

simpler ones, like nanosecond table top lasers. Furthermore, single photon processes can

be used instead of multiphoton schemes.

Up until recently, PECD studies were focused on neutral chiral molecules. It was not

clear if PECD asymmetries for chiral anions can be experimentally detected or even exist

since photodetached electrons were described as plane waves [49], which can not carry

an asymmetry. Neither experimental nor theoretical studies were available to this topic

for a long time and also when this project started. However, one study from Dreiling et

al. [50] already gave hope for a working PECD effect in photodetachment. In this study,

the quasi-elastic scattering of spin-polarized electrons on neutral 3-bromocamphor lead

to an asymmetry in electron transmission in the range of 10−4, hence, proving that

electrons can be scattered on a neutral chiral core and still pickup (detectable) chiral

asymmetries. If the PECD effect on neutrals is seen as scattering process, then PECD

1. Introduction

asymmetries could also occur in chiral anions, where the electron interacts with the

remaining neutral core.

Experimental and theoretical studies for PECD asymmetries on anions emerged in

the last few years. The first experimental conformation came from Kr¨uger et al. who

found a PECD effect for anionic (2S)-2-amino-3-(3,4-dihydroxyphenyl)propanoic acid

(L-DOPA) and glutamic acid of around 4.6 and 3.6%, respectively [2]. In a subsequent

study, they also found a PECD asymmetry of around 0.5% for the peptide gramicidin

[3]. Unfortunately, both experimental studies do not provide any energy dependence or

resolution of the PECD effect since only a split electron detector and only one photon

energy (355 nm) were used to determine the difference between for- and backward emit-

ted number of electrons. In a theoretical study from Artemyev et al. [4] a simple model

of a chiral molecule is designed and a non-vanishing anion PECD effect is calculated.

Our studies started years before the publication of theoretical and experimental proof

by Artemyev and Weitzel. The problem at this time was the choice of a good chiral

molecule or chiral system, which creates a (strong) PECD effect in photodetachment.

As already described for conventional PECD asymmetries, the chemical or physical

rules to determine the (ideal) molecule with a good PECD signal are not yet known.

In the end, several anionic systems like various gold complexes (chiral molecule + Au−)

and deprotonated molecules have been studied. Of these, only deprotonated 1-indanol

showed a significant PECD effect [48].

1.4. Outline of this thesis

The main focus of this work lays in the search for a PECD effect in the two classes of

chiral anions, namely gold complexes and deprotonated molecules. First, for this thesis

relevant scientific background is given in chapter 2. It covers briefly basics of molecular

structure, photodetachment, selection rules and angular distributions always in compar-

ison of linear and circular polarized light. The scientific conventions for determining

(R)- and (S)-enantiomers of chiral molecules and the polarization of light (left circular

polarized (LCP) or right circular polarized (RCP)) complete this chapter.

Experimental and computational methods are presented in chapter 3. The experimen-

tal methods summarize the setup, an illustration of the choice of molecules and tools

for analysis. Finally, density functional theory (DFT) is described and relevant energies

are defined.

The following two chapters present the experimental results, analysis and discussion

of the gold complexes (chapter 4) and the deprotonated chiral molecules (chapter 5).

The chapters are subdivided in a similar way to not only show the results for PECD

asymmetries but also present mass spectra, photoelectron spectra measured with linear

polarized light and DFT calculations. Next to PECD asymmetries, the focus in the

chapter for the gold complexes is also on hydrogen bonding. Parts of these chapters are

already published in [51] and [48].

The last chapter summarizes this work and gives an outlook for PECD asymmetries

on anions.

2. Scientific Background

2.1. Molecular Structures

Many molecules have the same molecular formula but are composed in different ways.

Such molecules have different properties only due to their structure and are called iso-

mers. Depending on how the molecules are structured they can be subdivided in further

groups from which some are shown in figure 2.1.1. Here, the main focus is on the enan-

Fig. 2.1.1.: Different categories of isomers with some examples. Tautomers and enantiomers

are highlighted since they are important for this work.

tiomers or chiral molecules. They belong to the stereoisomers (same connectivity but

different shape) and configurational isomers (isomers, which can not be interconverted by

rotating the molecule around a single bond). One famous example for a chiral molecule

is tartaric acid, which shows two enantiomers (figure 2.1.1)1.

However, other forms like tautomers are also present in the experiments. They be-

long to the constitutional isomers (same molecular formula but different connectivity)

1Tartaric acid can also be (2R,3S)-tartaric acid but it is not chiral anymore and belongs to the

diastereomers.

2. Scientific Background

and valence isomers (isomers, which differ in the amount and/or position of σ- and π-

bonds). Acetone and 2-propenol are examples for tautomers since an hydrogen – and

consequently a double bond – changes the position. In this work, tautomers become

important when a chiral molecule is deprotonated.

2.2. Anion Photoelectron Spectroscopy

Photoelectron detachment refers to the extraction of the excess electron e−from an

anion M−with photons that have an energy of at least the electron affinity (EA). If the

anion is singly charged, the corresponding neutral M is probed (equation 2.2.1).

M−hν

−→ M+e−(2.2.1)

The electron’s kinetic energy complies with energy conservation

EB,i =hν −Ekin,i (2.2.2)

with EB,i being the binding energy of the i-th state, the corresponding electron kinetic

energy Ekin,i and the photon energy hν.

Equation 2.2.2 is valid for isolated atomic systems. If molecules are considered, the

binding energy will not only describe electronic transitions but also contributions from

vibrations and rotations.

In figure 2.2.1, the photodetachment process is illustrated for a molecule: The photon

with an energy of Eph =hν detaches the excess electron and forms a neutral molecule,

which can be in a ground (M) or excited state (M∗). The electron probes the neutral

molecule and a measurement of its energy distribution (e.g. in form of photoelectron

spectrum/spectra (PES)) gives information about the (excited) states of the neutral

molecule. In a PES the measured quantity is (basically) the kinetic energy. However,

PES are often plotted over the electron binding energy rather than the kinetic energy

since it is independent from the chosen photon energy.

Experimentally, and as indicated in figure 2.2.1, not all transitions allowed by equation

2.2.2 have the same intensity or are observable. In other words, the transition proba-

bility varies for different states. In general, this probability or intensity variations need

to consider momentum conservation and symmetry principles next to the energy con-

servation (equation 2.2.2). This leads to quite simple selection rules, which determine if

a transition is allowed or how probable the transition is. In the end, information about

geometry changes between anion and neutral configuration can be gained from this.

2. Scientific Background

Fig. 2.2.1.: Energy diagram (left) and corresponding spectra (right) for anion photoelectron

spectroscopy on a molecule. A photon with energy Eph detaches an electron from the anion

M−. Thereby the electronic ground state M and excited states M∗of the neutral as well

as various vibrational states (black lines) can be probed. The intensity is described by the

Franck-Condon principle and determined by the overlap of the absolute squares of the wave

functions. Rotational levels are not shown.

2.2.1. Selection Rules and Transition Probabilities in Photoelectron

Detachment

The probability of a transition from state ito kis determined by the transition dipole

moment Mik. Only for non-zero values the transition is allowed. The conditions leading

to non-zero values are the selection rules for which the important steps of their derivation

are given here.

The following derivation uses the dipole approximation, which is valid for light with

a wavelength much larger than the dimensions of the dipole (e.g. the molecule). The

transition dipole moment is defined as

⎛

⎝

(Mik)x

(Mik)y

(Mik)z⎞

⎠=e·∫︂ψ∗

i⎛

⎝

z⎞

⎠ψkdr (2.2.3)

with ψ∗

ibeing the complex conjugated initial state wave function, ψkthe final state wave

function, e the charge of the detached electron and dr = dxdydz.

The requirement for one of the components of Mik being non-zero is demonstrated

for the hydrogen atom (H) in the following. Furthermore, the spin is neglected for now.

2. Scientific Background

The resulting selection rules are of course not restricted to the H atom but can be also

shown for the general case.

Usually, spherical coordinates (r,ϑ,ϕ) with a radial component r, a polar angle ϑand an

azimuth angle ϕare used to solve problems with the hydrogen atom since it catches the

symmetry of the system in a better way than e.g. the Cartesian system. If furthermore

the spherical symmetry of the H atom is used the wave function can be separated in two

parts: the radial function Rn,l(r) and spherical harmonic functions Ym

l(ϑ, ϕ), which are

solutions of the radial and angular part of the Schr¨odinger equation. n,land mdenote

the principal, azimuthal and magnetic quantum number, respectively.

With Ym

l(ϑ, ϕ)=1/√2πθl

m·eimϕ the wave function of the H atom can be written as

ψn,l,m =1

√2πRn,l(r)θl

m(ϑ)·eimϕ (2.2.4)

with ni,liand mibeing the quantum numbers for the i-th state. The quantum numbers

for the k-th state are noted correspondingly.

2.2.1.1. Polarized Light

If linear polarized light with E

= (0,0, E0) is interacting with the H atom, the zcom-

ponent of Mik can be written as

(Mik)z=e

2π∫︂∞

r=0

RiRkr3dr

·∫︂π

ϑ=0

θlk

mkθli

misin(ϑ) cos(ϑ)dϑ

·∫︂2π

ϕ=0

ei(mk−mi)ϕdϕ

(2.2.5)

with z=rcos(ϑ).

If circular polarized light (CPL) propagates in zdirection with an amplitude of E=

Ex+ iEy, the complex linear combinations of the xand ycomponent are considered

(Mik)x±i(Mik)y=1

2π∫︂∞

r=0

RiRkr3dr

·∫︂π

ϑ=0

θli

miθlk

mksin2(ϑ)dϑ

·∫︂2π

ϕ=0

ei(mk−mi±1)ϕdϕ

(2.2.6)

with x=rsin(ϑ) cos(ϕ) and y=rsin(ϑ) sin(ϕ).

2. Scientific Background

2.2.1.2. Selection Rules

Magnetic Quantum Number m In the case of linear polarized light the last factor of

equation 2.2.5 is non-zero for

∆m=mi−mk= 0 (2.2.7)

The selection rule for the magnetic quantum number changes for CPL with either left

or right polarized light (LCP and RCP) to

∆m=mi−mk={︄+1 for LCP

−1 for RCP (2.2.8)

since only here the last factor of equation 2.2.6 is not zero.

The selection rules in equation 2.2.7 and 2.2.8 are a result of the conservation of

the total angular momentum: Circular polarized light propagating in zdirection either

carries a photon momentum of +ℏfor LCP or -ℏfor RCP. Hence, the zcomponent of

the atom angular momentum has to change by either +ℏor -ℏafter photon absorption.

If linear polarized light is considered to be a superposition of LCP and RCP both photon

momenta cancel each other and mremains unchanged.

Parity Selection Rule or Selection Rule for the Angular Momentum l Let’s consider

the transition dipole moment in Cartesian coordinates and rewrite equation 2.2.3

Mik =e·∫︂∫︂∫︂∞

−∞

f(x, y, z)dxdydz(2.2.9a)

with f(x, y, z) = ψ∗

ir ψk(2.2.9b)

Integrals of the form as seen in equation 2.2.9a are always zero if f(x, y, z) is an uneven

function of (x, y, z) (meaning f(x, y, z) = −f(−x, −y, −z)). To achieve an even function

the product ψ∗

i·ψkmust be an uneven function since r = (x, y, z) is already an uneven

function.

Another word for (un)even function is parity. An uneven function corresponds to odd

parity while the even function refers to even parity. Consequently, ψiand ψkmust have

different parity for an allowed transition.

For a wave function of the hydrogen atom the parity is (−1)l. Hence, lhas to change

by an odd value for an allowed transition. Since a photon only carries one ℏ, the selection

rule is

∆l=li−lk=±1 (2.2.10)

This selection rule is valid for linear and circular polarized light and is connected to the

conservation of angular momentum: If a photon with a momentum of ℏis absorbed, the

atom angular momentum must change accordingly. For a many-electron system with

weak spin-orbit coupling, this selection rule changes to ∆L=±1 with the total angular

momentum L=∑︁ili.

2. Scientific Background

The second term in the transition dipole moment in spherical coordinates (equation

2.2.5) is only non-zero if equation 2.2.10 holds.

Selection Rule for Spin For the sake of completeness, the selection rule for the spin

is given. For a small spin-orbit coupling

∆S=Si−Sk=±1

2(2.2.11)

with the total spin S=∑︁isiis valid. In other words, the spin multiplicity 2S+ 1

must change by ±1. This means that the remaining neutral core must change its spin

to compensate for the spin the departing electron carries away.

For heavier atoms like Au, relativistic effects result in a strong spin-orbit coupling and

the selection rule changes to

∆J=Ji−Jk=±1

2,±3

2(2.2.12)

with the total momentum J=L+S(L-S coupling) or J=∑︁ijiwith ji=li+si

(jj-coupling). Normally, jj-coupling is used for atoms with Z > 40, which includes Au

(Z= 79).

Summary The selection rules for the dipole approximation are summarized in table

2.2.1. Under these conditions the transition dipole moment does not vanish and a peak

can emerge in the PES.

Table 2.2.1.: Summary of the selection rules in dipole approximation. Transitions fulfilling

these conditions are considered “allowed”, others forbidden.

Selection rule comments

∆l=±1 for one electron systems

∆L=±1 for many electron systems with L=∑︁ili

∆M= 0 for linear polarized light

∆M=±1 +1 for LCP and -1 for RCP

∆S=1

2for weak spin-orbit coupling

∆J=±1

2,±3

2for strong spin-orbit coupling

2.2.1.3. Transition Probability

The transition probability determines the intensity of a transition and can be given by

the golden rule of Fermi

I∼ |Mik|2·ρ(EB,i)·δ(∆E−hν) (2.2.13)

2. Scientific Background

with ρ(EB,i) being the density of the final states and ∆Ebeing the energy difference

between initial and final state. Basically, the delta function δ(∆E−hν) is another

expression for the conservation of energy in equation 2.2.2 for photoelectron spectroscopy.

The matrix elements of the transition dipole moments defines the probability or inten-

sity I of a transition. Transitions fulfilling the selection rules are referred to as allowed

transition (in the dipole approximation) and will most probably lead to high intensities.

Besides allowed transitions, transitions, which are forbidden in the dipole approximation

could emerge in the spectrum but are of much lower intensity or are less probable. Such

transitions could originate from e.g. magnetic dipole transitions or electric quadrupole

transitions.

2.2.1.4. Franck-Condon Principle

The principle known today under the name Franck-Condon principle (or short FC prin-

ciple) was first described 1926 for photoreactions by James Franck [52] and extended

by Edward Condon in the same year [53]. It describes transition probabilities between

different vibrational states and hence can be used for predicting the intensity of a tran-

sition. The Franck-Condon factor is given in equation 2.2.14.

FC(νi, νk) = |∫︂ψvib(νi)ψvib(νk)dR|2(2.2.14)

The principle is based on the assumption that electronic transitions happen immediately

in comparison to nuclei movements (Born-Oppenheimer approximation). An vibronic

transition becomes more probable/intense the more the vibrational wave functions of

both contributing states overlap or in other words if the maximum of both wave functions

are at (almost) the same position to the core (figure 2.2.1). In the special case of no

change between the potential curves of different electronic states (meaning minima at

the same core distance or according to figure 2.2.1 at the same normal coordinate)

transitions with νi−νk= 0 are most probable and will give the highest intensity. If the

potential curves are different other transitions will become more probable.

2.2.2. Photoelectron Angular Distribution

Apart from energy information (binding energy EB) the angular distribution can be ob-

tained by certain spectrometers like the VMI spectrometer. In this angular distribution,

anisotropies can occur, which give information about the orbital from which the electron

departed after photodetachment. For linear polarized light, the parameter describing the

anisotropy has been described by many researchers [54–57]. However, here, the focus of

the anisotropy parameter is mainly based on the work of Sanov et al. [58–61].

2. Scientific Background

In general, the angular distribution can be described by

dσ

dΩ=σtot

4π(1 +

∑︂

n=1

bnPn(cos(Θ))) (2.2.15a)

→I(Θ) ∼1 +

∑︂

n=1

bnPn(cos(Θ)) (2.2.15b)

with Pnbeing the n-th Legendre polynomial, dσ

dΩthe differential cross section, σtot the

total cross section and I(Θ) the corresponding signal intensity depending on the angle Θ,

which is measured between the electron flight path and the symmetry axis of the system.

Equation 2.2.15 is valid for non-chiral and chiral systems, which are photodetached by

n-photons. For the case of linear polarized light, the symmetry axis is the polarization

axis of the electrical field component. Circularly polarized light uses the direction of the

light as symmetry axis [62,63].

If only single photon detachment (n=1) is considered and pis introduced as light

polarization index (p=linear polarized (LIN), p=LCP, RCP) the equation is reduced

to equation 1.2.1 from chapter 1.2:

Ip= 1 + b1,pP1(cos(Θp)) + b2,pP2(cos(Θp)) (2.2.16)

Considering the different polarizations, the dichroism parameter b1and the anisotropy

parameter b2have the following relationship [62,63]:

b1,LIN = 0 (2.2.17a)

b1,LCP =−b1,RCP (2.2.17b)

b2,LCP/RCP =−1

2b2,LIN (2.2.17c)

From now on, b2will be mostly written as βand either called β- or anisotropy parameter

to be consistent with literature [54,58].

2.2.2.1. Anisotropy Parameter

An equation for the anisotropy parameter βwas derived by Bethe [64] and generalized

by Cooper and Zare [54] for atomic or atomic-like systems that experience photode-

tachment with linear polarized light. By restricting the problem to low kinetic energies,

Hanstrop et al. [57] could use the Wigner threshold law [65]

σ∼El+1/2

kin (2.2.18)

to simplify the equation for β.Ekin is the kinetic energy of the departing electron and lis

the orbital angular momentum from which the electron originates. Technically, equation

2.2.18 applies for all lbut just small llike l= 0 or 1 produce relevant cross sections in

the threshold limit for low kinetic energies (Ekin <1 eV).

2. Scientific Background

The simplified version for βis also called βin the Cooper-Zare-Hanstrop (CZH) for-

mulation and is given as

βCZH(Ekin) = l(l−1) + (l+ 1)(l+ 2)A2E2

kin −6l(l+ 1)AEkin cos(δl+1 −δl−1)

(2l+ 1)(l+ (l+ 1)A2E2

kin)]

(2.2.19a)

AEkin =χl,l+1

χl,l-1

(2.2.19b)

with δl+1 −δl−1being the phase shift originating from the interaction of the electron

with the neutral atom after photodetachment. The parameter Ais a proportionality

coefficient for the ratio of the radial matrix elements χof the outgoing partial waves l±1

and has the unit of a reciprocal energy. Since Awas introduced by Hanstrop et al. [57],

it is referred to as Hanstrop parameter.

In a figurative way, the Hanstrop parameter reflects the spatial extent of the anion

wave function and is sensitive to the diffusivity of the long-range tail of that wave

function. It roughly correlates with the size of the atom, e.g., the Hanstrop parameter

of O−and C−are 0.55 eV−1and 0.75 eV−1, respectively and correspond to the relative

sizes of the anions [58]. Apart from the size of the anion the relative electron affinities

give a hint of the size of the Hanstrop parameter since lower EA tend to more diffuse

tails (EA of O−is 1.46 eV and EA of C−is 1.26 eV) [58].

In order to guarantee a positive intensity (or cross section) in equation 2.2.16 for

linear polarized light, βhas to be restricted between the values -1 and 2. β= 2 is

achieved for the case of l= 0 (s-orbital). Furthermore, this is the only case where βis

independent of the kinetic energy and is a constant. Negative values, especially β= -1,

are determined by the strength of the interference term −6l(l+ 1)AEkin cos(δl+1 −δl−1)

(equation 2.2.19a) relative to the other non-interference terms.

2.2.2.2. s-pMixing Model from Sanov

For molecules and complexes no lcan be given due to the ”mixing“ of orbitals. Hence,

equation 2.2.19a is not valid anymore. A proper way to obtain βfor molecules is to

apply the s-pmixing model from Sanov [58]. As for βfor atomic and atomic-like systems

(2.2.19a), Sanov developed his model for the low kinetic energy regime and could define

a parameter for the outgoing partial waves similar to the Hanstrop parameter from

equation 2.2.19b. Being in the low kinetic energy regime, Sanov restricts the model for

l= 0 (s-orbital) and l= 1 (p-orbital) since here only small lcreate measurable cross

sections according to Wigners law 2.2.18. Furthermore Sanov uses the central-atom

approximations, meaning the detachment happens predominantly at one atom. The β

parameter in this model is then given as

2. Scientific Background

βsp(Ekin) = 2(1 −f)BEkin + 2fA2E2

kin −4fAEkin cos(δ2−δ0)

(1 −f)BEkin + 2fA2E2

kin +f(2.2.20a)

AEkin =χ1,2

χ1,0

(2.2.20b)

BEkin =χ0,1

χ1,0

(2.2.20c)

Fig. 2.2.2.: The anisotropy parameter βas a function of the kinetic energy plotted with the

s-pmixing model of Sanov (equation 2.2.20a). The curves correspond to different fractional

pcharacter f. For this plot A= 1 and B/A = 8/3 are set arbitrarily. Next to the plot, the

corresponding photoelectron angular distribution (PAD)s for the limits β= 2 (blue half moons)

and -1 (red half moons) are shown. The special case of β= 0 creates a circular PAD (green)

and is reached for tiny kinetic energies or for zero-crossings (green transparent ball). Dashed

contour lines indicate the sand ppartial waves of the departing electron. There are parallel

(blue) and perpendicular (red) transitions regarding the light polarization (black arrow). A

similar figure can be found in [58].

The parameter Adescribes the p→dand p→sphotodetachment channels like the

Hanstrop parameter. The newly introduced parameter Bis used for the s→pand

p→schannels. fis the fractional pcharacter of the orbital and describes the “amount

of p-orbital” in the s-pmixed molecular orbital. It ranges from 0 (pure s-orbital) to 1

(pure p-orbital) and reduces βsp for f= 0 or 1 to βczh with l= 0 (s-orbital) or l= 1

(p-orbital).

2. Scientific Background

fcan be gained from an orbital composition analysis. The ratio B/A depends on the

participating orbitals as well as the effective nuclear charges and can be calculated to

some extent if these orbitals are known [55,59]. B,Aor the nuclear charges need to be

determined by fitting the experimental data to the model of Sanov.

A visualization of equation 2.2.20a is given in figure 2.2.2. The effect on the angu-

lar distribution is given next to the plot, dependent on the light polarization. These

distributions can be imaged if a VMI spectrometer is used.

Since the s-pmixing model from Sanov is developed for low kinetic energies, the ques-

tion of a limiting kinetic energy arises. In general, the model becomes more inaccurate

for higher kinetic energies but can still be considered accurate in the range of Ekin <1 eV

according to Wigner’s law. However, according to Sanov et al. [59]2, the model can be

applied to a wider energy range of Ekin <5 eV due to the use of ratios rather than

absolute numbers. In this thesis, the used energy range is Ekin <3.4 eV.

For photodetachment it is assumed that the electron does not interact (in a noticeable

way) with the neutral atom or molecule. Hence, in both anisotropy parameter βCZH and

βsp no phase shift between the partial waves (cos(δ2−δ0) = cos(δl+1 −δl−1) = 1)

exists. However, for some systems, e.g., I−[61], O−[57] and O−

2[66] it is appropriate to

assume a small interaction (cos(δ2−δ0)=0.86 −0.96) to match the model better to the

experimental data [58]. Such interactions could arise from many-electron correlations

(between departing and remaining electrons) or via the polarizing field of the departing

electron on the neutral molecule [67].

Apart from electron correlations and polarizing fields, the departing electron can in-

teract with the dipole moment of the neutral core µ. However, instead of adjusting the

phase shift parameter, the Cooper-Zare model is expanded to the case of dipole moments

[61]. The βparameter is dependent on µand still reaches the value 2 for detachment

from the s-orbital.

Before evaluation of the βparameter, the type of molecular orbitals can be estimated

by their shape and defined more precisely with an orbital composition analysis. For some

molecules, like ortho-pyridinide, the shape of the molecular orbital of interest resembles

an atomic d-orbital. For such orbitals, the s-pmixing model from Sanov is not sufficient

and the model has to be expanded to d-orbitals [56,68].

With the central-atom approximation, the s-pmixing model can fail for system like

CS−, which are not approximated by a central atom. These cases have to be treated

differently [60]. Systems with molecules that are solvated with a heavy anion like iodine

are best suited for this model since the heavy atom iodine can be used as central atom

[61]. Among the systems investigated here, chiral molecules are solvated with the (heavy)

anion gold. With gold acting as central atom, the central-atom approximation can be

used and hence the s-pmixing model by Sanov is suited to describe this kind of systems.

However, the systems solvated with iodine and gold anions need to consider the dipole

moment to model the βparameter exactly. In the case of the iodine systems, the

experimental data might not be perfectly fitted by the model, which does not consider

the dipole moment but it gives the right form for β.

2This information is discussed in the supporting information of this paper

2. Scientific Background

2.2.2.3. Dichroism Parameter

Next to the anisotropy parameter, a second parameter becomes important if circular

polarized light and chiral molecules are used, the dichroism parameter, which describes

the PECD effect. The PECD asymmetry is twice the difference in electron counts for

LCP and RCP light with respect to the total amount and is given by

PECD = 2 ·ILCP −IRCP

ILCP +IRCP

(2.2.21)

The intensity for chiral systems, which are photodetached via a single photon process is

given in equation 2.2.16 and yields in combination with equation 2.2.21:

PECD = 2 ·b1P1(cos(Θp))

1 + b2,pP2(cos(Θp)) (2.2.22)

in which b1,LCP =−b1,RCP (equation 2.2.17b) was used. Since b2,p(β) is the same for LCP

and RCP (equation 2.2.17c), the subscript pwill be omitted for clarity in the following.

For specific angles, this equation can be simplified. If the maximum PECD signal is

of interest, the angles Θ = 0

or 180

(axis for light propagation) are taken and equation

2.2.22 simplifies to

PECD = ±2b1

1 + b2

(2.2.23)

Often, the relationship PECD ≈2b1can be found in the literature, which only con-

siders the asymmetry giving numerator [15,34]. While it is certainly the important

part for the PECD asymmetry, it should be emphasized that the full PECD signal also

depends on the anisotropy parameter.

b2can be avoided if the experiment is designed such that Θ is equal to the magic angle

Θm= arctan(√2) ≈54.7

.P2(cos(Θm)) will vanish and equation 2.2.22 then simplifies

PECD = 2 ·b1cos(Θm) (2.2.24)

and is important for PECD experiments with hemispherical analyzers [37]. Equation

2.2.23 and 2.2.24 are quite simple but are only valid for specific angles. If, however, the

full angular distribution is measured, the restriction to certain angles is not necessary

and instead the PECD signal over the full PAD is available. Since in this thesis, a VMI

spectrometer enables the measurement of the full PAD, the more general form of the

PECD equation (equation 2.2.21) is used.

2.3. Enantiomers and Circular Polarized Light

2.3.1. Nomenclature of Enantiomers

Molecules are chiral if there is a mirror image molecule (enantiomers) and they are

not superimposable. The enantiomers are discriminated by the labels (R) and (S) in

2. Scientific Background

combination with (+) and (-) or with D and L. Here, just a summarized version of the

labeling systems and how to apply them is given. A more comprehensive explanation

can be found, e.g., in the Beyer/Walter textbook [69].

The (R) and (S) system gives the absolute configuration since it is based on the

arrangement of different atoms or atom groups around the chiral center. The Cahn-

Ingold-Prelog (CIP) rules assign each atom or atom group priorities according to their

atomic numbers. With the help of the Fischer projection and molecule rotations, the

(R) and (S) label are assigned according to a clockwise or anti-clockwise order of the

priorities.

(+) and (-) are determined by the direction in which the plane of the polarized light is

rotated. If the light travels toward the observer, a clockwise rotation is labeled as (+),

in the other case as (-). It also can be labeled as d- or l- isomer.

The D- L- system determines the enantiomer relative to glyceraldehyde, which has

a clearly assigned D and L enantiomer. In contrast to (R) and (S), it is a relative

configuration system and not an absolute one. It is independent from the d- and l- or

(+) and (-) labeling system but can be easily confused.

The recommended system by International Union of Pure and Applied Chemistry

(IUPAC) is the (R) and (S) system and is exclusively used in this thesis since it gives

the absolute configuration [70].

2.3.2. Light polarization

2.3.2.1. Stokes Parameter

Polarized light with two independent orthogonal components xand ypropagating in z

direction can be described as

Ex(z, t) = E0xcos(ωt −kz +δx) (2.3.25a)

Ey(z, t) = E0ycos(ωt −kz +δy) (2.3.25b)

with E0x and E0y being amplitudes, ωbeing the optical frequency, kbeing the wave

number and δbeing the phase constants.

If the propagator ωt−kz is eliminated, a more visual form of equation 2.3.25 is found.

Ex(z, t)2

+Ey(z, t)2

0y −Ex(z, t)Ey(z, t)

E0xE0y

cos(δ) = sin2(δ) (2.3.26)

This is called the polarization ellipse and describes the polarization with its field compo-

nents E. Unfortunately, the field components and consequently the polarization ellipse

are not observable and need to be transformed in the observable intensity domain. The

transformation requires a time average over equation 2.3.26 and leads to

0=S2

1+S2

2+S2

3(2.3.27)

2. Scientific Background

with

S0=E2

0x +E2

y0 (2.3.28a)

S1=E2

0x −E2

y0 (2.3.28b)

S2= 2E0xEy0cos(δ) (2.3.28c)

S3= 2E0xEy0sin(δ) (2.3.28d)

Equations 2.3.28 define the Stokes parameters, which describe the polarization of light.

They are given in terms of intensity (squared amplitudes) and are therefore measurable.

The first parameter gives the total intensity while the others describe the amount of

polarization for certain directions: S1describes the polarization in horizontal (0

) and

vertical polarization (90

), S2is used for ±45

and S3is for LCP and RCP:

S0=Ix+Iy(2.3.29a)

S1=Ix−Iy(2.3.29b)

S2=I+45 −I-45 (2.3.29c)

S3=IRCP −ILCP (2.3.29d)

The Stokes parameter for different polarizations are summarized in table 2.3.1. If the

Table 2.3.1.: Stokes parameter describe the polarization of light.

S/polarization no 0

±45

LCP RCP

S01 1 1 1 1 1

S10 1 -1 0 0 0

S20 0 0 ±1 0 0

S30 0 0 0 -1 1

Stokes parameters are known, the degree of polarization P, can be calculated

P=√︁S2

1+S2

2+S2

.(2.3.30)

In other words, it describes the quality of polarization, which goes from unpolarized

(P= 0) to fully polarized (P= 1).

2.3.2.2. Convention for Circular Polarized Light

Circular polarized light comes in two forms: LCP and RCP whereas the definition of left

and right depends on what an observer or – in this thesis – the molecular beam “sees”

coming towards them. If the polarization of light is rotating in clockwise direction, the

light is called right circular polarized while a counter-clockwise rotation refers to as left

circular polarized. This convention coincides with the definition given by Born and Wolf

[71] and will be used throughout this thesis.

3. Experimental and Computational

Methods

3.1. Chiral Anions

3.1.1. Properties for Anions and Molecules

(a) (1R)-(-)-fenchone (b) (2S,5R)-(-)-menthone

(e) (R)-(-)-1-indanol

Fig. 3.1.1.: Chiral molecules used in this project. The chiral center is highlighted with a gray

* and its absolute configuration is given.

The molecules (1R)-(-)-fenchone, (2S,5R)-(-)-menthone, (R)-(-)-3-hydroxytetrahydro-

furan, (S)-(+)-alaninol and (R)-(-)-1-indanol (figure 3.1.1) were chosen to build the

chiral part of the anionic chiral system. (1R)-(-)-fenchone, (2S,5R)-(-)-menthone and

(R)-(-)-1-indanol were obtained from Sigma Aldrich while (R)-(-)-3-hydroxytetrahydro-

3. Experimental and Computational Methods

furan comes from Alfa Aesar and (S)-(+)-alaninol from TCI. Additionally, (S)-(+)-1-

indanol was purchased from Biosynth.

To create an anionic chiral system these molecules are either used in combination

with an anionic atom to form a complex or are deprotonated. The molecules itself and

the anionic systems containing these molecules need to fulfill certain criteria including

properties, which are beneficial for the PECD signal, anion production and measurement.

Properties for PECD

In section 1.2, it is shown that no obvious molecular properties are known, which could

lead to (strong) PECD signals. The only certain requirements seem to be that the

molecules have to be chiral and the sample enantiopure.

Not strictly necessary for the PECD effect itself but still helpful is a simple con-

formational space. It reduces the possibility of overlapping PECD signals originating

from different structural isomers that could cancel each other out like it is observed

for alanine [15,33]. Apart from PECD effects, simple conformational space can – in

combination with a simple structure – help to reduce the complexity of a photoelectron

spectrum, which simplifies the subsequent analysis and facilitates straightforward com-

parisons with DFT calculations. However, this is not a necessary condition for the chiral

system since the conformational space can be restricted by adequate experimental reso-

lution. However, the experimental setup might become more difficult if this constraint

is not met.

Another helpful property is the price and commercial availability of the other enan-

tiomer as well as the racemic mixture of the molecule. Both are needed to confirm the

PECD measurements and exclude other asymmetry sources.

Assuming that properties demanded for the PECD effect on neutrals are also valid

for the PECD effect on anions, the following properties can be required for the anionic

chiral systems:

1. It is chiral and the sample is enantiopure

2. Chiral structure remains intact after formation of the anion

3. Ideally, simple conformational space (and simple structure)

4. Ideally, it is based on a molecule with a strong PECD signal in the neutral case

5. Price and commercial availability of both enantiomers (and racemate) of the chiral

molecule the anionic chiral system is based on

The chosen molecules (figure 3.1.1) fulfill these properties. Especially, fenchone seems

to be a good fit since it shows quite large PECD values of ≈8-16% in conventional

PECD experiments [28,29,72] and is also a rigid molecule [32]. 1-indanol and 3-

hydroxytetrahydrofuran are also relatively rigid molecules and can reach PECD values

of around 5% [73,74]. Similar PECD values (3 - 5%) can be found in alaninol [31], which

has a relatively simple structure but can be pretty flexible [75]. Menthone belongs in

3. Experimental and Computational Methods

the same molecular category as fenchone and finds special interest in other asymmetry

studies like circular dichroism or 3-wave-mixing [11,76]. While the choice of the anionic

chiral system is relatively unconstrained regarding the PECD effect it will be restrained

more strictly by other factors like the production requirements.

Properties for Chiral Molecules

The following requirements imposed on the molecule for anion production in gas phase

are:

1. Easy to bring into gas phase (high vapor pressure, low sublimation enthalpy)

2. Stable molecule (no decomposition before or during evaporation)

3. Low toxicity

Since all sources used in this project are for gas-phase experiments, the chiral substance

should have relatively high vapor pressure when fluid and low sublimation enthalpy when

solid (assuming ambient environment). For example, the molecules shown in figure

3.1.1a -3.1.1d are good examples because they are liquid in the ambient environment

and require just a few mbar (<3 mbar) to evaporate at room temperature (≈25

C).

1-indanol (figure 3.1.1e) is also useful despite being solid (it is a powder) in the ambient

environment due to the low sublimation enthalpy; heating to around 100

C is enough to

bring a sufficient amount of it to the gas phase. In combination with the requirement of

a stable molecule an acceptable amount of stable anion signal for the photodetachment

process should be possible.

Finally, while requiring low toxicity neither helps with anion production nor with the

size of the PECD effect, it is preferential for the sake of the experimentalist. Luckily, all

presented molecules show this property.

Properties for Anions

After selecting the chiral molecules, beneficial characteristics for the corresponding anion

should be chosen:

1. Stable anion (positive electron affinity)

2. Electron affinity in range for “simple” laser systems (ns pulsed laser)

3. Precursor available or easy to produce

These properties are quickly explained: Long measurements are typically necessary

to get reliable statistics in a experiment with low repetition rates (here 10 Hz), which

demands stable anion production over the long measurement time and stable anions over

the timescale of an experimental cycle.

Another aspect is the electron affinity of the anionic chiral system. If the electron is

too strongly bound, more complicated laser systems are needed for detachment, which

3. Experimental and Computational Methods

(a) (b)

Fig. 3.1.2.: Two different anionic chiral systems exemplary shown for the chiral molecule

alaninol. The gold complex (left) consists of a gold anion Au−and a chiral molecule. A

second possibility to create an anion is the deprotonation of a chiral molecule (right). The

(transparent) hydrogen from the hydroxy group is most likely removed. The charge will be

located at the Au−for the gold complex and at the oxygen for the deprotonated molecule.

These structures are optimized with B3LYP-D3/aug-cc-pVTZ(-PP). Distances (yellow) are

given in nm.

contradicts the idea of being able to work with easy laser systems in anion PECD

experiments.

The last point refers to the availability of a precursor of the anionic chiral system or

of precursor elements, which can be easily combined to an anionic chiral system, e.g.

metal anion and chiral molecule to create a chiral metal complex. The (commercial)

availability of the chiral molecule is already demanded in a previous subsection but of

course this has to be valid for the precursor of the metal anion as well.

3.1.2. Creation of Anionic Chiral Systems

Many well-known chiral molecules – including the ones used in this thesis (figure 3.1.1)

– have closed-shell configurations and are expected to show low electron binding energy.

In table 3.1.1, the vertical detachment energy (VDE), which corresponds to the electron

binding energy, is given for some of the radical anions of the molecules used here and

features as expected quite low values. Consequently, the attachment of an additional

electron to these systems is difficult and an alternative to produce chiral anions is favored.

The used approaches are complexing atomic anions1with the neutral chiral molecules,

consequently creating an anionic chiral complex as shown in figure 3.1.2a, as well as

deprotonation of chiral molecules (figure 3.1.2b).

1molecular anions and clusters could be possible as well

3. Experimental and Computational Methods

Table 3.1.1.: Listed are the calculated vertical detachment energy (VDE) for the gold anion

and the radical anions of the chiral molecules as well as the experimental electron affinity for

the gold anion. Calculations are performed with B3LYP-D3 and aug-cc-pVTZ(-PP). Since the

VDE estimates the (electron) binding energy, small values indicate a system with a weakly

bound electron while for gold the electron is strongly bound.

system VDE (eV) exp (eV)

fenchone 0.249

menthone 0.157

3HTHF 0.335

alaninol 0.263

Au 2.215 2.309 [77]

Gold Complexes

The first approach – attaching an atomic anion to the neutral chiral molecule – was

realized with the existing laser ablation source. Here, Au−was chosen to provide the

extra electron to create an anionic chiral Au−-molecule complex (Au−-M). This decision

was made due to the following reasons:

1. Au−is relatively heavy with m/z 197, allowing the complex to be differentiated

easily from other substances in the mass spectrum.

2. Only one stable isotope of Au−(197Au−) exists, making the mass spectrum easy

to analyze.

3. Au−has a closed-shell configuration [Xe]4f145d106s2.



This makes Au−rather inert. Hence, Au−does not react much with other

components.



The electron is also strongly-bound with an electron affinity of 2.309 eV [77],

which is still easily accessible with ns-pulsed lasers.

4. The production of large amounts of Au−in the existing source is effortless and if

the connection between Au−and the chosen molecule is possible, the creation of

the anionic complex will be highly likely.

The calculated VDEs of table 3.1.1 show that Au has always a higher VDE than the

chiral molecules. Hence, the gold anion is more stable and the additional electron is

most likely localized at the gold atom. The chiral molecule can be polarized by the gold

anion, which gently forms and stabilizes the complex.

In the following these cluster anions are written as Au−-M, with M being either

fenchone (Fen), menthone (Men), 3-hydroxytetrahydrofuran (3HTHF) or alaninol (Ala).

3. Experimental and Computational Methods

Deprotonated Molecules

The second method used here is the production of a chiral molecular anion via deproto-

nation. Here, several properties have to be considered:

1. Easy to deprotonate, e.g., molecules with a hydroxy group.

2. Ideally, just one deprotonation site to avoid isomers. However, if several deproto-

nation sites can not be avoided, try to separate them (e.g. energetically).

3. No deprotonation at the chiral center

In order to find a molecule (M), which is easy to deprotonate, the enthalpy of the

reaction M−+ H+→M in gas phase needs to be considered whereas M−denotes the

deprotonated molecule M−≡(M-H+)−. In general, certain groups of molecules are easier

to deprotonate than others due to their functional groups. This is exemplary shown for

methyl-alcohol, -amine and -methane in table 3.1.2. Here, the molecule with the -OH

group is the easiest to deprotonate while the CH3is less likely to be deprotonated. The

molecule with -NH2lies in between. In a system like methyl alcohol or -amine the -OH

and -NH2group are considered as distinctive deprotonation sites since deprotonation will

happen most likely at this position. Methylmethane has no distinctive deprotonation

site since all positions are more or less equiprobable.

Another group of possible molecules, which can be deprotonated are carboxylic acids

(-COOH), like lactic acid. However, while deprotonation is relatively easy the photode-

tachment of the anion (-COO−) can be rather complicated due to the high electron

affinity (at least ≈5 eV for deprotonated lactic acid).

To avoid several isomers and a possible weaker averaged PECD signal, it would be ideal

to have only one distinct deprotonation site meaning that molecules with, for example,

two hydroxy groups like 2-propandiol, are not ideal since it is not instantly clear which

hydroxy group is deprotonated. However, even with only one distinct deprotonation

site deprotonations on other groups can sometimes not be avoided even if such groups

are less likely to be deprotonated. 1-indanol for example has only one hydroxy group

but can also be deprotonated at the -CH groups. Luckily, the differently deprotonated

1-indanols can be easily distinguished in a photoelectron spectrum due to their sufficient

different binding energies [48].

Table 3.1.2.: Enthalpy ∆rHofor the reaction M−+ H+→M in gas phase. M is the respective

molecule and M−≡(M-H+)−the deprotonated molecule. The values are from the “Reaction

Thermochemistry Data” of NIST [78].

molecule formula ∆rHo(eV)

Methyl alcohol CH3OH ≈16.6

Methylamine CH3NH2≈17.4

Methylmethane (ethane) C2H6≈18.2

3. Experimental and Computational Methods

Of course, the chirality has to be maintained after deprotonation meaning that the

most likely deprotonation site should not be the chiral center. 1-indanol and alaninol

can be deprotonated at the chiral center but since the main deprotonation site is not at

the chiral center, most of the created molecules are chiral.

In the case of deprotonation at the hydroxy group the excess electron will be located

at the deprotonation site (oxygen). This locates the excess electron closer to the chiral

center compared to the gold complex as can be seen for alaninol: The gold complex

Au−-Ala has a distance between Au−and the chiral center of around 0.4 nm while the

deprotonated form has a distance of around 0.2 nm between deprotonation site and

the chiral center. More importantly, the relevant electron is also no longer localized

at an achiral part like Au. If the localization is too strong, the electron might mostly

experience the atomic potential and not the chiral potential of the molecule, which could

probably suppress the PECD effect.

In the following, deprotonated molecules are written with “-H” indicating to the re-

moved H. The both molecules used for the experiments with deprotonation are [depro-

tonated alaninol (Ala-H)]−and [deprotonated 1-indanol (Ind-H)]−.

3.2. Setup and Data Treatment

Overview of Experiment

Roughly, the experiment consists of an anion source, two spectrometers and a laser

system. The whole experiment is operated under high vacuum and is pulsed with 10 Hz.

This experiment is already partly described by Gr¨une, H¨artelt and Yubero [68,79,80].

The anionic chiral systems of interest, i.e. chiral gold complexes (Au−-M) and depro-

tonated chiral molecules, are created with two different sources: For Au−-M, the existing

laser ablation source is ideal since Au−is easily produced in such sources. The plasma

entrainment source after the design of Lineberger et al. [81] was implemented for the

production of the deprotonated molecules since it is optimized for the deprotonation

process. Both sources are described in section 3.2.1.

Identifying the anions is possible with spectrometry: A linear time of flight mass

spectrometer (ToF-MS) separates substances according to their different mass-charge

ratios in their flight times and hence gives a first impression of the produced substances

(section 3.2.2). Furthermore, different flight times of the substances offer the possibility

of synchronizing a laser to a specific flight time and selecting the corresponding substance

for further spectroscopic study. Further measurements with an electron spectrometer are

needed to reveal the energy levels and substantiate the identification of the substance in

the ToF-MS. The spectrometer utilized in the experiments included in this thesis is an

anion-PES-VMI spectrometer, which yields, energy information and information about

the angular distribution (section 3.2.3). For PECD measurements, the polarization of

light is essential since it requires circularly polarized light in good quality and shot-

to-shot alternation to reduce the influence of long and short-term fluctuations (section

3.2.4).

3. Experimental and Computational Methods

Fig. 3.2.1.: Schematic setup of the experiment. In the source chamber (blue frame), anions

are created by either the laser ablation or the plasma entrainment source. After a skimmer, the

anions enter the chamber with a linear ToF mass spectrometer (red frame). Here the anions

are mass-selected and accelerated to the VMI chamber (green frame) where they are detected.

In the VMI chamber, a ns-pulsed OPO (1.1 - 5.77 eV) that is synchronized with the mass

spectrometer photodetaches electrons from the anions, which are subsequently directed to a

VMI lens system and are collected by a position sensitive detector.

Hardware Setup

Each element of the experiment (source, ToF-MS, VMI spectrometer) is in a separate

vacuum chamber equipped with a high-vacuum pump and can be separated from each

other through gate valves. A more detailed description of the vacuum system is given

elsewhere [79] and will thus be omitted for brevity. The three main vacuum chambers

contain, respectively, the source for anion production, the ToF-MS for mass separation

and the VMI lens system for photodetachment and PECD measurements (see figure

3.2.1). The source chamber holds a laser ablation source, which was later replaced by

a plasma entrainment source to investigate other molecular systems. A skimmer with

a 2 mm diameter orifice shapes the molecular beam of the source chamber and is the

only opening to the next chamber, which contains a linear ToF-MS. Even with a rela-

tively high pressure in the source chamber (10-4-10-3 mbar) during operation, this small

orifice aids in maintaining a pressure of around 10-6 mbar in the ToF-MS chamber (dif-

ferential pumping). Here, the anions in the molecular beam are extracted by a pulsed

electric field created by fast-rising, pulsed, negative, high voltages at the ToF-MS elec-

trodes, perpendicular to the molecular beam. The anion beam enters the VMI chamber

through an aperture of 5 mm in diameter, confining the anion beam and facilitating the

3. Experimental and Computational Methods

preservation of 10-7-10-8 mbar of pressure even when the source is operating. A 10 Hz

nanosecond Nd:YAG laser with an optical parametric oscillator (OPO) synchronized to

the arrival time of the desired anion, performs photodetachment about 17 cm in front

of the multichannel plate (MCP) detector of the ToF-MS (ToF-MCP detector). The

photodetached electrons are extracted to the MCP detector of the VMI spectrometer

(VMI-MCP detector) by pulsed high voltages on the VMI electrodes, while the neutrals

continue to travel to the ToF-MCP detector.

In general, the neutrals have the same kinetic energy as the corresponding anions,

which are accelerated in the ToF-MS to around 2-4 keV. Hitting the ToF-MCP detector

with such energies generates a measurable neutral signal if the anion intensity is high

enough2. A grid, placed in front of the ToF-MCP detector with a deflecting field for the

anions, allows the background-free observation of the neutral signal. The signal will be

at the same timing as the anion signal and can therefore be used to confirm the desired

photodetachment. Most importantly, both the PADs as well as the signal of the laser

produced neutrals can be measured simultaneously.

Software Setup

The experiment runs at 10 Hz and was controlled through a Software called KouDa,

which was designed in the Molecular Physics (MP) Department in collaboration with the

IT-Support Group (PP&B) at the FHI Berlin. KouDa allows the digital management of

power supplies and triggers as well as the real-time visualization of the ToF spectrum. A

16 bit digital-to-analog converter (16+8 channel Acromac IP231) transforms the digital

information to an analog signal for the power supplies, while the trigger information is

processed in four interconnected digitizer cards (BU 3008 delay generators manufactured

by the Electronics Workshop (E-Lab) of the FHI Berlin). The master clock was provided

by the Q-Switch of the laser. This setup was used in previous projects [68] as well as for

the measurements with the gold complexes. The hardware was updated to a National

Instrument system in 2019. Additionally, new software based on LabVIEW called SDaq

is used.

SDaq was implemented in the MP Department by Uwe Hoppe and provides a collection

of units for different applications. Out of those, programs for controlling the power

supplies and triggers, as well as the observation of the time-of-flight spectrum with a

digital oscilloscope are utilized. Each of these programs controls a hardware module from

National Instruments, which are all encased in a NI PXIe-1082 chassis and connected

to the computer via the remote control module NI PXIe-8381 MXI-Express x8. A NI

PXIe-6738 analog output device with a resolution of 16 bits for voltage control is used.

Two NI PXI-6602 Timing I/O – each with 8 channels, 32 bit resolution and a time base

of 80 MHz3– handle the triggers for the experiment. The conversion of the digital signal

to an analog signal (DAC) takes place in a digital counter panel 6602 (E-Lab # 6186)

built by the E-Lab for each of the timing I/O cards. The module NI PXIe-5160 is a

2Since the gain in neutral signal is low, a high anion signal is required.

3100 kHz and 20 MHz are available as well but are not used here

3. Experimental and Computational Methods

two channel, 500 MHz oscilloscope with a sample rate of 2.5 GS/s and permits real-

time observation of the ToF spectrum. The oscilloscope starts recording simultaneously

with the extraction voltages at the ToF-MS electrodes and stops recording after a time

depending on the minimum sample rate Smin and minimum record length Lmin. Here, a

minimum sample rate of 2.5·108Hz and a minimum record length of 5000 samples are

used and give a recording time of Lmin/Smin = 20µs. The data can be recorded in a

single shot mode or in two different averaging modes. The mode “scan” averages over

a specific amount of shot-to-shot measurements where each measurement has the same

weight, while in the mode “EWMA” (exponentially weighted moving average) the weight

of previous measurements decreases exponentially. During measurement, EWMA is used

to see the most up-to-date averaged data, while mass spectra are saved after measuring

in scan mode.

Since the oscilloscope only provides the flight time of anions and neutrals, a custom-

made program is added to the SDaq project for mass-calibration and for converting

the time-of-flight spectrum to a mass spectrum in real time. Another custom-made

program to fit specific peaks of the measured spectrum with a Gaussian function provides

information about the full width at half maximum (FWHM) of the mass peaks and thus

the resolution of the linear ToF-MS.

With SDaq, a photoelastic modulator (PEM) from Hinds Instruments was imple-

mented for shot-to-shot alternation of the polarization of the light for the PECD mea-

surements. Since the operation of the PEM is determined by material properties it can

not receive trigger signals but only provide trigger signals. Hence, the PEM has to be, in

combination with a pulse-delay generator (Quantum Composer 9420 Series), the master

clock of the experiment. More details about the functionality of the PEM and on how

it is connected with the pulse-delay generator to control the experiment can be found in

section 3.2.4.

3.2.1. Production of Anionic Chiral Systems

3.2.1.1. Laser Ablation Source

The production of anionic chiral complexes Au−-M is performed with an existing laser

ablation source [68,79] consisting mainly of a (gold) target, an ablation laser and a

pulsed electromagnetic valve (em-valve). Here, Au−is created in the laser ablation

region of the source. The neutral chiral molecules are introduced later with a second

perpendicular pulsed em-valve, i.e. reaction valve, and react with Au−to form the chiral

Au−-M.

Laser ablation sources were developed in the 1980s out of the ambition to produce and

investigate metal clusters. Smalley’s research group – as well as the group of Bondy-

bey – were the first to apply this technique in experiments [82–84] and are therefore

often referred to as its inventors. This technique combines two precursor methods: the

laser vaporization technique for creating metal vapors and the pulsed supersonic noz-

zle technique for subsequent cooling. This results in various vibrationally cooled metal

clusters with different charges and sizes, which provide a mass spectrum that is easy to

3. Experimental and Computational Methods

interpret. In comparison to previous methods (e.g. oven sources), extensive heating and

subsequent cooling is avoided, which would impede the formation of big, cooled clus-

ters. Due to these improvements, the laser ablation source – along with its numerous

variations – is still frequently used in modern cluster and material sciences [85].

The design of the here used laser ablation source is based on a source that is used in

another experiment for infrared spectroscopic studies of clusters and cluster complexes

[86]. The source has been described before in detail [68,79,80]. Hence, only a short

and more focused description is given here.

Fig. 3.2.2.: Laser ablation source with two pulsed em-valves. The main valve contains the

carrier gas helium, which crosses the laser ablation zone and entrains laser-ablated material

from a turning metal rod. A second valve, the reaction valve, releases another substance also

seeded in helium. This substance can react with the laser-ablated material and enters the

chamber through a nozzle. All dimensions are given in mm. The figure is not to scale.

Figure 3.2.2 shows dimensions and the essential parts of the laser ablation source,

which are the main stainless steel block for the laser ablation process and the copper

reaction block for reactions with other reactants. The copper block also gives the op-

portunity for temperature control with liquid nitrogen and a controllable heater.

Attached to the main block is a pulsed em-valve (General Valve, Series 9 from Parker,

≈0.8 mm orifice, 28 V, teflon poppet), the main valve, to provide carrier gas (helium).

The carrier gas flows inside the main channel while passing the laser ablation region.

Here, a gold rod (or target) is placed perpendicular to the main channel with a small off-

set to achieve contact between carrier gas and target without blocking the main channel.

A ns-pulsed BRIO Nd:YAG laser (Quantel, Model: Brio/IR-SB) serves as the ablation

laser. Its light passes through a third channel perpendicular to the other two while

3. Experimental and Computational Methods

being focused on the target with a movable convex lens with 250 mm focal length4. The

second harmonic (532 nm) provides enough energy (1-12 mJ/pulse) to create a plasma

and ablate material from the target, which is picked up by the passing carrier gas and

cooled while moving in the direction of the reaction block.

While ablating material from the target, the laser induces structural changes at the

surface of the rod. In order to prevent these changes from accumulating and impeding the

efficiency of laser ablation, the target is turned continuously (mostly ≈1.8 revolutions/h

for a gold target of 6 mm diameter) and simultaneously translated with a stepper motor

and a specially designed target holder (for details see [68,79]) allowing the laser to

always hit a fresh surface.

The reaction block contains a second pulsed em-valve (with the same specifications as

the main valve), the reaction valve, to introduce substances seeded in a carrier gas that

can react with the laser ablation products. In this particular case, chiral molecules like

alaninol are delivered to the laser ablation products.

Another feature of this reaction block is the temperature control between -180

C and

100

C resulting from a combination of liquid nitrogen flowing through a copper spiral

attached to the reaction block and a controllable heater bar (not shown in figure 3.2.2).

The reaction block is thermally insulated from the main block. In this experiment, the

source parts were never cooled but were sometimes heated by several degrees to facilitate

the vaporization of less volatile chiral substances.

Typical products from this laser ablation source are metal clusters. In this thesis a

gold target was used and hence Au−

nare mostly produced. With the introduction of

the reaction valve other types of atoms or molecules can be introduced additionally to

form metal cluster complexes. With the laser ablation source, the focus here is in the

production of the complexes Au−-M.

The formed laser ablation products enter the source chamber through a conical con-

verging-diverging nozzle and pass through a skimmer into the ToF chamber.

3.2.1.2. Plasma Entrainment Source

For the production of deprotonated molecules, a plasma entrainment source according

to Lineberger et al. [81] replaces the laser ablation source (figure 3.2.3). The important

components are two perpendicular em-valves from which one, the main valve, supplies

the chiral molecule via a supersonic expansion and the other, the plasma valve, produces

(mainly) OH−in a pulsed dc glow discharge plasma [87,88] from a special gas mixture.

Argon is used as carrier gas and is the main component of the gas mixture. The OH−is

entrained in the expansion of the main valve to deprotonate the chiral molecule. If the

entrainment happens close to the main valve, further cooling of the main expansion is

achieved. Compared to the laser ablation source, this source can produce deprotonated

molecular anions with higher intensity due to the increased controllability and at a lower

temperature.

4Sometimes a good signal is achieved when the focus is not directly on the target.

3. Experimental and Computational Methods

Fig. 3.2.3.: The plasma entrainment source consists of the main valve, which transports the

chiral molecule and a plasma valve with a hat consisting of electrodes (gray) and macor plates

(white) stacked in an alternating way. The main valve is fixed by a copper clip, which holds

a heater rod (dashed lines) to heat the valve. For heat distribution a copper wire is wrapped

around valve head and line (not shown). The plasma is formed between the electrodes (purple

dot) and produces OH−for the deprotonation of the molecule. The outer diameter of the hat

is ∅38.1 mm (for comparison: the size of a general valve head is ∅33.8 mm). The high voltage

electrode opens in a 40

cone. All dimensions are given in mm. The figure is not to scale.

Constructional Aspects

The em-valves used for this source are recycled from the former laser ablation source

(General Valve, Series 9 from Parker, ≈0.8 mm orifice, 28 V, teflon poppet). For the

sake of purity, the reaction valve, which delivered the molecules, will act as main valve

and is still responsible for the supply of chiral molecules, while the former main valve

will now act as plasma valve for the supply of OH−. In contrast to the laser ablation

source, the poppet in the main valve was changed from a teflon to a more robust PEEK

poppet when the valve was heated for 1-indanol.

Before the valves can be used for the plasma entrainment source some adaptations

need to be made. The plasma valve needs a “hat” in which the plasma can be created.

The hat is shown in figure 3.2.3 and contains the electrodes (stainless steel in gray) and

electrical insulators (MACOR in white) in an alternating way.

The first stainless steel plate is the ground electrode and has direct contact to the

pulsed plasma valve. The following plate is a MACOR plate, which insulates the ground

plate electrically from the subsequent stainless steel plate for high negative voltages

(around 0.5 - 2 kV). The top plate is another MACOR plate. The dimensions of these

3. Experimental and Computational Methods

plates are given in figure 3.2.3. Here, an important value is the channel size of the first

MACOR plate in comparison to the stainless steel electrodes: The channel is 0.5 mm

wider than the channel of the electrodes such that a discharge between the stainless steel

edges is (by design) facilitated.

It is crucial for optimal signal intensity and cooling to carefully select the vertical and

horizontal distance between the main and the plasma valve. The horizontal distance

between the orifice of the main valve and the plasma valve is set to 3 mm. If the distance

were smaller, the valve body would intrude in the plasma expansion and disturb the

entrainment. On the other hand, a larger distance would cause the plasma products to

be introduced after the cooling process and thus heat the molecules again. The vertical

distance between the MACOR surface and the orifice of the main valve is set to a value

of around 13 mm. Here, a closer distance is recommended by Lineberger et al. since the

gas beam from the plasma valves spreads in space and fewer molecules interact with the

main gas beam. [81]

To comply with the vertical and horizontal distances mentioned above, the original

33.8 mm diameter of the main valve’s front plate needed to be reduced. While Lineberger

et al. [81] created their own adapted front plate, here, an original front plate from Parker

is modified, instead, by decreasing its diameter to 20 mm.

Operational Aspects

Normally, a glow discharge plasma operates under low pressure conditions (10−3-

100 mbar) [87,88] with pulse length of 15 - 900 µs and several hundreds or thousands of

volts. The backing pressure can be around 2 - 8 bar for a 150 µs long gas pulse. [88–92]

According to Lineberger et al., voltage gradients between -500 and -2000 V applied for

40 to 140 µs are sufficient for plasma production. The plasma valve operates with around

2.8 bar for 110 - 160 µs, which is similar to the main valve, but the driving voltage is

set such that the plasma valve contributes only around 10% to the total source chamber

pressure. [81]

In this project, a voltage of around -2000 V for 70 to 200 µs is used. The backing

pressure is around 5 bar and the pulse trigger length can be between 170 and 300 µs.

However, the contribution to the total source chamber pressure remains around 10%.

Plasma

The type of plasma is a pulsed dc glow discharge plasma, which is named after the

“glow” generated by excitation collisions of electrons with the neutral part of the gas

(e.g. argon atoms) [88]. The color of the glow depends on the used gas mixture.

Here, the gas consists of 30% H2, 1% O2and 69% Ar and is supplied by the plasma

valve. This mixture is recommended by Lineberger et al. to achieve a significant OH−

signal [81]. The discharge itself occurs in the “hat” of the plasma valve between the

ground and high negative voltage electrode. A plasma is created in this region (purple

dot in figure 3.2.3) and glows in a purple-blueish color.

3. Experimental and Computational Methods

Possible chemical reactions happening in the plasma that lead to the creation of OH−

are

2H2+ O2−→ 2H2O + 6.3 eV (3.2.1a)

e−(3.2 eV) + H2O−→ H2+ O−(3.2.1b)

O−+ H2−→ OH−+ H + 0.1 eV (3.2.1c)

O−+ H2O−→ OH−+ OH −0.4 eV (3.2.1d)

Reactions 3.2.1b-3.2.1d (without the energies) are suggested by [93]. The energies given

here are calculated with B3LYP-D3/aug-cc-pVTZ. The energy of reaction 3.2.1a is

known to be around 5.9 eV, hence an error of 0.4 eV can be assumed for the other en-

ergies. Apart from reaction 3.2.1a water can also be created by heterogeneous processes

at the wall surface [93].

In this setup it is possible to confirm the production of plasma by observing the

discharge either through a window or by monitoring the discharge voltage on an oscillo-

scope. However, plasma formation can also be confirmed by the entrainment of electrons

in the main expansion. Slow and fast electrons have to be detected.

According to reference [81], slow and fast electrons are verified indirectly by the cre-

ation of O−

2and O−in the ToF-MS, respectively. Slow electrons attach to molecu-

lar oxygen and produce exited anionic molecular oxygen (O−

2)∗, which is subsequently

cooled collisionally and thereby stabilized in the presence of the carrier gas argon (equa-

tion 3.2.2b). The attachment of slow electrons to neutral molecules like O2in the main

expansion is possible due to the ambipolar diffusion of the plasma5. Hot electrons disso-

ciate O2into its components and create O−(equation 3.2.3). If the dissociation energy

of O2is considered, hot electrons need to have an energy of at least 5.1 eV, while slow

electrons have less [94].

O2+ e−→(O−

2)∗(3.2.2a)

(O−

2)∗+ Ar →O−

2+ Ar∗(3.2.2b)

O2+ hot e−→O−+ O (3.2.3)

Equation 3.2.1b and 3.2.3 represent two possibilities for the production of O−, which

can be used as proof for successful plasma entrainment and OH−production (equation

3.2.1c and 3.2.1d).

With successful plasma formation and entrainment, the deprotonation of a molecule

from the main expansion can be conducted with OH−. If the molecule is an alcohol, the

deprotonation will preferentially occur at the hydroxy group. For alaninol and 1-indanol,

this deprotonation process is shown in figures 5.2.1a and 5.2.1b in chapter 5.

In addition to deprotonated molecules and the plasma products (OH−, O−

2, O−), the

corresponding Ar clusters are observed by Lineberger. Here, the same products are

observed and it is possible even to observe an Ar cluster with [Ind-H]−.

5Electrons and ions move with the same diffusion rate since slow, heavy ions pull back on the electrons

while the electrons pull the ions forward.

3. Experimental and Computational Methods

3.2.1.3. Comparison of Laser Ablation and Plasma Entrainment Source

The laser ablation source is able to produce a variety of metal containing clusters and

complexes like gold anions. Via side channels placed after the laser ablation region, it is

possible to incite various interactions with other molecules, like chiral molecules, which

keeps the molecules often intact.

In contrast, the plasma entrainment source uses samples with comparably high vapor

pressure or low sublimation enthalpy and hence is more specialized for fluids, gases and

a few solid substances. Due to the presence of OH−, this source is specialized in depro-

tonation and molecules with hydroxy groups are of primary interest. The deprotonation

leads to modified molecules.

Apart from changing sources, the carrier gas is exchanged from helium to argon. This

influences the expansion conditions and should result in superior cooling in the case of

the plasma entrainment source.

Another difference is the different m/z region the mass spectra possess. Since Au is

used here, the mass spectra feature normally high m/z (m/z ≥197) while the plasma

entrainment source in this thesis features mass spectra (MS) at lower m/z. This affects

the resolution of the peaks in the mass spectrum since the ToF-MS has a resolution

dependent on the mass mand the FWHM ∆m(m/∆m) favoring low m.

(a) (b)

Fig. 3.2.4.: Exemplary mass spectra (MS) for the two sources. Left: MS for laser ablation

source with typical source products like Au−and Au−

2and Au−Fen. Right: MS for the

plasma entrainment source with the plasma products O−, OH−and O−

2. For OH−and O−Ar

complexes are observed. A more detailed analysis is given in section 4.2.

Mass spectra obtained with the laser ablation source and plasma entrainment source

are compared in figure 3.2.4. They give a first impression of the capability of the sources:

The mass spectra of laser ablation source working with a gold target (figure 3.2.4a) shows

Au−and Au−

2as well as Au−-fenchone (Au−-Fen). Au−

n>2can also be produced with

this source but are not shown here. Figure 3.2.4b is a mass spectrum from the plasma

entrainment source and features predominantly the plasma products O−, OH−and O−

For all these products respective argon clusters are possible as shown partly in figure

3.2.4b and to an larger extent later in figure 3.2.6. Carbon contaminations (e.g. m/z

3. Experimental and Computational Methods

24 - 26) may be the result from sputtering from stainless steel electrodes since this mass

spectrum was recorded before a (chiral) molecule was introduced to the source.

Although its specialization for ablation of solids, deprotonation is also possible for the

laser ablation source. Figure 3.2.5 shows next to typical laser ablation source substances

(Au−and Au-Ala−), the anion [Ala-H]−at m/z 74 and other substances like [Alan-H]−

and [Alan-OH]−. The deprotonation process could be performed with OH−, which is

probably produced in the plasma of the laser ablation region. However, oxygen and

hydrogen are not supplied actively, which makes the OH−production and, hence, the

deprotonation a rather erratic (side) effect. In contrast, the plasma entrainment source

offers a controlled and hence more effective way for the creation of OH−and consequently,

the deprotonation process.

It should be noted that this mass spectrum is optimized for [Ala-H]−and not for

the gold-alaninol complex. If the source parameters are optimized for the gold-alaninol

complex, the signal would be much stronger and outperform the [Ala-H]−signal easily.

The typical products of the plasma entrainment source depend on the chosen gas

mixture and are, for the here used gas mixture, the plasma products O−, OH−and

O−

2(figures 3.2.4b and 3.2.6). The strongest signals are O−and OH−, indicative of an

effective OH−production. A bond between O−, OH−and argon is also possible (ArO−,

ArOH−) via ion-induced dipole interactions [81,95].

Fig. 3.2.5.: Detection of deprotonation in the laser ablation source. Next to typical laser

ablation source products like Au−(m/z 197) and Au-Ala−(m/z 272), Ala-H (m/z 74), depro-

tonated clusters of alaninol ([Alan-H]−) and clusters with a removed OH group ([Alan-OH]−)

can be found. m/z 88, 101 and 110 can not be clearly assigned to a reaction product or frag-

ment of alaninol. They are considered to be contaminations.

3. Experimental and Computational Methods

Fig. 3.2.6.: MS obtained from the plasma entrainment source. It is possible to create O−

(m/z 16), OH−(m/z 17), O−

2(m/z 32) as well as ArnOH−-clusters at m/z (n·40 + 17) (with

n being the number of argon atoms) and thus reproduce the results of Lineberger et al. [81].

Furthermore, Ar-clusters with O−, O−

2or H−are possible as well, which is not reported in

[81].

However, besides the already reported species new ones are identified here as well:

ArnO−

2and ArnH−(subset of figure 3.2.6) indicating that – so far – every anion produced

in this source can connect to one or several argon atoms.

Another ability of the plasma entrainment source is the production of big argon clus-

ters. ArnOH−clusters with n >40 are reported in [81] and also measured here in

figure 3.2.7. Such clusters were not observed in the laser ablation source since the ex-

pansion conditions are different and argon is known for its high likelihood to cluster in

comparison to helium.

Figure 3.2.8 shows next to the typical products of the source different carbon clus-

ters (C2H−,C2H−

2and C2H2O−). They can also be considered typical source products

since they are generated in the plasma, which sputters material from the stainless steel

electrodes of the plasma valve hat. However, laser ablation also creates a plasma, which

can sputter carbon from the stainless steel of the main block and form various clusters

with Au−(m/z 200 - 260 in figure 3.2.4a). However, they could also be the result of

impurities of the gold target.

Apart from carbon clusters, figure 3.2.8 also shows [Ala-H]−at m/z 74 verifying the

deprotonation process. A relative comparison of signal strength and temperature of this

signal between both sources is not possible but the signal in the plasma entrainment

source is in general more stable and intense than in the laser ablation source. Fur-

3. Experimental and Computational Methods

Fig. 3.2.7.: MS illustrating the production of large Ar clusters with the new plasma entrain-

ment source. Large clusters indicate an effective cooling process of clusters.

thermore, due to the better cooling efficiency of Ar in comparison to He and due to

the supersonic expansion of the plasma entrainment source, the source products will be

cooler than in the laser ablation source.

3. Experimental and Computational Methods

Fig. 3.2.8.: MS from the plasma entrainment source showing typical products of this source

(O−, OH−, O−

2and ArO−

2) as well as Ala-H (m/ 74). Various carbon clusters (C2H−,C2H−

and C2H2O−) can also be considered typical products of this source since they originate from

stainless steel sputtering in the plasma region.

3. Experimental and Computational Methods

3.2.2. Linear Time-of-Flight Mass Spectrometer (ToF-MS)

Fig. 3.2.9.: Wiley McLaren-type ToF-MS with deflection plates to guide the anion beam. The

different species within one pulse are separated by their time of flight, which can be used to

synchronize one specific species with a pulsed laser (green). The species pass through the VMI

setup (partly shown) before reaching the ToF-MCP detector. The VMI setup is encased in a

grounded µ-metal shielding and its repeller can be used for ion gating. The ToF-MS electrode

plates have a dimension of 70x70x1 mm. All distances are given in mm. The figure is not to

scale.

Besides the target chiral anion, both the laser ablation and the plasma entrainment

source, also produce other products originating from e.g. ion-molecule reactions, clus-

tering, fragmentation etc. leading to various masses and charge states. Therefore, a

mass spectrometer is required to isolate the desired substance. One of the available

mass spectrometer types is the quite robust and simple linear Time-of-Flight mass spec-

trometer after the design of Wiley and McLaren (figure 3.2.9)[96]. The voltages on the

repeller and the extractor electrodes are pulsed on when the molecular beam is cen-

tered in between these electrodes. The anions are thus extracted perpendicularly to the

molecular beam, and are separated in time by their mass-to-charge ratio (m/z) in a

field-free drift zone after passing through two acceleration stages (repeller-extractor and

extractor-ground electrodes). The time of flight distribution can be converted to a mass

distribution after adequate calibration. Since this setup is already well established in

science and the ToF-MS for this project is described in detail by Gr¨une in [79] (including

calculation of the focal point) just a short description is presented here.

3. Experimental and Computational Methods

Function of ToF-MS

The physics of charged particles in a field-free drift zone, that were previously accelerated

in an electrical field is quite basic: The potential energy of particles with mass mand

charge q=z·e(ebeing the elementary charge and zthe charge number) is transformed

completely into kinetic energy Ekin and is experienced by all ionic particles in the same

way. If, furthermore, sis the length of the field-free drift zone and E=q·Uthe

effective accelerating field generated by the effective voltage Uthen the kinetic energy

is expressed as

Ekin =1

2m(︂s

t)︂2=z·e·U(3.2.4a)

→t=√︃m

√2U·e(3.2.4b)

For singly negative charged particles the equation z=−1 holds and Uhas to be

negative. Keeping both the distance sand the acceleration voltage Uconstant while

only focusing on the singly charged particle without initial kinetic energy (Ekin,0 = 0),

the arrival time depends solely on their mass m.

It should be noted that the time of flight given in equation 3.2.4b will be lower than

the true arrival time since the particles do not start from the ground plate but between

repeller and extractor (figure 3.2.9). Hence, the true arrival time is the sum of the time

needed to pass through the acceleration stages and the time needed in the field-free drift

zone. However, the time of flight in equation 3.2.4b remains a good first approximation

of the time of flight.

Resolution

In general, the overall resolution rMS is defined over the peak position in the time of

flight or mass spectrum (tor m) and the respective FWHM of the peaks (∆tor ∆m)

rMS =m

∆m=t

2∆t.(3.2.5)

The overall resolution of the ToF-MS is restricted by the space and energy resolution.

Space resolution depends on the initial space distribution (size of the ion package) while

energy resolution is influenced by the initial velocity vectors of two identical ions, which

have the same position and speed but opposite flight directions.

Although a single acceleration stage with a subsequent field-free drift zone would

suffice for mass-to-charge ratio (m/z) separation, adding a second acceleration zone

improves the space and energy resolution of this system clearly [96]. Further design

aspects have to be considered to optimize for space and energy resolution, e.g. the

distances between electrodes are crucial. For space resolution, the distance between

extractor and ground electrode as well as the length of the field-free drift zone should

increase. The energy resolution is also improved by an increased field-free drift zone

but also demands for a decreased distance between extractor and ground electrode.

3. Experimental and Computational Methods

Table 3.2.1.: Typical optimized voltages for ToF-MS for different situations. Above dashed

line: focus is at ToF-MCP. UR/UEis around 1.12. Below dashed line: focus is moved to

photodetachment region. UR/UEis around 1.14. The photodetachment region is around

17 cm before the ToF-MCP detector. Focusing in this region is important for subsequent VMI

measurements.

situation repeller (V) extractor (V)

high kinetic energy anions, focus at ToF-MCP -4000 -3587

lower kinetic energy anions, focus at ToF-MCP -3010 -2684

focus in photodetachment region -3010 -2634

This opposite design requirement demands a compromise between space and energy

resolution. The length of the field-free drift zone is not restricted by resolution but by

the sake of compactness and by the ion loss due to a velocity component perpendicular

to the axis of the flight tube. [96]

Once a satisfying design is found and the dimensions are fixed, the resolution will

be influenced by the applied voltages, the time the particles spend between repeller and

extractor electrode before acceleration as well as the transverse spread of the ion package

in the molecular beam. Good space focus or positioning of the focal point is achieved

by adjusting the voltage ratio between the repeller and extractor electrode. Also, the

decrease of the transverse spread of the ion beam package will improve the space focus.

Improved energy focusing can be achieved with the increase of the ratio between the

total energy of the ion to its initial energy. The initial energy is mostly thermal energy,

which can be reduced by cooling the ion beam. An easier way might be the increase

of the acceleration voltage (the voltage applied on the repeller electrode). For the sake

of space resolution, the voltage on the extractor will be increased accordingly. Another

way to improve the energy resolution is the introduction of a time lag. During the time

lag, ions move to new positions due to their initial velocities, which improves the energy

resolution but downgrades the space resolution. In the end, a compromise has to be

found and influence of time lag on the overall resolution have to be determined for the

individual setup. [96]

For the linear ToF-MS used for this project typical voltages for a good resolution are

given in table 3.2.1 for different situations. The resolution can be up to m/∆m= 500.

Calibration of ToF-MS

Calibration of the ToF-MS is performed with a rewritten form of equation 3.2.4b:

mi=c·(ti+toffset)2(3.2.6)

with t=ti+toffset, where toffset holds all experimental delays (e.g. electronic lag) as

well as the time the ions spend in the acceleration stages. The constant cincludes all

3. Experimental and Computational Methods

physical and geometric constants (s,Uand e). miand tiare the mass and corresponding

flight time for the i-th peak. The identity of at least two peaks in the spectrum need

to be known to define both calibration parameters (cand toffset). For the laser ablation

source, the gold anion and its clusters are taken for calibration since they are easy to

detect in the mass spectrum: Au−has a strong intensity and the clusters appear in

a certain pattern. The plasma entrainment source can be calibrated with its plasma

products (e.g. OH−) and corresponding Ar-clusters (ArOH−). SF−

6and S−are taken as

an additional calibration species.

With both calibration parameters known, the whole spectrum can be converted from

the time domain to the mass(-to-charge) domain. The calibration parameters are pretty

stable over long time periods and calibration is only repeated when the voltages (or the

geometry) change.

Setup and Abilities

Anions produced in the source need to fly approximately 30 cm (figure 3.2.1) from

the nozzle to the perpendicularly oriented ToF-MS and are extracted to the 81 cm

(figure 3.2.9) distant ToF-MCP by a set of three electrodes (repeller, extractor, ground).

Extractor and ground plate have a high transmitance Ni-mesh to guarantee homogeneous

electrical fields in the acceleration stages. Dimensions of the plates and distances between

them for this experiment can be found in figure 3.2.9.

The extraction of anions is accomplished by turning on high negative voltages for

the repeller and extractor plates with two identically constructed HV switches. If the

extractor is switched on 14 ns earlier than the repeller, an enhancement in resolution is

observed probably due to a small delay between the high voltage switches.

The already established HV switches (FHI ELAB 3962.3 and 3962.4) were “push”

switches, meaning the voltage rises fast but decreases slowly since the voltage drops

across a resistor. Later, these switches were replaced with “push-pull” switches (FHI

ELAB 4769), which creates a fast rising and falling voltage giving better control over

the mass spectrometer.

Two spatially separated pairs of deflection plates, placed after the ground plate of the

ToF-MS, are used to guide the ion beam to the MCP detector and rectify the initial

direction the anions possess before entering the ToF-MS as well as possible misalignments

of the ToF electrodes (figure 3.2.9). Later, these deflection plates were replaced with

an Einzel lens. The lens was meant to increase the resolution in the VMI spectrometer,

however it never worked satisfactorily and was then only used for deflection.

Ion-gating is a useful tool to remove certain components from the ion beam before

they reach the detector of the ToF-MS or in other words let pass only a desired m/z

region. The electrical field performing the gating comes from an additional deflection

plate, called the gating plate, and is switched by a “push-pull” switch. Only for the

m/z region of interest the voltages are switched off to provide a window for ions to pass.

This window is normally quite short emphasizing the importance of “push-pull” switches

over “push” switches and fast falling voltages. Ion-gating was initially not implemented

in this setup but can be achieved by exploiting the repeller (or extractor) of the VMI

3. Experimental and Computational Methods

spectrometer as the gating plate. The VMI-repeller is encased in a grounded µmetal

shielding and is placed perpendicularly to the ToF-MS. It is placed close to the ToF-

MCP where m/z separation is sufficient for ion gating (figure 3.2.9). Here, 500 V at the

VMI-repeller are sufficient for ion-gating, but 2000 V were also successfully used.

As already described in the beginning of this section, this ToF-MS is not only able to

detect anions but also neutrals due to a grid placed before the ToF-MCP detector: The

anions pass the grid held at ground potential if no preceding photodetachment is done

and are deflected for a grid voltage higher than the ToF-repeller (here: around 500 V

more) if photodetachment is performed (green circle with cross in figure 3.2.9). Thus

separating anions from the neutrals.

3.2.3. Velocity Map Imaging (VMI)

Next to mass spectrometry, anion photoelectron spectrometry is used to reveal the en-

ergy levels of neutrals by photodetaching one of the anion’s electrons and recording its

kinetic energy, which depends not only on the photon energy but also on the energy

level the electron is detached from. The type of photoelectron spectrometer, which is

used for this thesis, is the VMI spectrometer. Besides energies, the VMI spectrometer

can also measure the momentum of charged particles providing angular information,

which is important for PECD measurements. A description of this technique as well

as corresponding data handling techniques (reconstruction methods), resolutions and

calibration procedures are given here.

Photoelectron spectra and PECD measurements are recorded with a Velocity Map

Imaging spectrometer inspired by the design of Eppink and Parker [97]. It is an electron

lens system made out of three electrodes (repeller, extractor and ground) like shown in

figure 3.2.10. The design reminds of the setup of the ToF-MS, but while for the ToF-MS

homogeneous electrical fields between the electrodes are desired, the VMI spectrometer

is meant to form an electrostatic lens. This is achieved by removing the meshes from the

openings of the extractor and ground electrode6. The electrostatic lens forms between

extractor and ground electrode and focuses every electron with the same velocity vector

(direction and absolute value) on the same point of a detector even if the starting point

of each electron is different. Hence, Eppink and Parker called this technique Velocity

Map Imaging.

Typical VMI images are closed or open rings with diameters, which increase with

increasing electron speed (figure 3.2.10). Open rings look like two half moons, which

can be either parallel or perpendicular to the laser polarization axis. The type of ring

(closed or open) and the alignment of these half moons is connected to the anisotropy

parameter and is reflected in the direction of the electron’s velocity vector (figure 2.2.2).

An important property of the VMI spectrometer is that the absolute resolution can be

adjusted (to some extent) with the repeller voltage since it determines also the spread

in velocity. Best absolute resolutions are achieved with slow electrons, which are yielded

with small VMI-repeller voltages. This is discussed further in section 3.2.3.5.

6Grid wires also remove signal and cause grid deflections blurring out sharp details in the data.

3. Experimental and Computational Methods

Fig. 3.2.10.: Electron Velocity Map Imaging spectrometer according to Eppink and Parker.

The lens setup is covered in a double µ-metal shielding. The molecular (blue) and laser beam

(green) meet in the interaction zone between repeller and extractor plate. Electrons (orange)

with the same velocity vector are focused on the same point of the detector, which consists

of a MCP, a phosphor screen and a CCD-camera. Only the CCD-camera is outside of the

vacuum chamber (indicated by the window). A typical VMI image is shown in orange under

the CCD-camera: Electrons accumulate in closed or open ring structures, where the diameter

is determined by the absolute velocity of the electrons. All electrodes are discs with an outer

diameter of ∅100 mm and a thickness of 2 mm. Other distances are given in mm. The figure

is not to scale.

Since the original publication, several new and more complex designs have emerged to

fulfill different purposes like investigating high-lying Rydberg states, which are sensitive

to electrical fields and therefore require small extraction fields [98], or the recording of

high-resolution data with additional field-correcting electrostatic lenses [99]. Despite

the available sophisticated VMI designs, a simple design like the one of Eppink and

Parker can suffice for vibrationally-resolved spectra if a cold molecular beam is used in

combination with the SEVI method (Slow Electron Velocity Map Imaging) by Neumark

et al. [100,101].

The three electrode design from Eppink and Parker is applied here as well and its

dimensions are shown in figure 3.2.10. The ion packages interacts with a pulsed laser

beam between the repeller and extractor electrodes, leading to photodetachment in the

VMI electrodes center, around 170 mm before the ToF-MCP (figure 3.2.1). The released

electrons are extracted through switched electric fields to the 317 mm distant detection

system composed of a MCP (VMI-MCP) detector with an active diameter of 45 mm, a

phosphor screen (P47) and a CCD camera from Basler. During measurement with gold

3. Experimental and Computational Methods

complexes, the camera model A102f with 1392 x 1040 pixel and a pixel size of 6.45 x 6.45

µm was used but exchanged later for a model with increased resolution. The new model

acA1600-20gm has 1626 x 1236 pixel with a pixel size of 4.4 x 4.4 µm and was mainly

used for measurements with deprotonated molecules. The VMI electrodes are encased

in a double layer µ-metal shielding to suppress interaction of photo-detached electrons

with earth magnetic fields. The shielding ends just before the detection system and is

on ground potential. The material of the VMI electrodes started out as stainless steel.

These electrodes were used mainly for the gold complex measurements7. In the case

of deprotonated molecules, the electrodes were exchanged with electrodes made out of

molybdenum. Molybdenum is paramagnetic and hence can not retain a magnetic field

(without an external one), which can disturb the photodetached electrons. Furthermore

it has a high melting point making it resilient in the case of high voltage discharges and

it does not (quickly) form an isolating oxidation layer if exposed to air.

As mentioned in the beginning of this chapter, the perpendicular setup of the VMI

spectrometer allows simultaneously recording the PES with the VMI-MCP detector

and the signal of neutrals created in the photodetachment process with the ToF-MCP

detector. Unfortunately, the perpendicular setup also causes a spacial displacement of

the photoelectron distribution from the center of the detector since electrons detached

from the ion package always have a velocity component parallel to the ToF axis. This

displacement becomes more important for a smaller acceleration of detached electrons

and for lighter investigated molecules but can be reduced by decreasing the acceleration

voltage at the ToF plates or can be compensated by applying a tilt to the VMI setup.

Here, the VMI spectrometer is tilted and the acceleration voltage of the ToF-MS reduced.

However, the decrease of the acceleration voltage is limited since the energy resolution of

the ToF-MS gets worse for smaller ToF-repeller voltages (section 3.2.2). Another point

is that with a perpendicular setup, the resolution of the VMI spectrometer is coupled to

the energy spread of the ions in the molecular beam. The ToF-repeller voltage influences

this spread but is, again, limited due to the energy resolution of the ToF-MS.

3.2.3.1. Data Acquisition

The electrons are recorded with a imaging quality MCP detector with an active diameter

of 45 mm followed by a P47 phosphor screen, which converts the electron hits into visible

light for a CCD camera to record. For noise/background reduction, the VMI-MCP is

pulsed to an operating voltage of around 1600 - 1800 V for 0.15 µs during measurements

to ensure that only electron signal arising from the photodetachment process is recorded.

Compared to other switched potentials in this experiment, the voltage does not fall to

0 V after a measurement but to a standby voltage of around 1200 V, which is below

the threshold voltage required to detect electrons. Hence, fast (but gentle) switching is

achievable for the VMI-MCP.

7The stainless steel plates were later gold plated to elevate the work function and avoid electron

background but Nickel was probably taken as intermediate layer (acting as “glue”), which is ferro-

magnetic.

3. Experimental and Computational Methods

The data is visualized, collected and saved with a custom LabVIEW program called

“VMI Imaging” that was modified for PECD measurements as well as for continuous

saving within this project. The measurement program has several measurement modes:

normal, continuous, Area-of-Interest (AOI), event and PECD mode. In short, the normal

mode records electron hits as spots, which cover several pixel. The size of the spots

depend on the camera focus and the voltage applied to the VMI-MCP detector. It is

used for calibration measurements due to the fast recording time. If the measurement

restarts several times automatically, the continuous mode is used. This allows for rough

camera alignment work. AOI mode selects (virtually) the region of interest on the CCD

chip of the VMI camera, which will be recorded. The event mode uses centroiding to

assign one pixel to one electron hit resulting in superior resolution in comparison to the

normal mode, which records spots. It is used for the main measurements with linear

polarized light. The PECD mode works in the event mode and saves two alternately

recorded data sets simultaneously and individually. Here, the mode is synchronized with

the shot-to-shot polarization alternation to separate LCP and RCP data (more details

can be found in section 3.2.4). This mode is important, but not restricted to, PECD

measurements.

An electron hit is translated into light by the phosphor screen. If a certain intensity

treshold is satisfied the electron hit is registered and interpreted by the computer as 1.

The hit is saved in a 1236x1060 matrix, which can be illustrated as VMI image. The VMI

image of the current experimental cycle is added to the sum of VMI images of previous

cycles. Only the resulting sum is stored and used further. In the end, one 1236x1060

matrix is created. If operating in PECD mode two matrices are saved, however the

storing concept remains like described for the individual image.

3.2.3.2. Reconstruction of the Original 3D Distribution

Already 35 years before the first VMI spectromter, Herschbach [102] described for reac-

tive collisions in crossed beam experiments reaction products, which have to expand in

spheres (originating from the same center) according to the conservation of energy. The

radius of these spheres are determined by the (kinetic) energy of the reaction products.

Furthermore, the conservation of angular momentum leads to an angular distribution

of the products with cylindrical symmetry. All this was derived by applying Newtonian

mechanics. Even if Herschbach is not naming it as such, he described what is known

today as Newton sphere. The same concept is applicable for other processes as well like

photodissociation, ionization or photodetachment [103–105].

For photodetachment, a Newton sphere consists of electrons and expands until it is

projected as a 2D distribution on the VMI detector leading to the typical (open and

closed) rings visible in VMI images (orange ring in figure 3.2.10). This sphere contains

the information about the kinetic energy of electrons in form of the sphere radius r

and their angular distribution in the form of polar and azimuth angle θand ϕ(figure

3.2.11), respectively. Image reconstruction is required to extract this three-dimensional

information from the projected 2D detector image.

3. Experimental and Computational Methods

Methods for Inversion and Fitting Procedures

One of the earliest reconstruction methods is the inverse Abel method, which was already

applied by Eppink and Parker [97]. It was first introduced by Niels Henrik Abel [106] and

is covered in several text books like from Whitaker [107]. If the y-axis is the direction

the extraction field accelerates the Newton sphere, and if the symmetry axis (e.g. laser

polarization vector for linearly polarized light) defines the z-axis (figure 3.2.11), then the

2D projection f(x, z) of the 3D distribution F(x, y, z) is given in Cartesian coordinates

f(x, z) = ∫︂∞

−∞

F(x, y, z)dy = 2 ·∫︂∞

F(x, y, z)dy (3.2.7)

where the property of F(x, y, z) being an even function is used. Since the VMI exhibits

cylindrical symmetry, r2=x2+y2, the following relation

dy =r

√r2−x2dr (3.2.8)

leads to the Abel transform

f(x, z) = 2 ∫︂∞

|x|

F(z, r)r

√r2−x2dr (3.2.9)

By performing the inverse Abel transformation

F(z, r) = −1

π∫︂∞

|r|

∂f(x, z)

∂x

√x2−r2dx (3.2.10)

a given projected 2D image yields the desired 3D distribution.

This approach is relatively easy to implement and was successfully applied for particles

where the kinetic energy Ekin is small compared to the energy of the extraction field EU

(EU/Ekin ≈1000) but showed discrepancies when both energies become more similar

(EU

Ekin ≪1000) [108]. Unfortunately, further problems like the computationally costly

integration required by the inverse Abel method, a calculation impediment due to the

singularity at r2=x2, and the tendency of noise amplification owing to the derivation

of the 2D image in equation 3.2.10 diminish the allure of this approach [107]. These

problems are tackled with the Fourier-Hankel technique, which is based on the Hankel

transformation of the Fourier transformed projection of equation 3.2.7. The singularity

from before is avoided and noise is reduced. However, the problems with the noise are not

completely solved. In fact, noise is accumulated along the center line (coinciding with the

symmetry axis) of the reconstructed image. Particularly for PECD measurements this

might be a problem since, here, the symmetry axis is defined by the propagation direction

of the light and, hence, is the axis where maximal PECD asymmetry is expected.

The BAsis SEt EXpansion (BASEX) method [109] avoids the direct calculation of the

cumbersome inverse Abel integral in equation 3.2.10 by employing basis set functions

(similar to Gaussian functions) with well-known inverse Abel integrals. Hence, this

3. Experimental and Computational Methods

Fig. 3.2.11.: Projection and reconstruction of the 3D distribution. The Newton sphere ex-

pands until it is projected on the detector. The 2D projection will contain ϕ= 0 contributions

from the 3D sphere, which will be iteratively removed by the POP approach. The full 3D

distribution is recovered assuming cylindrical symmetry.

approach is efficient and computationally inexpensive but – among other things – still

poses the continuing problem of the accumulation of noise at the center line in the

reconstructed image. If prior to inversion with BASEX a transition from Cartesian

to polar coordinates is performed to match the given symmetry of the problem, the

accumulation of noise at the center line is replaced by a less disturbing accumulation

of noise at the center. Furthermore, superior resolution and accuracy, in comparison

to the inverse Abel transformation or (Cartesian) BASEX method, makes this method

more appealing. Since this method employs BASEX in polar coordinates, it is called

pBASEX (polar BASEX) [110].

Another reconstruction method is the Polar Onion Peeling (POP) approach by Zhao et

al. [108], the successor of the (Cartesian) Onion Peeling Method. The fundamental

assumption is that a cylindrical symmetry is present and that the 2D projection contains

ϕcontributions from the 3D Newton sphere, which must be “peeled away” in order to

reconstruct the 3D distribution (shown in figure 3.2.11). This is achieved by repeated

numerical simulations of the 2D image at different values of rwith a numerical fit of the

experimental data, thus completely evading the costly derivation of the 2D image.

In this approach, the distribution of the Newton spheres is expressed in spherical

coordinates (r, θ, ϕ) with an angular distribution independent of ϕdue to the cylindri-

cal symmetry. The corresponding 2D projection on the other hand is described with

R, θ′(figure 3.2.11). Since electrons have a radial (speed) distribution described by the

3. Experimental and Computational Methods

delta function δ(r), they can contribute to a signal on the 2D distribution, which has

a smaller radius than the radius determined by the velocity of the electrons (e.g. at

R<r) [108]. This is the influence of the ϕ= 0 components of the Newton spheres on

the 2D distribution. If the experiment has more than one transition - or rather many

Newton spheres with different radii -, the 2D projection will contain these contribu-

tions as well. The only circumference without the influence of other Newton spheres or

ϕ= 0 contributions is the outermost ring at rmax, which is removed (or “peeled away”)

from the experimental 2D image by subtracting a simulated image gained from fitting a

sine/cosine or Legendre polynomial type function to the experimental image. A “slice”

of the 3D contribution containing the largest rcontribution and a modified experimen-

tal image remain. Afterwards, another simulation of the modified experimental image is

calculated and the peeling process starts once more. The slicing and peeling process is

performed for every value of rand is repeated until the center of the image is reached.

Hence the name “onion peeling”. Finally, with cylindrical symmetry the full 3D distribu-

tion is obtained. Unfortunately, the permanent calculation of the simulated distribution

for every ris time-consuming and slows down the reconstruction process [111]. To speed

up the polar onion peeling (POP) method of Zhao et al. [108], the ideas of pBASEX are

applied to avoid the direct calculation of the simulation of the experimental image and

using basis set functions in polar coordinates, as demonstrated by Roberts et al. [111].

This method is fast enough to perform POP during data acquisition and thus permits

real-time analysis of the 2D images.

All the presented methods to reconstruct the Newton sphere (Abel, BASEX, pBASEX,

POP) are briefly compared for photoelectron imaging by Le´on et al. [99]. All methods

produce a satisfying reconstructed result, with the BASEX method performing a little

better than the others. However, since BASEX faces the problem with center line noise

it is not suitable for PECD measurements and therefore another procedure is chosen.

From the here mentioned reconstruction methods, only POP by Roberts et al. [111] is

used in this thesis. However, other methods like rBasex from the PyAbel package [112]

and Meveler by Dick [113] are also employed. rBasex can be seen as an update to pBA-

SEX, which enables the representation of Newton spheres as linear combinations of the

basis functions. Meveler on the other hand uses a different approach by reconstructing

the distribution with probability theory.

Polar Onion Peeling: Reconstruction Method using Fitting Procedures

In this project, the real time POP method from Roberts et al. [111] is mainly applied

to reconstruct photoelectron spectra measured with linearly and circularly polarized

light. Here, the 2D projection is captured by a CCD camera in Cartesian coordinates

and needs to be mapped on a polar array to convert to polar coordinates (R, θ′) prior

to reconstruction [111]. In order to achieve comparable information content, the polar

pixel size is chosen similar to the Cartesian pixel size. Thus, the differential area remains

almost constant, and the number of polar pixels necessary to form one complete ring at

Rwill scale with R. The intensity of a polar pixel is defined by rotating it by θ′around

its pivot point and combining the signals from the four surrounding Cartesian pixels,

3. Experimental and Computational Methods

which overlap it. Hence the number of angles, at which pixels can be specified, scales

linearly with R, leading to a triangular-shaped 2D image in polar coordinates or polar

image p(R, θ′) (figure 3.2.12). As described in [111], the polar image can be considered

as a sum over individual 2D projections g(r;R, θ′) for all rcomponents of the full 3D

distribution

p(R, θ′) = ∫︂rmax

g(r;R, θ′)dr (3.2.11)

with R < r. The semicolon indicates that the 2D projections are given at a specific

radius r. Assuming there is no signal beyond the edge of the detector, the outermost

ring contains no ϕcontribution and the substitution

g(r;R, θ′) = h(r, θ) (3.2.12)

at r=Rcan be used whereas h(r, θ) can be considered as “3D” distribution without

the ϕcontribution.

Beginning with the largest radius, h(rmax, θ) is fitted to the angular distribution:

I(θ) = N(r)∑︂

bn(r)Pn[cos(θ)] (3.2.13)

where Pnare the nth order Legendre polynomials, N(r) is an intensity factor and bnare

the anisotropy parameters (with b2=β). In this case, nis determined by the physics

of the process. The factors N(r) and bn(r) are the result of the fitting process and lead

to the function gfit(r;R, θ′), which subsequently is subtracted or “peeled away” from

p(R, θ′) for every R≤rmax. This procedure is repeated iterative until the center of the

image is reached.

The main difference to Zhao et al. [108] is that the function gfit(r;R, θ′) is not calcu-

lated but rather obtained with idealized radial distribution functions dr(R). They are

the result of angular integration of isotropic images and create a basis set D(R, r) [111].

D(R, r) only has to be calculated once. dr(R) are loaded once at the start of the routine.

Given the number of polar pixels at r,ρ(r, R) along with their intensities an idealized

isotropic polar image can be computed now:

gideal(r;R, θ′) = ρ(r, R)dr(R) (3.2.14)

Finally,

gfit =gideal(r;R, θ′)N(r)∑︂

bn(r)Pn[R

rcos(θ′)] (3.2.15)

In the case of photoelectron spectra acquired with circularly polarized light, the same

reconstruction methods can be used if the symmetry axis is changed to the axis of light

propagation instead of polarization direction. Simply put, the image is rotated by 90

prior to reconstruction.

3. Experimental and Computational Methods

Fig. 3.2.12.: Elements of the reconstruction program “manip POP v5” used for this thesis.

The “Raw image” contains the recorded image. It can be taken as it is or smoothed prior

to further processing if it was recorded in event mode (not shown). Symmetrization leads

to one quadrant (blue frame). After POP all windows with a green frame are generated: the

deconvoluted Cartesian and polar image as well as the radial PES, which is the result of angular

integration. The anisotropy parameter is calculated in another subroutine (figure 3.2.13).

3.2.3.3. Implementation of POP

The POP method is incorporated in an existing LabView program “manip POP v5”

(figure 3.2.12), which not only enables reconstruction of the image but also has other

features for image preparation. The important steps of the procedure to obtain the

radial PES and anisotropy parameter from a recorded image are as follows:

1. The recorded image is loaded and taken as “Raw image”. If the image is recorded

in event mode, the image is smoothed with a subroutine “Smooth”, which performs

Gaussian convolution on the raw image (A squared matrix of pixels is assigned to

every pixel of the raw image. The size can be set manually).

2. In the case of images recorded with circularly polarized light, the image has be

rotated by 90

, which is done with the self written subroutine “RotateData”.

3. The center of the (smoothed) raw image is estimated with the help of an artificial

red circle (in the raw image of figure 3.2.12)

4. Quadrants of the raw image can be selected

5. The (smoothed) raw image is symmetrized via folding the selected quadrants on

top of each other. This creates the “Symmetrized Quadrant” (blue frame in figure

3.2.12)

3. Experimental and Computational Methods

Fig. 3.2.13.: Elements of the “betaplotter”, which is a subroutine from the main program

“POP” 3.2.12. The interpolated deconvoluted polar image is loaded from the main program.

The “Cut” is the zoomed-in area between the cursors of the interpolated deconvoluted polar

image and also selects the area, which is considered for the determination of the anisotropy

parameter. Integrated cut and fit are shown next to the cut and give the βas well as its

standard deviation.

6. Reconstruction with POP is performed, which generates a deconvoluted Cartesian

and polar image and the radial distribution, which corresponds to a PES.

7. The PES is saved and loaded as reference spectrum, a new image center is chosen

and the procedure is repeated beginning from step 5. The new PES is compared to

the reference PES by eye or with the help of a self written subroutine “Gaussfit”,

which fits a Gauss function to the spectrum and gives for example the FWHM. The

new spectrum replaces the reference PES if it is the better spectrum (resolution).

This is repeated until the best spectrum is obtained.

A former version of this program was already described and used by Yubero [68] but

modified by the addition of the subroutines “Gaussfit” and “Rotate” to analyze the PES

within the same program and adapt it for PECD measurements, respectively.

The anisotropy parameter is obtained via the subroutine “betaplotter” (figure 3.2.13)

after the best spectrum is found. The deconvoluted polar image is loaded from the main

program and is interpolated. Stripes visible in this image correspond to transitions and

can be selected via the cursors. In the example of figure 3.2.13 only one stripe is visible

since only one transition is recorded with the VMI spectrometer. If the area of interest

is chosen with the cursors, a “Cut” is shown, which is a magnified part of the area of

interest. Only the cut is used for the fitting procedure and βcalculation. Here a non-

linear curve fit with the Levenberg-Marquardt algorithm (damped least-squares method)

is used. In short: The errors between model function and a data set are determined,

squared and added together. If the sum is minimized, the ideal fit is found.

Next to POP other reconstruction methods are used, namely rBasex and Meveler.

However, POP will be the main reconstruction program in this thesis and will always be

used if not stated otherwise. It is used for all spectra (obtained with linear or circular

3. Experimental and Computational Methods

polarized light) and for PECD analysis of deprotonated molecules and gold complexes

as well as for the anisotropy parameter in gold complexes.

rBasex

In this thesis, rBasex implemented in the PyAbel package is used [112,114]. Its main

application in this thesis is for the anisotropy parameter of deprotonated molecules and

the reconstruction of PECD images. rBasex can be seen as an improved version of

pBasex. Like pBasex, rBasex uses basis sets in polar coordinates, but applies radial

distributions as basis functions from Ryazanov [115]. They are more convenient since

they have analytical Abel transformations. The 3D Newton sphere can now be described

as linear combination of these basis functions.

A finite number of spherical harmonics Ynm(Θ, ϕ) (with m= 0) describes the 3D New-

ton sphere at each speed and this can also be described in form of Legendre polynomials

Pn(cos(Θ)). A PAD recorded as N×Nimage has only Nr×Nadegrees of freedom, if Nr

is the amount of radial samples and Nathe number of angular terms. Nais, similar to

nfrom equation 3.2.13, determined by the physics of the process and is usually a small

number. Nris normally N/2. Radial distributions obtained from transformed images of

other abel-transformed methods correlate with these degrees of freedom.

Despite the similar implementation to pBasex, there are some major differences:



Projected basis functions are separable into radial and angular contributions since

cosine powers instead of Legendre polynomial are used



Triangular basis functions instead of Gaussian ones, which are more compact; only

neighboring functions overlap



Custom pixel weighting is possible, which helps if part of the images is broken,

blocked or occupied by unwanted signal



Expansion coefficients arise from a simple linear problem, which improves calcula-

tion performance



Less noise in reconstructed images due to restraints on the angular behavior



Denoising experimental images with low electron counts due to non-negativity

constraint

Another important property of this method is that PECD images can be reconstructed

and the dichroism parameter can readily be extracted. In contrast to POP, it is designed

to be a more adequate method for PECD measurements.

Implementation of rBasex

The program reconstructing the image via rBasex is called “rBasex” and is implemented

in python since the PyAbel package is a python package. The program is executed in the

python environment of the command promt and guides the user through the different

3. Experimental and Computational Methods

steps of image preparation, e.g. image transposing and center determination. The center

determined by the corresponding PyAbel function can be calculated via various methods

including a center-of-mass calculation. Unfortunately, the calculated centers do not lead

to a good PES and can merely be taken as a starting point. Like in POP, the true

center has to be found iteratively by comparing PES with different centers until the

best PES is found. If the center is determined with the POP program beforehand, the

POP-center can be used in the rBasex program, which produces better PES than the

calculated centers from rBasex.

MEVIR, MEVELER and MELEXIR: Reconstruction with Probability Theory

Alongside the POP method from Roberts et al. [111] and rBasex, MEVELER (Maxi-

mum Entropy VElocity LEgendre Reconstruction) from Dick [113] – which is based on

the maximum entropy concept – is also used for this project. MEVELER is used to

extract the anisotropy parameter from measured photoelectron spectra and its results

are validated against POP and rBasex. However, POP and rBasex remain the main

reconstruction methods and are used for every spectrum in this thesis.

In addition to MEVELER, two other variants based on the same general concept

are developed by Dick, called MEVIR (Maximum Entropy Velocity Image Reconstruc-

tion) [113] and MELEXIR (Maximum Entropy Legendre EXpansion Image Reconstru-

tion) [116]. Each variant has different advantages and disadvantages: MEVELER and

MELEXIR both assume that the velocity distribution of the electrons can be expanded

in Legendre polynomials. However, while MEVELER only works with the 0th and 2nd

order of these polynomials, MELEXIR employs higher and odd order Legendre polyno-

mials. Because of this, MEVELER is primarily suited for experiments, which use single-

photon detachment (or ionization) with linear polarized light while MELEXIR can also

be used for spectra from multiphoton experiments and even PECD experiments. MEVIR

reconstructs the image without making any assumptions about the velocity distribution

(except the assumption of rotational symmetry around the laser polarization axis) and

can therefore handle data containing higher and odd order Legendre polynomials. How-

ever, similar to other reconstruction methods, MEVIR creates centerline noise and does

not handle low intensity data as good as MEVELER and MELEXIR. Nevertheless, all

these versions perform better than pBASEX, especially in the low intensity region (0.01

counts per pixel) [113,116]. A comparison to POP and rBasex is not made in these

publications.

According to Dick [113], the following four matrices are introduced for all variants: F

is defined as the velocity map, which is the slice cut through the velocity distribution at

y= 0. The (forward) Abel transform (in matrix form) of Fcreates the simulated image

A, which can be compared to the data D. The optimization process is performed on a

hidden map H, which is described later.

All variants work on the same basic principle: Instead of applying inversion to the

data or approximations by fitting functions, the most likely velocity map for the given

data is selected with the help of probability theory. In particular, the method selects the

velocity map that maximizes the probability Pr(F|D), which denotes the likelihood that

3. Experimental and Computational Methods

a given velocity map was produced by the given data. Casually speaking, the “trust”

one has in the solution Fbased on the actual data Dis maximized. This conditional

probability can be rearranged according to Bayes’ theorem

Pr(F|D) = Pr(D|F)Pr(F)

Pr(D)(3.2.16a)

Pr(D|F) = 1

Zexp(−L) (3.2.16b)

Pr(F) = αS (3.2.16c)

Pr(D) = const. (3.2.16d)

with Pr(D|F) being the likelihood that the data Dis produced given velocity map F,

Pr(D) the probability of D, Pr(F) probability of F.Zis a normalization constant, L

the maximum likelihood estimator, which is a measure for the similarity of the simulated

image A(obtained from F) to D.Sis the entropy and reflects the information content

of the velocity map F.

S=−

∑︂

i=1

Filn Fi

eBi

(3.2.17)

for a strictly positive map. Biis a default map for the situation before data is recorded.

If Fis of dimension NxM,NFis one of the dimensions of the map F.

Maximizing Pr(F|D) is equivalent to maximizing Pr(D|F) and Pr(F). In other words,

Lhas to be minimized and Sto be maximized. Hence, this is called the maximum

entropy concept.

First Lis minimized below a certain threshold L0. For this, from all possible velocity

maps, those that create simulated images Awith the most similarity to the actual data

are chosen. The size of this map selection depends on the desired accuracy defined by

L0. From this selection, the map with the smallest information content (= the maximum

entropy) is then selected as F to maximize S. Consequently, information not supported

by the data is not contained in F.

The optimization process, minimizing Land maximizing S, is performed on a hidden

map Hand gives F. The hidden map is connected to Fvia a linear transformation and

introduces correlations between adjacent rows of F. Different “layers”, with each layer

replacing a pixel value by a weighted average of this pixel and its eight adjacent ones,

are possible. Often just one, or a few, layers are needed for the reconstruction. However,

if working with low intensity measurements (0.01 counts per pixel), the layers increase

the quality of the reconstruction and create spectra in a better quality than pBASEX

[113].

Since the velocity map in MEVIR is (largely) free of assumption, all information

is contained in the velocity map Fand Legendre polynomials are not needed for the

map itself. However, for this kind of experiment, the velocity distribution Qn(v) is

needed, since they give the anisotropy and dichroism parameter. Qn(v) is obtained from

the map and projection with Legendre polynomials and can be expanded in Legendre

3. Experimental and Computational Methods

polynomials. The anisotropy parameters are then obtained by

bn(v) = Qn(v)

Q0(v)(3.2.18)

with nbeing the order of Legendre Polynomials. For an anionic chiral system pho-

todetached via a single photon process only n= 1 and 2 will be of importance, where

b1describes the dichroism parameter for PECD measurements and b2the anisotropy

parameter (or β).

In MEVELER, the size of matrix Fis reduced by employing a small number of Leg-

endre polynomials8. The number of polynomials depends on the type of experiment

conducted. In contrast to MEVIR, an assumption about the velocity distribution is

made before the optimization process. Hence, a map is not the result of the optimiza-

tion process but a velocity distribution. The anisotropy parameters are calculated like

in MEVIR (equation 3.2.18).

So far only the velocity distribution is expanded with Legendre polynomials but this

expansion can be done with the image data as well. This is the idea of the program

MELEXIR [116]. Images containing higher order or odd order Legendre polynomials are

of better quality and can be reconstructed faster9than with MEVELER. Consequently,

MELEXIR is technically not only adequate for PES with linear polarized light but also

for PECD experiments.

Implementation of MEVELER and MELEXIR

The MEVELER program provided by Dick [113] works via the command promt (cmd)

and needs two command lines: one command line for the preparation of the image,

which includes quadrant selection, image transposing and the calculation of the image

center. The center can either be entered by the user or is calculated by the program

by calculating the center of mass. The second command line is responsible for the

reconstruction itself. Here, the method (MEVIR, MEVELER or MELEXIR) can be

chosen as well as the order of Legendre polynominals and if only even or also odd orders

need to be considered (odd order only for MEVIR and MELEXIR). Output files include

a summary of the selected options, a reconstructed quadrant of the image (only for

MEVELER) and velocity distributions. The velocity distributions are used for the radial

PES and anisotropy (and dichroism) parameters. Instead of writing command lines, a

LabView program was designed here as operational help, which writes the command

line in the command promt depending on the selected buttons.

Comparison: POP, rBasex and Meveler

For the comparison, the PADs of two atomic anions, namely Au−and S−, are recon-

structed with all three reconstruction methods, POP, Meveler and rBasex. The resulting

8In MEVIR the size of Fis the same as for the data matrix

9This means reconstruction in real time like the POP method from Roberts [111].

3. Experimental and Computational Methods

photoelectron spectra as well as the anisotropy parameter are compared in figure 3.2.14

and 3.2.15.

(a) (b)

Fig. 3.2.14.: Photoelectron spectra for Au−(a) and S−(b) analyzed with different recon-

struction methods. The FWHM is given for the most intense peak in the spectrum for each

reconstruction method. POP, Meveler and rBasex perform similar in both spectra but POP

gives slightly narrower peak widths. In the PES for Au−POP is visibly better than Meveler

and rBasex.

The photoelectron spectra have for all reconstruction methods the same general spec-

tral content and differ only slightly in peak width. However, POP could be declared the

“winner” by a small margin since it has the lowest FWHM (best resolution) in the main

peak of the Au−and S−spectra (figure 3.2.14a).

The easiest case for the analysis of the anisotropy parameter is Au−since the electron

originates from a 6sorbital, which corresponds to the transition from 1S0(anionic ground

state) to 2S1/2 (neutral ground state) and should have, according to the Cooper-Zare

formula (equation 2.2.19a), an anisotropy of 2 regardless of the kinetic energy (parallel

transition). This will be used as benchmark for the three reconstruction methods and

helps to identify the uncertainty of all methods dependent on the kinetic energy.

Unfortunately, relatively big deviations can be seen for all methods, especially at low

kinetic energy for POP and rBasex. The reason for this deviation can not be explained

with the way the data was analyzed, e.g. quadrant selection was used, the determined

center of the PAD and the correct extractor voltage were confirmed. Furthermore, the

circularity of the PAD is checked and higher order anisotropy parameter (e.g. b4) are

considered as “correction parameters” for possible deformations. Last but not least, the

data was also plotted over the radius of the transition (not shown) since reconstruction

methods based on polar coordinates are known to accumulate more noise in the vicinity

of the image center. However, no correlation could be made out. The experimental setup

of the VMI seems to be not ideal for anisotropies measured at low kinetic energies.

Meveler seems to give the best performance in the lower kinetic area regime (Ekin <

1.5 eV), but it is suspicious that the values given from Meveler are error free and did

not deviate from 2 for all digits given (2.0000), whereas POP and rBasex always have at

least little deviation. Furthermore, Meveler does not perform differently from the other

methods in the S−case (figure 3.2.15b). This leads to the assumption that Meveler

3. Experimental and Computational Methods

(a) (b)

Fig. 3.2.15.: Anisotropy parameter obtained from three different reconstruction methods

applied for Au−(a) and S−(b). For Au−the electron originates from an sorbital and should

give β= 2 according to the Cooper-Zare equation (equation 2.2.19a). These deviations between

the experimental and theoretical values are used as error for the reconstruction methods. For

S−, the electron stems out of a porbital. Several unresolved contributions can influence the β

parameter especially in the high kinetic energy range but all relevant ones also have pcharacter.

Fitting all three data sets to the Cooper-Zare equation leads to similar fit parameters A∼0.8.

The black dotted line represents the Cooper-Zare equation for this fit parameter A= 0.8. The

legend given for S−is also valid for Au−

(forcibly) caps the βparameter for values beyond the limit. In the kinetic energy regime

Ekin >1.5 eV, POP seems to give more accurate values than the other methods.

In the case of S−, the performance of the reconstruction methods is difficult to evaluate

since there seems to be no reported value for the anisotropy of S−or the Hanstrop

parameter needed for equation 2.2.19a. However, what is known is that the transition

known as electron affinity happens between 2P3/2 (anionic ground state) and 3P2(neutral

ground state). Overall, six transitions between an energy of 2.01 and 2.15 eV can be

found but are of weaker intensity than the origin band (which give the electron affinity).

Due to a too low intensity or energetically close transitions not all of these transitions

can be resolved. They are partly resolved for smaller kinetic energies but merge to just

one peak if the kinetic energy becomes too high. Concerning the analysis of β, the βat

high kinetic energies will probably be a mixture of these different transitions. Luckily,

all six transitions are of pcharacter and βwill not experience much manipulation due

to “orbital mixing”.

Despite missing literature values, it seems like all methods perform in a similar manner

in the energy regime up to Ekin = 2.5 eV. Beyond that region, Meveler and rBasex still

give comparable values but POP clearly deviates to higher values. A fit based on the

Cooper-Zare formula (equation 2.2.19a) with the Hanstrop parameter Abeing the fitting

parameter leads for all reconstruction methods to A≈0.8. The corresponding Cooper-

Zare formula is given as black dotted line in figure 3.2.15b.

Another aspect is quality of the reconstruction method on the PECD parameter but

there are no literature values for PECD on anionic gold complexes and deprotonated

molecules, which could be used to judge over the performance of POP, Melexir and

3. Experimental and Computational Methods

rBasex. However, only POP is used to analyze the PECD value since here rBasex and

Melexir, both, give obvious wrong results meaning that the calculated b1’s does not

coincide with the raw PECD images. In comparison to POP, rBasex is able to produce

reconstructed PECD images directly, which serve for visualization purposes. Melexir

should be able to do the same but extracting a reconstructed image is more difficult.

Estimation of Error

(a) (b)

Fig. 3.2.16.: Deviations of the βparameter from the theoretical value (∆β=|2−βAu|, with

βAu being the βparameter from figure 3.2.15a) for POP (a) and rBasex (b). This deviations

can be considered as error for the corresponding reconstruction method. The deviations are

arbitrarily approximated with a linear error function (black dashed lines) and approximate

errors over the whole kinetic energy range.

The size of the experimental error in the determination of βhas been estimated from

the deviation ∆βfrom the theoretical value of β= 2 for the transition 2S1/2 ←1S0in

the photodetachment of Au−. Only POP and rBasex are considered in the following

since Meveler is not used in this thesis for the determination of the βparameter. The

deviation ∆βfor POP and rBasex are visualized in figure 3.2.16 and are arbitrarily fitted

with a linear function:

∆βPOP =−0.20 ·Ekin + 0.45 (3.2.19)

for POP (figure 3.2.16a) and

∆βrB = 0.09 ·Ekin + 0.38 (3.2.20)

for rBasex (figure 3.2.16b). These functions will be used for the gold complexes in chapter

4and for the deprotonated molecules in chapter 5to estimate the error of anisotropy

parameters for different kinetic energies.

3.2.3.4. Calibration and Optimization

For a meaningful photoelectron spectrum, two important preparations have to be done:

voltage optimization and energy calibration. With voltage optimization the goal is to

3. Experimental and Computational Methods

obtain the best resolved PES. Calibration assigns the radial position a kinetic or binding

energy, which is needed in order to be able to assign the measured transition.

Voltage Optimization

To achieve sharp images, the voltage ratio between repeller and extractor needs to be

set accurately and has to remain stable during the whole measurement. An appropriate

voltage ratio is determined by the VMI geometry and identified in a voltage optimization.

For optimization (and calibration) atomic anions are best suited due to their simple and

well-known spectra [117]. The aim is to obtain the best resolved atomic spectra with a

FWHM that is only determined by the VMI setup. The voltages producing this spectrum

are then taken for the main measurement with the target anionic system.

First, the repeller voltage URneeds to be selected, which determines the maximum

of the kinetic energy for the electrons being detected. The repeller voltage is mainly

restricted by the limits of the power supply and HV switch. Here, this limit is around

5 kV and corresponds to a maximum kinetic energy of around 5 eV, which can be

recorded. The corresponding extractor voltage UEcan be set by performing different

measurements with iteratively modified extractor voltages and subsequent comparison

between the corresponding reconstructed photoelectron spectra. The ideal extractor

voltage is detected when the best-resolved spectrum is attained. In this setup, the

optimal voltage ratio UR/UEis at around 1.47. An example of this optimization is shown

for Au−with a repeller voltage of 750 V in figure 3.2.17. Here, the best resolved PES is

the one with the smallest FWHM at an extractor voltage of 510 V, which corresponds to

UR/UE= 1.471. This voltage optimization needs to be repeated every time the repeller

voltage, the light path and/or the extraction time of the electrons is changed.

For the gold complexes Au−is taken to optimize the voltages. Two exceptions are

Au−-Men and Au−-3HTHF at Eph = 3.49 eV for which the complex itself was taken for

voltage optimization after the binding energy of the complexes had been determined.

This is quite unusual but the aim was to get the best (relative and absolute) resolution

(section 3.2.3.5) while keeping the transition at large radius and to be able to measure

PECD asymmetries at low kinetic energies. Unfortunately, Au−had no transition in that

region and other calibration material like Cu−did not work out. For the deprotonated

molecules S−is mainly used.

The optimal ratio of ≈1.47 for repeller and extractor voltage is used if VMI measure-

ments are performed (VMI mode). However, if the voltages of repeller and extractor

are almost equal, the VMI is operating in spatial imaging mode [118]. Here, the detach-

ment (or ionization) coordinate is mapped one-to-one to the detector coordinate. The

resulting image is a spatial map of the molecular beam [118]. This mode of operation

can reveal deviations of the molecular beam from the center line.

Voltage optimization for a PECD measurement does not only focus on the best re-

solved spectra but also on the intensity difference of the photoelectron spectra belonging

to the image halves for forward and backward direction with respect to the light propaga-

tion. Hence, the PAD is reconstructed for the forward and backward direction separately

and the intensities are compared with each other. The extractor voltage producing spec-

3. Experimental and Computational Methods

Fig. 3.2.17.: Voltage optimization exemplary on the transition 2S1/2 ←1S0of Au−with

Eph = 3.024 eV. The repeller voltage URis set to 750 V and the extractor voltage UEis varied.

The FWHM of the transition in the radial PES is determined for each UE. The best resolved

PES is obtained with UE= 510 V, which corresponds to UR/UE= 1.471.

tra of the same intensity in both halves, for a achiral molecule detached with linearly

polarized light, is taken as voltage for the PECD measurement.

At the moment, the reason for this intensity difference despite good voltage optimiza-

tion is not identified. Many tests were performed to resolve this issue but only lead

to theories, which can be excluded: the VMI-MCP detector does not have halves with

different qualities. Lens errors, like in an optical lens, could be checked to some extent.

Magnetic and electrical stray fields could be excluded and light polarization as well as

the measurement mode (Normal, Event) were considered. In the end, similar intensi-

ties in both detector halves can only be achieved by adapting the extractor voltage and

sacrificing some resolution.

Voltage Stabilization

The use of a wide voltage range in the VMI spectrometer makes a large amount of kinetic

energies available to the experiment and opens possibilities for the investigation of many

states (with high and low binding energies) at once leading to a “overview” spectrum

of the system. On the other hand, small kinetic energies and hence smaller voltages

are preferred if a specific state is wished to be studied in more detail since it leads to a

better absolute resolution (section 3.2.3.5). Reliably using these different voltage-ranges

requires the consideration of voltage resolution and accuracy of the power supplies.

3. Experimental and Computational Methods

Voltage resolution defines the smallest adjustable voltage interval and needs to be

small in order to come close to the ideal voltage ratio UR/UE≈1.47, consequently

obtaining a good resolved PES, e.g. for UR= 750 V, the power supply for UEhas to

be able to adjust the voltage by (at least) 1 V or else the ideal voltage ratio can not be

found (figure 3.2.17). Accuracy on the other hand gives the deviation the output value

can have from the set value and describes fluctuation. Keeping the fluctuations small is

important for long measurements since voltage drifts can change the quality of the PES

during the measurements, e.g. if the power supply drifts by 1 V over time the FWHM

can become worse (figure 3.2.17).

During voltage optimization UEis changed until the ideal, setup specific UR/UEratio

is reached. The variation (derivative) of UR/UEat the point of ideal UEbecomes smaller

for higher UR. For small URa change in UEof 1 V has a noticeable influence and UR/UE

will deviate from the ideal ratio resulting in a worse resolved PES (figure 3.2.17). The

same can be said for a constant UEbut with changing UR. Consequently, working with

voltage of different order requires different voltage resolutions and accuracies. If voltages

of e.g. UR= 10 V are used, power supplies with good resolution and accuracy have to

be taken while for e.g. UR= 1000 V less technical requirements can be demanded.

Three different power supplies are used for three diverse voltage ranges that are

adapted for voltage resolution and accuracy for the corresponding voltage ranges to

provide the VMI voltages. The NHQ215M power supply by ISEG Spezialelektronik

GmbH covers the range from 2 to 5 kV. It has an accuracy of ±(0.05%Uoutput + 1V)

(Uoutput being the set output voltage), which peaks at ±2.5 V. The resolution is 1 V.

However, it becomes highly unstable for lower voltages. The range of 0.1 to 2 kV

is provided by SHQ222M from ISEG. Here, the resolution is 0.1 V and accuracy is

±(0.05%Uoutput + 0.4V) (maximum accuracy ±1.4 V). For even lower voltages of 0-

120 V, the PLH120-P from LXI is used since the resolution and accuracy is better with

0.01 V and ±(0.05%Uoutput +0.05V) (with maximum accuracy of ±0.11 V), respectively.

To obtain long-term stability a feedback loop is used via a NI AD/DA card and a PID

control through a LabView based software [68]. The voltages are stabilized by a ca-

pacitor of 0.5 µF before they enter the high voltage switches, which were identical in

construction to the ToF-MS HV switches. In order to improve jitter, rise time and noise

of electrons on the VMI detector, these switches were replaced by a double push-pull

switch with a rise and fall time of around 80 ns. Furthermore, the push-pull switch allows

ion-gating in ToF-MS by switching an ion-deflecting electrical field between VMI-repeller

and VMI-extractor like it is already explained in section 3.2.2.

Energy Calibration

Energy calibration is necessary to determine, which pixel radius belongs to which ki-

netic energy to thereby obtain the binding energies of a new (molecular) system. An

unambiguous calibration requires a spectrum measured with the optimized voltage ratio.

The raw VMI data after voltage optimization with the corresponding reconstructed

image and PES is shown in figure 3.2.18. A total of around 2 ·106electrons are recorded

within almost 3000 experimental cycles in normal mode. The color scale shows the

3. Experimental and Computational Methods

Fig. 3.2.18.: Raw data, reconstructed image and PES obtained with a VMI measurement of

the S−anion at hν = 4.28 eV. The direction of the laser and molecular beam are given in

the left down corner. The radii of the circles give the kinetic energies of the photo-detached

electrons and lead to the binding energy since the photodetachment energy is known. Two

features can be clearly discerned, which are at 2.08 eV and 3.22 eV. The first feature actually

consists of several unresolved transitions but the most prominent is the feature belonging to

the electron affinity 3P2←2P3/2 at 2.08 eV. The second feature belongs to 1D2←2P3/2. The

angular distribution (here: half moons) disclose the asymmetry parameter β.

normalized number of electron hits (“electron intensity”) at each pixel position of the

detector. Areas with the most hits are indicated with red or white color, while areas

with low hits are black/dark blue. Most of the hits accumulated in a ring-like structure

with a radius riin pixel (px).

Every ring with radius ricorresponds to electrons with a specific kinetic energy Ekin,i.

Ekin,i =k·r2

i(3.2.21)

where kis a calibration factor depending on the VMI geometry and the voltages applied

to the VMI electrodes.

Using the detachment laser energy Eph =h·ν, the binding energy EB,i is deduced as:

Eph =Ekin,i +EB,i (3.2.22a)

→EB,i =h·ν−k·r2

i(3.2.22b)

The constant kis determined in an energy calibration via an initial measurement of

a system with well-known energy levels, like atomic anions. The atomic anion is ideally

3. Experimental and Computational Methods

Fig. 3.2.19.: Trigger scheme (not to scale) for the measurement with S−in figure 3.2.18.

Gray values give the length of a trigger signal while the colored values at the trigger labels

give the start depending on another trigger signal, e.g. the plasma valve starts 786 µs before

the beginning of the the discharge voltage trigger indicated by the blue vertical line below the

blue horizontal line and is on for 299 µs.

chosen such that at least one energy level is close to the energy level of interest in the

desired molecule as resolution scales with kinetic energy (section 3.2.3.5).

Once kis known, every radius in every raw VMI image can be converted into a kinetic

energy, yielding the binding energy as shown in equation 3.2.22b and figure 3.2.18. While

kbarely changes in day-to-day operation, energy calibration must be repeated every time

changes occur at the VMI spectrometer, like electrode voltage changes or variations of

the detachment laser’s light path.

The calibration is performed using Au−, S−and Br−. Au−is used for the gold

complexes and is easy to obtain with a laser ablation source. For the plasma entrainment

source, Br−and S−are used and produced by introducing bromobenzene or OCS in the

discharge of the plasma valve, respectively. For the measurement of [Ala-H]−the VMI

spectrometer is calibrated first with Br−and later with S−, while for [Ind-H]−S−was

exclusively used.

3.2.3.5. Energy Resolution of VMI Images

To assess the quality of a VMI picture or the corresponding PES the resolution must

be taken into account. The aim is a PES with well separated features for unambiguous

assignment.

3. Experimental and Computational Methods

Here, resolution is distinguished between absolute kinetic energy resolution ∆Ekin

and relative kinetic energy resolution resr. The absolute energy resolution describing

the spread of the kinetic energy is obtained by

Ekin =1

2mv2(3.2.23a)

→∆Ekin =mv ·∆v(3.2.23b)

and increases with higher velocity. In other words: the best absolute resolution is

obtained with slow electrons.

Relative resolution is defined as

resr=∆Ekin

Ekin

(3.2.24)

and improves with better absolute resolution and higher kinetic energies. However, due

to the improvement of absolute resolution with low kinetic energies a contradiction is

found and a compromise is demanded.

Differentiation of equation 3.2.21 leads to the following relation between kinetic energy

and radius. ∆Ekin

Ekin

= 2∆r

r(3.2.25)

Consequently, transitions at a large radius rhave the best relative energy resolution,

but low energy electrons have the best absolute resolution. Additionally, low repeller

voltages used for slow electrons provide the highest degree of adjacent ring separation.

As already mentioned, in order to ensure voltage stability, three different power sup-

plies are used to cover three voltage ranges: 2-5 kV with NHQ215M, 0.1-2 kV with

NHQ222M and 0-120 V with PLH120-P. All three voltage ranges were used for calibra-

tion measurements with different atomic anions to demonstrate the reachable energy

resolution by Yubero [68]. Here, absolute resolution improves with smaller VMI-repeller

voltage (which determines the velocity of electrons) and is best for a repeller voltage

of 40 V with ∆Ekin = 1.35 meV. Yubero also shows a smaller relative resolution for a

transition at high kinetic energy in comparison to another transition within the same

measurement at a smaller kinetic energy. The best relative resolution could be achieved

with 3.4%. Overall, both the relative and the absolute resolution improve with smaller

repeller voltages.

Here, absolute and relative resolution for Au−and S−PES behave like observed for

Yubero [68]. However, an extensive investigation of the best possible resolution is not

undertaken but the best absolute resolution of 0.01 eV measured here for Au−can be

reported and four out of six transitions for S−between 577 - 614 nm can be resolved.

More details can be found in section 3.2.6.

3. Experimental and Computational Methods

3.2.4. Laser System and Polarization Techniques

The laser system described and used here provides a wide range of photon energies for

photodetachment. Additional optical elements like retarders and a PEM give control

over the polarization of the laser beam, which is important for anisotropy (β) and PECD

measurements.

The photoelectron detachment of the anions is realized with a laser system operating

at 10 Hz and is able to produce ns laser pulses in a range of 0.62 - 5.77 eV. This laser

system consists of a Nd:YAG laser (Surelite II, SL II-10 from Continuum) serving as

a pump laser for an Optical Parametric Oscillator (OPO Continuum Panther) used for

wavelength tuning. The pump laser is operated at its third harmonic (355 nm) and

produces pulses with a width of 5-7 ns and a jitter of less than ±1 ns. The light is

linearly polarized in horizontal direction and (the third harmonic light) has a pulse

energy of around 160 mJ. The subsequent OPO converts the wavelength to 205-2000 nm

through a combination of optical parametric oscillation and frequency doubling, leading

to a reduction of the initial pulse energy due to the non-linear nature of these processes.

The visible range (410-700 nm), called “signal”, and IR range (700-2000 nm), known

as “idler”, only require the optical parametric oscillation process and can reach pulse

energies up to 45 mJ and 25 mJ, respectively. The polarization of the signal is vertical

while it is horizontal for the idler. For the UV-purple regions (210 - 355 nm and 355 -

420 nm), frequency doubling is used. This further reduces the pulse energy to 3 mJ and

<1 mJ, respectively. 355 nm can be taken directly from the pump laser, which passes

the attenuator in the OPO but not the non-linear crystals, resulting in a higher output

pulse energy for the experiment.

For polarization manipulation waveplates and polarizers are used. Here, achromatic

waveplates from Thorlabs are implemented, which cover a large wavelength area: The

quarter waveplates (QWPs) cover 260 - 410 nm (AQWP05M-340) and 400 - 800 nm

(AQWP05M-600), respectively. The same spectral range can be achieved for the half

waveplates (AHWP05M-340 and AHWP05M-600). The polarizer is a Glan-Laser alpha-

BBO Polarizer (GLB10, SLAR MgF2) from Thorlabs and covers 210 - 450 nm. The

spectral range above 450 nm is reached with a polarizer from Standa (Glan polarizer,

220 - 2300 nm).

Several broadband mirrors and prisms guide the laser pulse into the VMI chamber.

Since reflections could lead to a change in polarization of the incident light if the incidence

angle is not 90

, a λ

2waveplate and polarizer is used to ensure vertical polarization right

before the VMI chamber. Instead of a polarizer, a Brewster window attached to the

VMI chamber can be employed, like it was done in earlier experiments with this setup

[68,80]. In this project, the Brewster window is replaced with a flat, UV-graded, fused

silica viewport (by VACOM) to allow PECD measurements with circularly polarized

light. In general, a λ

2waveplate sufficed for the restoration of vertical polarized light.

During the first attempts to measure a PECD signal, the same λ

2waveplate is used like

for the measurements with linearly polarized light to provide a correct initial polarization

for the subsequent static λ

4waveplate with fast axis position at 45

or -45

for LCP or

RCP light, respectively. In order to check for the quality of circular polarization, a

3. Experimental and Computational Methods

Fig. 3.2.20.: Optical setup to generate LCP/RCP light with a static waveplate and the

measurement of the Stokes parameter with the rotating quarter waveplate method (black

dashed box). The second quarter waveplate is turned in e.g. 22.5

steps and the modulated

intensity is measured at the detector. The position of the fast axis and the intensity lead to the

Stokes parameter. Optical elements in the black dashed box are removed for measurements.

second static λ

4waveplate, a polarizer and a photodiode were installed to receive and

analyze the Stokes parameter with the rotating λ

4waveplate method as described in

[119]. Of course, the analyzing optical elements were removed for measurements. A

scheme of this optical setup is shown in figure 3.2.20.

With this setup, the change between LCP and RCP light is quite slow since the

waveplate has to be turned manually. Consequently, signal changes due to short and

long term laser intensity fluctuations and drifts of source conditions [120] can add up

differently in measurements for LCP and RCP measurements and lead to spurious signal

differences, which are not originating from a dichroism effect. In order to alleviate this

behavior, a shot-to-shot alternation of the polarization is required. An optical retarder

that can create circularly polarized light within the wavelength range of the previously

described laser system and that is suitable for quick axis changes with at least 10 Hz is

necessary to perform the shot-to-shot measurement.

For this a photoelastic modulator (PEM, Hinds Instruments, Model I/FS50) is added

to the experiment. The optical element of a PEM is an isotropic material like fused

silica where oscillating strains impose a varying birefringence and, therefore, modify the

retardation of a light beam passing through the silica. This oscillation frequency is

inherent to the PEM since it depends only on material properties such as length and

speed of sound of this material [121,122]. The model I/FS50 used in this experiment

operates at approximately 50 kHz (50.02 kHz to be exact).

The main consequence of this inherent oscillation is the necessity for synchronization

with the laser and the whole experiment, which is described below. Another possibility of

alternating the polarization in a fast way would be to use Pockels or Kerr cells, but these

materials already have an intrinsic birefringence that does not have the same direction as

the electrically induced one. Hence, for a laser beam that is only 1-2

off-axis, the light

would already experience a superposition of a fraction influenced by the electrically

induced birefringence and a fraction influenced by the intrinsic birefringence, which

therefore leads to a significant change in polarization. In contrast, the PEM tolerates a

3. Experimental and Computational Methods

much bigger angle of off-axis beams (50

if a 10% retardation deviation is accepted)[121]

and, therefore, facilitates straightforward alignment work.

3.2.4.1. Synchronization

Since the 50 kHz frequency of the PEM is inherent to the mechanical properties of

the optical element (e.g. its resonance frequency), no external trigger can be applied

and, consequently, the PEM has to be the master clock for the experiment. Also, the

50 kHz needs to be down-modulated to be compatible with the 10 Hz experiment and

synchronized in a way that a laser pulse passing through the PEM experiences a +λ

and −λ

4retardation, respectively.

In order to gain knowledge about the moment when the PEM is in λ

4waveplate mode,

a preceding test is conducted as shown in figure 3.2.21: Polarized laser light from a cw

HeNe laser first passes through a λ

2waveplate with a fast axis at -22.5

. Afterwards, the

PEM (fast axis at 0

) and a static λ

4waveplate with the same fast axis position of 0

are

installed. If the PEM is in the state of ±λ

4retardation, the PEM and the waveplate act

together as a λ

2waveplate with a changing fast axis. In front of the detector, a polarizer

is mounted with a fast axis perpendicular to the first λ

2waveplate so that no light can

hit the detector until the PEM and the λ

4waveplate are installed.

Simultaneously monitoring the 50 kHz driving oscillation from the PEM control (green

square wave in figure 3.2.21) and the corresponding phase modulation from the PEM

(blue sine wave in figure 3.2.21) facilitates the identification of when the PEM is in λ

retardation state regarding to a fixed signal (here the driving oscillation). The state of

+λ

4or −λ

4retardation is reached when the sine wave of the phase modulation arrives at

a maximum or minimum, respectively. Between both these extrema the PEM produces

elliptically polarized light, and at zero-crossing it creates a linear polarization with an

orientation of 45

(figure 3.2.21). A comparison between the sine phase modulation and

the square driving oscillation reveals a clear time delay between maxima/minima of the

sine wave with respect to the rising/falling edges of the square wave, and must therefore

be considered if the system is triggered at the square wave of the driving oscillation.

A synchronization scheme for a PEM is shown in figure 3.2.21 and is analogous to

the asymmetric synchronization described in [120,123]. The driving oscillation from

the PEM controller triggers a pulse-delay generator (Quantum Composer 9420 Series).

First, the system mode is set to Duty Cycle with one on-pulse and 9999 off-pulses.

Second, two 5 Hz signals are created in channels A and B of the pulse-delay generator

by again using duty cycle with one on- and one off-pulse. The pulse length is the same

as for the PEMs driving oscillation (20 µs). In order to create a 10 Hz signal in channel

C, channel B needs to wait for one pulse (wait function set to one) and combined with

the signal from channel A. If the shift ∆t1between the sine wave of the PEM and the

square wave from the PEM controller is taken into account, channel A and B get an

extra time delay of ∆t1and ∆t2= ∆t1+20µs+δt, respectively. Here, δt is an adjustable

parameter, which is not necessarily zero due to a known effect for PEMs called residual

static birefringence [123]. Consequently, channel C creates an almost-10 Hz signal, which

offers an interaction of a light pulse with the PEM in the moment of ±λ

4retardation.

3. Experimental and Computational Methods

Fig. 3.2.21.: Intensity modulation of a cw laser beam (HeNe laser) by a PEM in quarter

waveplate mode. The square wave oscillation of the PEM control is shifted depending on the

sine wave received by the detector.

Furthermore, the almost-10 Hz signal now drives the remaining experiment. For data

acquisition, channel D is created to distinguish between LCP and RCP measurements.

The signal is on (or off) for every second signal of channel C. The signal passes through

a digital I/O device of National Instruments (NI USB-6501) to convert it into a digital

signal before it is send to a computer. Here, a custom LabVIEW routine separates both

measurements by the two states of channel D, and sends the acquired data to different

locations (see PECD mode in section 3.2.3.1). For a measurement with linear polarized

light the switching is disabled by removing the PEM from the light path and disabling

channel D, which stores all data in one file.

3.2.4.2. Testing the PECD mode with the PEM

If the polarization optics are placed before the VMI chamber, the PECD mode mentioned

in section 3.2.3.1 can be tested. A similar setup was described earlier in figure 3.2.21

with the main difference being that a pulsed instead of a cw laser is used here. If the

PEM is in +λ/4 (or −λ/4) retardation state, channel D is in the on (or off) state.

However, in this setup, a ±λ/4 retardation state of the PEM means that light can

either pass through the VMI chamber or is blocked in front of it. Consequently, in a

fully running experiment, a photoelectron spectrum is created only in one of the two

relevant retardation states of the PEM. If the PECD mode is working, one file contains

the photoelectron spectrum while the other file should be empty or only contains noise.

Additionally, the PECD mode counts how often the LCP and RCP modes are entered.

3. Experimental and Computational Methods

Fig. 3.2.22.: Timing scheme of PEM and how the trigger of the detachment laser is manip-

ulated in order to hit the PEM with the laser when the PEM is in ±λ

4mode. A Time-Delay

Generator is triggered by the PEM driving oscillation and creates 5 Hz signals in two separated

channels (A and B), which are either synchronized with the maxima or with the minima of the

sine wave. Channel C combines both signals to an almost-10 Hz signal. Channel D creates a

signal for the computer to distinguish between ±λ

4polarization.

Ideally, these numbers should be equal, especially when working with LCP and RCP

light, since an (almost) equal number of electrons in both modes is required for PECD.

3.2.4.3. Quality of Polarization

The quality of polarization is determined by the quality of waveplates, polarizer and

PEM. The error for the waveplates is determined by several factors: the waveplates

are inserted manually in their rotation mounts and the fast axis is aligned to the zero

position with the help of a polarizer and a linear polarized laser. This manually setting is

determined by the polarization quality of the used laser. Furthermore, the dial reading

of the rotation mounts only offers an accuracy of 1-2

. There are rotation mounts

offering indexing in 22.5

steps, which proves helpful for the adjustment of the fast axis

but the accuracy of the indexing again influences the error of the fast axis position.

Even if the fast axis can be adjusted perfectly, the quality of polarization is influenced

by a wavelength dependent retardation. Thorlabs specifies its half waveplates with a

deviation in retardance of around 0.45 - 0.54 waves. The QWPs deviate between 0.23 -

0.27 waves in retardance for waveplates in the area of 260 - 410 nm and 0.20 - 0.27 waves

for 400 - 800 nm. These will influence the PECD measurements with only the static

waveplates as well as the one with the PEM since it is used in combination with these

3. Experimental and Computational Methods

waveplates. However, with Stokes parameter and an intensity comparison between an off

and on pulse, the quality of light polarization can be estimated for the static waveplate

and the PEM measurement, respectively.

The quality of light polarization for the static quarter waveplates is determined by the

Stokes parameter gained from the rotating λ

4waveplate method [119]. The S3parameter

should be either +1 or -1 regarding the type of circular polarization. Averaged over

all experiments using the quarter waveplates a mean S3of 0.98 is determined but the

value can vary with ±0.09 between experiments. The polarization quality P (considering

all Stokes parameter) is also averaged and has a value of 0.97±0.10. The polarization

quality is checked once before the experiment.

For the PEM, the polarization of the light is constantly verified during the experiment

by a λ

4waveplate, a polarizer and a detector, installed after the VMI chamber. The

combination of PEM producing either LCP or RCP light before the VMI chamber and

the static quarter waveplate (with a fast axis parallel to the axis of PEM) after the VMI

acts as half waveplate with switching fast axis. The subsequent polarizer either blocks

or lets the light pass depending on the polarization of the incident light. Consequently,

the detector sees a on-off behavior in a 5 Hz pattern.

To estimate the polarization quality, the intensity difference between on and off pulse

is measured. Ideally, this difference reaches theoretically its maximum for perfect po-

larization and has a non-detectable off pulse as well as an on pulse with maximum

intensity. However, the off pulse will mostly show a non-zero intensity especially for

high light intensities, which the polarizer can not absorb even if set perfectly. Therefore,

a new baseline for the off pulse has to be determined before the PECD measurement.

First, the initial polarization of the laser needs to be set (±45

). Then a polarizer is

placed after the VMI in a position, which minimizes the light output (either 45 or 315

The intensity is read out with an oscilloscope and taken as baseline for the off pulse.

Then, the PEM is installed before the VMI chamber and a static quarter waveplate is

positioned after the VMI chamber. The intensity of on and off pulse are measured and

compared taking the baseline for the off pulse in account.

Especially if working with UV light, the intensity can be completely absorbed by the

polarizer resulting in off pulses below the noise level and the only option is to maximize

the on pulses. If the noise level is taken for the off pulse intensity the polarization can

differ up to 3.3% from the ideal polarization. This represents the worst case scenario for

this kind of measurements.

In the case of visible light more intensity is available and the off pulse does not vanish

completely. Considering the new baseline of the off pulse, the off pulse barely differs

from this base line and the polarization could be considered ideal. However, in the cases

where it differed from the base line, the difference between minimum and maximum leads

to a 3.5% deviation from ideal polarization. This polarization deviation is comparable

to other PECD experiments [72].

3. Experimental and Computational Methods

3.2.5. Ascertaining a Single Photon Process and its Effectivness

Fig. 3.2.23.: Time of flight spectrum for the neutral signal at different grid voltages. The

neutral signal is produced with Eph = 4.77 eV and is not normalized. Intensity differences

originate from fluctuations in the source during the change of the grid voltage. The peak

at around 14.27 µs corresponds to m/z 133. If cations are present a peak should appear at

around 13.95 µs for a grid voltage of 3050 V (black) and at around 13.45 µs for a grid voltage of

4000 V. This assumes that the grid only affects the molecular beam after the µ-metal shielding

and that possible cations are not otherwise disturbed, e.g. by anions. µ-metal shielding and

MCP are around 70 mm apart. Since there is neither a peak at the estimated time nor a shift

of any peak observed, formation of cations is excluded.

The analysis of the photoelectron spectra in this thesis is based on the assumption that

an electron is detached via a single photon process from the anion leaving a neutral

core behind. These photodetached electrons alone (with the exception of background

and noise electrons) should contribute to the PES and PECD signals. If additionally

electrons are photoionized from the neutral core leaving cations behind, any PECD

signals could also stem from this process, like it is the case in conventional PECD

experiments. This measurement would merely have a “photodetachment background”

and consequently mask any PECD effect from pure photodetachment.

On the example of deprotonated 1-indanol, two experiments show that neither cations

are formed nor that multiphoton processes enabling the creation of cations can be de-

tected. One involves the grid in front of the ToF-MCP detector and the other the

measurement of photon energy in dependence of the kinetic energy.

3. Experimental and Computational Methods

Fig. 3.2.24.: Anion-neutral (signal) ratio for photodetachment at Eph = 4.77 eV. Laser pulse

energy before/after VMI chamber around 0.5/0.1 mJ. Anion signal (black) and corresponding

neutral signal (red) are measured at the same MCP voltage. The neutral signal is around 1%

of the anion signal.

3.2.5.1. Cation Measurement with Grid of ToF-MS

In the experiment, a grid is placed just before the MCP detector for ion detection (figure

3.2.1). Applying a negative potential to this grid can be used to effectively deflect (or

reflect) anions before reaching the detector (as described in section 3.2.2). If the anions

are accelerated in the ToF-MS to -3010 V, than, with a grid voltage more negative

than -3010 V, the anions are deflected, leaving only the neutral signal. If there is also

photoionization, cations are formed and accelerated toward the grid. Consequently, a

time-of-flight spectrum should show the neutral peak at the same time of flight as the

anions and an additional “cation peak” at shorter flight times, which should change

position with changing grid voltage.

Figure 3.2.23 shows time-of-flight spectra at different grid voltages. The main feature

is the neutral signal of m/z 133 created by photodetachment of [Ind-H]−with Eph =

4.77 eV. Some neighboring peaks matching m/z 132 and 134 also seem to appear but are

too small to contribute significantly to the electron signal. Anyway, over the full time

scale (figure 3.2.23 only shows an interval of 1.4 µs) no additional peak can be made out

and no peak is changing position if the grid voltage is changed. The same result can

be obtained with a photon energy of Eph = 3.49 eV (355 nm) where considerably more

light intensity is available10.

10Laser pulse energy before/after VMI chamber 3/0.5 mJ.

3. Experimental and Computational Methods

(a) (b)

Fig. 3.2.25.: Kinetic energy of the peak maxima in the PES of [Ind-H]−plotted over photon

energy for some selected transitions. The transitions are labeled B (a), B1(b), A (c) and C (d)

according to section 5.3.2. The data points can be fitted with a linear function with a slope

of 1 and an intercept, which matches the binding energy of the corresponding peak (section

5.3.2). Therefore, a single photon process is assumed.

3.2.5.2. Anion-Neutral Ratio

Comparing the anion and neutral signal of m/z 133 measured with the same MCP volt-

age, gives an estimate for the effectivness of the photodetachment process. This assumes

that neutral and ion signal have (almost) the same detection efficiency at the MCP de-

tector, which is reasonable for high kinetic energies [124,125]. Other factors like the

overlap between molecular and light beam as well as the cross section for photodetach-

ment define the intensity of the neutral signal relative to the anion signal. Since the

spot size (and alignment freedom) of the light beam is restricted by light baffles (and

an adjustable aperture before the VMI chamber) the light might not hit all molecules if

the width of the anion beam should be broader than the light beam leading to an higher

anion signal in comparison to the neutral signal.

In figure 3.2.24, the anion signal is compared to a neutral signal generated with a

photon energy of Eph = 4.77 eV. The neutral signal is around 1% of the anion signal.

A similar result is obtained with Eph = 4.13 eV with almost 1% (not shown). The best

anion-neutral ratio is reached with a photon energy of Eph = 3.49 eV (355 nm) with

around 6%, using a larger pulse energy. These percentages do not account for the PECD

values measured at the photon energies.

3. Experimental and Computational Methods

3.2.5.3. Kinetic Energy vs Photon Energy

In this project, the first PECD signal was recorded for [Ind-H]−at a photon energy of

3.49 eV. Unluckily, some (neutral) alkoxy radicals show optical transitions in a similar

energy regime (around 3.5 - 3.8 eV [126]) making resonant absorption feasible after pho-

todetachment. Photoionization via multiphoton processes of the neutral radical Ind-H

(after photodetachment) seems possible and the recorded PECD signal could be a result

of conventional PECD effects instead of photodetachment. In order to exclude (or prove)

multiphoton processes, more photoelectron spectra are recorded and the dependence of

the kinetic energies of several peaks on the photon energy is observed.

In a single photon process, the kinetic energy related to a given feature in the PES

and photon energy used for the detachment follow Einstein’s photoelectric law Ekin =

hν −EB. Indeed, all peaks evolve in a linear manner when the kinetic energy of the

peak maximum is plotted over the photon energies (figure 3.2.25). A linear regression

of these data points results in a line with the slope of 1 that crosses the kinetic energy

axes at the (in section 5.3.2) experimentally determined binding energies (within the

given errors) confirming the single photon process. Furthermore, a multiphoton process

would reveal itself by discrete changes of the peak positions in the PES by hν, i.e. the

slope(s) in figure 3.2.25 would change from 1 to nif nphotons are required.

If the electrons are the result of a multiphoton process, such shifts or changes should

have been seen according to the calculated photoionization energy of the neutral radical

Ind-H of 9.321 eV. For example, for the PES recorded at Eph = 4.77 eV two additional

photons are needed for the ionization of the neutral Ind-H radical while in the visible

region at least four additional photons are required. Even if an arbitrary error of 0.5 eV

is assumed for the calculated values, at least one shift should be observable.

In summary, neither cations nor a multiphoton process could be detected, which

would have indicated photoionization of neutral species. Consequently, all spectra (and

most importantly all presented PECD asymmetries) presented here are the result of

photodetachment in a single photon process.

3.2.6. Data Handling

3.2.6.1. PES of gold and sulfur anion

Optimization of the VMI spectrometer voltages and calibration of the PES are done

with the gold anion for the gold complex measurements and (mainly) with the sulfur

anion for the deprotonated molecules. Exemplary spectra at different photon energies

are shown in figure 3.2.27 for Au−and figure 3.2.30 for S−.

Gold anion

In general, peaks are represented with Gaussian line profiles. In the case of more complex

systems with overlapping vibrations and/or isomeric effects, peaks are approximated

with several (overlapping) Gauss profiles. For atomic systems like Au−only one Gaussian

profile is needed to describe one measured electronic transition. An energy level diagram

3. Experimental and Computational Methods

Fig. 3.2.26.: Energy level diagram for photodetachment from Au−. The transition to the

ground state of Au is 2S1/2 ←1S0and is marked with X. The binding energy is 2.309 eV.

The first excited state is reached for the transition 2D5/2 ←1S0and is indicated with A. The

energy is 3.444 eV. [77,117]

Table 3.2.2.: Energies, resolution and applied VMI voltages for the Au−spectra. ∆Ecorre-

sponds to FWHM. * photoelectron spectra are depicted in figure 3.2.27.

Eph (eV) rep (V)/ext (V) state EB(eV) Ekin (eV) ∆E(eV) resr

4.77* 3700/2475 X 2.31 2.46 0.16 0.07

A 3.45 1.32 0.08 0.06

4.35 2000/1355 X 2.31 2.04 0.09 0.04

A 3.45 0.90 0.05 0.06

4.13* 2500/1690 X 2.31 1.82 0.08 0.04

A 3.45 0.68 0.04 0.06

3.49 1450/989 X 2.31 1.18 0.06 0.05

3.02* 800/538 X 2.31 0.71 0.04 0.06

2.70 800/546 X 2.31 0.39 0.03 0.08

2.58* 500/340 X 2.31 0.27 0.01 0.04

for the detachment from Au−is given in figure 3.2.26 and the corresponding measured

PES is in figure 3.2.27. Dependent on the kinetic energy the FWHM and hence the

resolution ∆Evaries (figure 3.2.27 and table 3.2.2). As expected (from section 3.2.3.5),

the resolution improves with decreasing kinetic energy (figure 3.2.28) and repeller voltage

(table 3.2.2). The relative resolution of a peak should be compared to other peaks within

the same spectrum. Peak A shows, as expected, an inferior resolution than X since peak

A is at smaller kinetic energies than X (section 3.2.3.5). The PES at Eph = 4.77 eV

behaves slightly in the opposite way.

3. Experimental and Computational Methods

Fig. 3.2.27.: Selected PES of Au−at different Eph and hence different Ekin measured in

normal mode. The transition to the ground state (X) is at a binding energy of 2.309 eV and

the transition to the first excited state (A) at 3.444 eV. An energy level diagram can be found

in figure 3.2.26. The ground and excited state feature smaller FWHMs for smaller kinetic

energy and have a better resolution as can be seen in figure 3.2.28. Furthermore a shoulder is

observed for PES with high kinetic energy and vanishes the smaller the kinetic energy gets.

(a) (b)

Fig. 3.2.28.: Absolute resolution ∆Eplotted over the kinetic energy for the X transition in

(a) and the A transition in (b). For smaller kinetic energies ∆Ebecomes smaller and hence

better. The values for these figure can be taken from table 3.2.2.

3. Experimental and Computational Methods

Besides the expected behavior for the resolution, a shoulder at the side with higher EB

emerges. It is also observed in the literature [127] and appears in PES of other anions

like Br−and F−(not shown). Since no additional contributions like vibrations can be

present, this shoulder is considered to be an experimental artifact or rather an artifact of

image processing/deconvolution. This shoulder will be also visible in the PES of Au−-M

and the deprotonated molecules and should not be confused with additional overlapping

Gaussian peaks origination from isomeric, vibrational or rotational contributions.

Sulfur anion

Fig. 3.2.29.: Energy level diagram for photodetachment from S−. Transition 3P2←2P3/2

(“2”) is the electron affinity and has an energy of 2.077 eV. Other transitions, including excited

states of the anion and neutral, are given in table 3.2.3. Only the black, labeled transitions

can be resolved in this experiment. Since they are energetically close and can not be resolved

for PES with high kinetic energies, they are summarized in the label “X”. The transition to

the excited state “A” is 1D2←2P3/2 and has an energy of 3.222 eV. [77,117,128]

A better visualization of improving resolution with decreasing kinetic energy is repre-

sented by the sulfur anion. The atomic S−is known to have six anion to neutral atomic

transitions in the visible energy regime (577 - 614 nm), which appear as one peak for Eph

= 4.77 eV and start splitting for PES recorded at lower photon (or kinetic) energies (fig-

ure 3.2.30a). The best image is obtained for the lowest photon energy (Eph = 2.38 eV)

and if the spectrum is measured in event instead in normal mode (figure 3.2.30b). This

leads to a PES where four features can clearly be discerned. Two features are unfor-

tunately not resolved but would explain the imperfect Gaussian shape of peak 2 since

they are pretty close in energy. A corresponding energy level diagram can be found in

figure 3.2.29.

Since only four transitions are resolved an unambiguous assignment of all peaks is

not possible before calibration. Consequently, not all peaks can be incorporated in the

calibration process. However, the most intense peak (2) can assumed to be the electron

affinity at 2.0771 eV [128]. On this basis, the EBof the other peaks are evaluated,

3. Experimental and Computational Methods

(a) (b)

Fig. 3.2.30.: (a) Three PES for S−in normal mode. For Eph = 4.77 eV (black), two features

at 2.077 eV and 3.222 eV are visible corresponding to ground and an excited state, respectively.

The ground state peak splits up with smaller photon energy. (b) The best resolved PES (Eph

= 2.38 eV) has been measured in normal and event mode. The event mode shows a cleaner

PES and up to four features are resolved. Peak 2 has a FWHM of 0.014 and 0.013 eV in normal

and event mode, respectively. The assignments and measured energies are given in table 3.2.3.

Table 3.2.3.: Energies and assignment for the S−spectra at Eph = 2.38 eV from figure 3.2.30.

Measured values (meas.) are determined by fitting a Gauss function to the peak. The PES

is calibrated on peak 2, which is considered to be the electron affinity. The literature values

(lit.) are taken from [77,117,128]. An energy level diagram can be found in figure 3.2.29. Not

labeled values are not resolved transitions.

label Transition EB(eV) (lit.) EB(eV) (meas.)

13P2←2P1/2 2.0171 2.018 ±0.008

3P1←2P1/2 2.0663 not resolved

23P2←2P3/2 2.0771 (EA) 2.0771 (fixed)

3P0←2P1/2 2.0882 not resolved

33P1←2P3/2 2.1263 2.131 ±0.007

43P0←2P3/2 2.1483 2.151 ±0.006

3. Experimental and Computational Methods

which does not only provide a save assignment of the remaining peaks but also a quality

control of the calibration. In table 3.2.3, the measured values match to the literature

values enabling the peak assignment and confirming that the calibration is adequate.

3.2.6.2. Background Signal in VMI data

Fig. 3.2.31.: Background signal in VMI data measured in PECD mode. Here, background

signal originating from light at Eph = 4.77 eV for a measurement with [Ala-H]−is shown.

Up: Raw data from VMI measurements. The data containing the background is subtracted

from the data, which contains the signal and background. The result is data with reduced

background, called background corrected signal. The dashed line marks a center line of the

signal. The background deviates from this line. Down: Corresponding photoelectron spectra

to VMI raw data from above. Background signal is clearly visible in the UV region between

3 and 5 eV (red). Hence, the broad peak in this region for the violet spectrum is accounted

by background. The blue PES is the background corrected signal. All spectra are normalized

relative to the maximum of the violet spectrum.

Background signal measured at the VMI detector accompanies each experiment and

can not always be avoided but often reduced to acceptable levels. Here, two main

sources of background signal are identified: Background originating from the laser light,

especially UV light and background caused by the molecular beam. In both cases the

center of the background signal does not coincide with the center of the signal (figure

3.2.31), which hinders the reconstruction of the image. Hence the background has to be

minimized or separated from the signal.

Without a molecular beam being present, photoelectrons can be emitted due to scat-

tered light of the metallic surfaces inside the vacuum chamber through the photoelectric

3. Experimental and Computational Methods

effect. The work function of materials built in the VMI spectrometer is high enough that

this background appears only for UV light11. This background can be reduced by align-

ing the path of the light beam such that no or only a few counts reach the VMI-MCP

detector while the molecular beam is disabled. The light beam can also be narrowed

by a telescope or focused by a lens to avoid contact with the light baffles, which are

installed before and after the VMI lens system.

If the background reduction does not suffice, the background signal originating from

light can separately be measured by operating the ToF electrodes at 5 Hz while keeping

the rest of the experiment at 10 Hz. The PECD mode (introduced in section 3.2.3.1) will

then produce a file containing only the background data, which – in combination with

the measurement of the signal plus background –, can be used to judge the magnitude

and localization of the background. If the background data is subtracted from the

data containing signal and background, a background corrected spectrum is obtained

(figure 3.2.31). However, caution is advised since background from each trigger cycle

is independent from the cycle before. Technically, to be allowed to do this subtraction

the background should be measured simultaneously to the signal+background spectrum.

The setup is not able to do that but the 5 Hz switching of the ToF plates is “the closest

to simultaneity” possible for this experiment.

The other type of background originates from the molecular beam. Here, molecules

with high kinetic energy could encounter an obstacle and upon collision eject electrons,

which are detected as background. Such an obstacle could be background gas, which is

ionized or solid surfaces in form of apertures or µ-metal edges. In the case of collisions

with solid surfaces, the background can simply be reduced by redirecting the molecular

beam with the deflection plates of the ToF-MS. Background gas can be reduced if the

VMI chamber is baked out.

If that is not enough, the background of the molecular beam can be recorded similarly

to the background originating from light: Instead of operating the molecular beam at

5 Hz, the light will be operated at 5 Hz. Hence, a PES is recorded normally with a

molecular and light beam present in the VMI chamber and a PES where only the molec-

ular beam can be found while the light is off, consequently measuring the background

created by the molecular beam. However, the trigger rate of the laser is fixed to 10 Hz

and light must be blocked or let through alternatively with a combination of an optical

element acting as varying half waveplate and a polarizer. Again, the PECD mode is used

to record the two alternatively arriving data sets. In this project, the optical element

switching between both polarizations is the PEM, described in section 3.2.4.

Unfortunately, these background reduction mechanism comes with the downside of

causing the effective data collection rate to be halved from 10 Hz to 5 Hz. This means

that there is an inherent trade-off between the required run length of the experiment

and the desired level of background reduction.

Therefore it is preferred to reduce the background with the already mentioned meth-

ods e.g. improving the alignment of the path of the light and molecular beam. The

11Work function of stainless steel and of µ-metal are around 4 eV and 5 eV [129,130]. It varies for

different metal alloys [131].

3. Experimental and Computational Methods

background can also be reduced by gating the VMI-MCP detector (which was already

described in section 3.2.3.1) and restricting e.g. the recording time.

3.2.6.3. Data Handling for PECD Measurements

Fig. 3.2.32.: Flowchart for the analysis of PECD data. The first step (1) is the measurement

of LCP and RCP data and refers to figure 3.2.33. The second step (2) is the smoothing of the

data. For a reconstructed PECD image with rBasex the green path has to be followed (figure

3.2.34). If PECD values are to be extracted from the recorded data POP has to be used and

the blue path is taken. The third step (3) is shown in figure 3.2.35. The dashed box is not

strictly necessary. The fourth step (4) is illustrated in figure 3.2.36. Figure 3.2.37 shows the

below green box of step five.

PECD PADs

The extraction of PECD values from PADs measured with LCP and RCP light and the

reconstruction of PECD PADs is illustrated in the flowchart 3.2.32. Five main steps are

necessary to get to the PECD value and are all represented in the figures 3.2.33 -3.2.37.

Step 1: For PECD measurements, two images corresponding to detachment from LCP

and RCP light are measured alternatively in the PECD mode. Ideally, both images

have the same amount of electron counts after the same amount of measurements cycles

(loops), however they always show a count difference of around 0.01 - 3.20%. This count

difference neither correlates with the PECD signal nor signal-to-noise ratio or loops. It is

probably driven by the cross section of photodetachment and can depend on fluctuations

3. Experimental and Computational Methods

Fig. 3.2.33.: Step 1: Measurement of PECD data. Raw images of the LCP and RCP mea-

surement (left) as well as the resulting PECD image (right) for (R)-[Ind-H]−at Eph = 3.49 eV.

Approximately 4 Mio electrons were accumulated for each polarization. No smoothing and no

correction of the final counts is applied here.

in molecular and light beam intensity. Also, background fluctuations could have some

contribution.

However, this count difference does not necessarily prohibit a PECD signal in the

raw images as can be seen in figure 3.2.33. Figure 3.2.33 shows exemplary the PECD

measurement of (R)-[Ind-H]−at Eph = 3.49 eV. Despite the missing 0.5% counts in

the RCP measurement a PECD asymmetry is visible (on the right of figure 3.2.33).

Anyways, for a quantitative analysis the count difference should be reduced to (almost)

zero.

To account for this difference, a second PECD measurement is performed right after

the first one and stopped when the count difference is met (“remaining measurement”).

If the PES of the main measurement (the first measurement) with the lowest electron

count is added with the corresponding remaining measurement and compared to the

main measurement of the other polarization, the count difference is just a few counts,

which is negligible in comparison to the overall electron counts.

Step 2: Both photoelecton distributions are subsequently smoothed in the same way

via Gaussian convolution with the “Smooth” subroutine of the main POP program

(section 3.2.3.3) and equation 2.2.21 for a PECD image can be applied. The resulting

smoothed and count corrected PECD image can be found in the upper, right image of

figure 3.2.34.

3. Experimental and Computational Methods

Fig. 3.2.34.: Step 2: Raw PECD image (up, left) from figure 3.2.33 and corresponding PECD

image after LCP and RCP data are smoothed (up, right). The reconstruction of the smoothed

PECD image via rBasex (down, left) leads to image artifacts in form of rings. The artifacts

are alleviated by applying an low-pass filter (down, right).

(a) (b)

Fig. 3.2.35.: Step 3: Photoelectron spectra of measurements with LCP and RCP light sepa-

rated in forward (a) and backward (b) direction. Between EB= 2 and 3 eV, PES for LCP and

RCP differ clearly in intensity, which also is visible in the PECD function (blue). The intensity

difference between LCP and RCP as well as the PECD function switches sign for the other

direction. This is recorded under similar conditions as figure 3.2.33 and 3.2.34 but instead of

4 Mio, 70 Mio electrons are accumulated for each polarization for better visualization of the

PECD signal. An energy region (green box) is selected for the subsequent analysis.

3. Experimental and Computational Methods

Fig. 3.2.36.: Step 4: Mean PECD values (PECD) for forward and backward direction of

[Ind-H]−at Eph = 3.49 eV in the energy region indicated in figure 3.2.35 with 70 Mio electrons

per polarization. Error bars are based on the standard error (SE) of the mean.

For a reconstructed PECD image, rBasex will be used. Unfortunately, this introduces

artificial frequencies in form of rings (bottom left of figure 3.2.34) and could be the result

of noise/background signal in the raw data. Since these rings are of high frequency a low

pass filter, namely the Savitzky-Golay filter [132], will be applied to the reconstructed

PECD image, In short, this filter uses convolution to fit a low-degree polynominal with

the linear least square method to subsets of the data in an iterative way. One advantage

to other methods is the consideration instead of the cutting off of high frequency portions.

In the end, this filter leads to an image without high frequencies and it appears smoothed

(bottom right of figure 3.2.34).

These images are just for visualization since, unfortunately, PECD values read out

from such images do not coincide with the values from the raw or smoothed PECD

images due to some internal scaling. The reconstructed as well as the filtered PECD

image are shown in the lower part of figure 3.2.34. The PECD “intensity” of the images

are scaled with the factor 275 to obtain visually comparable PECD intensities with the

raw and smoothed PECD images shown in the upper row.

3. Experimental and Computational Methods

Fig. 3.2.37.: Determination of ∆PECD with the absolute value of the mean PECD (PECD)

from figure 3.2.36. The forward and backward PECD value should have theoretically the

same absolute value but differ clearly. The difference can not be described by the standard

error (SE) of mean. Therefore the difference of both values ∆PECD is taken as error to

describe the difference in PECD of forward and backward direction.

PECD values

For a quantitative analysis of the PECD data, rBasex and Melexir are theoretically

applicable. Although rBasex and Melexir are supposed to reconstruct PECD images

and give directly the dichroism parameter, the dichroism parameters obtained here show

many (ridiculously high) spikes in value over a broad energy range and also do not

coincide with the values obtained from the not reconstructed PECD images even if the

spikes are ignored. Again, this could be a result of noise/background in the raw image,

which is not handled well in these reconstruction methods. Due to these difficulties,

POP will be used for the analysis of PECD data.

Since the main POP program is designed for measurements with linear polarized light,

the axis interpreted by POP as symmetry axis coincides with the polarization axis of

the light. In order to account for the changed symmetry axis for measurements with

circular polarized light, the smoothed PADs are transposed before further processing,

which turns the axis for the light path by 90

and hence matches now with the axis POP

interprets as symmetry axis.

The reconstruction in POP over the whole PAD would destroy the asymmetry since

POP averages over the whole image. While this is not helpful regarding the PECD, it

can be used to check on the image quality of LCP and RCP measurement. Both fully

reconstructed measurements should lead to PES with equal intensities. For measure-

3. Experimental and Computational Methods

Fig. 3.2.38.: Fully (all quadrants) reconstructed PES of the LCP (black solid) and RCP

(black dashed) measurement with POP. Both PES should have the same intensities and shape.

However, the RCP PES (black dashed line) needs to be scaled (here with a factor of 1.547)

to get equal intensities in the main peak of LCP and RCP (pink dashed line) measurement

(left). All PECD measurements with QWPs (and long term signal fluctuations) require such

scaling. This concerns the gold complexes. The PECD PAD of the unscaled data is shown on

the right. The data is recorded close to the edge of the detector, hence it is cut off on the left

side. However, all transitions are contained in the detector image.

ments with quarter waveplates (this concerns mainly the Au−-M measurements), there

is unfortunately a quite big difference, like seen for Au−-Fen measured at Eph = 4.13 eV

in figure 3.2.38. Despite the same amount of electron counts, a scaling factor of 1.547

is needed to make the main peaks equal. The electrons seem to be distributed differ-

ently over the PAD for RCP than for the LCP measurement. The cause of the “weird”

looking PAD, the corresponding PES and hence the huge scaling factor are explained

in more detail in section 4.6 but can be, in short, attributed to long-term drifts. The

scaling factors for the deprotonated molecules are around 1, which can be attributed

to the shot-to-shot measurements with the PEM and more stable signal intensity. In

the case for Au−-M all reconstructed PES (not the PECD PADs) are corrected with a

corresponding scaling factor. The PES of the deprotonated molecules are not corrected

since the fully reconstructed PES are (almost) equal.

Step 3: To obtain PECD values, the PADs can not be reconstructed fully in POP as

explained before but must be separated for each polarization in two image halves cor-

responding to forward and backward direction (regarding the propagation of the light).

The forward and backward half are reconstructed individually for both polarizations,

leading in the end to four reconstructed spectra. A comparison of the forward-LCP

PES with the forward-RCP PES should show an intensity difference (the PECD signal),

which has the same amount but different sign when backward-LCP PES is compared

with backward-RCP PES. This is illustrated in figure 3.2.35 for a PECD measurement

on (R)-[Ind-H]−at Eph = 3.49 eV (like before) but with 70 Mio instead of 4 Mio elec-

tron counts per polarization due to a less noisy PECD function (blue function in figure

3.2.35).

The PES in figure 3.2.35 are normalized to the maximum value of the PES with the

highest intensity for each direction. Hence, two spectra will be at 1 and the other two

3. Experimental and Computational Methods

will be below 1 according to the PECD difference, e.g. in the forward direction both

PES are normalized according to the maximum of the RCP measurement.

Step 4: The PECD asymmetry for each direction is calculated according to

PECDH= 2ILCP,H −IRCP,H

ILCP,H +IRCP,H

(3.2.26)

where H either stands for the forward half (FW) or the backward half (BW). Equation

3.2.26 is another notation of equation 2.2.21 and is obtained for the whole energy range

(blue function in figure 3.2.35).

However, certain energy regions are selected to account for the different features,

which are available in a spectrum. Here an energy range of 2.187 - 2.376 eV (green box

in figure 3.2.35) is used since it contains three transitions, which are not resolved for

this photon energy but become resolved when working with visible light [48].

Over the chosen energy range and for each direction, the mean PECD value

(PECDFw/Bw) and the standard error of PECDFw/Bw (SE of mean), which is a pure

statistical error, are extracted. The result for the measurement for (R)-[Ind-H]−at

Eph = 3.49 eV with 70 Mio electron counts per polarization can be seen in figure 3.2.36.

Step 5: Ideally, both image halves give the same PECD value but are opposite in

sign (PECDFw =−PECDBw). Unfortunately, there is a difference in the absolute value

of the PECD signal, which points to asymmetries coming from the experimental setup

rather than the chiral molecule. This difference can not be explained with the SE of the

mean alone (figure 3.2.37). The difference in the PECD signal for both directions could

be related to the intensity difference, which was already discovered in PADs measured

with linear light when the voltage optimization was described in section 3.2.3.4. Despite

the consideration of this intensity difference already in the voltage optimization step, the

influence on the PECD asymmetry is clearly visible in figure 3.2.37. Hence, ∆PECD,

describing this difference, is considered a machine asymmetry.

To obtain just one PECD value, the overall mean PECD (PECD) value of the forward

and backward mean PECD (PECDFw/Bw) is calculated according to

PECD = PECDFw −PECDBw

2.(3.2.27)

The PECD value (and its errors) is set to be zero if both image halves give the same

sign for the PECD asymmetry, else the SE of the mean and the difference of PECD

values for both images halves (∆PECD) are evaluated to describe the accuracy of the

PECD values. However, ∆PECD is in general bigger than the SE of mean (figure 3.2.37)

and represent a more realistic error, which is based on experimental conditions rather

than statistical ones. The data with SE as error is shown in [48] but ∆PECD will be

used here for measurements with non-zero PECD values.

3. Experimental and Computational Methods

3.2.6.4. PECD with PEM vs QWP

Fig. 3.2.39.: Comparison between PECD measurements performed with QWP and PEM at

Eph = 2.43 eV. The QWP is turned once for the polarization change while the PEM changes

the polarization shot-to-shot. The PECD asymmetry of the QWP is reversed in contrast to

the PEM. The PECD measurement with QWP by itself is consistent since it changes with the

enantiomer.

PECD measurements were mainly performed with quarter waveplates for Au−-M and

with the photoelastic modulator for the deprotonated species. For Au−-Ala and [Ind-H]−

quarter waveplates and the photoelastic modulator were used to compare both measure-

ment methods. Since the main difference between both methods is the switch frequency

of the light polarization, with the photoelastic modulator switching the polarization in a

shot-to-shot manner while the quarter waveplate was only switched manually after one

polarization measurement (after 3-4 hours), the influence of long and short term fluc-

tuation on the PECD signal is investigated. The photoelastic modulator is expected to

result in PECD signals with higher quality since long term fluctuations are handled bet-

ter than for the quarter waveplate method. In the following the discussion concentrates

on [Ind-H]−and not Au−-Ala due to the non-null PECD signal for [Ind-H]−.

The PECD asymmetry is measured for Eph = 2.43 eV with a quarter waveplate and

compared with the PECD measurements with the photoelastic modulator (figure 3.2.39).

For all transitions, A, B1, B2and B3(which are explained in more detail in section 5.3.2),

the mean PECD values are evaluated and shown in figure 3.2.40. In both figures a clear

3. Experimental and Computational Methods

(a) (b)

Fig. 3.2.40.: Mean PECD values for the PECD measurement performed with QWP (a) and

PEM (b) at Eph = 2.43 eV for the transitions A and B1,2,3. Full symbols represent the (R)- and

empty symbols the (S)-enantiomer. The mean PECD values are given with ∆PECD as error.

The worst quality has the measurement for the (S)-enantiomer with QWP due to the low total

electron counts per polarization (2 Mio). The mean absolute PECD values are comparable but

the used error is not sufficient in all cases.

but inverted PECD signal can be seen in each measurement, which is probably the result

of a mislabeled fast axis of one of the optical elements. One exception is the B1feature

for the (S)-[Ind-H]−measured with the quarter waveplate, which shows no PECD signal

probably due to low total electron counts/statistics. Considering the error ∆PECD,

the photoelastic modulator seems to produce data with smaller error and, hence, gives

results of better quality, as was expected.

The reason for the inverted PECD asymmetry for the quarter waveplate measurement

is unclear. A measurement with the photoelastic modulator was repeated the same day

to confirm the inversion. The way the PEM data is saved is controlled, e.g. if the data

saved in the correct file, and determination of the light polarization for the photoelastic

modulator and quarter waveplate was confirmed by a different person.

The position of the fast axis of the quarter waveplate and/or the photoelastic modula-

tor could be different from the company label or description. However, to control for the

fast axis position an experiment with a chiral molecule with known PECD asymmetry

would need to be performed. However, most PECD experiments are performed on neu-

trals for which this experiment is not designed. A professional polarimeter could also

help determining the absolute polarization after both optical elements and determine

which optical element could have the (in)correctly set or mislabeled fast axis.

In general, the error is smaller for the (R)-enantiomer than for the (S)-enantiomer since

for the (R)-enantiomer a more intense and more stable signal was at hand leading to

a better signal-to-noise ratio. Reproducing the source condition for the (S)-enantiomer

was not possible which lead to a weaker ion signal and also to lower electron counts

(or longer recording time for the same electron counts), e.g. only 2 Mio electrons are

recorded for the (S)-enantiomer for the measurement with the quarter waveplate. Signal

fluctuations in the case of the (S)-enantiomer can be handled to some extent by the

shot-to-shot measurement of the photoelastic modulator but has greater influence on the

3. Experimental and Computational Methods

measurement with the quarter waveplate. Such fluctuations lead to bigger errors and

can also be responsible for the zero mean PECD value for feature B1in the measurement

with the quarter waveplate for (S)-[Ind-H]−.

In the following, experiments are continued with the photoelastic modulator due to

the shot-to-shot measurement method leading to PECD results of better quality than

with the quarter waveplate.

3.3. Density Functional Theory

Apart from the experiment, theoretical results can be as important since they help with

model development, preparation of the experiment, predictions and analysis/assignment

of the experimental observation. For instance in the field of molecular physics, the

calculation of molecular properties like bond lengths, dissociation energies and electron

affinities are of interest to design and understand experiments, which investigate certain

molecules. Such properties are dependent on the molecular structure and can strongly

vary between isomers. DFT is one method to obtain the molecular structures and the

corresponding molecular properties.

DFT is based on the approximation of the electron density and has – in contrast to

ab-initio methods, which are based on the calculation of wave functions – only a small

number of spatial coordinates to consider. Furthermore, the number of coordinates does

not scale with the number of electrons in the system making it applicable to many-

electron systems and reducing the computational cost.

Despite the reduced computational complexity, DFT is based on assumptions and has

problems with e.g. strongly correlated systems and liquids [133]. However, DFT has

the flexibility to let the user choose between different approximations in form of various

functionals and basis sets. Consequently, DFT adapts to the problem at hand and leads

to satisfying results in a wide scientific community.

The prediction of structures for systems used in this thesis (gold complexes and de-

protonated molecules) as well as their electron affinities, dissociation energies etc are

obtained with DFT. Hence, an overview of the basics for DFT is addressed here. An

elaborate description or introduction for DFT can be found in e.g. [134–137].

Nonrelativistic, spinless quantum chemical problems can be described by the

Schr¨odinger equation. In these cases, instead of a wave function ψ, a (probability)

electron density n(r) (c.f. equation 3.3.28) is applied to the Schr¨odinger equation. In

comparison to a wave function, the electron density is an experimentally detectable

quantity and holds just three instead of 3N(4Nif spin is considered) spatial variables

for an N-electron system.

n(r) = N∫︂···∫︂|ψ(x1, x2, . . . , xN)|2ds1dx2. . . dxN(3.3.28)

with xiholding the three spatial coordinates riand the spin siof the i-th electron. n(r)

is the probability of locating one of the Nelectrons with arbitrary spin sinside the

volume element dr1. The other N−1 electrons have arbitrary spin and locations.

3. Experimental and Computational Methods

Thomas and Fermi [138] were the first to solve the Schr¨odinger equation with n(r).

Due to strong approximations applied to the Hamilton operator their model was not

able to describe complicated systems like molecules.

Another approach is described by Kohn and Sham [139]. Here, all terms, which

require assumptions (unknown terms) are separated from the terms, which are known.

What is known is for example operators for non-interacting (ni) reference systems like

the kinetic energy operator for a free electron T

ˆni =−1/2∇2(atomic units are used

here and will be used in the following equations of this section as well.). The Hamilton

operator holding all known terms or terms for non-interacting systems is the Kohn-

Sham operator H

ˆKS. The unknown terms, mostly terms describing interactions like

the electron-electron interaction, which require approximations are concentrated in a

remainder operator V

ˆr. The equation rising from the Kohn-Sham approach build the

foundation of DFT:

ˆn=En (3.3.29a)

ˆ=H

ˆKS +V

ˆr(3.3.29b)

ˆKS =−1

2∇2+V

ˆni (3.3.29c)

with V

ˆni being a local effective potential operator.

In principle, H

ˆis exact (for a nonrelativistic system without quantum electrodynam-

ics). However, approximations are necessary for the remainder potential and thus H

becomes an approximation as well. Meanwhile, there is a great variety of approxima-

tions from which a system adequate approximation can be chosen.

Unfortunately, even with the Kohn-Sham approach and an electron density, the rewrit-

ten Schr¨odinger equation 3.3.29 can not be solved exactly (except for hydrogen or hy-

drogen alike systems) and the real electron density remains unknown. However, with

the help of the variational principle the ground state wave function ψ0and ground state

electron density n0with corresponding ground state energy E0are obtained (and also

all excited states with time dependent DFT).

Here, all expectation values, like the energy, are functionals of the electron density

E[n] and need to be minimized by searching through all acceptable electron densities

until the density with the lowest energy is found. Certainly, this search technique is

unrealistic and rather a subset of electron densities has to be scanned. Hence, it could

be that the real ground state density is not in the chosen subset but can be approximated

by an electron density in this subset.

The minimization of the energy functional requires the self-consistent field (SCF)

procedure since the Hamilton operator is dependent on the electron density (the solution)

itself via the potential operator. The minimized electron density is an unique density

for the system due to the unambiguous assignment to the external potential operator

(e.g. the positive background field of the nuclei is considered as external potential for

electrons but is not restricted to it) and leads to the lowest energy if the minimized

density is the real electron density [140].

3. Experimental and Computational Methods

3.3.1. Functionals

In the Kohn-Sham approach the Hamilton operator is subdivided into a known and an

unknown part. The same can be done for the energy functional:

E[n] = Tni[n] + J[n] + Ene[n] + Er[n] (3.3.30a)

Er[n]=(T[n]−Tni[n]) + (Eee[n]−J[n]) = Tc+Enon-cl (3.3.30b)

The known part consists of the non-interacting kinetic energy T

ˆni, the energy between

nuclei and electrons Ene, and the classical electrostatic electron repulsion energy Jfor

which an explicit form can be given. The remainder energy Ercontains all unknown

energies – in particular the correlation part of the kinetic energy Tc– and all non-classical

effects like self-interaction corrections, exchange and correlation.

Approximations are needed for the remainder energy to derive an energy functional,

which describes the quantum system with sufficient accuracy and is computationally

cheap. The best choice of energy functionals depends on the quantum system at hand

with different systems requiring different approximations. Hence, the best way to choose

a functional is to apply candidates to both the system of interest and reference systems

and to then take the one that matches the experimental data best. One of the first ap-

proximations for the remainder functional is the Local (Spin) Density Approximation,

L(S)DA, which was introduced by Kohn and Sham [139]. Here, an uniform and homo-

geneous electron gas is assumed, since the correlation and exchange functional energies

are well known for this case. Even the spin is considered. However, it only works well

for an ideal metal, but poorly for atoms and molecules. The functional by Perdew and

Wang from 1992 (PW92) is a representative of this approach.

A better approximation is the Generalized Gradient Approximation (GGA), which

allows (slow) variations of the electron density and can be seen as an extension of the

L(S)DA approach. Becke’s functional B88 (or B) is an example functional for this

approach.

To account for inhomogenities present in molecules, the reduced density gradient is

introduced in the GGA approach. An example functional (for the correlation part) is

the one from Lee, Yang, Parr (LYP) [141]. Here, instead of a uniform electron gas, the

knowledge about the correlation energy of helium is applied.

Another class of functionals are the so-called hybrid functionals. In comparison to

the previous methods, these use exact functionals (e.g. from classical effects, uniform

electron gas) in combination with approximated functionals (e.g. from non-classical ef-

fects like electron-electron correlations, GGA and L(S)DA). An “interaction parameter”

determines the amount of interaction in a system and the influence of the approximated

functionals on the overall functional. Among the presented approximations, the hybrid

functionals are the most accurate ones [134].

Assuming that the exchange-correlation functionals of both the non-interacting and

the fully interacting system contribute with equal parts (half-half combination), the

exchange-correlation functional can be written as

3. Experimental and Computational Methods

EB3LYP

xc = (1 −a)EL(S)DA

x+aEni

xc +bEB88

x+cELYP

c+ (1 −c)EL(S)DA

c(3.3.31)

with Exas the pure exchange functional, Ecas the pure correlation functional, Exc

as the exchange-correlation functional and the three interaction parameters: a, b and

c. Equation 3.3.31 is the wide-spread B3LYP functional (Becke, 3 parameters, Lee,

Yang, Parr), with the exchange energy functional from Becke and the correlation energy

functional from Lee, Yang and Parr (LYP) [141]. It belongs to the class of hybrid

functionals.

So far, all discussed methods do not include dispersion effects and thus are not appro-

priate for problems involving hydrogen bonding, bonding of noble gases, protein folding,

or other highly polarizable systems like Au−. This is because methods like GGA are

local, while dispersion is a non-local, pure correlation effect. The dispersion correction

of Grimme [142] is a widely implemented solution for this problem due to its robustness,

speed, simplicity in programming and satisfying accuracy. For this method, atomic dis-

persion corrections (∝R−6) are added to standard functionals (GD)[143]. Later damped

dispersion correction terms were used and the GD functional was generalized as well as

reparametrized (GD2) [144]. The most recent and advanced functional of Grimme uses

structure-dependent dispersion coefficients (GD3) [142]. It handles all elements from

Z=1 to Z=94 consistently, and reproduces the asymptotic behavior for finite systems

(molecules) exactly.

If GD3 is used for e.g. B3LYP, the functional is written as B3LYP-D3. This is the

functional, which is chosen to calculate the gold complexes and deprotonated species in

this thesis.

3.3.2. Basis Sets

The application of DFT requires another ingredient: the basis sets, which yield the

Kohn-Sham orbitals ϕi. Almost all computational procedures are based on the linear

combination of atomic orbitals (LCAO) ansatz

ϕi=

∑︂

µ=1

cµ,iηµ(3.3.32)

with ηµbeing a finite basis set with Lfunctions. The density in that case is

n(r) =

∑︂

iϕ2

i(r)=

∑︂

cµ,icν,iηµ(r)ην(r).(3.3.33)

In order to solve the Kohn-Sham equation properly, all ϕi’s should be considered such

that L=∞(exact limit) but practically Lis finite (basis set limit) and should be

chosen big enough to achieve the desired accuracy. There are different kinds of basis sets,

which are designed for different problems: While Gaussian-type orbitals (GTO) feature

100

3. Experimental and Computational Methods

great computational advantages, Slater-type orbitals (STO) are more appropriate from

a physical point of view and model the behavior for r→0 and r→ ∞ better. However,

a STO is difficult to handle computationally. Because of that, contracted Gaussian

Functions (CGF) are introduced to combine the advantages of GTO (computationally

cheap) and STO (better treatment of radial behavior). Another basis set is the double-

zeta one, which assigns two functions per orbital. If chemical reactions are of interest,

the computational costs are reduced by applying the double-zeta basis set only to the

valence orbitals while the core orbitals use smaller, simpler basis sets (split-valence

type basis sets). This basis set can easily be extended to triple- or quadruple-zeta

and is used by the Dunning basis sets denoted cc-pVTZ and cc-pVQZ (correlation-

consistent polarized valence triple/quadrupole zeta), respectively. Additionally, basis

sets can be expanded by polarization functions, which contain higher angular momenta.

These functions describe also unoccupied states in atoms/molecules, e.g. the pstate in

hydrogen. These are the augmented basis sets (aug), which are appropriate for molecules

since the atomic orbitals are allowed to distort and thus can adapt to the molecular

environment.

When modeling heavier elements such as gold, relativistic effects like the stronger

coupling between the spin of the electron and the orbital angular momentum or the

velocity-dependent mass have to be considered. The last effect is particular important

since it results in core contractions, which must be considered for core states and their

influence on chemically relevant valence shells in every model for such systems. For this,

the core states are substituted by a potential imitating the core states and its influence

on valence states [137]. This is the effective core potential (ECP) or pseudo-potential

(PP). Since valence electrons are shielded from the core by the inner electrons, relativistic

effects become negligible and non-relativistic basis sets like aug-cc-pVTZ can be applied.

3.3.3. Energies

Once, a functional and basis set are chosen, structure optimization lead to the ground

state energy Eg(M) of a system (e.g. a molecule) M. Additional frequency calculations

lead to vibrational frequencies, confirm the convergence of the calculation and give the

zero-point energy (ZPE). The ZPE-corrected ground state energy of M, called E(M),

is then given by

E(M) = Eg(M) + ZPE (3.3.34)

and will be used predominantly.

The molecular constants of a diatomic system like VDE, ADE, dissociation energy D0

etc. can be explained with the aid of two interatomic potentials, which are approximated

by Morse potentials. Here, VDE and ADE describe transitions between two Morse

potentials while D0is explained by following one Morse potential to higher bond lengths.

In an analogous way, the interatomic potential(s) can be applied to an anionic pseudo-

diatomic model, which is created if one of the atoms is replaced by a neutral molecule,

called M, and the other atom by an anion, called A−(figure 3.3.1). In simplest terms,

this system can still be treated as diatomic system in a Morse potential.

101

3. Experimental and Computational Methods

Fig. 3.3.1.: Simplified potential scheme for electron detachment illustrating the definition

of VDE, adiabatic detachment energy (ADE), dissociation energy D0of the anionic diatom,

dissociation energy Dnof the neutral diatom and equilibrium bond length re. If structural

changes happen after photodetachment, rechanges and VDE=ADE.

If two elements form a diatomic molecule, the system is stable in the well of the inter-

atomic potential and has the energy E. During the dissociation process, the diatomic

molecule follows the interatomic potential to longer bond length until the bond breaks

and the constituent parts are separated (figure 3.3.1). The energy required for this pro-

cess is the dissociation energy D0. For the anionic pseudo-diatomic system (A−-M), D0

is the energy difference between the complexed system E(A−-M) and the sum of the

separated elements E(A−) and E(M)

D0=E(A−) + E(M) −E(A−-M) (3.3.35)

Analogously, a dissociation energy for the neutral complex Dncan be defined

Dn=E(A) + E(M) −E(A-M) (3.3.36)

If the neutral complex is not allowed to relax to its optimized structure than the

corresponding energy E∗(A−M) leads to an excited dissociation energy of the neutral

complex

D∗

n=E(A) + E(M) −E∗(A-M).(3.3.37)

Another process an anionic diatomic system can undergo is electron photodetachment,

where an electron is removed, leaving behind the neutral diatomic system. Computa-

tionally, an electron detachment energy can be computed from the energy difference of

102

3. Experimental and Computational Methods

the anion and neutral diatomic system, where constraining the neutral geometry to the

same geometry of the anion provides the vertical12 detachment energy (VDE) (equation

3.3.38).

VDE(A−M) = E∗(AM) −E(A−M) (3.3.38)

Allowing the neutral diatomic system to relax to its stable configuration yields the

ADE (equation 3.3.39).

ADE = E(AM) −E(A−M) (3.3.39)

Since ADE arises from the structural change after photodetachment and VDE assumes

an unchanged structure, the difference VDE - ADE gives a relaxation energy for the

neutral case, an energy needed to reach the ground state structure from an excited

state.

In experimental photodetachment studies, it is quite reasonable to assume no struc-

tural changes after photodetachment since such changes are too slow for this kind of

process (Born-Oppenheimer approximation). In other words, re, the minimum of the

interatomic potential, should be the same for both Morse potentials and VDE should be

equal to ADE. Here, the resulting measured electron binding energy EBis compared to

VDE.

The shift (∆VDE), the difference between the VDE of the pseudo-diatomic system

and the VDE of the bare atomic anion A−is defined in equation 3.3.40.

∆VDE = VDE(A−M) −VDE(A−) (3.3.40)

It gives (approximately) the interaction strength between A−and M. The corresponding

measured value is called ∆EB.

In general, many isomers belong to the same pseudo-diatomic system A−-M. They

are considered as stable system if the (ground state) energy or the inner energy of the

system is negative. Relative stability between isomers can be judged by comparing the

ground state energies or the ZPE-corrected minimum energies E0(A−M) (Emin + zpe =

E0) with each other. The isomer with the lowest minimum energy is considered to be the

most stable isomer and is called E0(most stable A−M). All other E0(A−M) are given

relative to this energy and only the difference to E0(most stable A−M) is considered

further (equation 3.3.41).

E0=E0(A−M) −E0(most stable A−M) (3.3.41)

3.3.4. Choice of Functional and Basis Set

From the vast functional/basis set combinations that are exist, B3LYP-

D3/aug-cc-pVTZ(-PP) is used as main calculation method on Gaussian16 (g16)

[145]. This decision was made after testing 12 different functional/basis set combi-

nations on reference systems (Au−and Au−-H2O) and one of the here investigated

gold complexes (Au−-Fen). The calculated results are compared to the experimental

12The transition from the anion to the neutral configuration describes a vertical line (figure 3.3.1)

103

3. Experimental and Computational Methods

values of the reference systems (Au−with EB= 2.309 eV [77] and Au−-H2O with

EB= 2.76 eV [146]) and the gold complex Au−-Fen (EB= 2.69 ±0.02 eV, section 4.3

or [51]).

Out of the 12 functional/basis set combinations, B3LYP-D3/aug-cc-pVTZ(-PP) gave

energies, which generally differ the least from literature and experimental values (not

shown). In particular, the literature and experimental values for Au−, Au−H2O and –

the most stable – Au−-Fen deviate by only 0.09 eV, 0.05 eV and 0.11 eV, respectively.

Some readers might think that 0.11 eV is a significant deviation. Better results could

be achieved if more functionals and basis sets were tested. However, this is a time

consuming process and hence was omitted here. Furthermore, in section 4.4.1 it is

demonstrated that there seems to be a simple linear relationship between the calculated

and the experimental results, which helps to predict experimental values more accurately

than the calculated results do and is also faster than searching for the perfect functional-

basis set combination.

For an orbital composition analysis, Hartree-Fock (HF) is used in combination with

aug-cc-pVTZ(-PP). Instead of electron densities, wave functions are used, which nor-

mally lead to more precise information on the (molecular) orbitals, e.g. their compo-

sition from different atomic orbitals. Orbitals with corresponding energies and orbital

composition analysis are obtained with the help of the Multiwfn software [147].

104

4. Gold Complexes of Chiral Molecules1

Fig. 4.0.1.: The four molecules used to create Au−-M, in skeletal representation (a subset of

figure 3.1.1). All molecules are chiral and have a non-superposable mirror image (not shown).

The stereogenic center is highlighted with a * and their absolute configuration is given.

This chapter will have two main foci: nonconventional hydrogen bonds of the

type Au−···H-C,N,O and the first PECD measurements on gold-chiral complexes

Au−-M with M being the chiral molecule fenchone (Fen), menthone (Men), 3-

hydroxytetrahydrofuran (3HTHF) or alaninol (Ala) (figure 4.0.1). Of particular interest

is the bond Au−···H-C and if the interaction between molecule and Au−is strong

enough for recognizable PECD signals.

4.1. Introduction and Motivation

The gold complexes were the first targets for the anion PECD measurements. The idea

behind these complexes were to create an anionic chiral system, which is easy to produce

and without (strongly) altering the chiral molecule itself yet providing an electron source

(Au−) from which an electron can easily be photodetached. The detached electron would

then interact with the chiral environment provided by the molecule and lead to the PECD

effect. While PECD measurements were the main focus in the beginning, analyzing PES

measured with linear polarized light and DFT calculations showed further interesting

results towards (unconventional) hydrogen bonding.

Historically, hydrogen bonds are interactions, between hydrogen and either oxygen,

nitrogen or fluorine, the most electronegative elements. However, evidence for hydrogen

bonds with alternative elements, which retained the hallmark properties of a hydrogen

bonded system accumulated over time [148–157]. Hence, the IUPAC redefines hydrogen

1This chapter is in part based on the article J. Triptow, G. Meijer, A. Fielicke, O. Dopfer,

M. Green, “Comparison of Conventional and Nonconventional Hydrogen Bond Donors in Au–

Complexes”, 2022, in: The Journal of Physical Chemistry A, ACS Publications, in press DOI:

10.1021/acs.jpca.2c02725

105

4. Gold Complexes of Chiral Molecules

bonds by discarding the idea of the use of specific atoms in favor of specific properties,

like geometric, energetic and electronic ones [158].

Now, IUPAC defines a hydrogen bond as an attractive interaction between three

elements: the hydrogen (H), which is covalently bound to an atom called the hydrogen

donor (X), interacts with an atom called the hydrogen bond acceptor (Y). X and Y

are both electronegative atoms with Y having electron donor character. In general,

a hydrogen bond is written as X-H···Y. A hydrogen bond is also considered a three-

center-four-electron (3c-4e) bond [159,160].

Some of the properties defined by the IUPAC are:

1. The bond X-H···Y is almost linear: ∠XHY = 110 - 180

2. H···Y length is smaller than the van-der-Waals radii of H and Y

3. Commonly, the bond length X-H increases for a hydrogen bond, leading to a

redshift in the stretching frequency of X-H

4. Involved forces are electrostatic (dipole-dipole interaction), inductive, dispersive.

Their contribution can depend on the charge character of proton donor and accep-

tor [161]

5. The electron density topology usually shows a bond path and a (3,-1) bond critical

point between H and Y

The IUPAC lists more than the here given properties like NMR characteristics but they

are not considered here since it is not possible with this experimental setup to test them

all and does not need to be fulfilled completely to call a bond a hydrogen bond anyways

[158]. This also concerns the measurement of the red shift for the stretching frequency

in point 3 since there is currently no setup for vibrational measurements. However, the

bond length is monitored via DFT calculations.

This more universal definition of the hydrogen bond motivated many studies to non-

conventional hydrogen bonds. Especially transition metals have been found to be good

hydrogen acceptors [157,162–166]. Brammer explained this property with electron rich

transition metals with filled dshells [149]. Especially, the class of late transition metals,

to which Au belongs, should be the best hydrogen acceptors.

Originally, Au−was chosen under the aspect of PECD measurements but it turned out

to be a good candidate for hydrogen bonding as well: The gold atom is relativistic mean-

ing that the atomic and ionic radii are contracted [137] leading to greater accessibility

for hydrogen donors. Furthermore, the relativistic effects are responsible for gold being

one of the most electronegative transition metals with 1.92 (Allen scale), which is similar

to heavy halogens. Au also has a high polarizability and behaves like a Lewis base. The

neutral atom, as well as, the anionic gold have been found to form (nonconventional)

hydrogen bonds [127,167], whereas the additional charge in the anion strengthen the

interaction leading to so called charge assisted hydrogen bonds [168–170].

Hydrogen bonds of the type Au−···H-X normally concerned conventional hydrogen

donors like O, N and F. Smaller systems found moderate and strong bonding [146,

106

4. Gold Complexes of Chiral Molecules

171–175]. Also, more complex systems like microsolvation and nucleaobases can be

found mainly with the common donor atoms [127,176,177]. Few studies focus on the

nonconventional donors and bonds like Au−···H-C. The problem is that they are either

overshadowed by other, stronger hydrogen bonds or that they can not conclusively be

identified as hydrogen bonds [152,177,178].

Although, there are only a few studies on Au−···H-C hydrogen bonds, the impor-

tance of such interaction can be significant. In catalysis, Au−···H-C is expected to

be an important secondary interaction [178,179]. Important molecules in biology and

chemistry often have no conventional hydrogen donors and can only offer H-C like fen-

chone and menthone. They only have a ketone as functional group, which can not act

as hydrogen donor. These molecules are part of a larger group of compounds, which are

being used for green synthesis of gold nanoparticles [180–182].

The other two investigated molecules, 3-hydroxytetrahydrufuran (3HTHF) and alani-

nol, can be considered as comparative molecules since they can offer in both cases OH

and additionally NH in the case of alaninol. 3HTHF is considered a standard in mea-

suring hydrogen bonding [183,184]. Alaninol even shows internal hydrogen bonding in

the form of N···H-O or O···H-N, depending on the isomer.

An analysis of these different complexes not only provides insight into the general

characteristics of nonconventional hydrogen bonding with gold, but also provides insight

into the potential of the interaction between the photoelectron source (Au−) and the

chiral component (Fen, Men, 3HTHF and Ala) being “chiral”. In other words, this

analysis gives a first look into the possibility of PECD asymmetries of these complexes.

The sections about hydrogen bonding are already partly published in [51].

4.2. Mass Spectra

The utilization of a gold target in the laser ablation source produces mass spectra, which

peaks at multiples of m/z 197 corresponding to Au−

mas evident in figures 4.2.1. If in

addition chiral molecules are introduced, the gold complexes Au−-M can form (figures

4.2.1)2. In particular, peaks appear in the spectrum at m/z 349 for Au−-Fen (figure

4.2.1a), m/z 351 for Au−-Men (figure 4.2.1b), m/z 285 for Au−-3HTHF (figure 4.2.1c)

and m/z 272 for Au−-Ala (figure 4.2.1d), where m/z consists of a contribution of the

gold anion m/z 197 and the corresponding molecule (m/z 152 for fenchone, 154 for

menthone, 88 for 3HTHF and 75 for alaninol).

Along side the desired complex Au−-M, different kinds of clusters (Au−

m-Mn) are ob-

served. In particular, Au−

m-Fennwith m= 1 and up to n= 4 (highlighted in green in

figure 4.2.1a) are observed as well as m= 2 with up to n= 2 (highlighted in blue). Also

Au−

m-Fennwith m= 3 and m= 1 are visible in the mass spectrum (highlighted in red).

Similar combinations are visible in the other mass spectra containing the other chiral

molecules.

2The presented spectra of figure 4.2.1 are not necessarily optimized for the target complex in order to

show various other features.

107

4. Gold Complexes of Chiral Molecules

(a)

(b)

(c)

(d)

Fig. 4.2.1.: Mass spectra of gold complexes. Au−(m/z 197) and clusters in yellow. Target

complex Au−-Fen at m/z 349 (a), Au−-Men at m/z 351 (b), Au−-3HTHF at m/z 285 (c),

Au−-Ala at m/z 272 (d), with molecule cluster in green. Various mixtures in other colors.

108

4. Gold Complexes of Chiral Molecules

It is also possible, that one mass spectrum shows peaks of two different complexes

Au−

m-Mnand Au−

m-M’n, e.g. the mass spectrum of the target complex Au−-3HTHF

(figure 4.2.1c) shows Au−

m-3HTHFnand Au−

m-Menn. Additionally, complexes with mul-

tiple chiral precursors Au−

m-Mn-M’p(“mixed complexes”) are possible (figures 4.2.1c and

4.2.1d). Au−

m-M’nand the mixed complexes observed in figure 4.2.1c and figure 4.2.1d

arise from residual molecules from previous measurements.

Other peaks in the mass spectra that are not marked in figure 4.2.1 can be assigned

to impurities: Au−

mcomplexes with carbon clusters, like Au−

m-Cn(-H) are assigned to

the small peaks between m/z 209 and 258, after Au−, and between m/z 406 and 454,

after Au−

2. In addition, the peak at m/z 229 in figure 4.2.1a is assigned to Au−-O2.

Furthermore, molecules like Cn(-H), H2O and O2can combine with the target complex

Au−

m-M, which is observed in figure 4.2.1a between m/z 364 - 381. While the oxygen

could be coming from the air, the carbon could have its origin from the steel wool used to

clean the gold rod or from sputtering in the laser ablation region. Fragments of organic

molecules could also be a reason. In general, despite the variety of anions that are visible

in the mass spectra, mass selection enables the isolation of the desired complex prior to

photodetachment.

4.3. Photodetachment of Gold Complexes with Linear

Polarized Light

4.3.1. Photoelectron Spectra

Photoelectron spectra of the complexes measured at Eph = 4.13 or 4.35 eV give an

overview and are compared to the PES of Au−in figure 4.3.1. Several features and

properties are visible in the PES of the gold complexes: The dominant peaks (X and A)

belong to the electronic transitions of the gold complexes and show a difference ∆ to the

respective Au−transitions, which will be called “shift”. Corresponding binding energies,

EB, and shifts, ∆, are extracted from the high resolution spectra, discussed in section

4.3.1.1, and are summarized in table 4.3.1. The shift is directly related to the strength

of the bond of the molecule with Au−and will be discussed in section 4.3.1.2. Secondary

features are visible for the complexes Au−-Fen and Au−-Men at around EB= 2.31 eV

Table 4.3.1.: Photoelectron transitions for the different Au−-M with errors and shifts ∆ to

Au−based on PES (figure 4.3.1). X indicates the ground and A the excited state.

System EB,X (eV) ∆X(eV) EB,A (eV) ∆A(eV)

Au−2.309 0 3.45 0

Au−-Fen 2.707 ±0.009 0.398 3.93 ±0.01 0.48

Au−-Men 2.775 ±0.008 0.466 4.05 ±0.03 0.60

Au−-3HTHF 2.99 ±0.04 0.68 4.22 ±0.04 0.77

Au−-Ala 3.00 ±0.02 0.69 4.22 ±0.02 0.77

109

4. Gold Complexes of Chiral Molecules

Fig. 4.3.1.: PES with linear polarized light at Eph = 4.13 eV (300 nm) or 4.35 eV (285 nm)

for all Au−-M in comparison to PES of Au−. The PES for the complexes look similar to the

one of Au−but are shifted by ∆, which correlates with the strength of the Au−-M interaction.

as well as for Au−-3HTHF and Au−-Ala at around EB= 3.4 eV. In the case of Au−-Fen

and Au−-Men, the complex is metastable and leads to an Au−contribution in the PES

of the complex. The feature in the PES of Au−-3HTHF and Au−-Ala can be attributed

110

4. Gold Complexes of Chiral Molecules

to an O-H (or N-H) stretch vibration, which is supported by DFT calculations (section

4.5.2). Both features will be discussed in section 4.3.1.3.

4.3.1.1. Resolution

Fig. 4.3.2.: PES with linear polarized light at different photon energies Eph for Au−-Men

compared to Au−. The peaks corresponding to the ground state are labeled XAu for Au−and

XM(or X’Mand X”M) for Au−-Men. The excited stated are labeled accordingly with A. If

the spectrum is measured at a different photon energy ’ is added to the label. For Au−-Men

the first transition (X) is around EB= 2.77 eV and the second (A) around 4.04 eV. The small

transition around 2.31 eV in the blue PES arises from Au−indicating a metastable state of

the complex. FWHM gets smaller with smaller Eph. Au−is measured in normal mode while

Au−-M is measured in event mode.

Apart from the PES presented in figure 4.3.1, more PES measured at smaller photon

energies are also recorded with the VMI spectrometer since they show an improved

absolute resolution of single peaks (section 3.2.3). The smallest photon energy for Au−-

Fen and Au−-Men is 3.024 eV. For Au−-3HTHF the smallest photon energy is 3.49 eV.

Au−-Ala is only measured at Eph = 4.35 eV. In all PES with different Eph an improved

absolute resolution is evident, which is only shown exemplary for Au−-Men in figure

4.3.2. The binding energies of table 4.3.1 are derived from these PES. For the high

intensity peak in figure 4.3.2, there is a clear narrowing of the band, but the increase in

absolute resolution did not reveal additional spectral structure. Therefore, representative

spectra of the Au−anion and Au−-M complexes, which show all observed transitions,

at comparable resolutions, are provided in figure 4.3.1.

111

4. Gold Complexes of Chiral Molecules

Spectra measured with relatively high photon energies show, at ground state peaks,

a shoulder on the side of higher binding energies. If this shoulder contains unresolved

vibrational or isomeric features, measurements at lower kinetic energies should resolve

this features according to absolute resolution. Instead of resolving any features, the

shoulder vanishes for smaller kinetic energies (figure 4.3.2). A shoulder with the same

behavior was visible in the PES of Au−from section 3.2.3.5 and can be attributed as an

artifact of a not perfect image reconstruction.

However, even if high resolution spectra could not resolve additional features, the PES

of Au−-3HTHF and Au−-Ala probably contain vibrational or isomeric features due to a

broadened FWHM of X in comparison to Au−PES measured at similar kinetic energies.

Especially for Au−-Ala, the FWHM could be dominated by isomeric effects since for

alaninol itself already 25 isomers could be found [75]. In contrast, the FWHM of the

X peak of Au−-Fen and Au−-Men seem similarly broadened to the X peak of the Au−

PES for high Ekin (>1 eV). However, the Au−PES could be broader than it could be

since it is measured in normal mode and not like the gold complexes in event mode,

which reduces the resolution as could be seen for S−in figure 3.2.30b. For lower Ekin

(<0.5 eV), the X peak for Au−-Fen and Au−-Men shows bigger broadening. In the end,

the PES of all gold complexes could contain more or less some unresolved vibrational or

isomeric features.

Comparing the corresponding excited state peaks (A), all Au−-M show an increased

FWHM with respect to the Au−peaks. Vibrational states and isomeric effects seem to

dominate this broadening.

Furthermore, it is important to consider the relative resolution or rather peaks with

similar kinetic energy as uncertainty in the resolution scales with electron kinetic energy

(section 3.2.3.5). Consequently, peaks corresponding to ground states are expected to

have better relative resolution than corresponding excited states. In contrast to the

absolute resolution, not a comparison between spectra of different photon energies is

made but a comparison between peaks within one spectrum. Hence, at least two peaks

(ground state and excited state) need to be in one spectrum, which is only fulfilled for

spectra measured with at least Eph = 4.22 eV. The expected better resolution for ground

state transitions can be observed in all the spectra (exemplary shown in figure 4.3.2 for

Au−-Men).

4.3.1.2. Blue shift ∆

The PES of Au−given as reference in figure 4.3.1 and 4.3.2 are measured with 4.13 eV

(300 nm) and 4.35 eV (285 nm), respectively. These photon energies are sufficient to

probe the transitions from the anionic electronic ground state 1S0to the neutral ground

state 2S1/2 (XAu in figure 4.3.1) and to the excited state 2D5/2 (AAu in figure 4.3.1),

which corresponds to a detachment from the 6sorbital with EB= 2.309 eV and from

the 5dorbital with EB= 3.445 eV, respectively (figure 3.2.26).

As expected, all Au−-M spectra resemble the spectrum of Au−indicating a photode-

tached electron that was mainly localized at Au−before photodetachment. The main

difference to the Au−spectra is the (blue) shift ∆ to higher electron binding energies,

112

4. Gold Complexes of Chiral Molecules

which is seen in figure 4.3.1 and table 4.3.1. Apparently, the Au−-M without conventional

hydrogen bond donors (i.e. fenchone and menthone) show smaller blue shifts. Similar

blue shifts of the ground state peaks (X) were already reported for related molecules by

several research groups [127,146,152,176,185]. Interestingly, blue shifts related to the

excited states (A) are larger than for the first transition and are also reported in [127].

The Born-Haber cycle is given by

Au + e−+M+EB(Au) →Au−+ M (4.3.1a)

Au−+M+D0→[Au]−M (4.3.1b)

[Au]−M−EB(AuM) →AuM + e−(4.3.1c)

AuM + e−−Dn→Au + e−+ M (4.3.1d)

with EBbeing the electron binding energy, D0the dissociation energy of the anionic

complex and Dnbeing the dissociation energy for the neutral complex. In equation 4.3.1,

the shift reflects (in zeroth order of approximation) the interaction between Au−and

the molecule M – or in other words, the dissociation energy – if the interaction between

Au and M is neglected.

Assuming the complex is held together solely by the extra electron, detaching it leads

to a neutral complex (Au-M) with a negligible dissociation energy. Hence Dnis set to

zero and the dissociation energy must be EB(AuM) −EB(Au) = |∆EB|=|D0|. This is

just a rough estimation and hence the shift reflects the interaction of Au−-M, or in other

words the dissociation energy, only approximately. However, it seems that a larger shift

can be connected to higher dissociation energies.

From the perspective of hydrogen bonding with Au−, the electronegativity values EN

for the atoms in the molecules (in Allen scale [186]: EN(H) = 2.30, EN(C) = 2.54,

EN(O) = 3.61 and EN(N) = 3.07) shows that O has the strongest electron withdrawn

ability and leaves the largest partial positive charge at its hydrogen. Consequently,

the interaction between Au−and a hydroxy group is stronger than with other groups

leading to larger dissociation energies and, according to the approximation made in the

Born-Haber cycle (∆EB≈D0), to larger blue shifts in the ground and also in excited

states.

For Au−-Fen and Au−-Men blue shifts of around 0.40 eV and 0.47 eV are found respec-

tively, which is much bigger than what was calculated for Au−-CH4[152] with 0.047 eV.

Other gas phase studies focusing on Au−···H-C interactions in similar complex systems

like done here seem not to be available for a comparison.

The blue shifts for Au−-3HTHF and Au−-Ala are around 0.7 eV in both cases. In

comparison to Au−-H2O, Au−-CH3OH, Au−-C2H5OH and Au−-C3H7OH this blue shift

is about 0.2 eV higher indicating to a stronger interaction between Au−and molecule

[127,146,176,187].

In these studies, smaller blue shifts were observed, in comparison to the complexes

studied, herein. This is assumed to be due to the number of attractive interactions that

can be sustained: with such small molecules, only a single H-bond interaction is expected,

where as the complexes here are much larger, and as will be shown later (section 4.4),

113

4. Gold Complexes of Chiral Molecules

can sustain numerous hydrogen bonding interactions. The amount of bonds and the

cooperation between them stabilize the system and leads to a higher blue shift.

On the other hand, nucleaobase-Au−show much higher blue shifts of 0.92 - 1.12 eV

[177]. These systems also show more than one bond to Au−and are characterized by

medium or strong Au−···H-N hydrogen bonds.

The blue shifts of the excited states ∆Aare around 0.1 eV larger than the shifts of

the ground state. Before this work, no satisfying explanation to this effect was given in

the literature. An explanation will be ventured in section 4.4.3.2. In summary, charge

transfer mechanisms could lead to a more diffuse 6sorbital and hence to the deshielding

of the 5dorbital in Au−. This lowers the energy for transition A.

The blue shifts in the PES are a clear indicator for the influence of the molecule on

the detached electron. Hence, the electron “feels” the molecular potential (more or less)

of each complex but it is not clear to what extent the chirality is felt by the electron

and how it is expressed in the PECD effect.

4.3.1.3. Secondary Features

Two secondary features are visible in the PES of the gold complexes:

First, spectra from Au−-Fen and Au−-Men both feature an unusual peak at

2.30±0.01 eV and 2.31±0.01 eV, respectively (figure 4.3.1, more pronounced in figure

4.3.2 for Eph = 3.024 eV (410 nm)). This peak matches the transition from the 6sorbital

of Au−at 2.309 eV. Thus, despite the huge m/z difference for Au−and Au−-M, both

substances seem to enter the interaction zone of the VMI spectrometer simultaneously

(hence reach the ToF-MS detector at the same time) and are photodetached with the

same laser pulse. This leads to the assumption of a metastable fraction of Au−-M, which

falls apart in the acceleration region of the ToF-MS. However, this offers the opportu-

nity to verify in retrospect the quality of optimization and calibration to some extent3

and can confirm a relatively flawless running experiment since every (major) error will

be reflected in the extra Au−peak.

Second, for Au−-3HTHF and Au−-Ala, a tiny peak around 3.4 eV or around 0.4 eV

higher in energy than the main peak X, emerges. It is labeled νXin figure 4.3.1. The

energetic position of this peak leads to two possibilities:

It can be the first excited transition A of Au−. Au−-Fen and Au−-Men already showed

that the complex might be meta stable and transitions from the bare Au−can appear

but this always concerned the X peak and never the A peak. If νXshould be the A peak

of Au−, the X peak should also be visible and be of much stronger intensity. However,

this is not observed, which makes this theory unlikely.

A more likely explanation is νXbeing the stretch vibration of O-H. A similar peak is

observed in Au−-H2O and it is assigned to the water stretch frequency [146]. Further-

more, DFT calculations support this assumption but will be discussed later in section

4.5, where experimental and computational results are compared. In the case of Au−-

Ala, the calculations indicate also to a N-H vibration.

3This does not replace a real calibration, since the intensity is too small

114

4. Gold Complexes of Chiral Molecules

4.3.2. Beta Parameter

Fig. 4.3.3.: Exemplary reconstructed PAD of Au−and Au−-Fen to visualize the angular

distribution of the electrons. Both spectra are taken at Eph = 4.13 eV and lead for Au−-Fen

to the red spectrum shown in figure 4.3.1. The different positions of rings between both PADs

correspond to different electron binding energies. The PAD of Au−-Fen features noise in the

center, which originates from the light and accumulates after hours of measurement. Au−does

not show this noise since the signal-to-noise ratio is much higher and the PAD can be taken

in several minutes. Hence, the noise can not accumulate. Both PADs are normalized to their

highest intensity value. Transitions are labeled according to figure 4.3.1.

The anisotropy parameter βis extracted from the photoelectron spectra with POP and

rBasex for all Au−-M. Since both methods produce (almost) identical results only the

POP data is depicted here in figure 4.3.4.

As already known for the isolated Au−, the anisotropy parameter is (in theory) exactly

2 for all kinetic energies since the electron detachment for the first transition happens out

of the 6sorbital. Electrons from other orbitals than pure sorbitals show a dependence

on the kinetic energy Ekin. Such a dependence is seen in the anisotropy parameters of

each Au−-M (figure 4.3.4). Some points could be, within the errors, 2 but most data

points are around 1 < β < 2 indicating to a photoedetachment process from an sorbital,

which is disturbed by the complexing molecule. The disturbing elements could be the

2porbitals from the carbons, oxygen and nitrogen, which mix with the 6sorbital of

Au−. The disturbance of the molecules might be subtle but is still large enough to be

recognized with the current setup.

The second transition A shows anisotropy parameter around zero indicating to a

more uniform distribution in the low kinetic energy region. This anisotropy parameter

is probably determined by the 5dorbital of Au−being disturbed by the molecule.

115

4. Gold Complexes of Chiral Molecules

(a) (b)

Fig. 4.3.4.: Anisotropy parameter βfor X and A transition of Au−-Fen (a), Au−-Men (b),

Au−-3HTHF (c) and Au−-Ala (d) obtained with POP.

Orbital images of the gold complexes in combination with an orbital composition anal-

ysis will help understanding the anisotropy parameters. However, this will be discussed

in more detail in section 4.5.

The change in beta, in conjunction with the blue shifts observed in the complex spec-

tra, provide evidence for the influence of the chiral molecule on the detaching electron.

However, it is still unclear whether the photodetachment will carry a chiral signal (i.e.

PECD signal).

4.4. Computational Results

4.4.1. Calculated Structures of Gold Complexes

4.4.1.1. Stabilization

The initial molecular geometries – which are taken to prepare Au−-M for calculations –

are shown in figures 4.4.1 for fenchone, 4.4.3 for menthone, 4.4.7 for 3HTHF and 4.4.9

for alaninol. They are arranged and labeled according to their stability (or minimum

energy E0).

116

4. Gold Complexes of Chiral Molecules

Fig. 4.4.1.: Structures for fenchone optimized with B3LYP-D3/aug-cc-pVTZ(-PP). This is

the only possible isomer due to the bicyclic structure of fenchone [32].

Especially the most stable configurations were initially extracted from the literature

[32,75,188,189], calculations were repeated with the level of theory given in the lit-

erature and a comparison of rotational constants confirms the reproduction of these

structures. Apart from isomers given in the literature, other structures were extracted

from websites like “PubChem”. This concerns for example the “chair” structure of men-

thone 4.4.3d. In the end, all structures were optimized with B3LYP-D3/aug-cc-pVTZ

in combination with harmonic frequency calculations to fit with the upcoming Au−-M

calculations.

Due to its bicyclic structure, fenchone has no torsional flexibility, leading to only one

possible conformation [32]. This structure is shown in figure 4.4.1.

In contrast, menthone, 3HTHF and alaninol, possess more than one isomer. For

menthone, four different isomers were found: M1.0 - M3.0 have almost a flat structure

and differ from each other by a rotated isopropyl group [188], whereas the structure

of M4.0 resembles a “chair”, due to the bending of the adjacent methyl group out of

the plane of the central ring. M1.0 (figure 4.4.3a) is the most stable configuration.

M2.0-M4.0 are structures, which lie 0.008, 0.029 and 0.094 eV above M1.0.

For 3HTHF, four isomers were reported in [189] from which just two are considered

here. Among them, the most stable structure H1.0 and an isomer located 0.02 eV above

H1.0 (figure 4.4.7). Both isomers are depicted in two different views: The top view for

H1.0 shows clearly the orientation of the hydroxy hydrogen pointing inside the ring and

towards the ether oxygen (O2), which might stabilize the system due to the internal

hydrogen bond O2···H-O1. The side view shows the form of the ring and the upwards

117

4. Gold Complexes of Chiral Molecules

(a) Structure F1 (b) Structure F2

Fig. 4.4.2.: Optimized structures for the complex Au−-Fen with various positions of the gold

atom adjacent to the chiral core obtained with B3LYP-D3/aug-cc-pVTZ(-PP) as well as the

distances to Au−in nm (yellow) and energies VDE, E0,D0in eV (black).

bending of the ether oxygen due to the hydrogen bond. This type of structure is called

a C2-endo structure and corresponds to the most predominant furanose ring structure,

which can be found in nucleotides [189].

For H2.0, the hydroxy hydrogen is pointing outside the ring, leading to a vanishing

interaction to the ether oxygen. Furthermore, the interaction between the ether oxygen

and the hydroxy oxygen is increased, which may support the ring puckering (side view

of H2.0). This is the C4-endo structure.

According to Fausto et al. [75], there can be up to 25 different isomers for alaninol

within a relative energy range of just 0.3 eV. Here, only five isomers are considered, which

mainly differ from each other by the rotation of the OH group and secondary by the

arrangement of hydrogens at the nitrogen. Among them, the most stable configuration

A1.0 in figure 4.4.10a. The stability of the system seems to be determined by two inter-

nal hydrogen bonds of the type N···H-O and O···H-N. For the most stable conformer

A1.0 and the two isomers below A2.0 and A3.0, the hydrogen bond N···H-O appears in

different strengths. In A4.0, no N···H-O but instead O···H-N emerges, which reduces

the stability of the system since N induces a smaller partial positive charge in its hydro-

gens than O. A5.0 is the least stable isomer since neither N···H-O nor O···H-N can be

observed as a bond rotation causes the hydroxy and amino groups to be separated.

118

4. Gold Complexes of Chiral Molecules

(a) Structure M1.0 (b) Structure M2.0

Fig. 4.4.3.: Optimized structures for menthone obtained with B3LYP-D3/aug-cc-pVTZ(-PP).

E0is the minimum energy given relative to the most stable structure M1.0. M1.0-M3.0 corre-

spond to the structures given in [188] and differ by a rotated isopropyl group. M4.0 resembles

a “chair” and is the least stable structure studied here.

Au−-M are prepared for all molecules (and their isomers) in the same manner: the neu-

tral molecule was fixed in one orientation and Au−was manually placed at six different

positions around it, then a geometry optimization was performed. After optimization,

the initial structures converged to the gold complexes presented in figure 4.4.2 for Au−-

Fen, figures 4.4.4 -4.4.6 for Au−-Men, figure 4.4.8 for Au−-3HTHF and figures 4.4.10 -

4.4.13 for Au−-Ala. The optimized structures of the most stable Au−-M are given in the

appendix A.1. Alongside the Au−-M structures, bond lengths and angles of the three

(sometimes four) shortest Au−···H bonds as well as energies like VDE, D0and E0are

extracted. They are given partly in the figures and completely in the corresponding

tables 4.4.1 -4.4.2. Both, figures and tables, are arranged by stability or in other words,

according to E0, starting with the most stable Au−-M isomer.

The label of the different Au−-M isomers are assigned depending on the initial molec-

ular isomer and the stability of the complex: In the case of Au−-Fen, the complexes are

labeled with F1 - F4, with F1 being the most stable complex and F4 the least stable one.

For the other Au−-M two numbers are needed: the first number always indicates the

parent molecular isomer and the second number is assigned according to their stability.

For example, the gold complexes Au−-3HTHF are labeled H1.x (with x = 1 - 4) and

H2.x (with x = 1, 2) according to the base structures H1.0 and H2.0, respectively. In

119

4. Gold Complexes of Chiral Molecules

(a) Structure M1.1 (b) Structure M2.1

Fig. 4.4.4.: First group (1) of optimized structures for the complex Au−-Men with various

positions of the gold atom adjacent to the chiral core obtained with B3LYP-D3/aug-cc-pVTZ(-

PP). This are the most stable isomers for Au−-Men. Predominantly, Au−binds with the ring

of menthone. Distances to Au−are given in nm (yellow) and energies VDE, E0,D0in eV

(black).

the group of H1.x isomers, the most stable one is H1.1 and the least stable one H1.4,

while H2.1 is the most stable complex in the group of H2.x. Other Au−-M are labeled

accordingly.

In general, two main stabilization effects can be discerned, which correlates with the

type of molecule in the complex: The complexes with ketone groups (Au−-Fen and

Au−-Men) are stabilized by geometry while the complexes with conventional hydrogen

bond donors (Au−-3HTHF and Au−-Ala) are stabilized through the strong electron

withdrawing ability of these donors.

The stability for Au−-Fen and Au−-Men seems to be determined by the position of

the Au−. In general the Au−seems to avoid the ketone group, which can probably be

explained by the negative partial charge sitting on the oxygen. For Au−-Fen the distance

of Au−to O is between 0.5 - 0.6 nm and a bit bigger for Au−-Men with 0.5 - 0.7 nm.

One could expect that the stability is increased for the isomers with the largest distance

of Au−and O but this is not what can be observed here: The most stable isomer of

Au−-Fen shows the largest distance but the smallest distance is seen for F3 and not F4.

In Au−-Men the least stable isomers show the biggest distances between Au−and O and

the most stable isomer even has the shortest one. Overall, the ketone group is avoided

120

4. Gold Complexes of Chiral Molecules

(a) Structure M1.2 (b) Structure M3.2

Fig. 4.4.5.: Second group (2) of optimized structures for the complex Au−-Men with various

positions of the gold atom adjacent to the chiral core obtained with B3LYP-D3/aug-cc-pVTZ(-

PP). This are the second stable isomers of Au−-Men. Au−binds predominantly to the boarder

of the ring of menthone. Distances to Au−are given in nm (yellow) and energies VDE, E0,

D0in eV (black).

by Au−but the attractive forces of the positively partial charged hydrogens seems to

have a bigger influence on the position of Au−at the molecule than the repellent effect

from the oxygen.

Something similar can be observed for Au−-3HTHF: Here, not a ketone group needs

to be avoided but the ether oxygen, which is part of the ring structure. However, the

reason will stay the same with the oxygen holding a negative partial charge, which repels

the Au−. Especially H1.3, H1.4 and H2.2 show this effect clearly: the oxygen always

bends away to the other side of the ring plane (ring puckering). Even more, in H2.2,

the hydroxy group is pointed away from the ring center and exposes O1 to the ether

oxygen. Normally, this leads O2 to bend to the other side of the ring plane but here it

rather stays on the same side with O1 than to be on one side with Au−.

Another aspect regarding the stability of Au−-Fen and Au−-Men is the position rela-

tive to ring structures: If Au−connects with H atoms of C’s, which are part of a ring

structure the most stable isomers are formed. This is the case for F1, where Au−bonds

with hydrogens of C’s, which form a rather deformed ring. For F2 - F4, Au−connects

to hydrogens from carbons not being part of a closed structure (ring).

121

4. Gold Complexes of Chiral Molecules

(a) Structure M4.3 (b) Structure M1.3

Fig. 4.4.6.: Third group (3) of optimized structures for the complex Au−-Men with various

positions of the gold atom adjacent to the chiral core obtained with B3LYP-D3/aug-cc-pVTZ(-

PP). This are the least stable isomers for Au−-Men. Here, the system is the least stable if Au−

binds to the isopropyl group. Distances to Au−are given in nm (yellow) and energies VDE,

E0,D0in eV (black).

(a) Structure H1.0 (b) Structure H2.0

Fig. 4.4.7.: Structures for 3HTHF optimized with B3LYP-D3/aug-cc-pVTZ. The bond

lengths of O-H are given in nm (red) and the minimum energies E0in eV. The structure

with the lowest E0is structure H1.0. H1.0 and H2.0 are discerned by ring puckering (up view)

and the orientation of the hydroxy group (side view). For H1.0, H is pointing inside the ring

and towards the ring oxygen, which stabilize the structure.

122

4. Gold Complexes of Chiral Molecules

(a) Structure H1.1 (b) Structure H1.2

(e) Structure H2.1 (f) Structure H2.2

Fig. 4.4.8.: Optimized structures for the complex Au−-3HTHF with various positions of the

gold atom adjacent to the chiral core obtained with B3LYP-D3/aug-cc-pVTZ(-PP) resulting

from the initial molecule H1.0 or H2.0. The isomers are arranged according to E0. H1.1 - H1.3

show a hydrogen bond between Au−and the hydroxy group (Au−···H-O), which increases

the OH bond length (compare to figure 4.4.7) and decreases the hydrogen bond length of

Au−···H-O in comparison to Au−···H-C. They are the most stable structures and belong

to the first group of isomers. H1.4, H2.1 and H2.2 do not have Au−···H-O resulting in less

stable structures and an unchanged OH bond length. These are the second group. Distances

are given in nm (yellow or red). The VDE, E0and D0energies are given in eV (black).

Due to the better arranged structure, this effect is observed more easy in Au−-Men:

The most stable isomers belong to structures where Au−interacts mostly with the ring

part of the molecule (figure 4.4.4). Here, the most H can participate in the Au−bonding

123

4. Gold Complexes of Chiral Molecules

(a) Structure A1.0 (b) Structure A2.0

(e) Structure A5.0

Fig. 4.4.9.: Structures for alaninol optimized with B3LYP-D3/aug-cc-pVTZ. Given are the

OH bond lengths in nm (red) and minimum energies E0in eV. The structure with the lowest

E0is structure A1.0, with H of the hydroxy group pointing directly at N.

stabilizing the bond. The fourth stable isomer is a structure obtained from M4.0 (the

“chair” structure). If the gold is “sitting down” a quite stable complex (M4.1) is created

from the least stable molecular structure. If Au−binds at the boarder of the ring part

of the molecule (figure 4.4.5) less stable isomers are created, which is accompanied by

increased hydrogen bond length between Au−and CH. The least stable isomers are

created if Au−is bound to the isopropyl group instead to the ring (figure 4.4.6).

Something similar could be expected from Au−-3HTHF due to the 5-membered ring

but here only the least stable isomers show a connection between Au−and the ring part

of the molecule. The stabilization effect by the ring seems to be secondary if an O-H

group is involved (e.g. compare H1.1 with H2.2 in figure 4.4.8).

124

4. Gold Complexes of Chiral Molecules

(a) Structure A1.1 (b) Structure A2.1

Fig. 4.4.10.: First group (1) of optimized structures for Au−-Ala with various positions of Au−

adjacent to the chiral core obtained with B3LYP-D3/aug-cc-pVTZ(-PP). They are ordered

according to E0and are the most stable ones of the Au−-Ala complexes. Common in all

configurations is the existence of the hydrogen bond Au−···H-O, which leads to an extended

OH bond length and a shorter hydrogen bond in Au−···H-O (in comparison to Au−···H-C

or Au−···H-N). In addition to Au−···H-O, A1.1 and A2.1 feature a hydrogen bond of the

type Au−···H-N. Distances are given in nm (yellow or red) and energies in eV (black).

Structure H1.1 is the most stable isomer of Au−-3HTHF with the hydrogen of the

hydroxy group pointing outside the carbon ring and towards Au−. It could be generated

with the structure H1.0 and H2.0. Indeed all complexes generated by H1.0 could also

be produced by H2.0 indicating to a low energy barrier for conversion between H1.0

and H2.0. This is also supported by the small E0difference of 0.022 eV (figure 4.4.7b).

The interaction between molecule and Au−is strong enough to overcome the energy

of 0.022 eV, which is needed to convert H1.0 into H2.0 or vice versa (or to cause OH

rotation and ring puckering).

In general, Au−-3HTHF and Au−-Ala show a clear trend regarding stabilization: The

most stable isomers are the ones with a hydrogen bond between Au−and the hydroxy

group Au−···H-O (H1.1 - H1.3 in figure 4.4.8 as well as all isomers in figure 4.4.10 and

4.4.11) while isomers without that hydrogen bond (no Au−···H-O) are the least stable

isomers (H1.4, H2.1, H2.2 in figure 4.4.8 and all isomers in figure 4.4.12,4.4.13). This

can be expected from bonds including one of the strongest hydrogen donors.

125

4. Gold Complexes of Chiral Molecules

(a) Structure A4.2 (b) Structure A3.2

Fig. 4.4.11.: Second group (2) of optimized structures for the complex Au−-Ala with various

positions of Au−adjacent to the chiral core obtained with B3LYP-D3/aug-cc-pVTZ(-PP).

This are the second most stable isomers of the Au−-Ala complexes. As for the first group,

the hydrogen bond Au−···H-O exists. A4.2, A3.1 and A2.2 also have the hydrogen bond

Au−···H-N. The hydrogen bond to N is shorter than for Au−···H-C or for the first group in

figure 4.4.10 indicating a stronger interaction between the hydroxy hydrogen and N. Distances

are given in nm (yellow or red) and energies in eV (black).

Comparing E0between the groups of isomers with and without Au−···H-O for Au−-

3HTHF, the isomers show a difference of around 0.3 eV emphasizing the importance of

the Au−···H-O hydrogen bond for stabilization. This energy jump between both groups

of isomers is much smaller for Au−-Ala, especially if the first subgroup of isomers without

Au−···H-O (A1.2, A1.3, A2.3 and A2.4 in figure 4.4.12) is considered. Looking at the

hydroxy group, a slightly increased bond length of 0.097 and 0.098 nm is observed in

contrast to the undisturbed OH bond of 0.096 nm. Au−is too far away to be responsible

for this kind of extension. However, a (internal molecular) hydrogen bond of the type

N···H-O, like observed in A1.0 - A3.0, can be responsible for the slight extension and

give some stabilization. If this internal molecular hydrogen bond is not present, the

energy jump in E0between both groups is around 0.2 eV (compare figure 4.4.11 and

4.4.13).

126

4. Gold Complexes of Chiral Molecules

(a) Structure A1.2 (b) Structure A1.3

Fig. 4.4.12.: Third group (3) of optimized structures for the complex Au−-Ala with various

positions of Au−adjacent to the chiral core obtained with B3LYP-D3/aug-cc-pVTZ(-PP).

In contrast to the first two groups, no Au−···H-O hydrogen bonds are observed. Instead,

hydrogen bonds with Au−···H-N occur. Like in the second group, the hydrogen bond in

Au−···H-N is shorter in comparison to Au−···H-C bonds. Since Au−is too far away from

the hydroxy group, the OH bond length is determined by the influence of N, which increases

the bond length slightly (figure 4.4.9). Distances are given in nm (yellow or red) and energies

in eV (black).

127

4. Gold Complexes of Chiral Molecules

(a) Structure A5.2 (b) Structure A5.3

Fig. 4.4.13.: The fourth group (4) of optimized structures for the complex Au−-Ala with

various positions of Au−adjacent to the chiral core obtained with B3LYP-D3/aug-cc-pVTZ(-

PP). Like for the third group, no hydrogen bonds of the type Au−···H-O occur and the

hydrogen bonds Au−···H-N are shorter in comparison to Au−···H-C. The difference to the

third group is the bond length of the OH group, which is the uninfluenced bond length since

neither N nor Au−interact with the hydroxy group. The distance between Au−and CH

hydrogens is around 0.3 nm. Distances are given in nm (yellow or red) and energies in eV

(black).

128

4. Gold Complexes of Chiral Molecules

4.4.1.2. Geometric Properties Supporting H-bonding in Au−-M

According to the IUPAC definition and listed properties for a hydrogen bond mentioned

in the beginning of this chapter, the bond length between hydrogen and hydrogen ac-

ceptor is usually smaller than the sum of the van-der-Waals radii of both atoms. Van-

der-Waals radii can be extracted from Bondi and Batsanov in [190] but relevant sums

are 0.272 nm for conventional hydrogen bonds involving X-H···O and 0.333 nm for the

nonconventional bonds X-H···Au, where X is an hydrogen donor, e.g. O, N or C. Here,

the van-der-Waals radius of neutral Au is taken, not the one of the anion, which might

lead to a (slightly) smaller radius than for the anion case.

Normally, bond lengths of H···O in a hydrogen bond are around 0.18 - 0.20 nm [191],

fulfilling the IUPAC definition. In the nonconventional case of O-H···Au, the bond

length also meets the condition set by IUPAC for some systems [127].

The more common case with O as hydrogen acceptor fulfills this condition always for

Au−-3HTHF and Au−-Ala: All bonds involving O lead to a Au−···H bond length of

around 0.23 nm, a bond length, which also fulfills the length condition as if Au−would be

an O. Concerning N, this property is also easily satisfied by the last two groups of Au−-

Ala with the length staying below 0.275 nm, where N is the only/primary hydrogen bond

donor (figure 4.4.12 and 4.4.13). Mostly the bond length is around 0.25 nm. However,

the most stable group (the first group) of Au−-Ala barely fulfills the condition with bond

length of 0.3 nm or higher where N operates as a secondary H-bond donor, second to O.

(figure 4.4.10).

Considering the Au−···H-C systems, most bond lengths stay below the limit of

0.333 nm. In the case of Au−-Fen all bond length are below that limit and also all

Au−-Men complexes except two examples in the least stable ones fulfill this condition.

Even in the systems with Au−···H-O and Au−···H-N bonds, there are complexes with

Au−···H-C with a bond length smaller than 0.333 nm. Among them are the most stable

ones, e.g. H1.1, H1.3, A1.1 and A2.1.

The smallest bond length of the type Au−···H-C can be found in M1.1 and M3.1

with 0.266 nm. It is no match for the Au−···H-O bond length but is comparable to

Au−···H-N (compare with figure 4.4.13).

Another aspect for hydrogen bonds is the bond angle ∠X,H,Au−with X being either

O, N or C. For a H-bond, the bond has to approach linearity (110 - 180

). Bonds of the

type Au−···H-O easily satisfy this condition since the angles are all between 159 - 175

The bonds involving N can be comparable to ∠O,H,Au−, but can also be pretty small

with one bond not fulfilling the angle condition. The angles are between 102 - 175

∠C,H,Au−satisfy in most cases the angle condition, too, but with a smaller average

bond angle compared to those mentioned above. In Au−-Fen and Au−-Men where C

does not need to compete with O or N the angles are between 128 - 168

for Au−-Fen and

84 - 173

for Au−-Men. Only two bonds are not fulfilling the angle condition. They are

in the two least stable Au−-Men and do not fulfill the bond length condition from earlier.

In general, Au−···H-C bond angles are comparable in linearity to the Au−···H-O and

Au−···H-N bonds. If Au−···H-C has to compete with the other bond types the angle

is in general smaller and is between 86 - 143

(Au−-3HTHF and Au−-Ala).

129

4. Gold Complexes of Chiral Molecules

Table 4.4.1.: Bond lengths and angles for selected Au−-M. The most stable isomer of each

isomer group is chosen as representative of this group. Number in brackets give the values

for the undisturbed molecule (no Au−). X = C, N or O. Other isomers can be found in the

appendix A.3.

Complex H-bond length (nm) length (nm) angle(

)

X-H H···Au−

F1 C3-H···Au 0.109 0.288 151.2

C4-H···Au 0.109 0.293 134.9

C5-H···Au 0.109 0.316 128.4

M1.1 C4-H···Au 0.111(0.110) 0.226 161.0

C6-H···Au 0.110 0.295 144.3

C9-H···Au 0.109(0.110) 0.291 144.8

M1.2 C7-H···Au 0.110 0.298 130.7

C9-H···Au 0.109 0.308 117.7

C10-H···Au 0.109 0.307 130.1

M4.3 C2-H···Au 0.109 0.293 149.3

C4-H···Au 0.109 0.315 125.3

C10-H···Au 0.109 0.312 119.3

H1.1 C1-H···Au 0.109 0.231 92.2

C4-H···Au 0.109 0.318 124.8

O-H···Au 0.099(0.096) 0.231 164.6

H1.4 C2-H···Au 0.110 0.299 139.5

C3-H···Au 0.109 0.325 121.9

C4-H···Au 0.109 0.292 131.1

A1.1 C3-H···Au 0.110 0.323 107.1

N-HN.1 ···Au 0.102(0.101) 0.331 102.0

N-HN.2 ···Au 0.102(0.101) 0.301 122.4

O-H···Au 0.099(0.097) 0.233 163.5

A4.2 C2-H···Au 0.109(0.110) 0.305 121.1

N-HN.1 ···Au 0.102(0.101) 0.297 138.5

O-H···Au 0.099(0.096) 0.232 170.0

A1.2 C1-H···Au 0.109 0.309 136.2

C2-H···Au 0.109 0.366 94.9

N-HN.2 ···Au 0.103(0.101) 0.251 157.9

A5.2 C1-H···Au 0.109 0.318 128.7

C2-H···Au 0.110 0.320 111.5

N-HN.2 ···Au 0.102(0.101) 0.263 149.6

130

4. Gold Complexes of Chiral Molecules

Interestingly, the most linear bond for Au−···H-C of 173.1

can not be found in the

most stable isomer M1.1 but in M4.1 indicating that the stability is not driven by a

solitary Au−···H-C bond but rather is a collaboration of several Au−···H-C bonds.

This is in contrast to isomers involving Au−···H-O bonds. This bond is always the

most linear bond and the corresponding isomer belongs to the most stable isomers.

Beside the bond length to Au−, internal bond lengths like O-H, N-H and C-H are

monitored to study the influence of Au−on this kind of bonds. The bond lengths

disturbed and undisturbed by the Au−can be found for selected Au−-M in table 4.4.1

and in the appendix A.3 for all other isomers (table A.6 -A.15).

For hydrogen bonding, it is usual to find an elongated bond between the donor and

H in comparison to the undisturbed bond. Without the perturbation of Au−, the OH

bond length is around 0.096 nm for 3HTHF isomers (figure 4.4.7) and for alaninol isomers

except for the most stable isomers A1.0 and A2.0 (figure 4.4.9). A1.0 and A2.0 have an

extended bond length of 0.097 nm due to the internal hydrogen bond N···H-O. Both,

OH bond lengths are within literature values [75,189,192]. If Au−is interacting with

the molecule, the bond length is increased clearly to 0.099 nm, which can be expected

for the common hydrogen donor O.

Another hydrogen donor is N, which can be found in alaninol. It forms weaker hydro-

gen bonds than the common donor O can offer but is nevertheless accepted as hydrogen

bond. The bond elongation is about 0.001-0.002 nm. Especially in the first two groups

of Au−-Ala (table A.12 and A.13) the elongation is mostly 0.001 nm since the N donor

is in competition with the O donor weakening the hydrogen bond involving the N and

hence lead to a smaller elongation. In contrast to the last two groups (table A.12 and

A.13), which have no hydrogen bonds with the O, most complexes show an increased

elongation of 0.002 nm.

Bonds involving C change the bond length maximal by 0.001 nm. Some seem to be

longer and even shorter after the bond with Au−(e.g. M1.1 in table A.7). This could be

due to rounding the values but in general the elongated bonds match with the elongation

seen in the N-H bond.

From a geometric point of view, all complex types demonstrate characteristics of hy-

drogen bonding indicating to a stronger (and potentially directional) interaction between

chiral molecule and Au−. This interaction is expected to be stronger and more perturb-

ing than weak van der Waals forces and might help the photoelectron to sense the chiral

potential facilitating a PECD effect.

131

4. Gold Complexes of Chiral Molecules

4.4.2. Calculated Energies of Gold Complexes

4.4.2.1. Global Energies

Table 4.4.2.: ZPE corrected energies calculated with B3LYP-D3/aug-cc-pVTZ(-PP) for Au−-

Fen and Au−-Men. VDE(Au−) = 2.215 eV. EB(Au−) = 2.309 eV. D0and Dnare always

related to the respective most stable molecular isomer. The structures are ordered by E0.

Hence, isomers of Au−-Men can be grouped according to the connectivity of Au−to Men:

Au−connects with (1) the ring structure (figure 4.4.4), (2) the border of the ring (figure 4.4.5)

and (3) isopropyl group of Men (figure 4.4.6).

Au−-Fen

Exp EB∆EB

2.707 0.398

DFT E0VDE ∆VDE D0ADE VDE-ADE Dn

F1 0 2.590 0.373 0.548 2.550 0.040 0.214

F2 0.065 2.528 0.313 0.483

F3 0.119 2.490 0.275 0.429

F4 0.128 2.490 0.275 0.420

Au−-Men

Exp EB∆EB

2.8 0.5

DFT E0VDE ∆VDE D0ADE VDE-ADE Dn

(1)

M1.1 0 2.669 0.454 0.680 2.606 0.063 0.289

M2.1 0.017 2.660 0.445 0.663

M3.1 0.024 2.674 0.459 0.656

M4.1 0.077 2.698 0.483 0.603

(2)

M1.2 0.186 2.551 0.336 0.494

M3.2 0.214 2.554 0.339 0.466

M2.2 0.217 2.544 0.329 0.463

M4.2 0.325 2.543 0.328 0.355

(3)

M4.3 0.398 2.439 0.224 0.282

M1.3 0.456 2.326 0.111 0.224

M2.3 0.468 2.325 0.110 0.212

132

4. Gold Complexes of Chiral Molecules

Table 4.4.3.: ZPE corrected energies calculated with B3LYP-D3/aug-cc-pVTZ(-PP) for Au−-

3HTHF and Au−-Ala. VDE(Au−) = 2.215 eV. EB(Au−) = 2.309 eV. D0and Dnare always

related to either H1.0 or A1.0, respectively. Isomers are ordered by E0and hence can be

grouped according to the connectivity of Au−to the molecule: Au−connects with the hydroxy

group of 3HTHF and Ala in (1), respectively (figures 4.4.8a -4.4.8c and 4.4.10). Also for (2)

in the case of Ala but Au−···H-O is not observed in (2) for 3HTHF as well as (3,4) for Ala.

Au−-3HTHF

Exp EB∆EB

2.99 0.68

DFT E0VDE ∆VDE D0ADE VDE-ADE Dn

(1)

H1.1 0 2.880 0.665 0.761 2.845 0.035 0.131

H1.2 0.031 2.860 0.645 0.730

H1.3 0.036 2.800 0.585 0.725

(2)

H1.4 0.268 2.560 0.345 0.493

H2.1 0.316 2.548 0.333 0.445

H2.2 0.326 2.539 0.324 0.435

Au−-Ala

Exp EB∆EB

3.00 0.69

DFT E0VDE ∆VDE D0ADE VDE-ADE Dn

(1)

A1.1 0 2.866 0.651 0.736 2.386 0.480 0.565

A2.1 0.010 2.881 0.670 0.726

A3.1 0.069 2.805 0.590 0.667

A4.1 0.079 2.823 0.608 0.657

(2)

A4.2 0.082 2.855 0.640 0.655

A3.2 0.084 2.869 0.654 0.653

A2.2 0.099 2.863 0.648 0.637

A5.1 0.112 2.837 0.622 0.625

(3)

A1.2 0.142 2.702 0.487 0.594

A1.3 0.180 2.622 0.407 0.557

A2.3 0.183 2.692 0.477 0.554

A2.4 0.183 2.688 0.473 0.553

(4)

A5.2 0.332 2.639 0.424 0.404

A5.3 0.354 2.532 0.317 0.382

A4.3 0.360 2.502 0.287 0.376

133

4. Gold Complexes of Chiral Molecules

Energies extracted from the various isomers of the gold complex can be found in the

tables 4.4.2 -4.4.3. Like the figures, the isomers are ordered according to their minimal

energy E0in ascending order.

However, ordering the isomers according to the VDE in descending order would lead

for Au−-Fen and Au−-3HTHF to the same order. The isomers in Au−-Men would

change places within the respective groups (figure 4.4.14a), e.g. M4.1 would be on the

first position instead of M1.1. In these cases, the VDE seems to correlate with the

general placement of Au−relative to the molecule and hence correlates with E0. Au−-

Ala would behave a bit differently: isomers with Au−···H-O would rearrange within

the first two groups (1) and (2), e.g. A3.2, a member of (2), would be on the second

position instead of A2.1 and hence be in (1). The same could be observed for the group

without Au−···H-O (3,4). Especially in the first two groups, if one Au−···H-N is

among the three closest bonds, the corresponding isomer shows the largest VDE values

(points above the blue horizontal line in figure 4.4.14b) while isomers without Au−···H-

N have lower VDE values (below the blue line). Hence, the VDE seems to be primarily

determined by Au−···H-O and secondary by Au−···H-N. From group (1) only A1.1

and A2.1 and from (2) A2.2, A3.2 and A4.2 are above the blue horizontal line. The

difference between these subgroups is the strength of the Au−···H-N bond, which is for

(1) weaker than for (2) according to the bond length. This seems to be important for

E0and less for the VDE.

(a) (b)

Fig. 4.4.14.: VDE vs minimum energy E0of (a) Au−-Men and (b) Au−-Ala. Vertically black

dashed lines are set arbitrarily to separate the different isomer groups. Group (1) and (2) of

Au−-Ala are further subdivided with an horizontal blue dashed line above which isomers show

Au−···H-N bonds. From (1) only A1.1 and A2.1 are above the blue line and differ from (2)

by the weaker Au−···H-N bond according to the bond length to Au−.

After photodetachment, the influence of Au is decreased due to the missing charge

and the complex can experience different structural changes before reaching a relaxed

state. The energy needed for this changes is ADE-VDE, which is given for only the most

stable isomers of all Au−-M. For Au−-Fen and Au−-Men, VDE-ADE is only 0.038 and

0.063 eV implying a relatively small structural change of the complex after photode-

tachment. For Au−-3HTHF a difference of 0.035 eV is needed. Without the additional

charge, the molecule in H1.1 (which resembles H2.0 more than H1.0) could transform

134

4. Gold Complexes of Chiral Molecules

in a molecule, which resembles more H1.0. In that case, around 0.022 eV are required

for the transformation from H2.0 to H1.0 (E0in 4.4.7). The remaining 0.013 eV could

be needed for additional hydrogen rotation. The largest structural change appears in

Au−-Ala with VDE-ADE = 0.480 eV. Once the charge is removed, alaninol in A1.1

seems to need big structural changes to reach the relaxed configuration.

4.4.2.2. (Local) Hydrogen Bonding Energetics

An analysis of the geometric properties of these complexes gives a qualitative assessment

of the hydrogen bonding in these complexes, but examining the local energetics of these

complexes, meaning the influence of individual hydrogens, could provide a more quanti-

tative understanding. Considering the whole complex, the dissociation energy is a good

first hydrogen bond strength estimator. However, with the help of Bader’s quantum

theory of atoms in molecules (QTAIM or just AIM) [161,193] analysis, strengths of

the individual hydrogen bonds can be estimated more precisely. Solely considering the

dissociation energy D0of an isomer with conventional bond donor and another with a

nonconventional hydrogen donor shows that the latter is not necessarily weaker bound.

For example, A1.1, the most stable isomer of the Au−-Ala, has an Au−···H-O only

shows a dissociation energy difference to M1.1 of 0.056 eV (table 4.4.2 and 4.4.3). Even

more interesting is the fact that D0of M1.1 is only smaller for the first two most stable

isomers of Au−-Ala, hence being more stable than some of the isomers, which show a

Au−···H-O bond (e.g. A4.1).

This small energy difference between the different types of complexes and even the

superiority of M1.1 over some isomers from Au−-Ala show the importance of identifying

hydrogen bond donors, the effect of cooperativity of several hydrogen donors on the total

bond energy and the influence of different forces like electrostatic forces, dispersion and

induction.

A first approximation of the individual hydrogen bond energy ebHB can be done under

the assumption of D0= -EHB with EHB being the sum of all hydrogen bonding interac-

tions between molecule and Au−. If only one H is contributing to the bond with Au−

and all other bonds are negligible then the individual hydrogen bond energy is simply

-EHB. However, this is just the lower limit (considering the minus sign) and probably an

overestimation of the magnitude. At the opposite end of the spectrum, if three hydro-

gens equally participating in the bond with Au−, the individual contribution is -EHB/3,

which can be considered as the upper limit if the minus sign is considered and represents

a lower limit of an overestimation. This arises from the assumption that there are no

other energetic contribution to the dissociation energy except the ones from hydrogen

bonding.

Considering only the most stable isomers, the individual H-bond energy range for each

complex is [-0.55,-0.18] eV for Au−-Fen, [-0.68,-0.23] eV for Au−-Men, [-0.76,-0.25] eV for

Au−-3HTHF and [-0.74,-0.25] eV for Au−-Ala. An energy of at least -0.2 eV is considered

to be a moderate strength in hydrogen bonds [158], which seems to be possible for all

complexes. Au−-Fen and Au−-Men will probably show energies, which are closer to

-EHB/3 since all bonds have the same hydrogen donor and will be equally strong. On

135

4. Gold Complexes of Chiral Molecules

the other hand, Au−-3HTHF and Au−-Ala could be closer to the other limit since they

possess the pretty dominant hydrogen donor O.

This is an overestimation, as it assumes all attractive forces and contributions to

the dissociation arise from solely the hydrogen bonding. Therefore, an AIM analysis is

performed to further confirm the hydrogen bond.

Fig. 4.4.15.: Electron density of the most stable gold complexes after AIM analysis. White

areas (density beyond scale) and brown dots (nuclear critical points) mark the atom positions.

Bond critical bonds are blue dots with white circles. The one with two big white circles is the

bond critical point considered in table 4.4.4. Ring and cage critical points are masked. Only

hydrogen bonds with the strongest bcp’s are considered here. H label according to figure A.1.

AIM analysis The result of the AIM analysis is given in form of electron densities ρ

and critical points in figure 4.4.15 for selected bonds of the most stable gold complexes.

Critical points are positions where the derivation of the density is zero and hence mark

extrema in the charge density. They can be categorized into four types:



(3,-3) or nuclear critical point (npc): ρis a local maximum. It overlaps (almost

perfectly) with the nuclear positions of (heavy) atoms.



(3,-1) or bond critical point (bcp): Saddle point in ρwith ρbeing a maximum

in two room directions and a minimum in one room direction. It occurs between

attractive atom pairs.

136

4. Gold Complexes of Chiral Molecules



(3,+1) or ring critical point (rcp): Like bcp a saddle point but with ρbeing a

minimum in two room directions and a maximum in one room direction. It marks

the center of ring systems and displays steric effects.



(3,+3) or cage critical point (ccp): ρis a local minimum. It describes cage systems

like pyramid shaped molecules.

Of special interest are the bcp’s since conclusions about type and strength of a bond

can be derived, which helps to judge about the (hydrogen) bonds in the gold complexes.

However, caution is advised for bcp’s since, contrary to their name, bcp’s do not always

indicate a (chemical) bond [194]. A bcp can also appear if two non-bonded atoms are

close together simply due to their topology. To avoid this confusion between bcp’s and

(chemical) bonds, Shahbazian [194] suggests to call bcp’s, line critical bond (lcp). Here,

bcp is used further to avoid confusion between the two abbreviations LCP and lcp.

In figure 4.4.15, the positions of the atoms are clearly visible by white areas, which

mark values beyond the density scale and by brown dots representing nuclear critical

points. Bond critical points are blue dots with a white ring and the one with two

rings is the one of interest. Table 4.4.4 lists all relevant bcp’s (two white rings) with

corresponding densities and energies (according to Emamian et al. [161]) for the most

stable gold complexes.

For Au−-Fen, four bcp’s concerning Au−and one completely without Au−could be

found. Interestingly, the one not involving Au−shows the highest density but it is

possible that this bcp does not indicate a true bond due to the repellent character of

both partially positively charged hydrogens. Four bcp’s for Au−-Men are revealed from

which the one with the lowest density does not include Au−but the ketone group.

Au−-3HTHF and Au−-Ala show each two bcp’s, which all include Au−and different

hydrogen donors. The found bcp’s agree more or less with the most likely bonds found

via Au−···H bond length and angles.

Emamian et al. [161] studied 42 different hydrogen bond complexes (28 neutral and

14 charged complexes) of various hydrogen bond strength and could not only classify

this strength from very weak to strong but also establish a relationship between electron

density and individual H-bond energies. Due to the variety of H-bond complexes studied

by Emamian et al., gold complexes will be compared to their electron densities and

energies. This enables also a categorization of the gold complex’ hydrogen bond strengths

according to Emamian et al. [161].

The determined electron densities of bcp’s of charged systems by Emamian et al. [161]

are at least 0.03 au (atomic units4), which is not reached by any bond of Au−-M (ta-

ble 4.4.4). The bond of the type Au−···H-O from Au−-3HTHF and Au−-Ala come

close but stay under that value. This could be due to the different kind of complex:

Emamian et al. [161] did not study charged complexes involving Au−but mostly conven-

tional hydrogen acceptors (and Cl, S), which may have greater influence on the H-bond

than unconventional anions like Au−. However, comparing the densities of bcp’s of the

Au−···H-O bonds to the ones of the gold(I)···indazol-3-ylidene complex from Park

4Not to be confused with arbitrary units a.u.

137

4. Gold Complexes of Chiral Molecules

Table 4.4.4.: Bond critical points (bcp) calculated with AIM for the most stable conformers

and ordered according to the density ρbcp. The density ρbcp is given in atomic units (au). The

bond energies for a single hydrogen bond ebHB are calculated according to equation 4.4.2 and

given in eV. Bonds with * are shown in figure 4.4.15. The bcp in C5-H···H-C8 of Au−-Fen

might not correlate to a true bond.

System bcp ρbcp (au) ebHB (eV)

Au−-Fen C5-H···H-C8 0.0120 -0.2192

Au−···H-C3* 0.0103 -0.1947

Au−···H-C4* 0.0098 -0.1875

Au−···H-C5 0.0067 -0.1428

Au−···H-C1 0.0033 -0.0938

Au−-Men Au−···H-C4* 0.0156 -0.2711

Au−···H-C9 0.0100 -0.1903

Au−···H-C6 0.0094 -0.1817

O···H-C1 0.0089 -0.1745

Au−-3HTHF Au−···H-O1* 0.0282 -0.4526

Au−···H-C4 0.0066 -0.1413

Au−-Ala Au−···H-O* 0.0273 -0.4397

Au−···H-N 0.0089 -0.1745

and Gabbai [167] (ρbcp = 0.026 and 0.017 au), which are confirmed moderately strong

hydrogen bonds, reveals that the here determined densities are greater. Of particular

interest is the gold(I)···indazol-3-ylidene complex with a bcp of a smaller density of

0.017 au since it is comparable to the Au−···H-C4 bond of Au−-Men.

Emamian [161] estimates the bond energy of each bond with a linear fit to the electron

density ρbcp of a specific bond critical point gained from fitting experimental and DFT

calculated results. The relationship between the individual bond energy ebHB, given in

kcal/mol, and ρbcp, given in atomic units (au) is presented in equation 4.4.2.

ebHB =−332.34 ·ρbcp −1.0661 (4.4.2)

The fit is based on a calculation with B3LYP-D3(BJ)/ma-TZVP [161] and equation 4.4.2

might vary for different DFT methods. Since, in this work a slightly different functional

and another basis set is used, equation 4.4.2 might show a different deviation than

given by Emamian [161]. However, a test calculation with F−-H2O shows that B3LYP-

D3/aug-cc-pVTZ and B3LYP-D3(BJ)/ma-TZVP lead to similar dissociation energies

(around 0.014 eV difference) indicating that the deviation given by Emamian could still

be similar in the here presented case. This test calculation is presented in table A.5.

The energies of the individual bonds with Au−are comparable and equally distributed

for Au−-Fen and Au−-Men like it can be expected for bonds involving the same atoms

(C, H, Au−). This confirms the assumption from earlier when the individual bond energy

was estimated based on D0, which also led to similar numbers like given in table 4.4.4.

138

4. Gold Complexes of Chiral Molecules

Table 4.4.5.: Calculated O-H and asymmetric N-H stretch frequencies for Au−-3HTHF and

Au−-Ala. Calculated frequencies from the optimized neutral complex and isolated molecules

are given. All calculated frequencies are given in cm−1and are scaled with a factor of 0.9636.

Vibration (cm−1) Au−-3HTHF Au−-Ala

OH stretch in Au−-M 3104.83 3147.26

OH stretch in Au-M 3627.49 3633.11

OH stretch in isolated M 3643.05 3582.18

NH stretch in Au−-Ala 3380.01

NH stretch in Au-Ala 3431.10

NH stretch in isolated Ala 3441.21

In contrast, Au−-3HTHF and Au−-Ala show energies that are not described well by

the estimation done with D0. It was correct to assume that the atom with the highest

electronegativity will have the strongest contribution but the energy of these bonds is

lower than the maximum assumed energy of D0. The bond involving the atom with

lower electronegativity has an energy smaller than estimated with D0/3. In general,

estimating the individual bonding energies with the help of D0and AIM leads to lower

values for AIM. This is pronounced for Au−-3HTHF and Au−-Ala while the AIM result

of Au−-Fen and Au−-Men is more comparable to the estimation with D0.

Redshift Apart from bond strength, a hydrogen bond can also be identified by a red-

shift upon hydrogen bonding, according to IUPAC. Such redshifts can be calculated for

the O-H and N-H bond. However, it remains experimentally not accessible due to the

experimental resolution.

The calculated frequencies can be found in table 4.4.5 and are scaled by a factor

of 0.9636, which is determined from [195]. The ratio of the B3LYP-D3/aug-cc-pVTZ

calculated frequencies of the asymmetric and symmetric stretch frequencies of H2O and

corresponding experimental values hereby define this scaling factor.

The relevant redshift is between the isolated molecule and the anionic complex. For

Au−-3HTHF and Au−-Ala, the frequency drops for O-H around 538 and 435 cm−1,

respectively. Something similar is observed in the N-H bond but weaker: the frequency

falls in total by around 61 cm−1. In general, this is the redshift, which is typical for

hydrogen bonds according to IUPAC.

A smaller redshift of around 16 and 10 cm−1can also be observed for the O-H bond

in the neutral complex Au-3HTHF and the N-H bond in Au-Ala, respectively. Hence,

a weak H-bond seems to be possible for the neutral complex as well indicating that the

charge is not necessary for a H-bond itself but is definitely enhancing it.

For a H-bond, an unusual blueshift of around 51 cm−1can be found for the O-H bond

in the neutral complex Au-Ala. The O-H frequency is probably altered in the molecule

due to the internal hydrogen bond N···O-H in the isolated molecule, which is broken

in the gold complex. In contrast to the internal bond, the neutral Au seems to create a

weaker H-bond, which only becomes stronger if the charge is added to the gold.

139

4. Gold Complexes of Chiral Molecules

4.4.3. Bond Character

Hydrogen bonds in charged complexes are governed mainly by electrostatic and induction

forces [161]. This includes charge transfer ∆Q and polarization α. With the help of a

natural bond orbitals (NBO) analysis, it is determined if the interaction between Au−

and molecule is of global nature (in the context of the complex’ size) or if the bond

character is driven by local properties (e.g. by single atoms of the complex). In order

to achieve that, the quantities are considered in combination with the stability of the

complex or the dissociation energy.

4.4.3.1. Global Property: Dipole Moment and Polarizability

Fig. 4.4.16.: Polarizability αof the excited molecules dependent on the dissociation energy of

Au−-M. The dashed colored lines are the αof the respective most stable molecular isomer. All

excited isomers M∗of the same molecule are polarized in the same way in the vicinity of Au−.

The polarizability of M∗differ not at all or just slightly (Au−-Men) from the polarizability of

the most stable molecular isomer.

Here it is hypothesized that, molecules with a strong polarizability αshould be the most

stable systems, i.e. having the largest dissociations energies D0due to the relationship

between dispersion forces and α. Also, molecules with a strong magnitude in dipole

moment and a dipole vector pointing towards Au−should attract Au−the most hence

leading to the most stable Au−-M.

While the polarizability and the magnitude of the dipole moment can readily extracted

after the DFT calculation, the dipole angle needs some more consideration: The orien-

tation of the dipole moment from the excited molecule is depicted by GaussView and a

bond parallel to the dipole vector is located, e.g. the O-C bond in fenchone. Now, the

corresponding gold complex is considered: a “gold vector” is defined, which has the same

origin as the dipole vector from M∗but ends at Au−(inset of figure 4.4.17e). The angle

between the dipole and gold vector is the dipole angle and is plotted over D0(figures

4.4.17e -4.4.17h).

140

4. Gold Complexes of Chiral Molecules

Figure 4.4.16 present the correlation between the polarizability αof the excited

molecule M∗over D0. The stability does not rise with αbut shows an (almost) constant

relationship to α. The dashed line indicates αof the most stable molecular isomer (e.g.

A1.0 in violet) and is in almost all cases not differing from αof M∗. Hence, if Au−

forms the external polarizing field, all isomers of the same molecules will displace their

charges in an (almost) equal amount in the vicinity of Au−. The only difference is the

polarizability of the different molecules with the largest molecules (fenchone in red and

menthone in blue) having larger αthan the smaller ones (3HTHF in green and alaninol

in violet). This is a known tendency since larger molecules offer more volume to the

electrons to occupy.

In figure 4.4.17 the magnitude and angle of the dipole moment µof the excited

molecules M∗is compared to D0of Au−-M. The expected correlation of a strong dipole

moment (magnitude µ) pointing in the direction of Au−(ϕ= 0

) leading to the most

stable systems is not observed here. Au−-Fen and Au−-Men stay more or less constant

for the magnitude µand even show the inverse expected correlation for ϕ. For Au−-

3HTHF and Au−-Ala no correlation at all seems to exist. Since neither the magnitude

nor the direction of the dipole show the expected correlation to D0, the breakdown of

the multipole expansion has to be assumed. It is valid at great distances but not for

short ones like 0.3 nm, which is observed for these complexes.

Global properties like the polarizability and the dipole moment of the whole molecule

seems to have no expected influence on the stability of the system or on the charge

transfer. Rather local effects, like the amount of hydrogen atoms participating in Au−

bonding (compare figures 4.4.4 -4.4.6) or local charge displacements of H in the vicinity

of Au−, seem to have the dominant role.

141

4. Gold Complexes of Chiral Molecules

(a) (b)

(e) (f)

(g) (h)

Fig. 4.4.17.: Magnitude (a-d) and angle (e-h) of the dipole moment of the excited molecules

dependent on the dissociation energy of Au−-M. Horizontal dashed lines in (a-d) indicate

the dipole moment of the most stable molecule (water in black, the other molecules in their

respective colors) for comparison. Vertical dashed lines are set arbitrary between the different

groups of gold complexes, according to the energy tables 4.4.2 -4.4.3. The inset of (e) shows

the definition of the angle between the dipole vector (blue, solid) (obtained from Fen∗and

copied to Au−-Fen (blue, dashed)) and the gold vector (black solid). The dipole vector is

parallel to the C-O bond, which can be used as reference. In (e-h) 0

means that dipole vector

and gold vector are parallel.

142

4. Gold Complexes of Chiral Molecules

4.4.3.2. Localization and Transfer of the Excess Charge

(a) (b)

Fig. 4.4.18.: A comparison of charge transfer ∆Qand dissociation energy D0. Black circles

mark the most stable structures. Vertical black dashed lines are set arbitrarily between the

different isomer groups according to the energy tables 4.4.2 -4.4.3.

A NBO analysis reveals that the extra charge mainly remains localized at the gold

part of the complex but is slightly reduced due to the “electron sharing” with or “charge

transfer” to the molecule (around 0.9 e remains at Au). The amount of negative charge

being transferred from Au−to the molecule, the charge transfer ∆Q, is calculated as the

difference of the charge located at the gold anion QAu−and the charge of a bare gold

anion Q= -1: ∆Q=|−1−QAu|. ∆Q(and Q) are measured in units of e.

∆Qis compared to the dissociation energy (figure 4.4.18), and the blue shift ∆VDE

(figure 4.4.19). In general, ∆Qrises with increasing ∆VDE or D0indicating that a

stronger bond correlates to the “electron sharing” with the molecule. Due to this cor-

relations, properties plotted against D0will in general show the same behavior as when

plotted over ∆Q, e.g. dipole moment and polarizability plotted over ∆Qwill still not

show the expected behavior. In figure 4.4.19, the most stable structures are among the

structures with the largest ∆VDE and ∆Qbut do not necessarily feature the strongest

electron bond or the most “electron sharing”. The same can be said about the VDE due

to the linear relationship to ∆VDE. Anyways, the most stable structures are among the

structures with the largest VDE and ∆Q.

143

4. Gold Complexes of Chiral Molecules

(a) (b)

Fig. 4.4.19.: A comparison of charge transfer ∆Qand ∆VDE. The most stable structures are

marked with black circles.

To further understand the bond character a more detailed look on the charge distribu-

tion and charge modification (due to Au−) among the other atoms within the complex

is performed. In figure 4.4.20 the charge distribution is shown for the most stable struc-

tures F1, M1.1, H1.1 and A1.1. The charge of the atoms may differ, slightly, within the

same kind of gold complex but the trend of charge distribution remains the same. As

already mentioned, the negative charge or excess electron remains mainly concentrated

at the gold atom (around -0.9 e). The hydrogens are weakly positively charged (dark

green), whereas the carbons tend to have almost no or a weak negative charge (dark

red). One exception is the C binding to O in fenchone and menthone: It clearly holds a

positive charge while the oxygen holds a negative one. In the case for Au−-3HTHF and

Au−-Ala, all hydrogens are mainly positively charged. However, the hydrogen in the

hydroxy group is a bit more positive than the others. In general, the charge distribution

matches with what can be expected if the electronegativities of the atoms are considered.

The change of NBO charges upon Au−bonding can also be seen in figure 4.4.20. Here,

all hydrogens relevant for the bond with Au−according to bond length and angle are

depicted with their charges when Au−is bond and in brackets when Au−is not there.

In general, all charges are more positive if Au−present. Two exceptions are a hydrogen

at H1.1 and another at A1.1: In the case of H1.1, AIM does not reveal a bcp between

that hydrogen and Au−indicating that there is no H-bond formed with Au−. For A1.1,

the difference arises from breaking the internal H-bond when going from bare molecule

to the gold complex.

144

4. Gold Complexes of Chiral Molecules

(a) (b)

Fig. 4.4.20.: NBO of the most stable structure for the different Au−-M: F1 (a), M1.1 (b), H1.1

charge (e) from +1 (green) to -1 (red). The negative charge or the electron remains mainly

with Au−. Black numbers are relevant for (hydrogen) bonding with Au−. Numbers in brackets

give the charges of the bare molecule (no Au−).

In the case of the most stable isomers, figure 4.4.18 and 4.4.19 already show that

complexes with an OH group show a (slightly) bigger charge transfer ∆Q than gold

complexes with a ketone group. The same can be observed in figure 4.4.20. This can be

explained by the different strong interactions between Au−and the different participating

atoms in the hydrogen bond. In figure 4.4.20, the charge increase in the hydogens is

greater in magnitude than what can be explained by the lost charge of Au−indicating an

enhanced H-X bond polarity due to induction, an important force in hydrogen bonding.

The NBO analysis revealed the electron donation character of the complexes. In all

cases electron donation happens predominately from the 6sorbital of Au−into the σ*

orbital of all X-H bonds: the CH bonds of Au−-Fen and Au−-Men, the OH and CH of

Au−-3HTHF as well as significantly into OH and secondary into NH and CH from Au−-

Ala. Such a donation behavior is typical for three-center-four-electron (3c-4e) bond,

which is expected for a hydrogen bonds.

145

4. Gold Complexes of Chiral Molecules

4.5. Experiment vs Computational Results

All the energies obtained from the previous presented structures will be compared to the

experimental values to verify if the generated structures are appropriate for describing

the Au−-M system that have been observed. Since, just the (electron) binding energy is

measured in these experiments, only a comparison between EBand VDE (figure 4.5.1a)

as well as the resulting shifts to Au−, ∆ (figure 4.5.1b) are possible. A comparison

between experiment and calculated value is not restricted to peak X but can be extended

to peak νXand A as well if frequency calculations and Koopmans’ theorem [196] are

used, respectively. Here, D0,Dnand E0do not have an experimental counterpart.

4.5.1. Peak X and Blue Shift

The comparison between the binding energies of peak X in figure 4.5.1a, as well as

the shifts in figure 4.5.1b, for the most stable isomers show that the calculated binding

energies and shifts underestimate, in all cases, the experimental values. This is indicated

by a linear fit without offset and a slope of slightly larger than one (1.04 for the most

stable systems).

If instead the VDE of the most stable isomers is replaced with the best matching

VDE, the comparison between VDE and EBgives a worse fit, e.g. not matching the

error bars of the data points. The fit for the most stable complexes seems to be more

reliable and hence the factor 1.04 is recommended for an estimation of experimental

values given the calculated values. The proximity of the fit parameter to 1 is another

indicator of the adequate choice of functional and basis set for these systems.

The DFT calculations can also be used to test the assumption from section 4.3.1, that

the shift ∆VDE or ∆EBfrom the Au−PES can be fully described by the dissociation

energy due to the negligence of D∗

n(equation 3.3.37). For this test, the Born-Haber cycle

(a) (b)

Fig. 4.5.1.: (a) Experimental electron binding energy (EB) over the calculated electron binding

energy (VDE) of the most stable structure and (b) the corresponding shifts ∆EBover ∆VDE.

A linear fit with slope 1.04 (orange dotted line) shows in both cases how the experimental

energies are underestimated by the calculated ones. The experimental values for Au−-H2O are

taken from Zheng et al. [146] while the VDE is calculated with B3LYP-D3/aug-cc-pVTZ-PP.

146

4. Gold Complexes of Chiral Molecules

introduced in equation 4.3.1 of section 4.3.1 is applied. All concerned energies, VDE

of Au−and Au−-M as well as the dissociation energies for Au−-M and Au-M have to

compensate each other to close the Born-Haber cycle: VDE(Au−)+D0−VDE(Au−-M)−

D∗

n= 0. Instead of Dn,D∗

nhas to be chosen to close properly the cycle since the

VDE energy assumes detachment without relaxation into the neutral ground state5.

The compensation of energies and closing of the Born-Haber cycle can exemplary be

done with the most stable isomers. In general, the excited dissociation energy of the

(a) (b)

Fig. 4.5.2.: ∆VDE vs dissociation energy D0. If the dissociation energy of the neutral complex

is negligible, the points would follow the orange dotted line with slope of 1 (Born-Haber cycle).

Vertically black dashed lines are set arbitrarily to separate the different isomer groups. Group

(1) and (2) of Au−-Ala are further subdivided with an horizontal blue dashed line above which

isomers show Au−···H-N. (b) and (d) are related to figure 4.4.14 since ∆VDE and VDE as

well as D0and E0are only shifted by system specific constants.

neutral D∗

nis a quite small value but non-zero. Hence, D0alone can not compensate

completely the VDE shift ∆VDE = VDE(Au−)−VDE(Au−-M). Figure 4.5.2 illustrates

this difference and relationship between D0and ∆VDE. Approximately, large shifts lead

to high D0but are by a value of D∗

nbelow the dissociation energy (or being by a value

of D∗

nbelow the orange dotted line indicating the line of equality). In conclusion, the

assumption made in section 4.3.1 about the dissociation energy of the neutral being weak

5The cycle can also be closed without exchanging Dnwith D∗

nbut then ADE instead of VDE has to

be taken.

147

4. Gold Complexes of Chiral Molecules

and maybe even negligible does not quite fit. Nevertheless, figure 4.5.2 shows clearly

that larger D0also lead to larger ∆VDE, which validates the statement of section 4.3.1

that the most stable isomers lead to the largest shifts. Since the calculations matches

pretty well with the experimental values (figure 4.5.1), the same statements can probably

made for the experimental values even if not all values of the Born-Haber cycle are

experimentally measured.

4.5.2. The Peak νXin Au−-3HTHF and Au−-Ala

In the spectra of Au−-3HTHF and Au−-Ala a peak at 3.42 and 3.43 eV is visible,

respectively. The other two complexes do not reveal such a peak. This peak was already

discussed in the experimental section 4.3.1.3 and it is assumed that it could be a O-H

stretch vibration, which motivated the label νX. Here, this assumption is supported by

DFT calculations:

A similar peak is observed for Au−-H2O at around 3900 cm−1(0.49 eV) [146]. A test

calculation for Au−-H2O gives a scaled6calculated frequency of around 3700 cm−1for

the water stretch vibration, which is in line with literature values and supports the use

of the here applied DFT method and basis set.

For Au−-3HTHF and Au−-Ala, the peaks are higher in energy to the X transition by

0.43 eV in both cases. This corresponds to a transition of 3470 ±330 cm−1for Au−-

3HTHF and 3470 ±250 cm−1for Au−-Ala above the ground states of these complexes.

The scaled calculated frequencies (in table 4.4.5) deviate around 200 cm−1from the

experimental value and fall all within the confidence area of the experimental value

indicating a relatively good match to the O-H stretch vibration in Au−-3HTHF and Au−-

Ala. For Au−-Ala, the asymmetric stretch vibration of N-H also fits pretty well and could

be another possibility for the νXpeak. A Franck-Condon simulation is not conducted

but according to the harmonic frequency calculations from the gaussian calculations the

O-H vibration should be more probable.

4.5.3. Peak A and Molecular Orbitals

Examining the molecular orbitals can provide information to compare the binding

energy of peak A to DFT calculations as well as give further insight into the observed

anisotropy of photodetachment. The molecular orbitals for the most stable Au−-M are

shown in figure 4.5.3 for HOMO and in figure 4.5.4 for HOMO-1. The HOMO and

HOMO-1 of all Au−-M are dominated by the 6sand 5dorbital of Au−, respectively.

However, they are deformed slightly in the complex due to the different (and mostly) p

type atomic orbitals of the molecule.

Orbital energies are extracted with Multiwfn after an orbital composition analysis

(table 4.5.1). The detachment energy of the excited peak A is then estimated with

Koopmans’ theorem [196] given by

VDE(A) = VDE(X)+(EHOMO −EHOMO−1) (4.5.3)

6scaling factor 0.9636 from [195]

148

4. Gold Complexes of Chiral Molecules

Table 4.5.1.: Orbital energies and their difference to the corresponding orbital of Au−∆ for

the most stable Au−-M are given in eV. Orbital composition shows only contributions to the

orbital, which are bigger than 0.5%. In all cases, only Au shows a contribution of greater than

0.5%.

System Orbital orbital energy (eV) ∆ (eV) orbital composition (%)

Au−HOMO -0.04

HOMO-1 -1.18

Au−-Fen HOMO -0.58 0.54 Au, 6s, 99.1

HOMO-1 -1.77 0.59 Au, 5d, 99.9

Au−-Men HOMO -0.72 0.68 Au, 6s, 98.7

HOMO-1 -1.96 0.77 Au, 5d, 100.0

Au−-3HTHF HOMO -0.77 0.73 Au, 6s, 98.3

HOMO-1 -1.93 0.75 Au, 5d, 99.7

Au−-Ala HOMO -0.80 0.76 Au, 6s, 98.2

HOMO-1 -1.99 0.81 Au, 5d, 100.0

Table 4.5.2.: Experimental (EB) and calculated (VDE) energies from the most stable com-

plexes compared to each other. VDE(A) is calculated with the orbital energies from table 4.5.1

and Koopmans’ theorem.

System EB(X) (eV) VDE(X) (eV) EB(A) (eV) VDE(A) (eV)

Au−2.309 2.215 3.45 3.3603

Au−-Fen 2.707±0.009 2.590 3.93±0.01 3.7789

Au−-Men 2.775±0.008 2.669 4.05±0.03 3.9055

Au−-3HTHF 2.99±0.04 2.880 4.22±0.04 4.0450

Au−-Ala 3.00±0.02 2.866 4.22 ±0.02 4.0522

149

4. Gold Complexes of Chiral Molecules

(a) HOMO of F1 (b) HOMO of M1.1

Fig. 4.5.3.: HOMO of most stable Au−-M. The molecular orbitals are created with the pro-

gram Multiwfn. Blue and green refer to positive and negative regions. The isosurface value is

0.01 for all figures. The sorbital of Au−is deformed slightly by molecular orbitals.

with VDE(A) being the estimated detachment energy of A, VDE(X) the already deter-

mined VDE of transition X and EHOMO as well as EHOMO-1 being the orbital energies

given in table 4.5.1. The results are summarized in table 4.5.2.

In all cases, the calculated energy is lower than the experimental evaluated binding

energy. For the X transitions this was already determined before but not in comparison

to the excited state A. Au−shows for X and A the same deviation of 0.9 eV. The devia-

tion in the X transition for the gold complexes ranges from around 0.11 to 0.13 eV, while

a stronger deviation of 0.14 - 0.17 eV is observed in A. Such different deviations can be

expected from Koopmans’ theorem since it assumes unaltered orbitals (no reorientation)

as well as identical relativistic energies (only relevant for inner electrons) and electron

correlation energies between (an)ion and molecule [197]. Especially the assumption of

identical correlation energies contributes to the different deviations of X and A since this

energy is not only different in ion and molecule but can also be different between states

of the ion/molecule [197]. However, the deviations from the experimental values are still

relatively low validating the use of Koopmans’ theorem for these gold complexes.

In the experiment, a greater shift in binding energy is observed for the A peak than

for the X peak in comparison to the Au−peaks. This shift is observed in other works as

well (e.g [127]) but no satisfying explanation has been provided. Given what has been

determined about the complexes herein, an explanation will be attempted: If electrons

150

4. Gold Complexes of Chiral Molecules

(a) HOMO-1 of F1 (b) HOMO-1 of M1.1

Fig. 4.5.4.: HOMO-1 of most stable Au−-M. Colors are defined like in figure 4.5.3. The

isosurface value is 0.004. The dorbital of Au−is deformed slightly by molecular orbitals.

are shared upon complexation, the energy of the HOMO is lowered, which leads to a

more diffuse 6sorbital. Hence, deshielding the 5dorbital, which lowers the HOMO-1

orbital energy and blue shifts peak A. This is supported by the calculated HOMO and

HOMO-1 orbital energies in table 4.5.1.

A more qualitative way to analyze the individual orbital contributions to the whole

system is an orbital composition analysis (table 4.5.1). Only orbitals with a contribution

of bigger than 0.5% are shown, which is only fulfilled by the gold atom. In all cases,

the contribution of gold is between 98 and 100% emphasizing the dominance of the gold

orbital over the whole system. Hence, the excess electron will mainly originate from

Au−instead of the molecule, which is consistent with the results in the discussion about

the charge transfer.

Considering the results of the anisotropy parameter from section 4.3.2, the orbitals

match to what one would expect from the experimental βvalues for the X transition.

βis around 1 and 2, which indicated to a system still dominated by the 6sorbital of

Au−but being disturbed by the molecule. This is affirmed by the orbital image in figure

4.5.3, which shows the 6sorbital of Au−deformed by the molecular orbitals.

151

4. Gold Complexes of Chiral Molecules

Fig. 4.6.1.: PECD PADs of Au−-Fen (not scaled). Images are recorded close to the edge of

the detector (clipped circle on the left of each image). Below the PADs are the photon energy

and electron counts per polarization. The light propagates from down to up. The forward and

backward half are separated by a dashed line.

Fig. 4.6.2.: Mean PECD of Au−-Fen. LCP and RCP spectra were scaled before PECD values

are calculated.

4.6. Photoelectron Circular Dichroism

The results and analysis of the previous section have confirmed the interaction and

influence between Au−and four chiral molecules, but also revealed that the probed

electron mostly retains the character of an electron from atomic Au−. The question

if this interaction is enough to elicit a chiral response (i.e. PECD asymmetry) in the

photodetachment is answered here.

The PECD results for Au−-M can be found in figures 4.6.1 -4.6.8 containing the

(unscaled) PECD PADs and mean PECD values, which where obtained by scaling the

RCP PES according to table A.16 before PECD evaluation (section 3.2.6). The mean

152

4. Gold Complexes of Chiral Molecules

Fig. 4.6.3.: PECD PADs of Au−-Men. Below the PADs are the photon energy and electron

counts per polarization. The light propagates from down to up. The forward and backward

half are separated by a dashed line.

Fig. 4.6.4.: Mean PECD of Au−-Men. LCP and RCP spectra were scaled before PECD values

are calculated.

PECD value is evaluated over the FWHM of all peaks. Measurements for all Au−-M

are performed with quarter waveplates (4.6.1 -4.6.7(up) and 4.6.8a). For Au−-Ala, a

measurement with the photoelastic modulator, with shot-to-shot polarization switching

were additionally performed to assure that the null-PECD result is not a consequence

of the quarter waveplates (figures 4.6.7(down) and 4.6.8b).

Except for the measurements with the PEM and the left PAD in figure 4.6.5, PADs

show a weird red-blue (positive and negative PECD values) pattern: It seems like the

colors are accumulating at positions of transitions or background, e.g. first PAD in

figure 4.6.1 for Au−-Fen shows how red (positive PECD values) accumulates where the

transition is located while the region between the transitions is blue. If the PAD is fully

reconstructed (all four quadrants considered), then the corresponding PES looks like the

black curves in figure 3.2.38 of section 3.2.6. Here, the LCP-PES shows clearly a higher

153

4. Gold Complexes of Chiral Molecules

Fig. 4.6.5.: PECD PADs of Au−-3HTHF. Next to the PADs the photon energy and electron

counts per polarization are given. The light propagates from down to up. The forward and

backward half are separated by a dashed line.

Fig. 4.6.6.: Mean PECD of Au−-3HTHF. LCP and RCP spectra were scaled before PECD

values are calculated.

intensity in the main transition (corresponding to red in the PAD) but less signal in the

region between the transitions (around 3.0 - 3.8 eV, blue region in PAD) in comparison

to the RCP-PAD. Since both images have the same electron counts, the electrons seem

to be differently distributed indicating to a worse signal-to-noise ratio in the RCP-PAD

in comparison to the LCP-PAD. This is supported by the needed loops, which is clearly

higher for the RCP-PAD than for the LCP-PAD. Since the PADs recorded with QWPs

are measured in series and not alternatively, and signal is optimized with respect to the

signal intensity, different experimental conditions existed probably during the measure-

ment of the LCP and RCP-PAD (long term effect). From the view of measurement,

alternatively switching the polarization and recording the PADs avoids this since both

PADs are equally affected by changed experimental conditions as can be seen in figure

4.6.7 (compare the four upper PADs with the four lower PADs). This is also reflected

in the scaling factors, which are generally closer to 1 than for the QWP measurements

(table A.16). However, the PEM was not available during the measurements shown in

figures 4.6.1 -4.6.7(up) and scaling the RCP-PAD according to table A.16 is used.

154

4. Gold Complexes of Chiral Molecules

PADs of Au−-Ala (figure 4.6.7 (up)) look a bit different, like the colors accumulating

in different quadrants (left image in third row of figure 4.6.7) or still accumulating in the

transition/background manner like above but the transition ring is “closing” in the upper

half of the image (right image in third row and left image of fourth row of figure 4.6.7).

If the color accumulation is related to the transition, then this indicates to an incorrect

anisotropy (β) since the ring should be symmetric around the Fw-Bw axis (white dashed

line). Despite checking the polarization before PECD measurements, the polarization

seems not to be ideal in these kind of images or changed during the measurement. A

better approach would be to constantly monitor the quality of polarization to recognize

such changes in time like it is done in the measurements with the PEM.

Overall, the data does not indicate that a (real) PECD signal was measured for any

of the Au−- M complexes. Most mean PECD values are either set to zero since forward

and backward direction give the same sign or are zero within the SE. Only two points,

namely Au−-Men at Eph = 4.35 eV (figure 4.6.4) and Au−-Ala at Eph = 3.02 eV (figure

4.6.8a) seem to reveal a PECD asymmetry but are on closer inspection not real:

For Au−-Men the determined PECD signal is rather small at -0.8% and the SE is

small enough to not reach zero. However, looking at the corresponding PAD image in

figure 4.6.3, the expected PECD pattern is not visible (even if the PAD is scaled like

it is done before PECD value evaluation). The SE seems not to be an adequate error

description for this measurement.

Au−-Ala gives seemingly a mean PECD value of around 3% at Eph = 3.02 eV but

shows not the typical PECD pattern in the PAD (left PAD in second row of figure 4.6.7):

Blue is predominantly on one side but as no corresponding red part on the other side.

Furthermore, the red part is not contained within one image half but spills over to the

other half. This could be due to wrong/changed polarization. Additionally, the mea-

surement was repeated for smaller VMI-repeller voltages to focus on the corresponding

region (right PAD in second row of figure 4.6.7 and of figure 4.6.8a) and also with the

PEM (right PAD in the last row of figure 4.6.7 and 4.6.8b) but the earlier PAD pattern

and the PECD signal could not be reproduced, probably because polarizations are set

more correctly in the latter cases.

While no PECD asymmetry could be measured for neither quarter waveplates nor

the photoelastic modulator, the measurements involving the PEM result in better null-

PECD PAD, meaning they are distributed like one would expect for a noisy PAD. Hence,

using the PEM seems to be more promising for a PECD measurement since non-PECD-

asymmetries are not contained in the PAD and will not overlapping with any real PECD

signal.

155

4. Gold Complexes of Chiral Molecules

Fig. 4.6.7.: PECD PADs of Au−-Ala recorded with QWPs (up) and PEM (down). Next to the

PADs the photon energy and electron counts per polarization are given. The light propagates

from down to up. The forward and backward half are separated by a dashed line. URis the

used repeller voltage of the VMI spectrometer.

156

4. Gold Complexes of Chiral Molecules

(a)

(b)

Fig. 4.6.8.: Mean PECD of Au−-Ala measured with (a) QWP and (b) PEM. LCP and RCP

spectra were scaled before PECD values are calculated. URis the repeller voltage of the VMI

spectrometer.

157

4. Gold Complexes of Chiral Molecules

Possible Reasons for the null-PECD Result

The null-PECD results for Au−-M elicit the question of why no PECD effect is ob-

served despite having a chiral system. Several reasons can be considered for potential

explanation:

1. PECD signal under the detection limit of this setup

2. Unlucky selection of chiral molecules and kinetic/photon energy

3. The photodetached electron does not feel the chiral potential of the molecule

(enough)

4. Contributions by too many isomers and/or vibrational states with different PECD

asymmetries, which superimpose and cancel each other out

The detection limit depends from the noise or background level, which can depend

on several factors like different noise from light (dependent on photon energy and align-

ment) or molecular beam. The amount of electron counts also plays an important role

since more electrons mean a smaller statistical error. Here, 2.6 - 11 Mio electrons per

polarization are recorded but it was not known if this is sufficient to measure the PECD

signal at that time. As will be shown in section 5.4.2 with [Ind-H]−, the smallest mea-

sured PECD signal still being over the standard error (SE) is around 1% and required

4 Mio electron counts per polarization. With 40 Mio electron counts per polarization

a PECD asymmetry of around 0.5% could be measured. If the PECD values for gold

complex are below 1% (or 0.5%) than it is excessively difficult to measure.

Another instrumental limitation are the artificial asymmetries in the PECD measure-

ments with QWPs, which are probably caused by long term fluctuations or unstable

anion signal. This could be clearly avoided with a shot-to-shot measurement with the

PEM. However, even with the PEM a PECD signal could not be measured.

Every chiral system should show a PECD asymmetry but not every chiral molecule will

show a strong one. Additionally, since the PECD asymmetry is dependent on the kinetic

(or photon) energy, the PECD effect can become quite small. An unlucky combination

of a bad chiral system and kinetic energy could lead to a non-detectable PECD effect.

Of course, chiral molecules were chosen such that a (large or) measurable PECD

asymmetry (or a chiral response in the case of Men) exists in the neutral case too avoid

such an scenario. Especially fenchone is known to have a strong PECD asymmetry of

around 8 - 16% for valence shell [28,29] in the neutral case. However, the situation

might change to the worse for the anionic system or within the gold complex.

Regarding the kinetic energy, low kinetic energy electrons are known to result in PECD

signals while (too) high kinetic energy electrons do not have time to probe the chiral

molecule and result in no PECD asymmetry. In the neutral case the limit was around

10 or 20 eV (section 1.2). However, for the anion case the assumption of having only

short-range interactions guided to the conclusion that even slower electron are needed for

PECD signals in anions to ensure enough interaction time. However, what slow means

was not known when the Au−-M measurements started. PECD measurements were

158

4. Gold Complexes of Chiral Molecules

conducted for 0.1 eV < Ekin <1.6 eV to stay (hopefully) in the slow regime necessary

for anion PECD signals.

Other reasons for the electron not to feel the chiral environment of the molecule apart

from being too fast could be the distance of the electron to this chiral environment or

the strength of localization on the achiral part of the system: The DFT calculations of

Au−-Fen and Au−-Men give distances of around 0.3 nm between the gold anion and the

hydrogens of the chiral molecule. If the short-range interactions necessary for PECD

effect are already negligible at this distance, the electron will not feel the chirality of

the molecule. The distance between gold anion and molecule can become shorter for

molecules with stronger H-bond donating functional groups, as seen for Au−-3HTHF

and Au−-Ala. These complexes had Au−···H-O bond distances of 0.23 and 0.25 nm

but these distances might not suffice for the short range interactions. However, the

hydrogen bond length to Au−corresponding to the distance of the detached electron to

the chiral molecular is just an approximation since neither the extension of the atom

nor the uncertainty in position of the electron is considered.

The localization of the negative charge stays mainly with the gold (0.9 e). However, a

measurable influence of the chiral molecule is happening since the anisotropy parameter

of the gold complexes is not 2, which would be the case for the pure gold anion. The

localization could still be strong enough for the electron to not feel the chiral environment

of the molecule effectively and hence does not produce a detectable PECD asymmetry.

With DFT calculations from section 4.4 several structures for the gold complex are

revealed. Such structures are often energetically close and one can assume that several

conformers are produced in the laser ablation source. Unfortunately, for PECD mea-

surements, this might be not ideal as the PECD effect is known to be sensitive to even

slight structural changes. PECD asymmetries can be different for all conformers and

even cancel each other out. (Of course, the opposite effect of enhancing each other is

also possible.) Hence, adding Au−to the chiral molecule could have been not ideal, since

it leads to many isomers due to the various possible binding positions, e.g. for Au−-Fen

four isomers are calculated despite having just one molecular isomer (Fen).

A similar problem is on hand if vibrational states are considered, since – beside con-

former sensitivity – PECD asymmetries can feature different values for different vibra-

tional states. Unfortunately, the experiment is neither able to cool down the complexes

efficiently to reduce the amount of isomers and vibrational states nor can it resolve the

isomers and vibrational states. Therefore, target molecules that can assume many dif-

ferent conformations and are expected to have significant thermal population are most

likely not the most ideal targets for initial anion PECD studies.

4.7. Summary for Gold Complexes

Gold complexes (Au−-M) were the first target systems for anion PECD experiments in

this project. The idea was to complex a chiral molecule with an electron source (Au−)

such that the chiral molecule remains (mainly) unaltered and that leads to a chiral

response in the photodetachment of the electron from the Au−-M. Apart from PECD

159

4. Gold Complexes of Chiral Molecules

measurements, gold complexes could be used to make statements about (unconventional)

hydrogen bonding.

Four different gold complexes, namely Au−-Fen, Au−-Men, Au−-3HTHF and Au−-

Ala are produced in gas phase. PES (with linear polarized light) and DFT calculations

revealed the interaction between Au−and the chiral molecule: Blue shifts and anisotropy

parameter indicated to an influence of the chiral molecule, however, the photodetached

electron remained mainly controlled by the unchiral part of the complex, the Au−.

Many isomers of the Au−-M are calculated with DFT and could be created in the

experiment. They are used to characterize the interaction as hydrogen bonding and can

provide quantitative predictions. Regarding hydrogen bonding, even Au−···H-C fulfills

the IUPAC requirements for hydrogen bonding and can be called as such.

Unfortunately, no PECD signal could be seen for the gold complexes. While many

possible reasons are discussed, it is not clear what the main cause for the null-PECD

signal could be since these measurements started before any other (published) anion

PECD studies on this topic. At the start, there was no guiding principle and one had

to find the needle in the hay stack: What are good chiral systems/kinetic energies? Is

the detection limit of the experimental setup sufficient? How many electrons should be

recorded? Is a PECD effect for anions even possible?

Due to the various problems emerging from gold complexes for the PECD effect (e.g.

electron too strongly localized), another system – without any additionally attached

anion – should be chosen. Deprotonated chiral molecules are a possible choice: Here, the

charge is directly located in the molecule and should sense the chirality of the molecule

much better. Of course, due to structure sensitivity of PECD signals, it should have

a distinctive deprotonation side. Hence, fenchone and menthone are not suited since

deprotonation is (almost) equally probable at every position. On the other hand, chiral

molecules with hydroxy groups are ideal since deprotonation happens most likely at only

one position: the hydroxy group.

160

5. Deprotonated Chiral Species1

(a) Ala-H (b) Ind-H

Fig. 5.0.1.: 3D structures of deprotonated alaninol [Ala-H]−and deprotonated 1-indanol

[Ind-H]−with corresponding skeletal structures and labels.

The second approach pursued for the creation of chiral anions is the deprotonation

of chiral molecules. In contrast to the gold complexes, the chiral molecule is altered

due to the removal of the hydrogen but detachment happens now directly in the chiral

molecule. This could enhance the electron’s sensing of the chiral field. Here, [Ala-H]−

and [Ind-H]−, which are deprotonated at the hydroxy group are of main interest (figure

5.0.1).

However, not only the chiral system was changed, also several experimental modifi-

cations were undertaken. The source was changed to a plasma entrainment source to

adapt to the new kind of chiral anions. Furthermore, the software controlling the ex-

periment was updated from KouDa to SDaq since new hardware components like new

computers and a new VMI camera were integrated. Also, all polarisation optics changed

the positions such that the light does not need to pass through further prisms after the

PEM and only a window separates the PEM and the VMI interaction zone.

In addition, some improvements to the VMI system and VMI images were tested like

the gold platting of the stainless steel VMI plates to rise the working function and hence

minimizing the electron background/noise in the UV regime. Unfortunately, this was

not successful and it is assumed that nickel was used during the gold plating process as

1Results of [Ind-H]−are, to a large part, published in the article J. Triptow, A. Fielicke, G. Meijer,

M.Green, “Imaging Photoelectron Circular Dichroism in the Detachment of Mass-Selected Chiral

Anions”, 2022, in: Angewandte Chemie International Edition, Wiley Online Library, in press DOI:

10.1002/anie.202212020

161

5. Deprotonated Chiral Species

intermediate “glue” layer. A material, which is ferromagnetic and is unwanted in VMI

systems. In the end, new VMI plates made out of molybdenum were installed.

Two einzel lenses were added, one before and one after the extraction region of the

ToF mass spectrometer to reduce the waist of the anion beam and also to improve the

resolution of VMI measurements but could not give noticeable improvement. One einzel

lens replaces the deflection plates of the ToF-MS and now are only used for deflection.

Most of the changes happened during the measurements with alaninol. There are

for example mass- and photoelectron spectra of [Ala-H]−created with the laser ablation

and plasma entrainment source. Deprotonated 1-indanol was used when all experimental

modifications were finalized.

5.1. Mass Spectra

Fig. 5.1.1.: Mass spectrum obtained with plasma entrainment source with the target molecule

[Ala-H]−at m/z 74. Also, OH−, O−, O−

2and [ArO2]−are assigned, which are typical for this

kind of source (section 3.2.1.2). Isotopes of Br−at m/z 79 and 81 originate from bromobenzene

and serve for the calibration of subsequent VMI measurements. The break in the m/z axis

marks strong electronic noise originating from high HV switches that has been removed from

the picture.

Mass spectra for [Ala-H]−and [Ind-H]−created in the plasma entrainment source are

presented in figure 5.1.1 and 5.1.2, respectively. Typical for the plasma entrainment

source are the plasma products O−at m/z 16 and OH−at m/z 17. C2H−at m/z 25

visible in both mass spectra as well as other carbon-containing anions like C2H2O−in

figure 5.1.1 probably stemming from sputtering carbonaceous deposits or from fragments

162

5. Deprotonated Chiral Species

Fig. 5.1.2.: Mass spectrum obtained with plasma entrainment source using 1-indanol, showing

[Ind-H]−at m/z 133 and corresponding clusters with Ar (purple). Also S−, used for calibration,

is visible at m/z 32 and its clusters with Ar (yellow). Typical plasma entrainment products like

[ArnOH]−(orange) and [ArH]−can be found. Also, argon clusters of small carbon containing

molecules (green) appear. The red dotted circle indicates noise produced by HV switches. The

gray area is enlarged and shown in figure 5.1.3.

Fig. 5.1.3.: Enlarged part of the mass spectrum from figure 5.1.2 in the region around [Ind-H]−

at m/z 133. The resolution for m/z 133 is about m/∆m= 211.

of the organic molecules. Furthermore, Ar complexes of the produced molecular anions

can be detected (figure 5.1.2).

In the following experiments, Br−(m/z 79 and 81 in figure 5.1.1) and S−(m/z 32

in figure 5.1.2) are used to calibrate the kinetic energy scale of the VMI spectrometer.

They are introduced via bromobenzene or OCS and can be confirmed by their respective

isotopes and natural abundances, i.e. 79Br and 81Br with an abundance of 51% and 49%

163

5. Deprotonated Chiral Species

as well as 34S−with 5%. This is especially important for S−since O-

2also appears at

m/z 32. Another indicator for S−is a peak at m/z 33, which is assigned to SH−since

[O2H]−is unlikely. Additionally, S−and Br−can later be confirmed by anion PES.

At m/z 74 in figure 5.1.1 and m/z 133 in figure 5.1.2 (or 5.1.3) are the deprotonation

products of alaninol and 1-indanol. m/z 133 only appears after heating the reservoir

to around 100

C, which corresponds to the sublimation temperature of 1-indanol and

hence supports the assignment. In the case of 1-indanol, clustering with argon is also

observed.

Figure 5.1.3 shows a cutout of figure 5.1.2 and covers an area of m/z 130 - 140, which

includes [Ind-H]−at m/z 133 and [Ar3OH]−at m/z 137. The resolution at m/z 133 is

about m/∆m= 211, which is sufficient to separate the neighboring peaks and to ensure

that only m/z 133 is probed by the laser.

5.2. Computational Considerations

5.2.1. Isomers

(a)

(b)

Fig. 5.2.1.: Deprotonation process of alaninol (a) and 1-indanol (b). The hydroxy group is

deprotonated with OH−forming the molecular anion, water as well as an excess energy of

0.7 eV for alaninol and 0.9 eV for 1-indanol. The excess energy is calculated with B3LYP-

D3/aug-cc-pVTZ for the most stable conformer.

The conformeric landscape of neutral alaninol has been discussed before (figure 4.4.9 of

section 4.4.1) and will be the basis for the DFT calculations of [Ala-H]−. All molecular

isomers of figure 4.4.9 are considered in the calculations but the results will mostly be

presented for the most stable isomer since the results are similar (e.g. orbitals).

While for alaninol 25 isomers are predicted [75], only six conformers are found for

1-indanol. They can be separated into two groups based on the position of the C2 atom

(figure 5.0.1b) relative to the ring plane and are called equatorial (eq) or axial (ax)

position (figure 5.2.3). The eq and ax group each contain three conformers, which differ

164

5. Deprotonated Chiral Species

(a) (b)

Fig. 5.2.2.: Four conformers of [Ala-H]−: AH-1 (a), A-H2 (b), A-H3 (c), A-H4 (d) calculated

with B3LYP-D3/aug-cc-pVTZ. The energies, E0, are relative to the lowest energy conformer

and given in eV. Arrangement and label are according to their relative energy.

(a) (b)

Fig. 5.2.3.: Two conformers of [Ind-H]−calculated with B3LYP-D3/aug-cc-pVTZ. (a) is the

equatorial (eq.) and (b) is the axial (ax.) form. Distances of C-O are given in nm for [Ind-H]−

and in brackets for the optimized neutral radical Ind-H. For comparison, the C-O bond lengths

in the neutral 1-indanol conformers are 0.142 nm for eq and 0.144 nm for ax, respectively.

by the orientation of the H atom. In a supersonic expansion of Ar, however, only a

single conformer (eq) has been detected [198,199].

The deprotonation process with OH−is shown in figure 5.2.1 for the loss of H+at the

most acidic site, i.e. the OH group. Furthermore, water and an excess energy calculated

to be around 0.7 eV for alaninol and 0.9 eV for 1-indanol (for the most stable conformer)

165

5. Deprotonated Chiral Species

Table 5.2.1.: Isomers of [Ala-H]−obtained by deprotonation of the most stable conformer

of neutral alaninol. Different deprotonation sites (dep. site) are used. The label correspond

to figure 5.0.1a. Tautomers above the dashed line are energetically possible according to the

excess energy of 0.7 eV for formation of the most stable tautomer (figure 5.2.1a).

dep. site E0(eV) VDE (eV)

HO0 2.080

HN.1 0.478 1.670

HN.2 0.484 1.774

H1.1 1.172 0.950

H1.2 and H1.3 1.185 0.923

H2.1 1.226 0.856

H3.1 1.507 0.413

H3.2 1.630 0.568

are formed. All isomeric anions with a smaller relative energy than the excess energy can

be created as well. Next to the most stable isomer of [Ind-H]−, the equatorial form, the

axial configuration reappears since it is only ≈0.07 eV higher in energy (figure 5.2.3b).

After deprotonation and optimization four different conformers of [Ala-H]−are formed

(figure 5.2.2) since A1.0 and A4.0 result into the same deprotonated structure, A-H1,

which is the most stable conformer. The other three deprotonated conformers are en-

ergetically close to A-H1 (within 0.1 eV, figure 5.2.2) and may be formed during the

deprotonation process, too. Probably, even more conformers for [Ala-H]−can be ex-

pected since only a subset of the 25 alaninol conformers is considered. If around three

OH orientations per base structure are estimated, around eight conformers could sur-

vive after deprotonation (presupposed they fulfill the energy requirement set by the

excess energy). For [Ind-H]−, on the other hand, only two conformers are expected: eq.

[Ind-H]−and ax. [Ind-H]−, which should lead to a less complicated PES in comparison

to [Ala-H]−. The structures of the most stable isomers of [Ind-H]−and [Ala-H]−can be

found in the appendix B.1.

5.2.2. Tautomers

Aside from deprotonation of the O-H group, deprotonation can also occur at other

sites leading to tautomers. If the excess energy for deprotonation at the O-H group is

considered (table 5.2.2), three more tautomers for [Ala-H]−and two for [Ind-H]−may

be expected to be observable in the experiment. These tautomers have VDEs, which

are at least 0.3 eV ([Ala-H]−) or 1 eV ([Ind-H]−) lower compared to the ground state

isomer and hence should be easily differentiated in a photoelectron spectrum. To avoid

confusion between the lowest isomer and tautomers, [Ind(O)-H]−is used to mark the

deprotonation from the hydroxy group and [Ind(Ci)-H]−for deprotonation from the

166

5. Deprotonated Chiral Species

Table 5.2.2.: Relative energies (E0) and VDE’s of tautomers formed by deprotonation of

equatorial 1-indanol at different sites (dep. site). The atom labels correspond to figure 5.0.1b.

HOwould be the hydrogen bonded to the oxygen (not shown in figure 5.0.1b). Tautomers

above the dashed line are energetically possible according to the excess energy of 0.9 eV for

formation of the most stable tautomer (figure 5.2.1b). C3 and C2 each hold two hydrogens,

which lead to the same structure when deprotonated. * indicates the stereogenic center.

dep. site E0(eV) VDE (eV)

O 0 2.185

C3 0.466 1.047

C1∗0.603 0.949

C6 0.966 2.110

C2 1.001 1.122

C9 1.214 1.704

C8 1.322 1.617

C7 1.329 1.628

i-th C atom, e.g. [Ind(C1)-H]−and [Ind(C3)-H]−mean a deprotonation at C1 and C3,

respectively. [Ala-H]−is handled similar.

For tautomers with an intact OH group a variety of conformers associated with the

O-H orientation exist, similar to the neutral molecules, e.g. in total 12 conformers for

[Ind-H]−and even more for [Ala-H]−. Thus, the spectral signatures of the tautomers

predicted at around 1.7 eV ([Ala-H]−) or 1 eV ([Ind-H]−) may contain contributions

from several conformers of similar energy.

Achiral tautomers are formed by deprotonation at the sterogenic center, i.e. H2.1 in

alaninol or C1 in 1-indanol. In the case of alaninol, formation of such isomer is ener-

getically not feasible (table 5.2.1). However, for 1-indanol, the formation of an achiral

tautomer is energetically possible. A PECD asymmetry for [Ind-H]−photodetachment in

the energy region around 1 eV, therefore, may attributed to the tautomer [Ind(C3)-H]−.

5.2.3. Orbitals

For the lowest energy isomers of [Ala(O)-H]−(A-H1) and [Ind(O)-H]−(eq) depro-

tonated at the OH group, the HOMO, HOMO-1 and HOMO-2 orbitals are exemplary

visualized in figure 5.2.4 and figure 5.2.5, respectively. The orbitals of other isomers look

similar (not shown). The figures are created with Multiwfn [147].

Since HOMO and HOMO-1 are the O’s lone pair after deprotonation, the HOMO and

HOMO-1 of each conformer are mainly concentrated at the oxygen atom. HOMO-2, on

the other hand, is located predominately at other positions: at the nitrogen in the case

of [Ala(O)-H]−and the ring structure for [Ind(O)-H]−.

167

5. Deprotonated Chiral Species

(a) (b) (c)

Fig. 5.2.4.: Valence orbitals of the most stable isomer of [Ala(O)-H]−(A-H1). HOMO (a)

and HOMO-1 (b) are mainly localized at the oxygen atom, HOMO-2 (c) at the nitrogen atom.

All in all, the other isomers follow the same trend (not shown). Isosurface value is 0.08.

(a) (b) (c)

Fig. 5.2.5.: Orbitals of eq. [Ind(O)-H]−. HOMO (a) and HOMO-1 (b) are concentrated at the

oxygen, while HOMO-2 (c) is determined by the ring structure. Orbitals of ax. [Ind(O)-H]−

look similar (not shown). Isosurface value is 0.05.

An orbital composition analysis reveals in more detail, which atomic orbitals con-

tribute to the corresponding molecular orbitals: The most dominant participant atoms

and their contributions are given in table 5.2.3 for the HOMO and HOMO-1 of A-H1 as

well as in 5.2.4 for the HOMO, HOMO-1 and HOMO-2 of eq. [Ind(O)-H]−.

The strongest contributor for the HOMO in both molecules is the oxygen atom (2p)

with around 73% for A-H1 and around 64.5% for eq. [Ind(O)-H]−. The hydrogen atom

(1s) bound to the C, which is connected to the oxygen (for [Ind(O)-H]−this corresponds

to the stereogenic center) is the second strongest contributor with 12% for A-H1 and

10% for [Ind(O)-H]−. Overall, the HOMOs of both molecules are of 1s/2pcharacter

with a fractional pcharacter of f= 0.845 for A-H1 and 0.860 for eq. [Ind(O)-H]−. The

same is valid for HOMO-1 of eq. [Ind(O)-H]−but with f= 0.913. These results are

important for the s-p-mixing model from Sanov, which will be applied to the anisotropy

parameter (or β) analysis of both molecules.

168

5. Deprotonated Chiral Species

Table 5.2.3.: Orbital composition (comp.) analysis for HOMO and HOMO-1 of A-H1. The

atom labels are according to figure 5.0.1.∗marks the stereogenic center. The atoms are ordered

according to their contribution to the HOMO. Main contributor is oxygen with around 73%

for HOMO and 74% for HOMO-1. Contributions with less than 1% are not shown. The sum

of the total values is not 100% since contributions from other atomic orbitals are not shown.

atom type HOMO comp. (%) HOMO-1 comp. (%)

O 2p73.0 74.1

H3.1 1s12.0 1.1

C2∗2p5.5 4.4

C3 2p3.3 3.3

N 2p1.6 1.8

H3.2 1s12.4

total s14.8 14.9

total p84.5 84.5

5.2.4. Calculated Detachment Energies

Electronic Transitions

Vertical detachment energies are calculated to be 2.080 and 2.185 eV for the most stable

conformers of [Ala(O)-H]−and [Ind(O)-H]−, respectively (table 5.2.5 and 5.2.7). The

energy difference to other conformers is rather small with maximal differences of around

0.092 eV for [Ala(O)-H]−and 0.084 eV for [Ind(O)-H]−but these are still within the

resolution of this experiment. However, the smallest energy difference for [Ala(O)-H]−

is only 0.005 eV and it will be quite difficult to resolve these conformers experimentally.

Other conformers, which can be expected for [Ala(O)-H]−but are not considered here,

aggravate the situation, since it can be assumed that their are in a similar energy range.

The adiabatic energies are smaller by 0.105 eV for eq. [Ind(O)-H]−and 0.080 eV

for ax. [Ind(O)-H]−indicating that the axial configuration is closer to its most stable

form after photodetachment. With an ADE smaller by 0.169 eV the [Ala(O)-H]−is the

furthest away from its equilibrium structure.

Based on the VDE, Koopmans’ theorem and orbital energies the detachment energies

of HOMO-1 and HOMO-2 for [Ala(O)-H]−(table 5.2.6), for both conformers of [Ind(O)-

H]−(table 5.2.8) and for the tautomers [Ind(C1)-H]−, [Ind(C3)-H]−(table 5.2.9) are

estimated. However, the orbital energies for all HOMO’s and some HOMO-1’s obtained

from Multiwfn for A-H1 are positive. This indicates to an electron self interaction error

common in DFT. [Ind-H]−only shows this behavior for the HOMO’s of the tautomers,

else all orbital energies are negative.

Between HOMO and HOMO-1 of [Ind(O)-H]−, the energy difference is 0.118 eV for

eq. [Ind(O)-H]−and 0.035 eV for ax. [Ind(O)-H]−. Assuming the existence of both

conformers in the molecular beam, the energy range between around 2.1 and 2.3 eV can

169

5. Deprotonated Chiral Species

Table 5.2.4.: Orbital composition (comp.) analysis for HOMO, HOMO-1 and HOMO-2 of

eq. Ind(O)-H. The atom labels are according to figure 5.0.1.∗marks the stereogenic center.

The table is ordered according to the contribution of atomic orbitals to the HOMO. Main

contributor is oxygen with around 64.5% for HOMO and 76.7% for HOMO-1. Three carbon

atoms contribute to HOMO-2 with similar amounts. Contributions with less than 1% are not

shown. The sum of the total values is not 100% since contributions from other atomic orbitals

are not shown.

atom type HOMO comp. (%) HOMO-1 comp. (%) HOMO-2 comp. (%)

O 2p64.5 76.7 12.3

H (of C1∗) 1s10.3 4.6

C2 2p8.0 2.1

C1∗2p3.0 1.8

C8 2p3.0 22.4

C4 2p2.2 19.3

C5 2p1.8 8.0 24.7

C6 2p1.6 2.5

C2 2s1.4

C5 2s2.1

C7 2p12.9

H (of C3) 1s1.9

C3 2p1.2

total s13.1 8.1 2.8

total p86.0 91.3 96.8

Table 5.2.5.: Energies calculated with B3LYP-D3/aug-cc-pVTZ for four conformers of

[Ala(O)-H]−given in eV. Energies are zero point corrected.

[Ala-H]−E0VDE ADE

A-H1 0 2.080 1.911

A-H2 0.019 2.085

A-H3 0.042 2.070

A-H4 0.077 1.993

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5. Deprotonated Chiral Species

Table 5.2.6.: Detachment energies from orbitals calculated with Koopmans’ theorem for

[Ala(O)-H]−given in eV.

[Ala-H]−VDE (HOMO) HOMO-1 HOMO-2

A-H1 2.080 2.209 4.489

A-H2 2.085 2.203 4.525

A-H3 2.070 2.242 4.421

A-H4 1.993 2.041 4.574

Table 5.2.7.: Energies calculated with B3LYP-D3/aug-cc-pVTZ for [Ala(O)-H]−given in eV.

Energies are zero point corrected.

[Ind-H]−E0VDE ADE

eq 0 2.185 2.080

ax 0.069 2.101 2.021

Table 5.2.8.: Detachment energies from orbitals calculated with Koopmans’ theorem for

[Ind(O)-H]−given in eV.

[Ind-H]−VDE (HOMO) HOMO-1 HOMO-2

eq 2.185 2.303 4.728

ax 2.101 2.136 4.547

Table 5.2.9.: Detachment energies from orbitals calculated with Koopmans’ theorem for the

tautomers [Ind(C1)-H]−and [Ind(C3)-H]−given in eV. C1 is the stereogenic center.

tautomer VDE (HOMO) HOMO-1 HOMO-2

[Ind(C1)-H]−0.949 4.089 4.368

[Ind(C3)-H]−1.047 4.125 4.539

171

5. Deprotonated Chiral Species

already contain four transitions, which needs to be resolved properly due to the small

energy differences.

In the case of [Ala(O)-H]−, the energies of the respective orbitals are pretty similar.

For the here considered isomers, the difference in HOMO-1 can be as small as 0.003 eV

and for HOMO-2 as small as 0.04 eV (5.2.6). Since more isomers with similar energetics

can be expected, the PES may contain features of several overlapping isomers, which

will probably difficult to resolve.

Vibrationally Excited States

Fig. 5.2.6.: FC simulation for eq. [Ind(O)-H]−(green) and ax. [Ind(O)-H]−(blue). The

FC spectra are shifted in energy such that the first peak of eq. [Ind(O)-H]−matches the

calculated VDE of around 2.19 eV. The combination spectrum assumes a ratio of 1:1 between

both conformers (red) and resembles the spectrum of the eq. [Ind(O)-H]−the most. The

difference between the first peak (HOMO) and the second peak (C-O vibration) is about

0.144 eV (scaled with 0.9687 [200]). HOMO-1 is not considered.

Next to electronic transitions, vibrations are considered, which can broaden the PES

or give additional distinct features. Vibration frequencies are coupled to the geom-

etry like bond lengths, however their probability or activation is determined by how

much the geometry changed upon the transition from the anion [Ind(O)-H]−to the

(optimized) neutral radical Ind(O)-H and how the respective wave functions overlap

(Franck-Condon (FC) principle in section 2.2.1). Major geometry changes happen in

the 5-member ring, especially around the stereogenic center (C1) while the 6-member

ring stays basically the same. The most important change is the C-O bond length, which

172

5. Deprotonated Chiral Species

becomes longer by 0.003 nm in both isomers of Ind(O)-H compared to [Ind(O)-H]−(fig-

ure 5.2.3). This change is related to the detachment from the HOMO (and HOMO-1)

meaning the detachment of a localized electron from the oxygen (figure 5.2.5). Conse-

quently, oxygen orbitals are altered, which in the end influences the bond length to C1.

The calculated (B3LYP-D3/aug-cc-pVTZ) and scaled2frequencies related to the elon-

gated bond lengths are around 1058 cm−1(0.13 eV) for eq. Ind(O)-H and 1075 cm−1

(0.13 eV) for ax. Ind(O)-H. A Franck-Condon simulation performed on both conformers

confirms the activation of these frequencies and also their energy positions (figure 5.2.6).

The FC simulation is performed with Gaussian 16 with a simulation temperature of

300 K on [Ind(O)-H]−. A simulation with 0 K gives basically the same result. Tautomers

are not considered. For each peak a Gaussian distribution with HWHM of 160 cm−1

(0.02 eV) is used, which produces spectra with similar resolution than the experimental

spectra. The first two prominent peaks of the eq. and ax. [Ind(O)-H]−belong to the

HOMO and to a vibrational mode, which is dominated by the C-O stretch (figure 5.2.6).

Another smaller third feature appears at around 0.14 eV higher in energy than the C-

O stretch feature. The FC simulation shows that this peak is partly attributed to a

vibrational progression of the C-O stretch vibration.

In the case of ax. [Ind(O)-H]−, there are more significant vibrational contributions,

which broaden the spectrum clearly. Since the energies of eq. and ax. [Ind(O)-H]−

are pretty similar and the combination spectrum is dominated by the eq. [Ind(O)-H]−,

the influence of the ax. [Ind(O)-H]−to the experimental spectrum will be difficult to

determine. However, arbitrary a ratio of 1:1 is assumed like in [48] and in figure 5.2.6.

The transition from HOMO-1 is close to the one of HOMO in the case of eq. and

ax. [Ind(O)-H]−(table 5.2.8) and hence should be considered for further interpretations.

However, this requires the optimization of the excited neutral, which is beyond the scope

of this work. The interpretation is consequently restricted to the HOMO.

In the end, three different contributions (HOMO, HOMO-1 and the CO stretch) for

each isomer might appear in the experimental spectrum. However, since HOMO-1 is

not considered in the FC calculations not all possible features might be calculated. The

calculated features are energetically similar and good resolution is required.

5.3. Photoelectron Spectra with Linear Polarized Light

5.3.1. Photoelectron Spectra of Deprotonated Alaninol

Photoelectron spectra measured with linear polarized light are plotted over the binding

energy in figure 5.3.1. The measured values are given in table 5.3.1 and features are

assigned according to previous calculations.

One broad feature, called A, centered at EB= 2.23 ±0.09 eV is visible in both

spectra and matches the calculated VDE for HOMO and HOMO-1 of several [Ala(O)-H]−

isomers. Due to the close energies predicted in table 5.2.6, both HOMO and HOMO-1, of

the calculated structures may be contained in this peak. Additionally, more conformers,

2Scaling factor is 0.9687 [200]. The same scaling is used in the previous chapter 4.

173

5. Deprotonated Chiral Species

Fig. 5.3.1.: PES of [Ala-H]−plotted over the electron binding energy for Eph = 2.38 eV and

4.77 eV. More PES are recorded for Eph = 2.76 eV, 3.02 eV and 3.49 eV (not shown).

Table 5.3.1.: Electron binding energies for the signals seen in the PES of [Ala-H]−and possible

assignments according to computational results.

peak EBassignment

A” 1.44 ±0.02 -

A’ 1.76 ±0.01 tautomers (HN.1, HN.2)

A 2.23 ±0.09 HOMO and HOMO-1

A12.099 ±0.07 HOMO

A22.163 ±0.006 HOMO-1

B 4.47 ±0.02 HOMO-2

not considered in the calculation, as well as vibrational substructure can be expected

but can not be resolved in this spectrum leading to the relatively broad feature (covering

an energy area of ≈0.7 eV).

For a photon energy of 2.38 eV, peak A seems to split in two peaks, which are referred

to as A1and A2. Feature A1is centered at EB= 2.10 ±0.07 eV and matches way

better the calculated VDE of the HOMO from [Ala(O)-H]−isomers. A2is centered at

EB= 2.163 ±0.006 eV but could be adulterated in intensity and energy due to the close

proximity of the cutoff energy/center of PAD. Anyways, this feature could be assigned

to the HOMO-1 (table 5.2.6).

Other clear features visible in the same spectrum are A’ and A” at EB= 1.76 ±0.01 eV

and EB= 1.44 ±0.02 eV, respectively. While A’ matches well with the calculated

VDE of the tautomers, which are deprotonated at the nitrogen atom ([Ala(N)-H]−),

the assignment for A” is not clear since it does not match with any calculated electron

binding energies (table 5.2.6).

The last feature is B, which is only visible in the spectrum measured at 4.47 eV. It is

probably the excited state of HOMO-2.

174

5. Deprotonated Chiral Species

5.3.2. Photoelectron Spectra of Deprotonated 1-Indanol

Fig. 5.3.2.: Photoelectron spectra of [Ind-H]−plotted over the binding energy for photon

energies of 2.76 (blue) and 4.86 eV (black). Energies and assignments are given in table 5.3.2.

Table 5.3.2.: Experimental determined binding energies for [Ind-H]−with possible assignment

according to computational results.

Peak EB(eV) assignment

A 1.06 ±0.05 VDE (HOMO) of tautomers (C1∗, C3)

B12.21 ±0.01 VDE (HOMO of eq. [Ind(O)-H]−)

B22.28 ±0.01 HOMO-1 of eq. [Ind(O)-H]−?

B32.35 ±0.01 C-O vibration of [Ind(O)-H]−

C 4.64 ±0.02 HOMO-2 of [Ind(O)-H]−

D 3.78 ±0.02 HOMO-1 of tautomers?

For [Ind-H]−, in total, 18 photoelectron spectra have been recorded in the photon range

of 2.34 - 4.96 eV. Exemplary, two spectra are presented in figure 5.3.2 in dependence of

the binding energy for photon energies of 2.76 and 4.86 eV. The energies and possible

assignments according to computational results can be found in table 5.3.2.

The UV-PES, represented by the black PES in figure 5.3.2, show four features: peak

A spans over 0.9 - 1.5 eV and matches to the VDE’s of the tautomers deprotonated

at C3 and C1∗. B occupies the energy region from around 2 - 3 eV and contains –

according to the previous calculations – the HOMO and HOMO-1 for equatorial and

axial [Ind(O)-H]−as well as possibly the excitation of a C-O stretch vibration. Between

4.5 and 5 eV, feature C is visible and can be assigned to HOMO-2. Feature D, in the

region of 3.5 - 4.2 eV could be the HOMO-1 of the tautomers (table 5.2.9).

With smaller photon energies, photoelectron spectra gain a better absolute resolution

as can be seen in the vis-PES, represented by the blue PES in figure 5.3.2. The B peak

splits into three subfeatures located at 2.21 ±0.01 eV (B1), 2.28 ±0.01 eV (B2) and

175

5. Deprotonated Chiral Species

Fig. 5.3.3.: Comparison of the experimental spectrum (blue) with the combined FC simulation

of eq. and ax. [Ind(O)-H]−from figure 5.2.6 (red). The FC simulated spectra is energetically

shifted to match with the experimental spectrum. HOMO-1 is not considered in the FC

simulation but could explain the peak between “HOMO” and “CO vibration” in the exp.

PES.

2.35 ±0.01 eV (B3) (table 5.3.2). B1matches well with the calculated VDE of eq.

[Ind(O)-H]−(2.185 eV) or with the detachment energy from the HOMO.

The experimental spectrum resembles the combination spectrum of eq. and ax.

[Ind(O)-H]−, but also the simulated spectrum of eq. [Ind(O)-H]−. Assuming that the

PES is dominated by eq. [Ind(O)-H]−, B2can be assigned to the HOMO-1 of the eq.

[Ind(O)-H]−(calculated to be 2.303 eV). The observation of the HOMO-1 is supported

by the observation of HOMO-2, which is assigned to peak C.

B3lies around 0.14 eV above B1, which matches with the Franck-Condon simulation

with a (scaled) band spacing of 0.14 eV (figure 5.2.6).

Overall, the FC simulation matches with the experimental spectrum (figure 5.3.3):

The first two peaks in the FC simulation fit well to features in the experimental spectrum

but the third peak at higher binding energy, including the vibrational progression of the

C-O stretch, has no visible counterpart. It is either not resolved or has a too low intensity.

The observed band pattern and their widths agree better with the FC simulated spectra

of eq. [Ind(O)-H]−than with the ax. [Ind(O)-H]−, which is broader due to a richer

vibrational structure (figure 5.2.6). The contribution of the ax. [Ind(O)-H]−to the low

binding energy part of the HOMO peak is not clearly visible but the current experimental

resolution might not be sufficient to resolve that. A contribution of the ax. [Ind(O)-H]−

to the experimental spectrum is difficult to assign. Attempts to obtain better resolved

spectra, i.e. by using a photon energy of 2.43, 2.64 and 3.02 eV in combination with

smaller repeller voltages able to catch a maximum kinetic energy of around 1.1, 1.3 and

2.5 eV, respectively, did not lead to additional features in the spectrum. The contribution

of ax. [Ind(O)-H]−remains unknown.

176

5. Deprotonated Chiral Species

5.3.3. Anisotropy Parameter

Fig. 5.3.4.: Anisotropy parameter for peak A of [Ala-H]−determined with rBasex. The error

of Ekin is calculated with Gaussian error propagation and the one of βis estimated by the

error function 3.2.20 determined from Au−spectra. The attempted fit is determined with the

s-pmixing model of Sanov and is based on the assumption that the anisotropy parameter is

predominantly described by oxygen orbitals.

Anisotropy parameters are measured for the photoelectron spectra of [Ala-H]−(figure

5.3.4) and [Ind-H]−(figure 5.3.5 and 5.3.6) but are – in contrast to the spectra – obtained

with rBasex rather than POP. As mentioned in section 4.3.2, POP and rBasex lead to

similar results but an anisotropy analysis with POP becomes difficult for energetically

close transitions like it is the case for B1, B2and B3for [Ind(O)-H]−. The problem

is that only two transitions (B1and B3) are visible in the analysis program for the

anisotropy parameter (figure 3.2.13) even if all transitions appear in the radial PES

after reconstruction. The problem might be that B2is lost in the background of the

peak edges of its neighboring peaks and also in noise background. rBasex does not show

this problem. All transitions are available for the βanalysis. For [Ala-H]−this is not

a problem since the features are not as resolved as for [Ind-H]−, nevertheless for both

anions rBasex is used.

The error for the kinetic energy is based on Gaussian error propagation and the

assumption that there are uncertainties of ±1 px for the peak position as well as ±1 nm

for the wavelength of the laser. If the error bar is not visible in the plots, the error is

smaller than the dot size as can be seen in the first two data points of figure 5.3.4 as

well as in figure 5.3.5 and 5.3.6. By means of the Au−spectra, an equation for the error

of rBasex (equation 3.2.20) was established and used in figure 5.3.4 -5.3.6 to estimate

the error for the anisotropy parameter.

177

5. Deprotonated Chiral Species

Fig. 5.3.5.: Anisotropy parameter for feature B of [Ind(O)-H]−. The black dots correspond

to data obtained at high photon energy, mostly in the UV, where peak B was not further

resolved, while at lower photon energy contributions of B1(blue), B2(red), and B3(green)

could be separated. For low Ekin a fit is attempted according to the s-pmixing model of Sanov

and assume that βis dominated by the oxygen orbitals. The fits are in the same color as the

corresponding data points. The error for βis based on the error function 3.2.20 determined

from Au−spectra. The error of Ekin is smaller than the dot size.

Ramond et al. [201] investigated alcoxyides, like CH3O−at an kinetic energy of around

1.8 eV. They can show anisotropy parameters of around 1 or -0.9. The sign seems to

be determined by the symmetry of the vibronic state. However, the spectra presented

here do not resolve vibronic states. Furthermore, peak B of [Ind-H]−and peak A of

[Ala-H]−are not resolved at the kinetic energy of 1.8 eV. If vibronic states are present in

[Ala-H]−and [Ind-H]−similar to Ramond et al. [201] but unresolved than the different

βvalues overlap. Depending on the amount of vibronic states in a specific symmetry,

βmight tend to be more positive (e.g. 1), more negative (e.g. -0.9) or around 0 if

they cancel each other out. For [Ind-H]−the anisotropy parameter is 0.12 or 0.10 for a

kinetic energy of 1.78 or 1.92 eV, respectively. For [Ala-H]−,βcould be negative around

that energy. In the case of the alkoxides of Ramond et al. [201], this would indicate to

different symmetries in (dominating) vibrational states between [Ala-H]−and [Ind-H]−.

Attempted fits of the s-p-mixing model from Sanov to the data points under consid-

eration of some simplifications are included in figure 5.3.4 (black) and in figure 5.3.5

and 5.3.6 (colored). The simplifications concern B/A (ratio of Hanstrop parameter de-

scribing different detachment channels) as well as f(the fractional pcharacter), which

were introduced in section 2.2.2, and are based on the assumption that only the most

stable conformers (A-H1 or eq. [Ind(O)-H]−) are present. Furthermore, B2is assumed

178

5. Deprotonated Chiral Species

Fig. 5.3.6.: Anisotropy parameter for feature A (red) und C (blue) of [Ind(O)-H]−. The error

for βis based on the error function 3.2.20 determined from Au−spectra. The error of Ekin is

smaller than the dot size.

to be the, due to detachment out of, HOMO-1 and will be fitted with the corresponding

values from the orbital composition analysis. For [Ind-H]−the data points are only fit-

ted until 1 eV since the B peak is not resolved for higher kinetic energies and too many

contributions would need to be considered to create an appropriate fit.

The fitting parameters can be obtained from the orbital composition analysis for

[Ala-H]−(table 5.2.3) and [Ind-H]−(table 5.2.4). Some parameters like the Hanstrop

parameter Aand the evaluation of B/A are similar since the HOMOs (and HOMO-1)

are localized at the oxygen atom for both molecules. If the orbital is dominated by the

oxygen, the Aparameter can be estimated to be 0.55 eV−1, which is the same value

as for an isolated oxygen anion [58]. Furthermore, all orbitals are of the type 1s-2p

meaning that the ratio B/A can be calculated with (1/768)(ζ2p/ζ1s)7(ζ’s being the

effective nuclear charges) [58]. First differences appear for the fractional pparameter f,

which is 0.845 for [Ala(O)-H]−, 0.860 for the HOMO and 0.913 for the HOMO-1 of eq.

[Ind(O)-H]−. The remaining parameter is the ratio ζ:= ζ2p/ζ1s, which is used here as

a free parameter for fitting. The best fits are 3.43 for [Ala(O)-H]−, 3.96 for the HOMO

(blue) and 3.91 for HOMO-1 of [Ind(O)-H]−(red).

Further, the application of the s-pmixing model on the peak B3assigned to the C-O

vibration is waged even if no orbital composition is at hand. However, the vibration is

based on the HOMO and hence the same parameters as for the HOMO are used. A fit

to these data points leads to ζ= 4.03 (green).

179

5. Deprotonated Chiral Species

Concerning the HOMO of [Ala(O)-H]−, the s-p-mixing model from Sanov does not

produce a satisfying match to the data points. The function might be within errors bars

for most of the points but misses the last data point completely and is of different form

than the points seem to have (figure 5.3.4). A little bit better, but still not satisfying,

performs the fit for the HOMO of [Ind(O)-H]−. The fit is within error bars for all data

points and seems to follow the trend of the data points in the beginning but does not

accompany the downtrend starting at around 0.2 eV. The best fits are obtained with B2

and B3since the data points almost match the fitted curve but again the trend of the

fit at higher kinetic energies seems not to be ideal.

The fits, especially the ones for the HOMOs, can probably be improved by adapting

the assumptions. As for example, a better adapted Acan be determined since the orbital

might be dominated by oxygen but is certainly influenced by other contributions, which

need consideration and will change the value for A. Furthermore, other conformers or

different vibrational states (other than the C-O vibration) are not considered such that

the superposition of the anisotropies is not described well. Even the B peak in the PES

measured with vis-light for [Ind(O)-H]−could not be completely resolved and B1-3 might

still contain other contributions. The trend of the fit at the high kinetic energy end can

be explained by the area of validity of the used model. The s-p-mixing model is in

general valid for low kinetic energies and becomes more inaccurate with higher kinetic

energy. This is especially important for [Ala-H]−, where the fit does not catch the data

point at Ekin ≈2.4 eV at all. Furthermore, the PECD data of [Ind-H]−will show that

the here used assumption of a negligible phase shift (cos(δ2−δ0) = 1) due to negligible

interaction between electron and molecule can not be correct in photodetachment. A

PECD signal presumes an interaction, which should also be considered for the anisotropy

parameter in form of an adapted phase shift. As mentioned in section 2.2.2, several types

of interactions could influence the phase shift. However, in the case of a (strong enough)

dipole moment of the neutral radical an adapted model is recommended, which includes

the influence of the dipole directly instead of changing the phase shift. Mabbs et al. [61]

used such an adapted model for molecules with a (calculated) dipole moment of 2.03 D

(and higher). The dipole moments calculated here for [Ala(O)-H]−is around 2.5 D and

for [Ind(O)-H]−around 2.3 D, which would emphasize the use of this adapted model.

5.4. PECD

The PECD PADs are presented and the mean PECD values are calculated for certain

binding energy ranges to investigate the influence of different PES contributions to the

PECD signal. The standard error (SE) of mean is taken as error for the [Ala-H]−

measurements and for [Ind-H]−the difference of PECD signals between forward and

backward half (∆PECD) is given as an error.

180

5. Deprotonated Chiral Species

5.4.1. PECD of Deprotonated Alaninol

Fig. 5.4.1.: PECD PADs of [Ala-H]−. Next to each PAD the photon energy and electron

counts per polarization are given. The light propagates from down to up. The forward and

backward half are separated by a dashed line.

The PECD PAD for [Ala-H]−are given in figure 5.4.1 and the corresponding mean

PECD values are given in figures 5.4.2 and 5.4.3. In total six different binding energy

regions are shown for each PECD PAD to reduce the average over different contributions,

e.g. contributions from the tautomers deprotonated at the NH2group (A’ at EB≈

1.76 eV) are considered separately from features originating from isomers deprotonated

at the OH group (A at EB≈2.23 eV) since both features might carry different PECD

asymmetries.

Looking at the PECD PADs (figure 5.4.1), there is no PECD asymmetry recognizable

for Eph = 3.49 eV and 2.38 eV. However, there could be a faintly visible negative PECD

asymmetry for Eph = 4.77 eV in feature B (inner disk) and a positive PECD asymmetry

for Eph = 2.76 eV in the A feature. A PECD asymmetry for Eph = 4.77 eV is not

confirmed by an evaluation of the mean PECD value (PECD) as seen in figure 5.4.3b.

The PECD asymmetry has the same sign for forward and backward direction and hence

is set to be zero. On the other hand, a PECD effect for Eph = 2.76 eV seems possible

since the mean PECD value is around 1% and has a small enough standard error (SE)

(figure 5.4.2b). Considering that the standard error is only a statistical error and does

181

5. Deprotonated Chiral Species

(a) (b)

Fig. 5.4.2.: (a) PES at Eph = 4.77 eV with considered EBregions for the analysis of PECD

values of [Ala-H]−in the A peak (b-d). The error is based on the standard error of the mean

PECD value. (b) shows a PECD asymmetry of around 1%.

not reflect the complete error, e.g. polarization quality and substance purity are not

considered here, it is possible that additional error contributions allow an inclusion of

the zero value, too.

Despite the slight difference in structure between alaninol and [Ala(O)-H]−a compari-

son between them can be ventured since the HOMO is in both cases dominated by the 2p

orbital of the oxygen. Such comparisons to PECD studies on alaninol show how difficult

the measurement of a PECD effect can be: Turchini et al. [30] calculated the PECD

asymmetries of the HOMO (and more) for two isomers, which resemble the isomers A1.0

and A2.0 from figure 4.4.9 and most likely deprotonate to A-H1 and A-H2 (figure 5.2.2),

respectively. The PECD asymmetries of both isomers seem to partly cancel each other

out for the HOMO with the A1.0 having a stronger PECD asymmetry. The overlapping

PECD strength is reduced by half, which is also confirmed by their experiments. This is

just the interaction of two isomers and does not consider the other isomers for alaninol.

The same could be happening for [Ala(O)-H]−meaning that many isomers contributing

to the PECD signal and resulting in an overall low PECD value, which might barely be

in the order of the sensitivity of this experiment (1%).

In summary, the only potential candidate for a PECD asymmetry in [Ala-H]−is

measured with Eph = 2.76 eV. However, the asymmetry is around the same range as the

experimental limit (around 1%).

182

5. Deprotonated Chiral Species

(a) (b)

Fig. 5.4.3.: (a) PES at Eph = 2.38 and 4.77 eV with considered EBregions for the analysis

of PECD values of [Ala-H]−in the B (b), A” (c) and A’ (d) peak. The error is based on the

standard error of the mean PECD value. No PECD asymmetry is observed.

5.4.2. PECD of Deprotonated 1-Indanol

5.4.2.1. PECD vs Photon Energy

For each PES measured with LIN light there is a PECD measurement. Hence, the same

photon energies are used and the range is the same as for the LIN case with Eph =

2.07 - 4.96 eV. Selected smoothed, raw PECD PADs and corresponding reconstructed

images are presented in figure 5.4.4 alongside with the photon energy and electron counts

per polarization. In contrary to the gold complexes and [Ala-H]−a convincing PECD

signal is visible for most measurements: The signal is stronger than the limit of the

experimental setup (stronger than 1%). Furthermore, the PECD PADs show a relatively

clean inversion of the asymmetry between forward and backward direction (separated by

a white or gray dashed line in figure 5.4.4). Reconstructed images smooth out the PECD

signals more than in the experimental PADs. However, the reconstructed images also

seem to spill over into the other half of the image. Such imperfections can be caused by

slight deformation of the circularity of the raw image or by non-uniform sensitivity across

the detector. Hence they are only used for visualization purposes while other information

is extracted from the experimental PECD PADs (left column of figure 5.4.4).

The corresponding mean PECD value (PECD) is evaluated for each peak individually

over the binding energy range given in table 5.4.1 and is shown in figure 5.4.5 in the

183

5. Deprotonated Chiral Species

Fig. 5.4.4.: PECD asymmetries for [Ind-H]−exemplary shown for Eph = 4.77, 3.49 and

2.43 eV as raw, smoothed (left) and reconstructed image (right). The light propagates from

down to up. For- and backward half are separated by a dashed line.

combination with ∆PECD as error. This figure is published in a similar form in [48].

However, in contrast to [48] not the standard error (SE) is taken as error but ∆PECD is

preferred here since it considers differences between Fw and Bw images halves (section

3.2.6).

The subfeatures B1,2,3 can not be separated well by eye in the PADs for the visible

photon energies but can be treated individually after image reconstruction (figure 5.4.6,

with ∆PECD as error). In the UV region, peak B is not further resolved and the PECD

asymmetry is evaluated over the EBrange covering B1,2,3, thus resulting in an effective

184

5. Deprotonated Chiral Species

Fig. 5.4.5.: Mean PECD values for (R)-[Ind-H]−of the three main features plotted against

the photon energy. B is represented by the subfeature B1for the region Eph = 2.07 - 3.02 eV.

The error is based on the difference between the PECD values in forward and backward half:

error = PECDFW - PECDBW.

PECD signal due to superposition of the three different PECD signals. In figure 5.4.5

feature B1represents B in the Eph = 2.3 - 3.1 eV range. PECD values for the other

subfeatures can be found in figure 5.4.6. They show the same PECD trend and do not

cancel each other out (completely). If this trend continues in the UV region, then the

PECD asymmetry from B is (more or less) the result of positive superposition of three

different contributions.

A clear dependence on the photon energy and hence the kinetic energy is recognizable

in each (sub)feature. Each transition seems to have its own, individual PECD trend,

which also includes sign changes for features A and B. The strongest PECD asymmetry

is measured for feature C with around -11% at Eph = 4.77 eV or Ekin = 0.13 eV. Feature

B has its maximum in B2with around 7% at Eph = 2.43 eV or Ekin = 0.15 eV. A PECD

signal which peaks with -5% at Eph = 2.43 eV or Ekin = 1.37 eV is seen in the feature

A. Also, feature D shows a PECD signal and peaks with 4% before it vanishes. These

signals can only come from the chiral tautomer deprotonated at C3 seemingly dominating

feature A and D. The exact contribution of the achiral tautomer deprotonated at C1

remains unknown. Magnitude and energy dependence of this anion PECD effect is

generally consistent with the PECD experimentally seen in the photoionization of neutral

molecules

In general, the PECD asymmetry seems to maximize for low kinetic energies, which

speaks for the idea of increased interaction time between detached electron and chiral

185

5. Deprotonated Chiral Species

Fig. 5.4.6.: Mean PECD values for (R)-[Ind-H]−of the three subfeatures of B plotted against

the photon energy. The error is based on the difference between the PECD values in forward

and backward half: error = PECDFW - PECDBW

environment. As for higher kinetic energies (over 1 eV), a departing electron (in general)

is assumed to have no or a negligible interaction with the remaining neutral core in

photodetachment. In such a case the electron can be described as a plane wave and

hence the PECD signal has to vanish [49,202]. However, here, recognizable PECD

signals are shown for kinetic energies over 1 eV (A and B peak) and can be appear for

kinetic energies as high as 2.2 eV. Observing a PECD asymmetry at such energies shows

the failure of the plane wave ansatz for the PECD effect in photodetachment and the

importance of short range interactions. If short-range interactions are not ignored in

theory, PECD asymmetries could be observed for electrons with a kinetic energy of up

to 12 eV [4].

5.4.2.2. Anion PECD vs Neutral PECD

These findings for the anion [Ind(O)-H]−can be compared to Dupont et al. [73], who

investigated the PECD effect of (S)-(+)-1-indanol for HOMO, HOMO-1 and HOMO-

2. Apart from having opposite enantiomers, the molecules also differ structurally, i.e.

[Ind(O)-H]−has one less H. The PECD effect has shown to be quite sensitive to small

structural changes and could be quite different (section 1.2).

Despite the differences, there are some similarities in the electronic structure of anion

and neutral, which can be used to compare the PECD signals of the anion and neutral:

HOMO and HOMO-1 of [Ind(O)-H]−(feature B) are mainly non-bonding, lone-pair and

oxygen-centered orbitals (figure 5.2.5 and table 5.2.4), which are similar to HOMO-2

186

5. Deprotonated Chiral Species

Table 5.4.1.: The mean PECD value is determined over these binding energy ranges for each

peak. The (tentative) assignments for each peak are also given. The range given for B1,2,3 is

taken for the photon energies Eph = 2.34 - 3.02 eV since the features can be separated here.

Between Eph = 3.49 - 4.96 eV, the subfeatures are not resolved and the ranges are condensed

to one range, which is used for B. Other regions for B were also tested but did not change the

PECD signal significantly.

Peak assignment EBrange (eV)

A tautomers (C3, C1∗) 0.85 - 1.30

B1HOMO of eq 2.19 - 2.24

B2HOMO-1 of eq 2.26 - 2.30

B3C-O stretch vibration 2.33 - 2.38

B eq and ax? 2.19 - 2.38

C HOMO-2 4.62 - 4.67

D HOMO-1 of tautomers? 3.54 - 4.06

of neutral 1-indanol [73]. Dupont et al. [73] measured the PECD of HOMO-2 for a

kinetic energy of 0.7 and 1.7 eV to be around -3% and (-7)-(-6)%, respectively. PECD

measurements for [Ind-H]−are performed at similar kinetic energies, i.e 0.67 and 1.66 eV

for HOMO as well as 0.74 and 1.72 eV for HOMO-1 (assuming HOMO-1 is indeed B2).

The PECD asymmetry of the HOMO is around -2% for Ekin = 0.67 eV (Eph = 2.88 eV)

and +2% for Ekin = 1.66 eV (Eph = 3.87 eV). In the case of HOMO-1, a PECD signal

of around -3% is measured for Ekin = 0.74 eV (Eph = 3.02 eV) and +3% for Ekin =

1.72 eV (Eph = 4.00 eV).

In the case of small kinetic energy (around 0.7 eV), the PECD signals for the HOMO-1

of the anion and the HOMO-2 of the neutral are the same (in sign and magnitude). The

HOMO of the anion leads to a (slightly) smaller PECD signal than the HOMO-2 of the

neutral. However, different enantiomers are taken and hence the PECD asymmetries are

inverted for the same enantiomer. For higher kinetic energies (around 1.7 eV), the PECD

signal of the HOMO-2 of the neutral is clearly stronger with (-7)-(-6)% in comparison to

+2 or +3% of the HOMO or HOMO-1 of the anion, respectively. However, the direction

of the PECD asymmetry is in this case the same for the same enantiomer.

Different for 1-indanol and [Ind-H]−are the magnitude of the PECD asymmetry at

higher kinetic energies and the flip in sign between low and high kinetic energies for

[Ind-H]−but not for 1-indanol. This could be attributed to the slight structural differ-

ence in the (existing or missing) H at the OH group, which turns out to be significant

for the PECD signal. Another point is the localization of the HOMO-2 of 1-indanol in

comparison to the HOMO of [Ind(O)-H]−. It seems to be more delocalized if the or-

bital figure for HOMO-2 of 1-indanol from Dupont et al. [73] is compared to HOMO of

[Ind(O)-H]−(figure 5.2.5a). Unfortunately, they do not provide an orbital composition

analysis, which could be used for confirmation. Hence, eq. 1-indanol is calculated here

187

5. Deprotonated Chiral Species

with B3LYP-D3/aug-cc-pVTZ. The HOMO-2 is compared to HOMO of eq. [Ind(O)-

H]−via an own orbital composition analysis with Multiwfn. The orbital composition

analysis confirms that the HOMO-2 of 1-indanol is indeed more delocalized: the main

contribution for HOMO-2 of 1-indanol comes from the 2pshell of O (42%) as well as

from the 2pof the chiral center C1 (14%) and its neighbors C2 (15%) and C5 (11%). In

the case of HOMO of [Ind(O)-H]−, the 2pshell of O also contributes the most but with

around 64% while 2pof C1, C2, C5 barely contribute (in sum only around 6%) in com-

parison to the HOMO-2 of 1-indanol (table 5.2.4). These different orbital contributions

and hence delocalization might be responsible for the different PECD behavior between

anion and neutral.

Comparing the maximum PECD signal of [Ind-H]−(around -11%) to the maximum of

neutral (1S,4R)-(+)-fenchone (around -10% for PECD experiments on valence orbitals

[28]), the strength of the PECD asymmetry in anions can be as strong as in neutral

molecules. Hence, the PECD effect of anions is in no way inferior to the PECD effect

of neutrals strengthening the importance of short-range interactions.

5.4.2.3. PECD vs Counts

The evolution of PECD signal quality with the number of total electron counts is shown

for three selected PADs in figure 5.4.7 and, in terms of mean PECD values for all

measurements in figure 5.4.8. A comparison of the PECD signal measured with different

total electrons shall give an estimation of the lower electron count limit to see a PECD

asymmetry. These measurements are performed with a photon energy of 3.49 eV with

the same laser pulse energy of 4 mJ measured before the light enters the VMI chamber

and of 0.3 mJ after the VMI chamber. In contrary to the before presented PECD PADs,

the space focus of the ion beam is not in the interaction zone with the detachment laser

but at the ToF-MS detector. A PAD obtained with 70 Mio counts, measured with a

laser pulse energy of 3 mJ before and 0.5 mJ after the VMI chamber, is recorded with

the space focus in the interaction zone (middle row of figure 5.4.4).

In general, the error becomes smaller for more electron counts, which can be expected

since the statistics become better and the error scales with 1/√N(N being the electron

counts). This coincides also with better PAD image quality as can be seen in figure

5.4.7. All values agree within error bars or are within the gray stripe, which marks the

reference area for the measurement with the most electron counts (figure 5.4.8).

Considering the mean PECD value, the lowest limit should be something around 0.5

Mio counts for [Ind-H]−measured at Eph = 3.49 eV since the error is small enough to

not include the zero value. The same limit holds for the case of the statistical error SE

(not shown). If the PECD signal would be smaller, e.g. 1% more electrons of at least

4 Mio counts would be better. A smaller PECD asymmetry of 0.5% could be measured

of 40 Mio electron counts per polarization. However, such high total electron counts

require a stable and high ion signal, which is not easy to reproduce as can be seen for

the (S)-enantiomer. Hence, the detection limit of PECD signals is based on the lower

count number of 4 Mio and is estimated to be around 1%.

188

5. Deprotonated Chiral Species

Fig. 5.4.7.: PECD PADs of [Ind-H]−at Eph = 3.49 eV for three different electron counts.

The PECD asymmetry becomes more visible for more electron counts.

Fig. 5.4.8.: Mean PECD values of [Ind-H]−at Eph = 3.49 eV plotted against electron counts

per polarization. All points were measured with a laser pulse energy of 4 mJ/0.3 mJ (be-

fore/after the VMI chamber) except the point at 70 Mio counts. Here 3 mJ/0.5 mJ were

recorded before/after the VMI chamber. The used EBrange for feature B is given in table

5.4.1. The error is based on ∆PECD. The gray bar marks a reference area of mean PECD

value and error from the measurement with highest counts. Within errors, all PECD values

are contained in the gray reference area.

In general, the exact electron count numbers are specific for [Ind-H]−since this also

depend on the width and shape of the feature in the PES. However, the general concept

of having smaller errors and better image quality after more electron counts does not

change since this is more in the nature of statistic than of the specific system. The

experimental limit of around 1% (or 0.5% after considerably more electron counts) will

also stay valid for other molecular systems.

Historically, the dependence of the PECD signal on the laser pulse energy was inves-

tigated at Eph = 3.49 eV to exclude that the measured PECD asymmetry arises from

the neutral radical Ind-H before the experiment with the grid was done and before the

kinetic energy dependence was known (section 3.2.5). PECD signal from the neutral

radical could arise from a multiphoton process, which depends on the laser pulse energy.

However, even with a laser pulse energy of 0.2 mJ measured before the VMI chamber still

189

5. Deprotonated Chiral Species

produces a PECD signal agreeing with the previous results from section 3.2.5. The total

count number scale linearly with the photon number and result in similar results than

shown in this section for the PECD signal’s dependence on the electron count number.

5.4.2.4. PECD vs Enantiomer

Fig. 5.4.9.: PECD PADs of (R)-, (S)- and racemate [Ind-H]−at Eph = 2.43 eV. The counts

per polarization are given next to the image. The racemic mixture shows no PECD signal

while (R) and (S) show a clear inversed PECD signal for two transitions.

Basic symmetry considerations demand not only an inversion of the electron flux

when the opposite circular light polarization is used but also when the other enantiomer

190

5. Deprotonated Chiral Species

Fig. 5.4.10.: Mean PECD values of (R)-, (S)- and racemate [Ind-H]−for the three main

features A (yellow), B (blue) and C (violet). Each photon energy (bottom) shows one feature

(top). The raw angular distributions are partially masked to highlight the corresponding

feature. Full raw images can be found in figure 5.4.9 (and in the figures B.1 and B.2 of the

appendix). The error is based on the difference between the mean PECD values of forward

and backward direction (∆PECD).

is taken. Furthermore, the PECD signal has to vanish for the racemic mixture. In

figure 5.4.9, the full PECD PADs are shown for the photon energy of 2.43 eV, in raw,

smoothed and reconstructed form for both enantiomers and the racemic mixture. Also

for photon energies of 3.49 and 4.77 eV, the two enantiomers and the racemate was

measured (figures in the appendix B.1 and B.2). The PECD inversion upon enantiomer

change is clearly visible and no PECD asymmetry for the racemic mixture can be seen.

The difference in quality of the PECD PADs between the enantiomers can be partly

attributed to different electron counts. In the experiments, there was a more intense

and more stable ion signal for the (R)-enantiomer than for the (S)-enantiomer or the

racemate leading to a much better SNR for the (R)-enantiomer. Somehow, the ion

intensity sensitively depends on source conditions (e.g., pressures, timings) but were

difficult to reproduce after a change of sample.

Selected mean PECD values for the three samples with corresponding PECD PADs

are shown in figure 5.4.10 with ∆PECD as error. For the photon energies 2.43, 3.49 and

4.77 eV the PECD values for the features A (yellow), B (blue) and C (violet) are shown,

respectively. The PADs here are partly masked to emphasize the considered transition.

B1-3 could also be measured with the photon energy of 2.43 eV but are not shown in

these figures.

191

5. Deprotonated Chiral Species

Both enantiomers show for feature B and C the same but opposite PECD asymmetries

within error bars (figure 5.4.10). Feature A, however, has a slightly smaller PECD sig-

nal for the (S)-enantiomer, which is catched neither by the SE (not shown) nor ∆PECD

(figure 5.4.10). Two main reasons could be responsible for that: different source condi-

tions leading to a changed tautomer distribution and a lower enantiomeric purity of the

(S)-enantiomer.

The enantiomeric purity of (R)-(-)- and (S)-(+)-1-indanol from Sigma Aldrich was

measured with chiral high-performance liquid chromatography (HPLC) by Synvenio.

While the (R)-enantiomer has a good purity with an enantiomeric excess (e.e.) of around

99.1%, the e.e. of the (S)-enantiomer could vary around 70 and 90% within the same

batch and even within the same bottle since the enantiomers seem not evenly distributed.

This shows that manufacturer information about enantiomeric purity should be looked

at critically, even if the here used (S)-enantiomer stems from another company.

Furthermore, deviations between the PECD values for the (R)- and (S)-enantiomer

might be attributed to the enantiomeric purity but the stronger deviation for feature A

in comparison to B and C can not be solely described by this. A more likely theory is dif-

ferent source conditions for the three samples leading to different tautomer distributions

and PADs of different qualities as described earlier.

5.5. Summary

Anions of deprotonated alaninol and 1-indanol are investigated for their anion PES and

PECD effect via a VMI spectrometer, which not only allows energy resolved measure-

mens but also PECD PADs as seen in figure 5.4.4. DFT calculation of these anions

revealed several isomers even if only the hydroxy group is considered for deprotonation.

In the case of [Ind(O)-H]−, the isomers are eq. and ax. [Ind-H]−. More isomers can be

expected for [Ala(O)-H]−since alaninol is a relatively flexible molecule.

All calculated energies could be assigned in the PES of both anions: HOMO and

HOMO-1 of [Ala(O)-H]−are contained in the A peak and HOMO-2 could be assigned

to feature B in the PES of [Ala-H]−. Further resolving peak A even revealed a transition

matching well with the calculated tautomers [Ala(N)-H]−but HOMO and HOMO-1 of

[Ala(O)-H]−could not be resolved. Probably many isomers of [Ala(O)-H]−are overlap-

ping in A leading to the relatively broad feature. Only one peak in this PES could not

be assigned.

For [Ind-H]−, HOMO and HOMO-1 are contained in feature B, which could be resolved

for smaller photon energies (B1, B2). A third feature (B3) is assigned to a C-O stretch

vibration of [Ind(O)-H]−after a FC simulation. HOMO-2 is assigned to feature C. The

contribution of ax. [Ind(O)-H]−to the PES is not clear but the experimental PES

resembles more the simulated spectrum of eq. [Ind(O)-H]−or the combination of eq.

and ax. [Ind(O)-H]−. The tautomers [Ind(C3)-H]−and [Ind(C1)-H]−match with the

transitions A (HOMO) and D (HOMO-1) but could not be resolved further.

For [Ala(O)-H]−and [Ind(O)-H]−, HOMO and HOMO-1 are energetically close since,

in both cases, these orbitals are dominated by the 2pshell of the oxygen, hence, detach-

192

5. Deprotonated Chiral Species

ment happens in states, which are nearly degenerate. Only HOMO-2 is dominated from

other parts of the molecule, which is the nitrogen for [Ala(O)-H]−and 2pshells of some

members of the benzene ring for [Ind(O)-H]−. This is reflected more or less in the mea-

sured anisotropy parameters which follow more or less a trend known for a pdominated

orbital in the s-pmixing model from Sanov (figure 2.2.2 in section 2.2.2). Unfortunately,

the attempted fits do not agree well with the data but effects like the influence of the

neutral radical on the departing electron, e.g. the dipole moment, were neglected, which

could account for some of the disagreement. Furthermore, lots of not resolved isomer

contributions and vibrations could overlapping, hence give a superimposed anisotropy

parameter. In the case of [Ind-H]−, the anisotropy parameter could agree with other

studies if certain symmetries of vibrational states dominate [201].

The first successful PECD signal was measured for [Ind-H]−. Even [Ala-H]−seems

to show a PECD asymmetry in feature B but it is relatively small and almost at the

detection limit of the experiment, which was determined with the help of total electron

counts measurements of [Ind-H]−and is around 1%. [Ind-H]−shows a more convincing

PECD signal in all features and changes sign upon switching the light polarization and

enantiomer without giving a PECD signal for the racemic mixture. The dependency of

the PECD signal on the photon energy (or kinetic energy) shows an individual trend for

all features, e.g. feature A (HOMO of the tautomers, especially [Ind(C3)-H]−) has always

a PECD signal with opposite sign than feature B (HOMO and HOMO-1 of [Ind(O)-H]−).

The strongest PECD signal of around -11% is measured for feature C. In comparison to

other experimental PECD studies on anions by Kr¨uger et al. [2], the strongest PECD

signal reported so far was around 4.6% for glutamic acid. Feature B peaks at -6-(-5)%.

Even feature A and D, which are assigned to the tautomers, shows a quite strong PECD

signal hinting to a contribution of the [Ind(C3)-H]−tautomer. They peak at around -5%

and 4%, respectively. Furthermore, the PECD signal of feature A and B always have

the opposite sign, which emphasizes the importance of energy resolved measurements,

since else the total PECD signal is a result of the superimposed PECD signals of A and

B making the total PECD signal appears weaker.

In comparison to PECD asymmetries on neutral molecules, e.g. 1-indanol [73] and

fenchone [28], the signal strength in anion PECD is in no way inferior. HOMO/HOMO-1

of [Ind-H]−and HOMO-2 of 1-indanol, which can be quite similar, e.g. 2pof oxygen

dominates these orbitals, but also different, e.g. weaker localization of HOMO-2 of 1-

indanol, can have similar PECD strengths but also have to opposite PECD asymmetries

for low kinetic energies.

PECD signals are measured for kinetic energies between 0.04 eV up to 3.90 eV. The

highest kinetic energy with a PECD signal is around 2.2 eV for feature B (Eph = 4.59 eV).

Measuring a PECD signal at such high kinetic energies is in contrast to the idea of

treating the departing electron as a plane wave and neglecting short-range interactions

with the neutral core. The electron is neither a plane wave nor is the influence of

short-range interactions unimportant.

193

6. Summary and Outlook

The aim of this work was to measure PECD signals on anions. Next to experimental ad-

vantages like mass spectrometry before photodeteachment and the use of table-top laser

instead of e.g synchrotron facilities, the role of short-range interactions regarding the

creation of a PECD asymmetry can be studied since long-range monopole interactions

are missing. The departing electron is then only influenced by short-range interactions

occurring, e.g., due to the presence of bond dipols or scattering potentials. In the be-

ginning, PECD effects on anions were predicted to be non-existent, since photodetached

electrons are considered to be a plane wave [49], which can not carry any asymmetry. The

lack of PECD experiments on anions seemed to support such assumptions. Initially, only

the study of Dreiling et al. [50] gave hope on a working PECD experiment on anions.

They used quasi-elastic electron-bromocamphor scattering to show that transmission

asymmetries of spin-polarized electrons through neutral chiral molecules are non-zero.

However, new studies reporting theoretically and experimentally on a non vanishing

PECD signal emerged recently and gave new hope in the direction of detecting anion

PECD asymmetries [2–4]. Not long after these studies, [Ind-H]−also showed the wanted

PECD signal. In addition, not only PECD values could be extracted but also PECD

images containing the full spatial and energy information are obtained.

The PECD effect for anions was studied on gold-metal complexes and deprotonated

molecules. Gold-metal complexes consists of Au−, which acts as electron source, and a

neutral chiral molecule. Deprotonated molecules, on the other hand, carry the charge di-

rectly at the molecule itself and have no achiral part, where the electron can be (strongly)

localized.

Gold complexes are produced in a laser ablation source, while deprotonated molecules

are created in a plasma entrainment souce. Subsequent mass spectrometry separates the

desired system from other source products in time. A tunable pulsed laser is synchronized

with the time of flight of the desired system and detaches the electrons, which are imaged

by a VMI spectrometer on a position sensitive detector. Depending on the polarization

of the light, photoelectron spectra can be used to extract binding energies, anisotropy

parameters and PECD images. DFT calculations support the experimental findings and

reveal the presence and nature of isomers.

While gold complexes do not show a PECD effect, photoelectron spectra recorded

with linear polarized light and DFT calculations reveal the bond nature of these com-

plexes. Hydrogen bonds occur between a nonconventional hydrogen acceptor (Au−),

conventional hydrogen donor (O and N) and the hydrogen. However, this was already

seen in other studies [127,176] and could be shown as well for Au−-3HTHF and Au−-

Ala. A more interesting focus is directed towards nonconventional acceptors and donors

(C), forming Au−···H-C and if they can be called a hydrogen bond as well. Indeed, all

195

6. Summary and Outlook

considered properties of this bond type, e.g. electron donation character, show hydro-

gen bond characteristics and also fulfill the definition from IUPAC. In comparison to

other studies, Au−···H-C can in fact be called a hydrogen bond of weak strength. This

hydrogen bond shows that the Au−has an effect on the molecule and that the electron

indeed interacts with the chiral molecule. Hence, a PECD asymmetry is not excluded

but the interaction might be too weak for measuring one.

Fortunately, the deprotonated molecules [Ala-H]−and [Ind-H]−show a PECD signal

in the photodetachment. However, the [Ala-H]−anion showed a weak PECD asymmetry

for one photon energy, which is (almost) at the detection limit of the experiment (around

1%). Only for the [Ind-H]−anion a recognizable PECD signal could be observed. The

measured PECD signal depends on the photon energy (or the kinetic energy), reverses

its sign upon change of the enantiomer and vanishes for the racemate, just like for the

PECD effect on neutrals. For each transition, even for certain subfeatures, an individual

PECD signal could be recorded. The strongest PECD signal was around -11 %. For

comparison, the strongest PECD signal reported before for electron detachment is 4.6%

for deprotonated glutamic acid [2]. Other features for [Ind-H]−are similar strong with

around -6%. These values are comparable to PECD asymmetries on neutral molecules

like 1-indanol [73] and fenchone [28], indicating that, in general, the PECD effect in an-

ions is not inherently weaker than in anions and that short-range effect play an important

role regarding PECD signals.

Outlook

[Ind-H]−revealed already a nice set of results but some open question remain for the

moment: Peak A, assigned to an achiral and a chiral tautormer, could be resolved further

to separate the different contributions, which are probably making up this feature. The

contribution of the ax. [Ind-H]−to the overall spectrum are not completely clear at the

moment and require separation from the eq. [Ind-H]−before or a better resolution of the

VMI spectrometer. Furthermore, the question of the correct sign of PECD values is still

unsolved since measurements with PEM and quarter waveplate (QWP) give different

signs probably due to a wrong or mislabeled fast axis. However, the absolute values

and zero-crossings will still be correct maintaining the non-zero PECD asymmetry for

[Ind-H]−in photodetachment.

Other potential candidates are [Ala-H]−, deprotonated 3HTHF or even Au−-1-indanol.

[Ala-H]−already showed a potentially weak PECD signal and repeating this experiment

will probably be successful. 3HTHF has less conformers than alaninol and the depro-

tonated form could also be a good candidate with an easier PES than [Ala-H]−. Going

back to the gold complexes could also be considered since now, after a successfully mea-

sured PECD signal, null-PECD values can be excluded to be from the experimental

method. Au−-1-indanol could work due to the success with [Ind-H]−.

More general questions regarding the anion PECD effect itself could be a comparison

in the capabilities between neutral and anion PECD effects. Here, [Ind-H]−already

shows that anion PECD experiments produce PECD signals in comparable strength to

196

6. Summary and Outlook

neutral PECD methods but how does the PECD asymmetry look for the neutral radical

Ind-H in comparison? What else is similar/different? Neutral PECD signals vanish if

the electrons have a too high kinetic energy supporting the theory of electron having

not enough time to scatter properly with the chiral potential. Is there a cutoff energy?

And if yes, where is this cutoff energy for anion PECD asymmetries? Artemyev [4]

calculated a cutoff energy of around 12 eV for a model chiral system but this was not

experimentally confirmed so far and might be vary for different models/chiral systems.

Do the PECD signals of vibrational excitations in anion PECD experiments behave in

a similar manner than the neutral PECD experiments? Other experiments on neutral

PECD asymmetries involved lasers with quite short pulses to follow the evolution of

PECD signals. Can there be differences in the evolution of anion and neutral PECD

signals?

Anion PECD methods also seemed to be a difficult topic among experimentalists since

some groups seemed to have tried such kind of experiments but could not successfully

report on it as was indicated by Lai-Sheng Wang and Manfred Kappes in private cor-

respondence. This study also showed problems in the beginning especially with the

gold complexes, which do not reveal any detectable PECD asymmetry. For this project,

[Ind-H]−is – so far – the only successful candidate. What unifies the (un)successful

chiral systems regarding anion PECD measurements? Can anion PECD experiments

work if an achiral anion, like Au−, dominates the system or if the charge is too strongly

localized at such places? Apart from gold complexes, does the dipole moment of the

neutral radical play an important role?

First steps towards anion PECD experiments are done with [Ind-H]−. However, more

work needs to be done in this only a few years old technique to reveal further the nature

of the PECD effect.

197

7. Appendix

A. Gold Complexes

A.1. Structures

(a) (b)

Fig. A.1.: Labeled molecules for Au−-Fen (a), Au−-Men (b), Au−-3HTHF (c) and Au−-Ala

(d) for tables A.1 -A.4.

199

7. Appendix

Table A.1.: Structure of F1. Labels according to figure A.1a.

Label Tag Symbol NA NB NC Bond Angle Dihedral

O 1 O

C22 C 1 2.4540083

C63 C 2 1 2.2845373 97.7357356

C74 C 3 2 1 1.5565402 77.3292524 -1.2497460

C35 C 3 2 1 1.5422892 42.3444709 -125.9357763

C46 C 2 1 4 1.5671834 110.4757214 77.7575505

C57 C 3 2 1 1.5405022 77.4632584 113.7942513

C10 8 C 1 4 3 1.2117133 31.2401638 -1.8694603

C19 C 2 1 8 1.5106483 94.2016902 -163.5625129

C210 C 4 3 2 1.5313436 116.2591866 119.8785848

C911 C 4 3 2 1.5377218 111.6051247 -115.0549714

H6.1 12 H 3 2 1 1.0904550 158.1213584 -121.6102703

H3.1 13 H 5 3 2 1.0913231 114.6665852 118.1950140

H3.2 14 H 5 3 2 1.0912130 112.9333190 -115.7649346

H4.1 15 H 6 2 1 1.0917505 107.9124007 145.4285549

H4.2 16 H 6 2 1 1.0918161 111.6602544 25.8415521

H5.1 17 H 7 3 2 1.0892052 113.6796597 -127.7261680

H5.2 18 H 7 3 2 1.0909839 109.5212046 111.2133377

H1.1 19 H 9 2 1 1.0920401 111.0515224 66.9201612

H1.2 20 H 9 2 1 1.0904893 109.4841608 -172.8227618

H1.3 21 H 9 2 1 1.0914928 110.7590731 -52.5790028

H8.1 22 H 10 4 3 1.0884149 112.2384176 -59.0090586

H8.2 23 H 10 4 3 1.0927883 110.4227209 61.7200571

H8.3 24 H 10 4 3 1.0906825 109.8060299 -178.6528451

H9.1 25 H 11 4 3 1.0926329 109.7334536 -71.5400713

H9.2 26 H 11 4 3 1.0889911 112.3544114 48.5349805

H9.3 27 H 11 4 3 1.0908195 110.1634671 169.0058786

Au 28 Au 6 2 1 3.7769983 95.9107105 177.2728170

200

7. Appendix

Table A.2.: Structure of M1.1. Labels according to figure A.1b.

Label Tag Symbol NA NB NC Bond Angle Dihedral

O 1 O

C14 2 C 1 2.4140363

C10 3 C 2 1 1.5447253 123.1071723

C74 C 3 2 1 2.5395873 91.2160675 50.2242824

C95 C 3 2 1 1.5281514 111.6406693 78.0240867

C36 C 2 1 3 1.5371931 88.9942738 -120.1910955

C67 C 4 3 2 1.5410125 88.5678868 -1.4958669

C58 C 1 7 4 1.2198943 32.2404149 64.3197472

C89 C 4 3 2 1.5282351 145.2187833 123.9794530

C110 C 6 2 1 1.5325717 113.6916911 72.2923401

C211 C 6 2 1 1.5321520 111.0896292 -161.5457525

H4.1 12 H 2 1 8 1.1074416 114.6376694 68.0446834

H10.1 13 H 3 2 1 1.0952574 109.8959839 -44.1108012

H10.2 14 H 3 2 1 1.0915957 108.9768666 -160.9598349

H7.1 15 H 4 3 2 1.0985412 91.6302650 -109.3332617

H9.1 16 H 5 3 2 1.0944170 108.6637261 63.4090614

H9.2 17 H 5 3 2 1.0948197 110.0205011 -179.0212575

H3.1 18 H 6 2 1 1.0928394 105.7718341 -44.9155568

H6.1 19 H 7 4 3 1.0906992 111.6021446 -148.2601537

H6.2 20 H 7 4 3 1.1007487 107.8565432 91.8925217

H8.2 21 H 9 4 3 1.0929895 111.1010915 61.9266304

H8.1 22 H 9 4 3 1.0927095 111.3393461 -177.5835445

H8.3 23 H 9 4 3 1.0916869 109.9510677 -57.7504803

H1.1 24 H 10 6 2 1.0926838 111.3201841 67.3139590

H1.2 25 H 10 6 2 1.0930013 110.4223530 -173.5890399

H1.3 26 H 10 6 2 1.0892833 110.9196637 -53.7332813

H2.1 27 H 11 6 2 1.0927194 111.4303273 -67.1521861

H2.2 28 H 11 6 2 1.0932073 110.6758274 173.4577332

H2.3 29 H 11 6 2 1.0906785 111.0370105 52.8026138

Au 30 Au 2 1 8 3.7261243 113.0613903 53.4576132

201

7. Appendix

Table A.3.: Structure of H1.1. Labels according to figure A.1c.

Label Tag Symbol NA NB NC Bond Angle Dihedral

O21 O

O12 O 1 3.1640680

C13 C 2 1 1.4143126 45.6982440

C44 C 3 2 1 1.5368473 111.8472878 74.8198879

C25 C 1 4 3 1.4406270 73.5968189 -13.5954730

C36 C 1 5 3 1.4374186 108.4829591 -3.2045412

H1.1 7 H 3 2 1 1.0937392 110.4895257 -160.4060944

H4.1 8 H 4 3 2 1.0934770 110.1874688 162.3526680

H4.1 9 H 4 3 2 1.0879639 110.5013891 41.7861427

H2.1 10 H 5 1 6 1.0943230 107.9898825 -124.1269828

H2.2 11 H 5 1 6 1.0917764 109.8969631 116.7129245

H3.2 12 H 6 1 5 1.0952583 109.9500930 -92.5693274

H3.1 13 H 6 1 5 1.0912121 107.5667887 148.7526284

HO.1 14 H 2 1 6 0.9918573 141.0091808 -33.3103656

Au 15 Au 2 1 6 3.2814733 131.9377092 -41.8874732

Table A.4.: Structure of A1.1. Labels according to figure A.1d.

Label Tag Symbol NA NB NC Bond Angle Dihedral

O 1 O

N 2 N 1 2.9372079

C23 C 2 1 1.4659447 56.5534170

C34 C 1 3 2 1.4134254 35.3449397 -130.7738724

C15 C 3 2 1 1.5265772 109.7600290 -150.2010976

H2.1 6 H 3 2 1 1.0959128 106.8197215 92.0427850

H3.1 7 H 4 1 3 1.0973328 110.1894885 121.5766587

H3.2 8 H 4 1 3 1.0970525 107.7650208 -120.6406687

H1.1 9 H 5 3 2 1.0928596 111.4044613 -178.4143879

H1.3 10 H 5 3 2 1.0932861 110.2475562 61.8775801

H1.2 11 H 5 3 2 1.0904932 110.5688384 -57.3344337

HN.2 12 H 2 1 4 1.0189387 93.2743968 -80.0425928

HN.1 13 H 2 1 4 1.0156141 59.2689268 177.1633113

HO14 H 1 4 3 0.9889543 107.0913182 -91.8358229

Au 15 Au 1 4 3 3.2931470 95.5017829 -90.7586859

202

7. Appendix

A.2. Calculations

Table A.5.: Comparison of D0for B3LYP-D3/aug-cc-pVTZ(-PP), B3LYP-D3(BJ)/def2-tzvp

and B3LYP-D3(BJ)/ma-tzvp given in eV. ma-tzvp is the def2-tzvp with the sand pdiffuse

basis functions on non-hydrogenic atoms. Hence, def2-tzvp is taken for a reference calculation.

ma-tzvp does not contain a basis set for Au. Therefore F−is taken as substitute for a closed-

shell (anionic) system. B3LYP-D3/aug-cc-pVTZ(-PP) and B3LYP-D3(BJ)/ma-tzvp lead to

similar results and are closest to the literature values in the case of F−-H2O.

D0(eV) F−-H2O Au−-H2O

literature 1.136 [203] 0.45 eV [146]

B3LYP-D3 1.172 0.515

aug-cc-pVTZ(-PP)

B3LYP-D3(BJ) 1.478 0.567

def2-tzvp

B3LYP-D3(BJ) 1.186 -

ma-tzvp

203

7. Appendix

A.3. Bond Lengths and Angles of Au−-M

Table A.6.: Bond lengths and angles for Au−-Fen. The undisturbed C-H bond length is in

all cases 0.109 nm.

Complex H-bond length (nm) length (nm) angle(

)

C-H H···Au−

F1 C3-H···Au 0.109 0.288 151.2

C4-H···Au 0.109 0.293 134.9

C5-H···Au 0.109 0.316 128.4

F2 C6-H···Au 0.109 0.292 141.1

C8-H···Au 0.109 0.304 145.8

C9-H···Au 0.109 0.306 144.4

F3 C1-H···Au 0.109 0.321 144.0

C3-H···Au 0.109 0.273 158.5

C9-H···Au 0.109 0.297 166.4

F4 C4-H···Au 0.109 0.309 129.0

C5-H···Au 0.109 0.294 136.7

C8-H···Au 0.109 0.294 168.4

Table A.7.: Bond lengths and angles for Au−-Men. If the C-H bond length changed due to

the disturbance of Au−the undisturbed bond length is given in brackets else the brackets are

omitted.

Complex H-bond length (nm) length (nm) angle(

)

C-H H···Au−

M1.1 C4-H···Au 0.111(0.110) 0.226 161.0

C6-H···Au 0.110 0.295 144.3

C9-H···Au 0.109(0.110) 0.291 144.8

M2.1 C4-H···Au 0.110 0.274 158.2

C6-H···Au 0.110 0.292 147.0

C9-H···Au 0.109(0.110) 0.290 145.7

M3.1 C4-H···Au 0.111(0.110) 0.266 162.0

C6-H···Au 0.110 0.293 145.1

C9-H···Au 0.109(0.110) 0.292 144.4

M4.1 C3-H···Au 0.109 0.281 173.1

C6-H···Au 0.110(0.109) 0.278 147.5

C9-H···Au 0.109 0.293 142.1

204

7. Appendix

Table A.8.: Bond lengths and angles for Au−-Men. The C-H bond lengths remain unchanged

despite disturbance of Au−

Complex H-bond length (nm) length (nm) angle(

)

C-H H···Au−

M1.2 C7-H···Au 0.110 0.298 130.7

C9-H···Au 0.109 0.308 117.7

C10-H···Au 0.109 0.307 130.1

M3.2 C7-H···Au 0.110 0.298 130.9

C9-H···Au 0.109 0.308 117.7

C10-H···Au 0.109 0.307 130.3

M2.2 C7-H···Au 0.110 0.303 126.9

C9-H···Au 0.109 0.298 122.4

C10-H···Au 0.109 0.322 124.3

M4.2 C7-H···Au 0.109 0.305 121.3

C8-H···Au 0.109 0.319 125.9

C9-H···Au 0.109 0.308 123.1

Table A.9.: Bond lengths and angles for Au−-Men. The undisturbed C-H bond length is

0.109 nm.

Complex H-bond length (nm) length (nm) angle(

)

C-H H···Au−

M4.3 C2-H···Au 0.109 0.293 149.3

C4-H···Au 0.109 0.315 125.3

C10-H···Au 0.109 0.312 119.3

M1.3 C1-H···Au 0.109 0.306 151.6

C2-H···Au 0.109 0.289 159.5

C3-H···Au 0.109 0.427 87.9

M2.3 C1-H···Au 0.109 0.288 164.5

C2-H···Au 0.109 0.308 153.1

C3-H···Au 0.109 0.442 83.9

205

7. Appendix

Table A.10.: Bond lengths and angles for Au−-3HTHF. If the C-H or O-H bond length

changed due to the disturbance of Au−the undisturbed bond length is given in brackets else

the brackets are omitted. A clear change is visible for the O-H bond length.

Complex H-bond length (nm) length (nm) angle(

)

C,O-H H···Au−

H1.1 C1-H···Au 0.109 0.231 92.2

C4-H···Au 0.109 0.318 124.8

O-H···Au 0.099(0.096) 0.231 164.6

H1.2 C1-H···Au 0.109 0.337 96.3

C2-H···Au 0.109 0.339 111.2

O-H···Au 0.099(0.096) 0.231 162.1

H1.3 C2-H···Au 0.110 0.321 127.2

C3-H···Au 0.110(0.109) 0.312 128.6

C4-H···Au 0.109 0.319 115.5

O-H···Au 0.099(0.096) 0.234 169.0

Table A.11.: Bond lengths and angles for Au−-3HTHF. If the C-H bond length changed due

to the disturbance of Au−the undisturbed bond length is given in brackets else the brackets

are omitted.

Complex H-bond length (nm) length (nm) angle(

)

C-H H···Au−

H1.4 C2-H···Au 0.110 0.299 139.5

C3-H···Au 0.109 0.325 121.9

C4-H···Au 0.109 0.292 131.1

H2.1 C1-H···Au 0.109 0.298 124.5

C2-H···Au 0.109 0.309 130.5

C4-H···Au 0.109 0.313 130.7

H2.2 C1-H···Au 0.109 0.304 119.4

C2-H···Au 0.110(0.109) 0.316 125.9

C3-H···Au 0.110(0.109) 0.327 123.3

C4-H···Au 0.109 0.319 113.8

206

7. Appendix

Table A.12.: Bond lengths and angles for Au−-Ala. If the C-H, N-H or O-H bond length

changed due to the disturbance of Au−the undisturbed bond length is given in brackets else

the brackets are omitted. A clear change is visible for the O-H bond length. The N-H bond

length changes like C-H.

Complex H-bond length (nm) length (nm) angle(

)

C,O,N-H H···Au−

A1.1 C3-H···Au 0.110 0.323 107.1

N-HN.1 ···Au 0.102(0.101) 0.331 102.0

N-HN.2 ···Au 0.102(0.101) 0.301 122.4

O-H···Au 0.099(0.097) 0.233 163.5

A2.1 C3-H···Au 0.110 0.324 107.0

N-HN.1 ···Au 0.102(0.101) 0.300 122.6

O-H···Au 0.099(0.097) 0.233 164.0

A3.1 C2-H···Au 0.110 0.307 133.6

C3-H···Au 0.110(0.109) 0.350 93.1

O-H···Au 0.099(0.096) 0.232 165.1

A4.1 C2-H···Au 0.109(0.110) 0.322 127.6

C3-H···Au 0.110 0.330 100.0

O-H···Au 0.099(0.096) 0.232 162.2

Table A.13.: Bond lengths and angles for Au−-Ala.If the C-H, N-H or O-H bond length

changed due to the disturbance of Au−the undisturbed bond length is given in brackets else

the brackets are omitted. A clear change is visible for the O-H bond length. The N-H bond

length changes like C-H but for A2.2 where N-H is elongated more.

Complex H-bond length (nm) length (nm) angle(

)

C,O,N-H H···Au−

A4.2 C2-H···Au 0.109(0.110) 0.305 121.1

N-HN.1 ···Au 0.102(0.101) 0.297 138.5

O-H···Au 0.099(0.096) 0.232 170.0

A3.2 C3-H···Au 0.110 0.390 85.9

N-HN.2 ···Au 0.102(0.101) 0.254 174.7

O-H···Au 0.099(0.096) 0.232 175.3

A2.2 C1-H···Au 0.109 0.373 126.8

N-HN.1 ···Au 0.103(0.101) 0.253 171.6

O-H···Au 0.099(0.097) 0.232 173.5

A5.1 C2-H···Au 0.109(0.110) 0.317 127.5

C3-H···Au 0.110(0.109) 0.324 101.6

O-H···Au 0.099(0.096) 0.236 159.4

207

7. Appendix

Table A.14.: Bond lengths and angles for Au−-Ala. If the C-H or N-H bond length changed

due to the disturbance of Au−the undisturbed bond length is given in brackets else the brackets

are omitted. The N-H bond length is clearly changed and is (almost) always longer than in

the first two groups of Au−-Ala (with Au−···H-O).

Complex H-bond length (nm) length (nm) angle(

)

C,N-H H···Au−

A1.2 C1-H···Au 0.109 0.309 136.2

C2-H···Au 0.109 0.366 94.9

N-HN.2 ···Au 0.103(0.101) 0.251 157.9

A1.3 C1-H···Au 0.109 0.301 140.3

C3-H···Au 0.110 0.343 131.6

N-HN.1 ···Au 0.103(0.101) 0.252 167.3

A2.3 C1-H···Au 0.109 0.314 134.5

C2-H···Au 0.110 0.363 95.2

N-HN.1 ···Au 0.103(0.101) 0.253 150.8

A2.4 C2-H···Au 0.110 0.320 112.7

C3-H···Au 0.110 0.350 122.3

N-HN.2 ···Au 0.103(0.101) 0.252 151.5

Table A.15.: Bond lengths and angles for Au−-Ala. If the C-H or N-H bond length changed

due to the disturbance of Au−the undisturbed bond length is given in brackets else the brackets

are omitted. Only A5.2 shows a clear elongation for N-H. The rest changes like the C-H bond.

Complex H-bond length (nm) length (nm) angle(

)

C,N-H H···Au−

A5.2 C1-H···Au 0.109 0.318 128.7

C2-H···Au 0.110 0.320 111.5

N-HN.2 ···Au 0.102(0.101) 0.263 149.6

A5.3 C1-H···Au 0.109 0.321 137.1

C3-H···Au 0.109(0.110) 0.310 134.0

N-HN.2 ···Au 0.103(0.101) 0.255 161.4

A4.3 C1-H···Au 0.109 0.298 143.4

C3-H···Au 0.109 0.308 141.8

N-HN.2 ···Au 0.102(0.101) 0.273 156.6

208

7. Appendix

A.4. Scaling Factors for PECD measurements with Au−-M

Table A.16.: Scaling factors for the PES of Au−-M for the PECD measurements. Maximum

of fully peeled LCP spectrum divided by the maximum of the RCP spectrum gives the scaling

factor. Au−-Ala produces more spectra with scaling factors being closer to 1 than for the other

Au−M. In the case for the quarter waveplate (QWP) this can be attributed to signal stability

while the measurements with PEM benefit from the shot-to-shot measurement. URis the used

repeller voltage of the VMI spectrometer.

System Eph (eV) scaling factor (LCP/RCP) comments

Au−Fen 4.13 1.5468

3.02 0.9953

2.79 0.9138

Au−Men 4.35 0.8466

4.13 7.6512

2.85 0.9429

Au−3HTHF 4.40 1.0179

3.49 0.8291

Au−Ala (QWP) 4.13 0.9932

3.49 1.0184

3.02 0.9522 UR= 800 V

3.02 1.0349 UR= 100 V

Au−Ala (PEM) 4.35 1.0392 UR= 1900 V

4.35 0.9502 UR= 700 V

3.49 0.9588

3.02 0.9657

209

7. Appendix

B. Deprotonated Molecules

B.1. Structures

Table B.1.: Structure of A-H1.

Label Tag Symbol NA NB NC Bond Angle Dihedral

1 O

2 N 1 2.8175384

C23 C 2 1 1.4762404 59.3828344

C34 C 1 3 2 1.3375980 36.3555748 -135.2480684

C15 C 3 2 1 1.5209991 110.8617700 -148.8439681

H2.1 6 H 3 2 1 1.0970319 106.4452257 92.5459148

H3.1 7 H 4 1 3 1.1386138 114.2278594 119.1573187

H3.2 8 H 4 1 3 1.1318903 115.0989910 -121.1436237

H1.1 9 H 5 3 2 1.0937463 110.4355486 -179.7182482

H1.3 10 H 5 3 2 1.0955159 110.4282384 61.5853330

H1.2 11 H 5 3 2 1.0937035 111.9132687 -58.6503937

HN.2 12 H 2 1 4 1.0196691 101.5298644 -74.9414458

HN.1 13 H 2 1 4 1.0252842 45.4189881 -173.0212732

210

7. Appendix

Table B.2.: Structure of eq. Ind-H.

Label Tag Symbol NA NB NC Bond Angle Dihedral

C51 C

C42 C 1 1.3950314

C93 C 2 1 1.3883794 120.6957794

C84 C 3 2 1 1.3974118 119.1805217 -0.0462083

C75 C 4 3 2 1.3954994 120.0670447 0.6644738

C66 C 1 2 3 1.3859441 120.2349155 -1.0686706

C37 C 2 1 6 1.5137947 109.9439474 177.6432044

8 H 3 2 1 1.0858467 120.7096044 178.8841178

9 H 4 3 2 1.0839052 119.9856304 179.4298517

10 H 5 4 3 1.0847592 119.4492265 178.8593845

11 H 6 1 2 1.0836841 118.5454010 -176.9699089

C112 C 1 6 5 1.5420134 127.4411389 179.5791170

C213 C 7 2 1 1.5421002 102.5681207 -19.0449251

14 H 7 2 1 1.0972242 110.0128174 98.4225519

15 H 7 2 1 1.0943030 112.5097288 -142.6873616

16 H 13 7 2 1.0940651 110.6040823 -83.7828960

17 H 13 7 2 1.0914588 113.8142979 153.7879706

18 O 12 1 6 1.3228990 117.8870667 -30.8248088

19 H 12 1 6 1.1417610 102.5214933 95.3487313

211

7. Appendix

B.2. PECD

Fig. B.1.: PECD PADs of (R)-, (S)- and racemate [Ind-H]−at Eph = 4.77 eV. All images have

the same counts of 5 Mio electrons. Despite the same counts, the (S)-[Ind-H]−measurement

shows a less pronounced PECD signal than the (R)-[Ind-H]−. This can be explained by the

worse signal-to-noise ratio. The racemic mixture shows no PECD signal.

212

7. Appendix

Fig. B.2.: PECD PADs of (R)-, (S)- and racemate [Ind-H]−at Eph = 3.49 eV. The counts per

polarization are given next to the image. The racemic mixture shows no PECD signal while

(R) and (S) show a clear inversed PECD signal.

213

Bibliography

[1] V. Ulrich, S. Barth, S. Joshi, U. Hergenhahn, E. Mikajlo, C. J. Harding, I. Powis,

The Journal of Physical Chemistry A 2008,112, 3544–3549.

[2] P. Kr¨uger, K.-M. Weitzel, Angewandte Chemie 2021, DOI 10 . 1002 / anie .

202107150.

[3] P. Kr¨uger, J. H. Both, U. Linne, F. Chirot, K.-M. Weitzel, The Journal of Physical

Chemistry Letters 2022,13, 6110–6116.

[4] A. N. Artemyev, E. Kutscher, P. V. Demekhin, The Journal of Chemical Physics

2022,156, 031101.

[5] G. Nagendrappa, Resonance 2007,12, 38–48.

[6] I. Ilisz, R. Berkecz, A. P´eter, Journal of pharmaceutical and biomedical analysis

2008,47, 1–15.

[7] X. Yu, Z.-P. Yao, Analytica Chimica Acta 2017,968, 1–20.

[8] A. V. Orlova, R. R. Andrade, C. O. da Silva, A. I. Zinin, L. O. Kononov,

ChemPhysChem 2014,15, 195–207.

[9] V. Parchaˇnsk`y, J. Kapit´an, P. Bouˇr, RSC Advances 2014,4, 57125–57136.

[10] B. Ranjbar, P. Gill, Chemical biology & drug design 2009,74, 101–120.

[11] V. A. Shubert, D. Schmitz, M. Schnell, Journal of Molecular Spectroscopy 2014,

300, 31–36.

[12] S. Eibenberger, J. Doyle, D. Patterson, Physical review letters 2017,118, 123002.

[13] M. Pitzer, M. Kunitski, A. S. Johnson, T. Jahnke, H. Sann, F. Sturm, L. P. H.

Schmidt, H. Schmidt-B¨ocking, R. D¨orner, J. Stohner, et al., Science 2013,341,

1096–1100.

[14] K. Fehre, S. Eckart, M. Kunitski, M. Pitzer, S. Zeller, C. Janke, D. Trabert, J.

Rist, M. Weller, A. Hartung, et al., Science advances 2019,5, eaau7923.

[15] L. Nahon, G. A. Garcia, I. Powis, Journal of Electron Spectroscopy and Related

Phenomena 2015,204, 322–334.

[16] B. Ritchie, Physical Review A 1976,13, 1411.

[17] N. B¨owering, T. Lischke, B. Schmidtke, N. M¨uller, T. Khalil, U. Heinzmann,

Physical review letters 2001,86, 1187.

[18] T. Jahnke, T. Weber, A. Landers, A. Knapp, S. Sch¨ossler, J. Nickles, S. Kammer,

O. Jagutzki, L. Schmidt, A. Czasch, et al., Physical review letters 2002,88,

073002.

214

Bibliography

[19] J. Viefhaus, L. Avaldi, G. Snell, M. Wiedenh¨oft, R. Hentges, A. R¨udel, F.

Sch¨afers, D. Menke, U. Heinzmann, A. Engelns, et al., Physical review letters

1996,77, 3975.

[20] M. Tia, M. Pitzer, G. Kastirke, J. Gatzke, H.-K. Kim, F. Trinter, J. Rist, A.

Hartung, D. Trabert, J. Siebert, et al., The journal of physical chemistry letters

2017,8, 2780–2786.

[21] S. Beaulieu, A. Ferr´e, R. G´eneaux, R. Canonge, D. Descamps, B. Fabre, N. Fe-

dorov, F. L´egar´e, S. Petit, T. Ruchon, et al., New Journal of Physics 2016,18,

102002.

[22] M. Wollenhaupt, New Journal of Physics 2016,18, 121001.

[23] T. Lischke, N. B¨owering, B. Schmidtke, N. M¨uller, T. Khalil, U. Heinzmann,

Physical Review A 2004,70, 022507.

[24] U. Hergenhahn, E. E. Rennie, O. Kugeler, S. Marburger, T. Lischke, I. Powis,

G. Garcia, The Journal of chemical physics 2004,120, 4553–4556.

[25] I. Powis, The Journal of Chemical Physics 2000,112, 301–310.

[26] D. Di Tommaso, M. Stener, G. Fronzoni, P. Decleva, Chemphyschem: a European

journal of chemical physics and physical chemistry 2006,7, 924–934.

[27] G. A. Garcia, H. Dossmann, L. Nahon, S. Daly, I. Powis, Physical Chemistry

Chemical Physics 2014,16, 16214–16224.

[28] I. Powis, C. J. Harding, G. A. Garcia, L. Nahon, ChemPhysChem 2008,9, 475–

483.

[29] L. Nahon, L. Nag, G. A. Garcia, I. Myrgorodska, U. Meierhenrich, S. Beaulieu, V.

Wanie, V. Blanchet, R. G´eneaux, I. Powis, Physical Chemistry Chemical Physics

2016,18, 12696–12706.

[30] S. Turchini, D. Catone, G. Contini, N. Zema, S. Irrera, M. Stener, D. Di Tommaso,

P. Decleva, T. Prosperi, ChemPhysChem 2009,10, 1839–1846.

[31] D. Catone, S. Turchini, G. Contini, T. Prosperi, M. Stener, P. Decleva, N. Zema,

Chemical Physics 2017,482, 294–302.

[32] D. Loru, M. A. Berm´udez, M. E. Sanz, The Journal of chemical physics 2016,

145, 074311.

[33] M. Tia, B. Cunha de Miranda, S. Daly, F. Gaie-Levrel, G. A. Garcia, L. Nahon,

I. Powis, The Journal of Physical Chemistry A 2014,118, 2765–2779.

[34] G. A. Garcia, L. Nahon, S. Daly, I. Powis, Nature Communications 2013,4,

2132.

[35] S. Turchini, N. Zema, G. Contini, G. Alberti, M. Alagia, S. Stranges, G. Fronzoni,

M. Stener, P. Decleva, T. Prosperi, Physical Review A 2004,70, 014502.

[36] S. Malerz, H. Haak, F. Trinter, A. B. Stephansen, C. Kolbeck, M. Pohl, U. Hergen-

hahn, G. Meijer, B. Winter, Review of Scientific Instruments 2022,93, 015101.

215

Bibliography

[37] M. N. Pohl, S. Malerz, F. Trinter, C. Lee, C. Kolbeck, I. Wilkinson, S. Th¨urmer,

D. M. Neumark, L. Nahon, I. Powis, et al., Physical Chemistry Chemical Physics

2022,24, 8081–8092.

[38] M. Tia, B. Cunha de Miranda, S. Daly, F. Gaie-Levrel, G. A. Garcia, I. Powis,

L. Nahon, The Journal of Physical Chemistry Letters 2013,4, 2698–2704.

[39] A. Kastner, G. Koumarianou, P. Glodic, P. C. Samartzis, N. Ladda, S. T. Ra-

necky, T. Ring, S. Vasudevan, C. Witte, H. Braun, et al., Physical Chemistry

Chemical Physics 2020,22, 7404–7411.

[40] A. Kastner, T. Ring, H. Braun, A. Senftleben, T. Baumert, ChemPhysChem

2019,20, 1416–1419.

[41] R. E. Goetz, C. P. Koch, L. Greenman, Physical review letters 2019,122, 013204.

[42] M. M. R. Fanood, N. B. Ram, C. S. Lehmann, I. Powis, M. H. Janssen, Nature

communications 2015,6, 1–8.

[43] C. S. Lehmann, N. B. Ram, I. Powis, M. H. Janssen, The Journal of Chemical

Physics 2013,139, 234307.

[44] C. S. Lehmann, K.-M. Weitzel, Physical Chemistry Chemical Physics 2020,22,

13707–13712.

[45] J. Miles, D. Fernandes, A. Young, C. Bond, S. Crane, O. Ghafur, D. Townsend,

J. S´a, J. Greenwood, Analytica chimica acta 2017,984, 134–139.

[46] A. Comby, C. M. Bond, E. Bloch, D. Descamps, B. Fabre, S. Petit, Y. Mairesse,

J. B. Greenwood, V. Blanchet, Chirality 2020,32, 1225–1233.

[47] I. Powis, S. Daly, M. Tia, B. C. de Miranda, G. A. Garcia, L. Nahon, Physical

Chemistry Chemical Physics 2014,16, 467–476.

[48] J. Triptow, A. Fielicke, G. Meijer, M. Green, Angewandte Chemie International

Edition 2022, DOI 10.1002/anie.202212020.

[49] S. Gozem, A. O. Gunina, T. Ichino, D. L. Osborn, J. F. Stanton, A. I. Krylov,

The journal of physical chemistry letters 2015,6, 4532–4540.

[50] J. Dreiling, T. J. Gay in Journal of Physics: Conference Series, Vol. 635, IOP

Publishing, 2015, p. 012015.

[51] J. Triptow, G. Meijer, A. Fielicke, O. Dopfer, M. Green, The Journal of Physical

Chemistry A 2022, DOI 10.1021/acs.jpca.2c02725.

[52] J. Franck, E. Dymond, Transactions of the Faraday Society 1926,21, 536–542.

[53] E. Condon, Physical Review 1926,28, 1182.

[54] J. Cooper, R. N. Zare, The Journal of chemical physics 1968,48, 942–943.

[55] C. Melania Oana, A. I. Krylov, The Journal of chemical physics 2007,127,

234106.

[56] J. A. DeVine, M. C. Babin, K. Blackford, D. M. Neumark, The Journal of Chem-

ical Physics 2019,151, 064302.

216

Bibliography

[57] D. Hanstorp, C. Bengtsson, D. Larson, Physical Review A 1989,40, 670.

[58] A. Sanov, Annual review of physical chemistry 2014,65, 341–363.

[59] A. Sanov, E. R. Grumbling, D. J. Goebbert, L. M. Culberson, The Journal of

chemical physics 2013,138, 054311.

[60] E. Surber, R. Mabbs, A. Sanov, The Journal of Physical Chemistry A 2003,107,

8215–8224.

[61] R. Mabbs, E. Surber, A. Sanov, The Journal of chemical physics 2005,122,

054308.

[62] M. H. Janssen, I. Powis, Physical Chemistry Chemical Physics 2014,16, 856–

871.

[63] K.-N. Huang, Physical Review A 1980,22, 223.

[64] H. A. Bethe, E. E. Salpeter, Quantum mechanics of one-and two-electron atoms,

Springer Science & Business Media, 2012.

[65] E. P. Wigner, Physical Review 1948,73, 1002.

[66] R. Mabbs, F. Mbaiwa, J. Wei, M. Van Duzor, S. T. Gibson, S. J. Cavanagh, B. R.

Lewis, Physical Review A 2010,82, 011401.

[67] V. Ivanov, Radiation Physics and Chemistry 2004,70, 345–370.

[68] D. Y. Valdivielso, PhD thesis, Technische Universit¨at Berlin, 2022.

[69] T. Schirmeister, C. Schmuck, P. R. Wich, Beyer/Walter— Organische Chemie,

Hirzel Verlag, 2015.

[70] G. P. Moss, Pure and applied chemistry 1996,68, 2193–2222.

[71] M. Born, E. Wolf, Principles of optics: electromagnetic theory of propagation,

interference and diffraction of light, Elsevier, 2013.

[72] V. Svoboda, M. D. Waters, D. Zindel, H. J. W¨orner, Optics Express 2022,30,

14358–14367.

[73] J. Dupont, V. Lep`ere, A. Zehnacker, S. Hartweg, G. A. Garcia, L. Nahon, The

Journal of Physical Chemistry Letters 2022,13, 2313–2320.

[74] A. Giardini, D. Catone, S. Stranges, M. Satta, M. Tacconi, S. Piccirillo, S. Tur-

chini, N. Zema, G. Contini, T. Prosperi, et al., ChemPhysChem 2005,6, 1164–

1168.

[75] R. Fausto, C. Cacela, M. Duarte, Journal of Molecular Structure 2000, 365–388.

[76] J. Schiller, J. Hormes, Nuclear Instruments and Methods in Physics Research

Section A: Accelerators Spectrometers Detectors and Associated Equipment 1986,

246, 772–775.

[77] T. Andersen, H. Haugen, H. Hotop, Journal of Physical and Chemical Reference

Data 1999,28, 1511–1533.

217

Bibliography

[78] P. Linstrom, E. W.G. Mallard, NIST Chemistry WebBook, NIST Standard Ref-

erence Database Number 69, National Institute of Standards and Technology,

Gaithersburg MD, 20899, 2023.

[79] P. Gr¨une, PhD thesis, Technische Universit¨at Berlin, 2009.

[80] M. H¨artelt, PhD thesis, Technische Universit¨at Berlin, 2012.

[81] Y.-J. Lu, J. H. Lehman, W. C. Lineberger, The Journal of chemical physics 2015,

142, 044201.

[82] T. G. Dietz, M. A. Duncan, D. E. Powers, R. E. Smalley, The Journal of Chemical

Physics 1981,74, 6511–6512.

[83] D. E. Powers, S. G. Hansen, M. Geusic, A. Puiu, J. Hopkins, T. Dietz, M. Duncan,

P. Langridge-Smith, R. Smalley, The Journal of Physical Chemistry 1982,86,

2556–2560.

[84] V. Bondybey, J. English, The Journal of Chemical Physics 1981,74, 6978–6979.

[85] M. A. Duncan, Review of Scientific Instruments 2012,83, 041101.

[86] A. Fielicke, G. Von Helden, G. Meijer, The European Physical Journal D-Atomic

Molecular Optical and Plasma Physics 2005,34, 83–88.

[87] H. Conrads, M. Schmidt, Plasma Sources Science and Technology 2000,9, 441.

[88] A. Bogaerts in Encyclopedia of spectroscopy and spectrometry/Lindon, JC [edit.]

2000, pp. 669–676.

[89] C. Budtz-Jørgensen, J. Bøttiger, P. Kringhøj, Surface and Coatings Technology

2001,137, 104–110.

[90] P. Hartmann, R. Haubner, B. Lux, Diamond and related materials 1996,5, 850–

856.

[91] D. L. Osborn, D. J. Leahy, D. R. Cyr, D. M. Neumark, The Journal of chemical

physics 1996,104, 5026–5039.

[92] D. W. Boo, Y. Ozaki, L. H. Andersen, W. Lineberger, The Journal of Physical

Chemistry A 1997,101, 6688–6696.

[93] M. Jim´enez-Redondo, E. Carrasco, V. J. Herrero, I. Tanarro, Plasma Sources

Science and Technology 2015,24, 015029.

[94] P. Brix, G. Herzberg, The Journal of Chemical Physics 1953,21, 2240–2240.

[95] S. T. Arnold, J. H. Hendricks, K. H. Bowen, The Journal of chemical physics

1995,102, 39–47.

[96] W. Wiley, I. H. McLaren, Review of scientific instruments 1955,26, 1150–1157.

[97] A. T. Eppink, D. H. Parker, Review of Scientific Instruments 1997,68, 3477–

3484.

[98] D. A. Horke, G. M. Roberts, J. Lecointre, J. R. Verlet, Review of Scientific

Instruments 2012,83, 063101.

218

Bibliography

[99] I. Le´on, Z. Yang, H.-T. Liu, L.-S. Wang, Review of Scientific Instruments 2014,

85, 083106.

[100] A. Osterwalder, M. J. Nee, J. Zhou, D. M. Neumark, The Journal of chemical

physics 2004,121, 6317–6322.

[101] C. Hock, J. B. Kim, M. L. Weichman, T. I. Yacovitch, D. M. Neumark, The

Journal of chemical physics 2012,137, 244201.

[102] D. R. Herschbach, Discussions of the Faraday Society 1962,33, 149–161.

[103] M. N. Ashfold, N. H. Nahler, A. J. Orr-Ewing, O. P. Vieuxmaire, R. L. Toomes,

T. N. Kitsopoulos, I. A. Garcia, D. A. Chestakov, S.-M. Wu, D. H. Parker, Phys-

ical Chemistry Chemical Physics 2006,8, 26–53.

[104] A. Bodi, P. Hemberger, R. P. Tuckett, Physical Chemistry Chemical Physics

2017,19, 30173–30180.

[105] M. G´en´evriez, K. M. Dunseath, M. Terao-Dunseath, A. Hibbert, A. Dochain, R.

Marion, X. Urbain, Physical Review A 2018,98, 033410.

[106] N. H. Abel, 1826, DOI 10.1515/crll.1826.1.153.

[107] B. Whitaker, Imaging in Molecular Dynamics, Technology and Application, Cam-

bridge University Press, 2003.

[108] K. Zhao, T. Colvin, W. T. Hill, G. Zhang, Review of Scientific Instruments 2002,

73, 3044–3050.

[109] V. Dribinski, A. Ossadtchi, V. A. Mandelshtam, H. Reisler, Review of Scientific

Instruments 2002,73, 2634–2642.

[110] G. A. Garcia, L. Nahon, I. Powis, Review of Scientific Instruments 2004,75,

4989–4996.

[111] G. M. Roberts, J. L. Nixon, J. Lecointre, E. Wrede, J. R. R. Verlet, Review of

Scientific Instruments 2009,80, 053104.

[112] S. T. Gibson, D. D. Hickstein, R. Yurchak, M. Ryazanov, D. D. Das, G. Shih,

2022, DOI 10.5281/zenodo.5888391.

[113] B. Dick, Physical Chemistry Chemical Physics 2014,16, 570–580.

[114] D. D. Hickstein, S. T. Gibson, R. Yurchak, D. D. Das, M. Ryazanov, Review of

Scientific Instruments 2019,90, 065115.

[115] M. Ryazanov, PhD thesis, University of Southern California, USA, 2012.

[116] B. Dick, Physical Chemistry Chemical Physics 2019,21, 19499–19512.

[117] J. E. Sansonetti, W. C. Martin, Journal of physical and chemical reference data

2005,34, 1559–2259.

[118] P. Johnsson, A. Rouz´ee, W. Siu, Y. Huismans, F. L´epine, T. Marchenko, S.

D¨usterer, F. Tavella, N. Stojanovic, H. Redlin, et al., Optics letters 2010,35,

4163–4165.

219

Bibliography

[119] B. Schaefer, E. Collett, R. Smyth, D. Barrett, B. Fraher, American Journal of

Physics 2007,75, 163–168.

[120] A. Hong, C. M. Choi, H. J. Eun, C. Jeong, J. Heo, N. J. Kim, Angewandte Chemie

International Edition 2014,53, 7805–7808.

[121] J. C. Kemp, J. Opt. Soc. Am. 1969,59, 950–954.

[122] D. Yang, J. Canit, E. Gaignebet, Journal of optics 1995,26, 151.

[123] M. Bonmarin, J. Helbing, Chirality: the pharmacological biological and chemical

consequences of molecular asymmetry 2009,21, E298–E306.

[124] S. Hosokawa, N. Takahashi, M. Saito, Y. Haruyama, Review of Scientific Instru-

ments 2010,81, 063301.

[125] K. Tobita, H. Takeuchi, H. Kimura, Y. Kusama, M. Nemoto, Japanese journal

of applied physics 1987,26, 509.

[126] S. Gopalakrishnan, PhD thesis, School of The Ohio State University, USA, 2003.

[127] Y. Wang, C. Han, Z. Fei, C. Dong, H. Liu, The Journal of Physical Chemistry A

2020,124, 5590–5598.

[128] M. L. Green, PhD thesis, Emory University, Atlanta, 2020.

[129] R. Wilson, Journal of Applied Physics 1966,37, 2261–2267.

[130] T. Maeda, S. Saito, Japanese journal of applied physics 1986,25, 1623.

[131] R. Ishii, K. Matsumura, A. Sakai, T. Sakata, Applied surface science 2001,169,

658–661.

[132] A. Savitzky, M. J. Golay, Analytical chemistry 1964,36, 1627–1639.

[133] K. Burke, The Journal of chemical physics 2012,136, 150901.

[134] W. Koch, M. C. Holthausen, A Chemist’s Guide to Density Functional Theory,

Wiley-VCH Verlag GmbH, 2001.

[135] N. Argaman, G. Makov, American Journal of Physics 2000,68, 69–79.

[136] N. Harrison, Nato Science Series Sub Series III Computer and Systems Sciences

2003,187, 45–70.

[137] R. Coquet, K. L. Howard, D. J. Willock, Chemical Society Reviews 2008,37,

2046–2076.

[138] L. H. Thomas in Mathematical proceedings of the Cambridge philosophical soci-

ety, Vol. 23, Cambridge University Press, 1927, pp. 542–548.

[139] W. Kohn, L. J. Sham, Physical review 1965,140, A1133.

[140] P. Hohenberg, W. Kohn, Physical review 1964,136, B864.

[141] C. Lee, W. Yang, R. G. Parr, Physical review B 1988,37, 785.

[142] S. Grimme, J. Antony, S. Ehrlich, H. Krieg, The Journal of chemical physics

2010,132, 154104.

220

Bibliography

[143] S. Grimme, Journal of computational chemistry 2004,25, 1463–1473.

[144] S. Grimme, Journal of computational chemistry 2006,27, 1787–1799.

[145] M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R.

Cheeseman, G. Scalmani, V. Barone, G. A. Petersson, H. Nakatsuji, X. Li, M.

Caricato, A. V. Marenich, J. Bloino, B. G. Janesko, R. Gomperts, B. Mennucci,

H. P. Hratchian, J. V. Ortiz, A. F. Izmaylov, J. L. Sonnenberg, D. Williams-

Young, F. Ding, F. Lipparini, F. Egidi, J. Goings, B. Peng, A. Petrone, T. Hen-

derson, D. Ranasinghe, V. G. Zakrzewski, J. Gao, N. Rega, G. Zheng, W. Liang,

M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima,

Y. Honda, O. Kitao, H. Nakai, T. Vreven, K. Throssell, J. A. Montgomery, Jr.,

J. E. Peralta, F. Ogliaro, M. J. Bearpark, J. J. Heyd, E. N. Brothers, K. N. Kudin,

V. N. Staroverov, T. A. Keith, R. Kobayashi, J. Normand, K. Raghavachari, A. P.

Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, J. M. Millam, M. Klene,

C. Adamo, R. Cammi, J. W. Ochterski, R. L. Martin, K. Morokuma, O. Farkas,

J. B. Foresman, D. J. Fox, Gaussian˜16 Revision A.03, Gaussian Inc. Wallingford

CT, 2016.

[146] W. Zheng, X. Li, S. Eustis, A. Grubisic, O. Thomas, H. de Clercq, K. Bowen,

Chemical Physics Letters 2007,444, 232–236.

[147] T. Lu, F. Chen, Journal of computational chemistry 2012,33, 580–592.

[148] I. Alkorta, I. Rozas, J. Elguero, Chemical Society Reviews 1998,27, 163–170.

[149] L. Brammer, Dalton Transactions 2003, 3145–3157.

[150] R. H. Crabtree, Science 1998,282, 2000–2001.

[151] R. H. Crabtree, P. E. Siegbahn, O. Eisenstein, A. L. Rheingold, T. F. Koetzle,

Accounts of chemical research 1996,29, 348–354.

[152] Y. Gao, W. Huang, J. Woodford, L.-S. Wang, X. C. Zeng, Journal of the American

Chemical Society 2009,131, 9484–9485.

[153] S. J. Grabowski, The Journal of Physical Chemistry A 2001,105, 10739–10746.

[154] L. Jiang, L. Lai, Journal of Biological Chemistry 2002,277, 37732–37740.

[155] E. Kryachko, S. Scheiner, The Journal of Physical Chemistry A 2004,108, 2527–

2535.

[156] S. Tsuzuki, A. Fujii, Physical Chemistry Chemical Physics 2008,10, 2584–2594.

[157] L. Epstein, E. Shubina, Coordination chemistry reviews 2002,231, 165–181.

[158] E. Arunan, G. R. Desiraju, R. A. Klein, J. Sadlej, S. Scheiner, I. Alkorta, D. C.

Clary, R. H. Crabtree, J. J. Dannenberg, P. Hobza, et al., Pure and applied

chemistry 2011,83, 1637–1641.

[159] E. S. Kryachko, Journal of Molecular Structure 2008,880, 23–30.

[160] H. Schmidbaur, Angewandte Chemie International Edition 2019,58, 5806–5809.

221

Bibliography

[161] S. Emamian, T. Lu, H. Kruse, H. Emamian, Journal of computational chemistry

2019,40, 2868–2881.

[162] A. Albinati, F. Lianza, P. S. Pregosin, B. Mueller, Inorganic Chemistry 1994,

33, 2522–2526.

[163] A. Albinati, P. Pregosin, F. Wombacher, Inorganic chemistry (Print) 1990,29,

1812–1817.

[164] J. L. Atwood, F. Hamada, K. D. Robinson, G. W. Orr, R. L. Vincent, Nature

1991,349, 683–684.

[165] D. Braga, F. Grepioni, E. Tedesco, K. Biradha, G. Desiraju, Organometallics

1997,16, 1846–1856.

[166] L. Brammer, J. M. Charnock, P. L. Goggin, R. J. Goodfellow, A. G. Orpen, T. F.

Koetzle, Journal of the Chemical Society Dalton Transactions 1991, 1789–1798.

[167] G. Park, F. P. Gabbai, Journal of the American Chemical Society 2021,143,

12494–12498.

[168] B. Bankiewicz, P. Matczak, M. Palusiak, The Journal of Physical Chemistry A

2012,116, 452–459.

[169] M. Jansen, Chemical Society Reviews 2008,37, 1826–1835.

[170] A. L. Jesus, J. Redinha, The Journal of Physical Chemistry A 2011,115, 14069–

14077.

[171] H. Schneider, A. D. Boese, J. M. Weber, The Journal of chemical physics 2005,

123, 084307.

[172] D.-Y. Wu, S. Duan, X.-M. Liu, Y.-C. Xu, Y.-X. Jiang, B. Ren, X. Xu, S. Lin,

Z.-Q. Tian, The Journal of Physical Chemistry A 2008,112, 1313–1321.

[173] E. Kryachko, F. Remacle, The Journal of chemical physics 2007,127, 194305.

[174] E. S. Kryachko, F. Remacle in Topics in the Theory of Chemical and Physical

Systems, Springer, 2007, pp. 161–191.

[175] E. Kryachko, A. Karpfen, F. Remacle, The Journal of Physical Chemistry A

2005,109, 7309–7318.

[176] X. Wu, K. Tan, Z. Tang, X. Lu, Physical Chemistry Chemical Physics 2014,16,

4771–4777.

[177] G.-J. Cao, H.-G. Xu, R.-Z. Li, W. Zheng, The Journal of chemical physics 2012,

136, 014305.

[178] A. Z. Msezane, Z. Felfli, K. Suggs, A. Tesfamichael, X.-Q. Wang, Gold Bulletin

2012,45, 127–135.

[179] H. Darmandeh, J. L¨offler, N. V. Tzouras, B. Dereli, T. Scherpf, K.-S. Feichtner, S.

Vanden Broeck, K. Van Hecke, M. Saab, C. S. Cazin, et al., Angewandte Chemie

2021,133, 21182–21192.

222

Bibliography

[180] S. P. Dubey, M. Lahtinen, M. Sillanp¨a¨a, Process Biochemistry 2010,45, 1065–

1071.

[181] A. Jafarizad, K. Safaee, S. Gharibian, Y. Omidi, D. Ekinci, Procedia Materials

Science 2015,11, 224–230.

[182] A. K. Mittal, Y. Chisti, U. C. Banerjee, Biotechnology advances 2013,31, 346–

356.

[183] Y. Luo, H. Ma, S. Zhang, D. Zheng, P. Che, X. Liu, M. Zhang, J. Gao, J. Xu,

Journal of the American Chemical Society 2020,142, 6085–6092.

[184] Y. Luo, H. Ma, Y. Sun, P. Che, X. Nie, T. Wang, J. Xu, The Journal of Physical

Chemistry A 2018,122, 843–848.

[185] X. Wu, L. Senapati, S. Nayak, A. Selloni, M. Hajaligol, The Journal of chemical

physics 2002,117, 4010–4015.

[186] L. C. Allen, Journal of the American Chemical Society 1989,111, 9003–9014.

[187] Z. Qin, R. Cong, X. Wu, Z. Liu, H. Xie, Z. Tang, L. Jiang, H. Fan, The Journal

of Chemical Physics 2013,139, 034315.

[188] D. Schmitz, V. A. Shubert, T. Betz, M. Schnell, Frontiers in chemistry 2015,3,

15.

[189] R. J. Lavrich, R. L. Rhea, J. W. McCargar, M. J. Tubergen, Journal of molecular

spectroscopy 2000,199, 138–143.

[190] S. S. Batsanov, Inorganic materials 2001,37, 871–885.

[191] J. P. Lommerse, S. L. Price, R. Taylor, Journal of computational chemistry 1997,

18, 757–774.

[192] J. Demaison, M. Herman, J. Li´evin, International Reviews in Physical Chemistry

2007,26, 391–420.

[193] R. F. Bader, T. Nguyen-Dang in Advances in Quantum Chemistry,Vol. 14, El-

sevier, 1981, pp. 63–124.

[194] S. Shahbazian, Chemistry–A European Journal 2018,24, 5401–5405.

[195] T. Shimanouchi, H. Matsuura, Y. Ogawa, I. Harada, Journal of physical and

chemical reference data 1978,7, 1323–1444.

[196] T. Tsuneda, J.-W. Song, S. Suzuki, K. Hirao, The Journal of chemical physics

2010,133, 174101.

[197] W. Richards, International Journal of Mass Spectrometry and Ion Physics 1969,

2, 419–424.

[198] A. O. Hernandez-Castillo, J. Bischoff, J. H. Lee, J. Langenhan, M. Karra, G.

Meijer, S. Eibenberger-Arias, Physical Chemistry Chemical Physics 2021,23,

7048–7056.

[199] A. Bouchet, J. Altn¨oder, M. Broquier, A. Zehnacker, Journal of Molecular Struc-

ture 2014,1076, 344–351.

223

Bibliography

[200] J. P. Merrick, D. Moran, L. Radom, The Journal of Physical Chemistry A 2007,

111, 11683–11700.

[201] T. M. Ramond, G. E. Davico, R. L. Schwartz, W. C. Lineberger, The Journal of

Chemical Physics 2000,112, 1158–1169.

[202] A. F. Ordonez, O. Smirnova, Physical Review A 2018,98, 063428.

[203] P. Weis, P. R. Kemper, M. T. Bowers, S. S. Xantheas, Journal of the American

Chemical Society 1999,121, DOI 10.1021/ja9842161.

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Acknowledgements

I express my gratitude to my colleagues, friends, and family without whom this thesis

and the accompanying research would not have been possible.

First and foremost, I thank my group leader, Andr´e Fielicke, who not only proposed

this research topic but also provided guidance throughout my entire journey as a Ph.D.

student. I extend my appreciation to Otto Dopfer and Gerard Meijer, who enabled my

scientific career at the TU Berlin and FHI and also were there for help and advise.

Special recognition is due to fellow group members David Yubero Valdivielso, Sascha

Schaller, Mallory Green, and Viktoria Brandt. Besides research our discussion topics

also extended to the simple pleasures in life, such as dogs and cats.

I am grateful to Wolfgang Erlebach, Henrik Haak, Uwe Hoppe, Sebastian Kray, Klaus

Peter Vogelgesang (KPV), the workshop and the E-Lab of the FHI, whose invaluable

contributions were indispensable for the essential designs and updates to the experiment.

My thanks is extended to Jes´us R´ıos and Xiangyue Liu, who got me started on DFT

calculations, which played an important role for this thesis.

I also thank my (former) coworkers from the FHI and TU: Johannes Bischoff, Bruno

Credidio, Sandra Eibenberger-Arias, Marko F¨orstel, Sandy Gewinner, Nadia Gonzalez

Rodriguez, Karin Grassow, Alan G¨unther, Uwe Hergenhahn, Manuela Misch, Pablo

Nieto, Evely Prohn, Christian Schewe, Stefan Schlichting, Wieland Sch¨ollkopf, Johannes

Seifert, Russel Thomas, America Torres, Florian Trinter, Bernd Winter, Sidney Wright

and many more for interesting discussions and fun activities.

Appreciation is extended to our external collaborators, including Christiane Koch and

V´ıt Svoboda, who initiated first calculations in the realm of anion PECD. I also have

to mention C. William McCurdy, whom I had the privilege of meeting at the Gordon

Research Conference 2018. He recommended a paper, which infused renewed hope during

a time when doubts first emerged about the feasibility of our anion PECD experiment.

Last but certainly not least, I express my gratitude to my friends for countless

adventures in board games, quizzes and bouldering. I reserve special thanks for

my boyfriend, Max Heimel, and my parents, Sabine and Klemens Triptow, whose

unwavering support took many forms.

To each and every one of you, whether explicitly mentioned or not, I extend a

sincere thank you for contributing to a period of my life that was both enriching and

enlightening.

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