Document [original]

Marija Semialjac · Dissertation

Computational Studies on

the Rearrangement Reactions

of Some Biologically Relevant Radicals

von Diplom-Chemikerin

Marija Semialjac

Von der Fakultät II

-Mathematik und Naturwissenschaften-

der Technischen Universität Berlin

zur Erlangung des akademischen Grades

Doktor der Naturwissenschaften

-Dr. rer. nat.-

genehmigte Dissertation

Promotionsausschuss:

Vorsitzender: Prof. Dr. rer. nat. Jörn Müller

Berichter: Prof. Dr. rer. nat. Dr. h.c. mult. Helmut Schwarz

Prof. Dr. rer. nat. Karola Rück-Braun

Tag der mündlichen Prüfung: 2. März 2004

Berlin 2004

D 83

mami i tati

(to my parents)

VII

Zusammenfassung

Semialjac, Marija: Computational Studies on the Rearrangement Reactions of Some

Biologically Relevant Radicals

In der vorliegenden Arbeit sind intramolekulare Umlagerungen von biologisch

wichtigen Radikalen mit Hilfe von theoretischen Methoden untersucht worden.

(I) Die Ionisierung von Valeramid und die sich daran anschließende Umlagerung

bzw. Fragmentierung des Radikalkations wurden mit quantenchemischen Methoden

untersucht. Die energetisch bevorzugte Umlagerung umfasst zunächst eine γ-C–H

Bindungsaktivierung mit anschließender McLafferty-Umlagerung. Die anderen energetisch

tiefliegenden Kanäle beginnen mit einer β-C–H und δ-C–H Bindungsaktivierung und

führen zu spezifischen Umlagerungen, die ebenfalls im Detail analysiert worden sind.

Trotz vieler Übereinstimmungen zwischen den theoretischen und experimentellen

Ergebnissen, konnten statische Rechnungen keine Erklärung für den ungewöhnlichen

Temperatureffekt des Dissoziationskanals des Valeramid-Radikalkations liefern, der in

massenspektrometrischen Experimenten festgestellt wurde. Deswegen wurden

molekulardynamische Rechnungen nach Car-Parrinello durchgeführt, und zwei

Erklärungsmöglichkeiten für den ungewöhnlichen Temperatureffekt konnten

vorgeschlagen werden.

(II) Die Umlagerung von 2-Aminoethanol, die von Coenzym B12-abhängiger

Ethanolamin-Ammonia-Lyase katalysiert wird, ist mit theoretischen Methoden untersucht

worden. Zwei Hauptumlagerungswege, die über freie Radikale verlaufen, wurden

detailliert analysiert, und nur die direkte Migration der protonierten Aminogruppe und die

direkte Eliminierung des Ammoniumions haben sich als mögliche Wege der 2-

Aminoethanol-Deaminierung herausgestellt. Der Einfluss des aktiven Zentrums des

Enzyms auf die Energetik der Umlagerung wurde ebenfalls untersucht, wobei die

Wechselwirkung zwischen dem Substrat und einigen Aminosäuren (Asp/Glu and His)

modelliert wurde. Unabhängig von der Natur des die NH2-Gruppe protonierenden

Moleküls, ist die intramolekulare Migration der NH3-Gruppe energetisch günstiger als die

Eliminierung von NH4+. Partielle Protonierung wie auch eine partielle Deprotonierung der

OH-Gruppe des Substrats verlaufen „katalytisch“, da alle berechneten

Aktivierungsenthalpien niedriger sind als die für die Umlagerung des „freien“ Substrats.

Trotzdem überschreiten sie die Aktivierungsenthalpie des geschwindigkeitsbestimmenden

Schrittes (d.h. die Wasserstoffabstraktion aus 5’-Deoxyadenosin durch das

Produktradikal). Nur im Fall eines synergistischen Zusammenspiels von partieller

Protonierung der NH2-Gruppe und partieller Deprotonierung der OH-Gruppe mit den zwei

möglichen katalytischen Hilfsgruppen (Asp/Glu und His) ist die Aktivierungsentalpie

kompatibel mit den experimentellen Ergebnissen. Ein solches synergistisches

Zusammenspiel von zwei katalytischen Gruppen ist in dem physiologisch realistischen pH-

Bereich 6 – 9.5 möglich. Im Gegensatz zur oben genannten Umlagerungsreaktion ist für

die die Gesamtreaktion einleitende Wasserstoffabspaltung aus 2-Aminoethanol durch das

5’-Deoxyadenosylradikal bereits eine partielle Protonierung ausreichend, um die

Aktivationsbarriere genügend abzusenken.

Abstract

Semialjac, Marija: Computational Studies on the Rearrangement Reactions of Some

Biologically Relevant Radicals

Methods of computational chemistry are used to investigate rearrangement reaction

of biologically relevant radicals:

(I) The ionization of valeramide, its subsequent rearrangements and further

fragmentations of the radical cation are studied by quantum-chemical methods. The

energetically preferred rearrangement route involves initial γ-C–H bond activation that

proceeds into the McLafferty rearrangement. Other, low-lying channels commence via β-

C–H and δ-C–H bond activations, respectively, leading to specific fragmentation reactions,

which are analyzed in detail. Even though these theoretical results agree nicely with the

experimental data in many respects, they do not provide a rationalization for the unusual

temperature effect on the dissociation pattern of ionized valeramide as observed in mass

spectrometric experiments. Therefore, Car-Parrinello molecular dynamics studies of

neutral and ionized valeramide were performed, which have provided two rationals for the

puzzling experimental results.

(II) The rearrangement of 2-aminoethanol as catalyzed by coenzyme B12 dependent

ethanolamine ammonia lyase is investigated by computational means employing DFT and

ab initio molecular orbital theory. Two major types of rearrangements involving free

radical intermediates as well as their protonated forms are discussed in detail. Only the

direct migration of the protonated amine group and the direct loss of an ammonium ion

represent feasible pathways of 2-aminoethanol deamination as catalyzed by the enzyme.

Further, the influence of the enzyme’s active site on the rearrangement barrier is

investigated, in that the interactions of the substrate with conceivable amino acids

(Asp/Glu and His) are considered. Irrespective of the nature of the protonating species at

the amino group of the substrate, intramolecular migration of the NH3 group is

energetically less demanding than elimination of NH4+. The partial protonation as well as

the partial deprotonation of the substrate’s OH-group was shown to act catalytically

because all computed activation enthalpies are lower than the barrier computed for the

rearrangement of the “free” substrate; however, they exceed the activation enthalpy for the

rate determining step, i.e. the hydrogen abstraction from 5’-deoxyadenosine by the product

radical. Only for the synergistic interplay of partial protonation of the NH2 group and

partial deprotonation of the OH group by the two conceivable catalytic auxiliaries Asp/Glu

and His, the activation enthalpy is compatible with the experimental data. This synergistic

action of the two catalytic groups is expected to take place in a physiologically realistic pH

range of 6 – 9.5. In contrast to the rearrangement reactions, where the synergistic effects of

two auxiliaries are essential to pull the barrier below the upper limit, for the initial

hydrogen abstraction from 2-aminoethanol by the 5’-deoxyadenosyl radical only a partial

protonation of the substrate suffices.

Acknowledgments

First of all I would like to thank my supervisor, Prof. Dr. h.c. mult. Helmut Schwarz,

for giving me the opportunity to do my Ph.D. in his group. I want to especially thank him

for the independence in choosing my own subject of research, as well as for many fruitful

discussions, which greatly contributed to my scientific work. I am as well grateful to Prof.

Dr. Karola Rück-Braun for being the second examiner.

The Schering Research Foundation is gratefully acknowledged for a fellowship and the

Konrad-Zuse Zentrum for the generous allocation of computer time.

In addition, I would like to thank Prof. Michele Parrinello (CSCS, Switzerland) for the

opportunity to learn the Car-Parrinello molecular dynamics technique in his group and

Dr. Daniel Aktah who introduced me to the CPMD method.

My thanks are due to Dr. Detlef Schröder for his support and many useful scientific

discussions. I am very grateful to Dipl.-Chem. Jessica Loos, Dipl.-Chem. Claudia Trage

and M.Sc. Mark Fitzgerald for their proofreading of this thesis. Special thanks go to Dipl.-

Chem. Jessica Loos and Dr. Detlef Schröder for performing numerous mass-spectrometric

experiments on valeramide that actually inspired my further theoretical investigations. Dr.

Thomas Weiske's maintenance of the windows-computer systems is gratefully appreciated,

as well as Dr. Martin Diefenbach’s help with the Linux computers. All other members of

the group I want to thank for making my graduate studies a real pleasure.

Last, but not least, I would like to thank my parents and Christian for all one can think

of.

XIII

TABLE OF CONTENTS

1. INTRODUCTION.............................................................................................................................................1

2. THEORETICAL APPROACH........................................................................................................................5

2.1. QUANTUM-CHEMICAL METHODS ..................................................................................................................5

2.1.1. The Schrödinger Equation in the Born-Oppenheimer Approximation ..................................................................5

2.1.2. Hartree-Fock Self-Consistent Field ........................................................................................................................7

2.1.3. Molecular Orbitals..................................................................................................................................................9

2.1.4. Electron Correlation Methods...............................................................................................................................10

2.2. DENSITY FUNCTIONAL THEORY .................................................................................................................12

2.2.1. The Hohenberg-Kohn Theorem............................................................................................................................12

2.2.2. The Kohn-Sham Equations...................................................................................................................................12

2.2.3. Local Density Approximation (LDA)...................................................................................................................14

2.2.4. Generalized Gradient Approximation (GGA).......................................................................................................14

2.3. CAR-PARRINELLO MOLECULAR DYNAMICS ...............................................................................................15

3. THEORETICAL EXPLORATION OF THE VALERAMIDE POTENTIAL-ENERGY SURFACE....21

3.1. BACKGROUND OF THE INVESTIGATION .......................................................................................................21

3.2. SECTOR MASS SPECTROMETRIC AND PHOTOIONIZATION EXPERIMENTS ......................................................21

3.3. COMPUTATIONAL METHODS .......................................................................................................................23

3.4. COMPUTATIONAL ACCURACY .....................................................................................................................24

3.5. CONFORMATIONAL ANALYSIS OF NEUTRAL AND IONIZED VALERAMIDE.....................................................26

3.6. ADIABATIC AND VERTICAL IONIZATION OF VALERAMIDE ...........................................................................27

3.7. UNIMOLECULAR DISSOCIATIONS OF IONIZED VALERAMIDE ........................................................................29

3.7.1. γ-C–H Bond Activation (C3-route) .......................................................................................................................30

3.7.2. δ-C–H Bond Activation (C2-route).......................................................................................................................33

3.7.3. β-C–H Bond Activation (C1-route).......................................................................................................................36

3.7.4. α-C–H Bond Activation (keto/enol tautomerism) ................................................................................................36

3.7.5. Exit Channels........................................................................................................................................................37

3.8. COMPARISON WITH LITERATURE THERMOCHEMISTRY ................................................................................40

3.9. IMPLICATIONS FOR THE FRAGMENTATION BEHAVIOR OF IONIZED VALERAMIDE .........................................41

3.10. CONCLUSIONS...........................................................................................................................................42

4. TEMPERATURE EFFECT ON THE DISSOCIATION PATTERN OF IONIZED VALERAMIDE ...44

4.1. AN UNPRECEDENTED TEMPERATURE EFFECT ON THE C3/C2 BRANCHING RATIO..........................................44

4.2. RATIONALIZATION OF THE TEMPERATURE EFFECT ON THE DISSOCIATION PATTERN:

AR – PARRINELLO MOLECULAR DYNAMICS STUDY ................................................................................47

4.3. COMPUTATIONAL METHODS .......................................................................................................................48

4.4. NEUTRAL VALERAMIDE..............................................................................................................................49

4.5. VALERAMIDE RADICAL CATION .................................................................................................................52

4.5.1. Simulations at 300 K ............................................................................................................................................52

XIV

4.5.2. Simulations at 500 K........................................................................................................................................... 57

4.6. CONCLUSIONS ............................................................................................................................................ 60

5. REARRANGEMENT OF AMINOETHANOL AS CATALYZED BY THE VITAMIN

12-DEPENDENT ETHANOLAMINE AMMONIA LYASE.....................................................................65

5.1. MIGRATION VS. ELIMINATION OF THE (PROTONATED) AMINO GROUP......................................................... 65

5.2. COMPUTATIONAL METHODS....................................................................................................................... 67

5.3. AMINOETHANOL......................................................................................................................................... 69

5.4. INTRAMOLECULAR MIGRATION .................................................................................................................. 71

5.4.1. Dissociation-association Mechanism................................................................................................................... 72

5.4.2. Sequential Intramolecular Isomerizations............................................................................................................ 73

5.4.3. One-step Migration of NH2/NH3.......................................................................................................................... 74

5.5. DISSOCIATION PATHWAYS.......................................................................................................................... 75

5.5.1. Elimination of the NHx (x = 2, 3) Group as the Initial Step................................................................................. 76

5.5.2. O-H Bond Cleavage as the Initial Step ................................................................................................................ 77

5.5.3. Direct Ammonia/Ammonium Eliminations......................................................................................................... 77

5.6. FORMATION OF ETHANAL ........................................................................................................................... 79

5.7. REACTION ENTHALPIES – A COMPARISON OF CALCULATED AND EXPERIMENTAL VALUES.......................... 81

5.7. SUMMARY AND CONCLUSIONS................................................................................................................... 82

6. HIS AND ASP/GLU ACTING SIMULTANEOUSLY AS CATALYTIC AUXILIARIES.......................84

6.1. COMPUTATIONAL METHODS....................................................................................................................... 86

6.2. MIGRATION VS. ELIMINATION .................................................................................................................... 87

6.2.1. Hydroxonium and Ammonium Ions as Protonating Groups................................................................................ 87

6.2.2. Active Site – What is the Most Probable pH?...................................................................................................... 90

6.2.3. His Serving as a Proton Donor............................................................................................................................. 92

6.2.4. Asp/Glu Serving as Proton Donors...................................................................................................................... 94

6.2.5. Résumé............................................................................................................................................................... 97

6.3. INFLUENCE OF THE OH GROUP CONFORMATION ON THE MIGRATORY APTITUDE...................................... 98

6.4. ACETIC ACID AND IMIDAZOLE – MORE RELIABLE MODEL SYSTEMS FOR ASP/GLU AND HIS ................... 102

6.5. PULL MECHANISM.................................................................................................................................... 104

6.6. SYNERGISTIC ACTION OF TWO CATALYTIC AUXILIARIES ........................................................................ 107

6.7. SUMMARY AND CONCLUSIONS................................................................................................................. 110

7. A HYDROGEN ABSTRACTION FROM 2-AMINOETHANOL BY A MODEL SYSTEM FOR

THE 5’-DEOXYADENOSYL RADICAL...................................................................................................113

7.1. COMPUTATIONAL METHODS..................................................................................................................... 115

7.2. HYDROGEN ABSTRACTION SCENARIOS FROM AMINOETHANOL BY 1,5-DIDEOXYRIBOSE-5-YL RADICAL... 117

7.2.1. Non-protonated Substrate.............................................................................................................................. 119

7.2.2. Fully Protonated Substrate ............................................................................................................................ 120

7.2.3. Partially Protonated Substrate....................................................................................................................... 122

7.2.4. Substrate Captured by Two Amino Acids from the Active Site.............................................................. 123

7.3. CONCLUSIONS...........................................................................................................................................125

8. CONCLUSIONS AND OUTLOOK............................................................................................................. 127

9. SUPPORTING MATERIAL........................................................................................................................ 131

APPENDIX I......................................................................................................................................................131

APPENDIX II ....................................................................................................................................................133

APPENDIX III...................................................................................................................................................140

10. REFERENCES AND NOTES.................................................................................................................... 141

PUBLICATION INDEX ..............................................................................................................................155

CURRICULUM VITAE............................................................................................................................... 157

Introduction 1

1. Introduction

Understanding the properties and functions of important biochemical species,

ranging from small biological signaling agents up to enzymes as well as the processes in

which these are involved, has been for a long time of great interest for the scientific

community. The last couple of decades brought rapid methodological improvements in the

ability to identify, isolate and characterize biological molecules resulting eventually in one

of the most fascinating discoveries, i.e. the elucidation of the human genome. However,

despite fast developments of the experimental techniques, many biologically relevant

problems are very difficult if not impossible to investigate only by experimental means

because of short life-times and/or high reactivities of the often elusive intermediates,

especially in the case of the elucidation of detailed mechanisms of the enzymatic reactions.

Recently, theoretical/computational chemistry has undergone great expansion owing to the

development of more powerful computers as well as of new theoretical methods and

algorithms with the consequence that computational methods present a welcome and useful

complement to experiment, and in most of the cases this information is provided at much

lower cost. Quite clearly, it is the synergy between theory and experiment that brings us

closer in answering important (bio)chemical questions.

In this Thesis computational methods were employed in order to investigate some

biologically relevant radicals and processes in which these species are involved. After a

brief presentation of the theoretical methods used, in the first part of the thesis, we will

deal with valeramide, which presents a model system for the investigation of higher amides

(and peptides). The second part is dedicated to an interesting enzyme, the vitamin B12

dependent ethanolamine ammonia lyase, and its catalytic activity in a seemingly simple

rearrangement process.

The interest in valeramide is based on the fact that this molecule belongs to an

important class of compounds, i.e. amides, and further, being a relatively small model

system, it enables extensive computational investigation at relatively high levels of theory.

The presence of the -CO-NH- bond in many molecules of biological relevance

makes amides a group of compounds of paramount importance for living organisms.

Further, recent studies have shown that primary fatty acid amides constitute a novel class

of mammalian hormones and neuromodulators.1 In particular, oleamide (cis-9-

2 Introduction

octadeceneamide) induces physiological sleep upon intravenous injection,2 potentiates

serotonin receptor subtypes,3 and inhibits gap cell communication.4 It is clear that fatty

acid amides play a yet unknown, but important role in normal neurological processes and

therefore, abnormal levels of fatty acid amides can be diagnostic for those diseases.

Besides oleamide, several other fatty acid amides have been shown to exhibit hormon-like

activity.5

It is well-known that, as reactive species, free radicals interact readily with many

physiologically important substances in the human body, resulting in cell damage and

hence various diseases.6 Lipids of biological membranes, especially those from the brain

cells, contain easily oxidazable polyunsaturated fatty acids, and thus are particularly

affected. Moreover, free radicals are implicated in the aging process as well as in some

severe afflictions such as the Alzheimer, the Parkinson disease, arthritis, myocardial

infarction, artheriosclerosis, and cancer.7 Because of the cellular damage caused by the free

radical impact, many substances have been studied to uncover details of the radical

scavenging properties, and some amides were shown to be successful in this sense as well.

By varying both the acid and amine part of the amides, for example chroman amide, has

been synthesized and its radical-scavenging abilities have been found to make it one of the

most potent compounds.8

The elucidation of questions concerning the reaction mechanisms of amide

rearrangements upon chemical activation and electron transfer might hopefully lead to a

better understanding of biological systems. As a result of radiation or oxidative damage, an

intramolecular hydrogen atom transfer occurs in peptide and in protein radicals.9 The

investigation of rearrangements of smaller amides (e.g. valeramide) may help to uncover

some of the interesting molecular features and thus aid in understanding some of the

processes that result in serious degenerations. In this thesis the rearrangement pathways of

valeramide radical cation have been investigated by theoretical means and the results are

presented in Chapters 3 and 4.

Another interesting system, which also forms a subject of this Thesis, is

ethanolamine ammonia lyase; its catalytic activity is discussed in detail in Chapters 5, 6

and 7. Ethanolamine ammonia lyase is a coenzyme B12 dependent enzyme that catalyzes

the rearrangement of 2-aminethanol into ethanal and ammonia. Even though this enzyme

can be found only in bacteria, because of the pronounced structural and functional

similarities between all coenzyme B12 dependent enzymes, the insight gained by studying

Introduction 3

this particular system might be useful in explaining the action of other coenzyme B12

dependent enzymes as well. The specific catalytic activity of these enzymes is due to the

presence of a cofactor common to all of them, i.e. the coenzyme B12.

Coenzyme B12 is a naturally occurring organometallic compound that contains a

unique Co-C σ-bond, and it serves as one of the most important cofactors for enzymatic

radical reactions. Since Barker’s discovery in 1958 of the light sensitive coenzyme form of

the vitamin B12 related corrinoid for the interconvesion of glutamate into 3-

methylaspartate,10 coenzyme B12 has fascinated many scientists in various research fields

by its peculiar function that itself is based on its particular structure (Figure 1.1).

The paradigm of action of B12

dependent enzymes was put forth in the 60-

ties,11 and about 10 enzymes requiring

coenzyme B12 were reported to catalyze

carbon skeleton rearrangements, heteroatom

eliminations and intramolecular amino group

migrations. From biochemical studies on

ethanolamine ammonia lyase12 and diol

dehydrase13 a minimal mechanism of action

was established, which has now been

accepted as a general mechanism for other

B12 dependent enzymes that catalyze

rearrangement reactions, and in which a

hydrogen atom exchanges place with a

moiety X of the substrate in a formal

dyotropic rearrangement (Scheme 1.1).

However, most of the essential details

concerning the enzymatic catalysis remained

unclear because the tree-dimensional

structures of B12 dependent enzymes were not available until recently, when for some of

them the X-ray structure has been determined. Nevertheless, many questions concerning

catalysis and the role of the coenzyme B12 remain still open, e.g. how the enzymes form

radicals in the active site, and in which way they control highly reactive species like

radicals in the active site. These questions are essential from the perspective of the

ure 1.1. Coenz

me B12.

4 Introduction

enzymatic mechanism not only for the coenzyme B12 dependent enzymes but as well for all

other enzymes that catalyze reactions in which radicals are involved.

HC CH

CoA

HC CH

X R1R2Substrate Enzyme

CO-SCoA H COOH Methylmalonyl-CoA Methylmalonyl-CoA mutase

C(=CH2)COOH H COOH 2-Methyleneglutarate Methyleneglutarate mutase

CH(NH2)COOH H COOH (S)-Glutamate Glutamate mutase

NH2OH H 2-Aminoethanol Ethanolamine ammonia lyase

OH CH3OH Propane-1,2-diol Diol dehydratase

OH CH2OH OH Glycerol Glycerol dehydratase

Scheme 1.1. Rearrangement reactions catalyzed by the coenzyme B12 dependent enzymes.

Theoretical approach 5

2. Theoretical Approach

2.1. Quantum-chemical Methods14

Quantum chemical methods are based on the postulates of Quantum Mechanics,

according to which a system is fully described by a wavefunction that can be found by

solving the Schrödinger equation. This equation relates the stationary states of the system

and their energies to the Hamiltonian operator, which can be viewed as a recipe for

obtaining the energy associated with a wavefunction describing the positions of the nuclei

and electrons in the system. However, in practice the Schrödinger equation cannot be

solved exactly. Already for a system that contains only 3 particles approximations have to

be made in order to make the method applicable. Nevertheless, the approach is called "ab

initio" since it makes no use of empirical information, except for the fundamental constants

of nature such as the mass of an electron, Planck's constant, etc. In spite of the necessary

approximations, ab initio theory has the conceptual advantage of generality, and the

practical advantage that its successes, limitations and failures are predictable.

The major disadvantage of ab initio quantum chemistry is the heavy demand on

computer power. Therefore, further approximations have been applied, which led to a

number of semi-empirical quantum chemical methods that can be applied to larger

systems. However, compared with ab initio calculations their reliability is lower and their

applicability is limited by the requirement for empirical parameters.

2.1.1. The Schrödinger Equation in the Born-Oppenheimer Approximation

The energies and wavefunctions of stationary states of a system are given by the

solutions of the Schrödinger Equation, Eq. (2.1):

Ψ=E

Hne

ne ,

ˆ (2. 1)

A wavefunction Ψ is one of the solutions of the eigenvalue equation and depends on the

coordinates of the electrons and the nuclei. Ĥ is the Hamiltonian operator, which gives the

kinetic and potential energies of a system consisting of atomic nuclei and electrons. The

6 Theoretical approach

Hamiltonian is composed of three parts (see Eq. (2.2)): the kinetic energy of the nuclei, the

kinetic energy of the electrons, and the potential energy of nuclei and electrons.

TTH ne

en ˆ

ˆˆˆ ,

= (2. 2)

Two approximations are commonly made:

(i) time-independence, where only states stationary in time are concerned and relativistic

effects are neglected. This is warranted unless the velocity of the electrons approaches the

speed of light, which is the case only in heavy atoms.

(ii) Born-Oppenheimer approximation; which makes a separation of the motion of nuclei

and electrons. The Born-Oppenheimer approximation implies the separation of nuclear and

electronic wavefunctions, where the total wavefunction is presented as a product of the two

parts, Eq. (2.3):

ΨΨ =n

, (2. 3)

The idea behind this approximation is that the electrons, being much lighter than the

nuclei, can easily follow the nuclear motion. Therefore, the electronic wavefunction

e can

be obtained by solving the electronic Schrödinger equation (2.4):

)()()()(

ˆrR

Henen e

= (2. 4)

which contains positions of the nuclei, however not as variables but as parameters. The

electronic Hamiltonian contains three terms: kinetic energy, electrostatic interaction

between electrons and nuclei, and electrostatic repulsion between electrons, Eq. (2.5).

∑∑∑∑∆<===

−

−−= n

ji ij

AiA

111

ˆ (2. 5)

The total energy in the Born-Oppenheimer model is obtained by adding the nuclear

repulsion energy to the electronic energy, Eq. (2.6):

Theoretical approach 7

netot += (2. 6)

where

∑

<−

BA BA

nRR

E (2. 7)

The total energy defines a potential energy hypersurface, which can be used to

subsequently solve the Schrödinger equation for the nuclear motion, Eq. (2.8):

]

[

)()()(

ˆRRR

Tnnn

Φ=+

(2. 8)

2.1.2. Hartree-Fock Self-Consistent Field

The electronic Hamiltonian contains two terms that act on one electron at a time:

the kinetic energy and the electron-nucleus attraction (Eq. (2.9)), and a term that describes

the pairwise repulsion of electrons (Eq. (2.10)):

∑∑∑∆

∑===−

−−== n

AiA

irR

Hi111

1ˆ

ˆ (2. 9)

∑∑ <<

== n

ji ij

ji r

Hij

2ˆ

ˆ (2. 10)

The latter depends on the coordinates of two electrons at the same time, and has turned out

to be a practical computational bottleneck, which can be overcome only for very small

systems. To avoid this problem the independent particle approximation is introduced, in

which the interaction of each electron with all the others is treated in an average way, Eq.

(2.11).

∑∑ ==

ij V

ˆ2

2 (2. 11)

The Schrödinger equation, which initially depended on the coordinates χ (representing

spatial and spin coordinates) of all electrons, can be reduced to a set of equations (Hartree-

Fock equations, Eqs. (2.12) and (2.13)):

8 Theoretical approach

()

()()

∑=+

ixxx

xxx

VH nn

1,...,,...,

ˆˆ 2121

ψψ

(2. 12)

(

)

()

(

)

(

)

VH i

ii 111

1ˆ

ˆˆ

==+ (2. 13)

The wavefunctions

i(x1) present one-electron spin-orbitals. For each electron the potential

due to all other electrons has to be determined, however it is initially unknown. In practice

trial orbitals are used and iteratively modified until a self-consistent solution ("Self-

Consistent Field") is obtained, which is a solution of the Hartree-Fock equations. The

eigenvalues

i are interpreted as orbital energies.

In addition to being a solution of the electronic Schrödinger equation, the

wavefunction must be normalized and must satisfy the Pauli principle. The normalization

condition (Eq. (2.14)) is connected with the interpretation of the wavefunction as a

distribution function, which when integrated over entire space should give a value of one:

∫dx

ψψ

(2. 14)

The Pauli principle states that the wavefunction must change sign when two independent

electronic coordinates are interchanged, Eq. (2.15):

(

)

(

)

xxxxxxxxxx niknki ,...,,...,,...,,,...,,...,,...,, 2121

(2. 15)

An important property of the SCF method is that its solutions satisfy the Variation

Principle (Eq. (2.16)), which states that the expectation value of the energy evaluated with

an inexact wavefunction is always higher than the exact energy:

ψψ

exact

≥

(2. 16)

As a consequence the lowest energy is associated with the best approximate wavefunction

and therefore, the energy minimization is equivalent with the wavefunction optimization.

Theoretical approach 9

A common way of representing the electronic wavefunction is a Slater determinant

(Eq. (2.17)) that contains spin-orbitals (

1), which are dependent on the spatial and spin

coordinates of an electron:

ϕϕϕ

nn n...

2/1−

= (2. 17)

The energies of Slater determinants from a Hartree-Fock calculation are readily expressed

in one- and two-electron integrals and according to this notation ground state energy can be

represented as:

(

[

)

(

)

]

∑−

∑<

+= occ

occ

ijijjjii

Eii

1 (2. 18)

where

()

(

)

dxx

Hii

ϕϕ

ˆ1

1∫

== (2. 19)

( )

() ()

(

)

(

)

dxdxxx

klji lkji 2122

ϕϕϕϕ

∫∫

= (2. 20)

The two-electron integral (ii|jj) describes the repulsion between two electrons each

localized in one orbital (Coulomb integral), while for the (ij|ij) integral (exchange integral)

a classical description cannot be given.

2.1.3. Molecular Orbitals

Molecular orbitals

i are usually represented as a linear combination of atomic

orbitals

ϕµ

(LCAO), Eq. (2.21):

ϕφ µ

µµ

∑

(2. 21)

The expansion of the wavefunction in terms of basis functions leads to a limitation

of the accuracy of the ab initio Hartree-Fock approach only because of the limited number

of basis functions available. The greater the number of basis functions (provided they are

well chosen) the better the wavefunction, consequently, the lower the energy. However, the

10 Theoretical approach

two-electron integrals (Eq. (2.20)) over atomic basis functions give rise to a major practical

problem in the application of the ab initio HF method since a large number of basis

functions is required for a reasonable quality calculation, resulting in a very large number

of two-electron integrals. The limit of an infinite basis set is known as the Hartree-Fock

limit; however, even at the Hartree-Fock limit the obtained energy is still greater than the

exact energy that follows from the Hamiltonian because of the independent particle

approximation that the theory assumes. In order to overcome this shortcoming, as the post

Hartree-Fock methods have been introduced (see further in text).

The basis orbitals used in practical calculations are mostly atom-centered functions

that resemble orbitals of isolated atoms. The radial part of such orbitals is an exponentially

decaying function. Basis orbitals of this type are called Slater-type orbitals (STO; Eq.

(2.22)). However, for practical calculations they have the disadvantage that evaluation of

two-electron integrals involving such functions is time-consuming. Therefore, these

orbitals are approximated by a linear combination of Gaussian basis functions (GTO; Eq.

(2.23)):

ϕϕ

GTO

STO k

∑

≈

(2. 22)

()

rr2

−

= (2. 23)

The functional form of GTO (Gaussian-type orbital) is different from the atomic

orbitals, especially in the vicinity of the nucleus and therefore, a combination of several

GTO's with different exponents α is necessary to give a reasonable basis orbital. The

exponents α and contraction coefficients k can be determined in different ways, e.g. by

fitting to an STO or by optimizing the energy in ab initio calculations on atoms and small

molecules. Once these values are determined, they define a standard basis set.

2.1.4. Electron Correlation Methods

The Hartree-Fock method, even at its limit, has a limitation in accuracy due to the

independent particle approximation that the theory uses, where the instantaneous

correlation of the motions of electrons is neglected. The correlation energy, which is a

Theoretical approach 11

difference between the exact energy (determined by the Hamiltonian) and the HF energy,

may be important in order to obtain chemically relevant answers from computations.

Several approaches were developed in order to account for the correlation energy (post-HF

methods), such as (i) Configuration Interaction (CI), (ii)Møller-Plesset (MP) Perturbation

Theory and (iii) Multi-Configuration SCF (MCSCF or CASSCF).

(i) In the Configuration Interaction (CI) method a linear combination of Slater

determinants is constructed, taking the unoccupied "virtual" orbitals from the SCF-

calculation also into account. The total wavefunction is written as presented in Eq. (2.24):

...

+++= ∑∑

φφφ

lijk

HF cc (2. 24)

In principle, the exact correlation energy can be obtained from a full CI calculation in

which all possible configurations are taken into account. Unfortunately this is not possible

but for the smallest systems only. Moreover, the problem is aggravated when the size of

the basis set is increased on the way towards the Hartree-Fock limit. Thus, the theoretical

limit of the exact (time-independent, non-relativistic) Schrödinger equation cannot be

reached since even for small systems the number of excited configurations is enormously

large. Therefore, a popular way to truncate the CI expansion is to consider only singly and

doubly excited configurations (CI-SD).

(ii) A basic idea behind the Møller-Plesset Perturbation Theory is that the difference

between the Fock operator and the exact Hamiltonian can be considered as a perturbation.

Corrections can be made to any order of the energy (Eq. (2.25)) and the wavefunction (Eq.

(2.26)).

() ( )

(

)

...

321 ++++

HF (2. 25)

() ( )

(

)

...

321 ++++

ΨΨΨ=Ψ HF (2. 26)

The most popular method, MP2, takes into account only a second level of correction.

12 Theoretical approach

(iii) Multiconfiguration SCF (MCSCF) and Complete Active Space SCF (CASSCF) are

methods in which HF-orbitals are optimized simultaneously with a “small” CI. The

MCSCF method requires considerable care in the selection of the basis set and especially

the active space (orbitals). The MCSCF methods can be used to study problems where the

Hartree-Fock method is inappropriate (e.g. for systems with low-lying excited states), or to

generate a good starting wavefunction for a subsequent CI calculation. For processes in

which transitions between potential energy surfaces occur, such as in photochemical

reactions, the MCSCF methods are shown to be essential.

2.2. Density Functional Theory15

Density functional theory (DFT) is a powerful, in principle exact theory, which as a

distinction from quantum chemical methods, is non-interacting and does not yield a

correlated N-body wavefunction. In the Kohn-Sham DFT, the theory is the one-electron

theory and shares many similarities with the Hartree-Fock theory. DFT has come to

prominence over the last decade as a method potentially capable of providing very accurate

results at low computational cost.

2.2.1 The Hohenberg-Kohn Theorem

The Hohenberg-Kohn theorem (2.27) states that if N interacting electrons move in

an external potential Vext, the ground-state electron density n0 minimizes the functional

[] []

() ()

∫

+= dxrrnnFnE Vext (2. 27)

where F is a universal functional of n and the minimum value of the functional E is E0, the

exact ground-state electronic energy.

2.2.2. The Kohn-Sham Equations

Kohn and Sham derived a coupled set of differential equations enabling the ground

state density n0 to be found. F was separated into three distinct parts, so that the functional

E becomes

Theoretical approach 13

()

[]

()

[]

(

)

(

)

()

[]

() ()

∫∫ ∫

−

+= drrrnrndrdr

rnrn

rnrnE V

ET ext

XCS

1 (2. 28)

where TS is defined as the kinetic energy of a non-interacting electron gas with density n,

()

[]

() ()

∑∇

∫

−= N

iii

Sdxrrrn

ψψ

(2. 29)

being not the kinetic energy of the real system. Introducing a normalization constraint on

the electron density from Eq. (2.27) follows:

() ()

[]

()

[]

0=− ∫drrnrnE

(2. 30)

where

()

[]

()

rnE (2. 31)

Equation (2.31) can be rewritten in terms of an effective potential, Veff

()

[]

() ()

=+ r

rn V

eff

S (2. 32)

where

() ()

()

rdr

rr VVV XCexteff ∫+

−

+= '

' (2. 33)

and

() ()

[]

()

VXC

= (2. 34)

To find the ground state energy, E0, and the ground state density, n0, the one

electron Schrödinger equation (Eq.(2.35)) should be solved self-consistently together with

Eq. (2.32) and (2.33) and satisfying that the electron density is equal to the number of

electrons in the system. A self-consistent solution is required due to the dependence of Veff

on n.

() ()

12=

⎟

⎠

⎞

⎜

⎝

⎛−+∇− rr i

ieff

(2. 35)

14 Theoretical approach

The above equations provide a theoretically exact method for finding the ground state

energy of an interacting system provided the form of EXC is known. Unfortunately, the

functional EXC is in general unknown and in electronic structure calculations it is most

commonly approximated within the local density approximation or generalized-gradient

approximation.

2.2.3. Local Density Approximation (LDA)

In the local density approximation (LDA), the value of EXC is approximated by the

exchange-correlation energy of an electron in a homogeneous electron gas of the same

density n(r), i.e.

()

[]

drrnrn

EXC

LDA

XC )())((

∫

(2. 36)

The principle advantage of LDA-DFT over methods such as Hartree-Fock is that

many experimentally relevant physical properties can be determined to a useful level of

accuracy provided that the LDA performs well (correlation effects are well accounted for).

The LDA is often surprisingly accurate for systems with slowly varying charge densities.

However, the method has failed in treating several different cases; e.g. it has a tendency to

favor more homogeneous systems and over-binds molecules and solids. In weakly bonded

systems these errors are exaggerated and bond lengths are too short. The satisfactory

performance of the LDA was shown to be a result of a real-space cancellation of errors in

the LDA exchange and correlation energies.

2.2.4. Generalized Gradient Approximation (GGA)

For systems where the density varies slowly, the LDA tends to perform well.

However, in strongly correlated systems, where an independent particle picture breaks

down, the LDA fails. Further, the LDA does not account for van der Waals bonding, and

gives a very poor description of hydrogen bonding.

An obvious approach to improve the LDA is to include gradient corrections, by

making EXC a functional of the density and its gradient:

Theoretical approach 15

()

[

]

(

)

(

)

(

)

(

)()

∫

∇

∫+= drrnrn

drrnrnrn

EXC

GGA

XC ],[

(2. 37)

where FXC is a correction chosen to satisfy one or several known limits for EXC. Clearly,

there is no unique recipe for FXC, and several dozen functionals have been proposed in the

literature. They do not always represent a systematic improvement over the LDA and

results must be carefully compared against experimental findings. The development of

improved functionals is currently a very active area of research and although incremental

improvements are likely, it is far from clear whether the research will be successful in

providing the substantial increase in accuracy desired.

2.3. Car-Parrinello Molecular Dynamics16

Ab initio molecular dynamics methods, in contrast to the effective force field

methods, allow one to model chemical reactions that involve changes in the bonding in

which electrons play a crucial role. For each molecular dynamics (MD) simulation, in

which electrons are not being treated explicitly, a choice about the nature of the system has

to be made a priori. However, if the bonding in the system changes due to changes in

pressure, temperature or phase, the accuracy of the force-field suffers. In 1985 Car and

Parrinello showed that it was possible to perform a molecular dynamics simulation whilst

calculating the forces within density functional theory. For the first time in the molecular

dynamics calculations electrons were treated explicitly in an ab initio way. The method

proposed by Car and Parrinello works within the Born-Oppenheimer approximation; at any

instant the state of the electronic system can be well described by the electronic ground-

state that is being calculated for the ionic positions at that instant, and it responds

instantaneously to changes in ionic positions.

The Car-Parrinello method makes use of the following classical Lagrangian (Eq.

(2.38)):

}]{},[{

12RE

ML I

ψψψµ

−+= ∑∑ &

&& (2. 38)

16 Theoretical approach

to generate trajectories for the ionic and electronic degrees of freedom via the coupled set

of equations of motion (Eqs. (2.39) and (2.40)):

MCP

=−= ∂

∂}]{},[{

&& (2. 39)

ψµ

∂

−= }]{},[{

&& (2. 40)

where MI and RI are the mass and position, respectively, of atom I, ψi are the Kohn-Sham

orbitals which are allowed to evolve as classical degrees of freedom with inertial

parameters µi, and E is the Kohn-Sham energy functional evaluated for the set of ionic

positions RI and the set of orbitals ψi. The functional derivative of the Kohn-Sham energy

in equation (2.40) is implicitly restricted to variations of {ψi} that preserve orthonormality.

The idea behind the CPMD method is that by putting the electrons to their ground

state at a fixed set of ionic positions and then allowing the ions to move according to

equation (2.39), the electronic orbitals should adiabatically follow the motion of the ions,

performing small oscillations around the electronic ground state. The electronic orbitals

will have a “fictitious” kinetic energy associated with their motion and the fictitious mass

parameter, µi. If µi is small enough, then the motion of the orbitals will be very fast relative

to the motion of the ions. It is generally believed that this motion consists of oscillations

around the ground state and therefore, by choosing for µi a value small enough, one can

ensure that the frequency spectra of the electronic orbitals and the ions are well separated

from one another if an energy gap exists between the occupied and unoccupied Kohn-

Sham orbitals. Within a harmonic approximation, the lowest frequency of oscillation of the

orbitals about the ground state may be written as:

()

⎟

⎠

⎞

⎜

⎝

⎛−

εε

22/1

0 (2. 41)

where εi and εj are the eigenvalues of the highest occupied and the lowest unoccupied

orbitals, respectively. Classical mechanics systems, which are well separated from each

another in frequency, remain energetically isolated from one another. Therefore, by using

for µi a value small enough, the electrons are isolate energetically from the ions. In this

Theoretical approach 17

way it can be ensured that thermalization between electrons and ions does not occur and

consequently, the electrons remain close to the electronic ground state, while the ions

dynamics can be performed at the desired temperature.

I. PART

DISSOCIATION BEHAVIOR OF IONIZED VALERAMIDE

Theoretical exploration of the valeramide potential-energy surface 21

3. Theoretical Exploration of the Valeramide

Potential-Energy Surface∗

3.1. Background of the Investigation

Amides are an important group of compounds for living organisms because of the

-CO-NH- structural motif that can be found in many molecules of biological relevance.

Consequently, there are numbers of publications on experimental and computational

research aiming at the prediction of some of the physical and chemical properties of the

peptide bond.17 Structural studies of small amides aid in a better understanding of peptide

bonds in biological molecules. Therefore, as a model molecule, valeramide, 1, was chosen;

this is a relatively small amide with a chain of only five carbon atoms, which nevertheless

may mimic the behavior of larger amides with respect to intramolecular hydrogen

migrations. The valeramide molecule is small enough to enable both extensive mass-

spectrometric studies as well as adequate computational treatment of the dissociation

process, out of which the McLafferty rearrangement seems the most interesting one. In the

McLafferty rearrangement18,19 an ionized carbonyl group of the substrate with a sufficient

chain length gives rise to specific 1,5-hydrogen transfers followed by β-C–C bond

cleavage affording an alkene and an enol. Thus, valeramide presents an ideal system for

investigation of this important process.20

3.2. Sector Mass Spectrometric and Photoionization Experiments

Unexpectedly large differences between the electron ionization and metastable ion

mass spectra of hexanoic acid and also its amide has been reported by Kreft and

Grützmacher.21 These findings triggered further mass-spectrometric experiments aiming at

a rationalization of the observed discrepancies. The dissociation behavior of ionized

valeramide 1 was investigated by several experimental methods in which the electron

∗ Results discussed in this chapter have been published in: Semialjac, M.; Loos, J.; Schröder, D.; Schwarz, H.

Int. J. Mass Spectrom. 2002, 214, 129.

22 Theoretical exploration of the valeramide potential-energy surface

ionization (EI), photoionization (PI), and metastable ion (MI) mass spectra were

compared.22,23

Scheme 3-1. Dissociation pattern of ionized valeramide 1+•.

Sector mass spectrometry and photoionization experiments provided an internally

consistent mechanistic picture for the unimolecular dissociation of ionized valeramide. The

γ-C–H bond activation according to the McLafferty rearrangement (C3-route)

predominates, while δ-C–H bond activation (C2-route) competes with it quite extensively

(Scheme 3-1). At elevated energies, also β-C–H bond activation (C1-route) as well as

direct C(3)–C(4) bond cleavage occur. The photoionization experiments revealed that the

C2- and C3-routes have rather low thresholds, where occurrence of the latter is observed

even at the photoionization threshold. Almost all experimental results, including several

mechanistic details such as the competition of direct and indirect C2H5• losses, are

consistent within both experimental approaches. Further, the labeling distributions can be

reproduced reasonably well by a kinetic modeling which explicitly includes the

competition of C2- and C3-routes. The most interesting result of the modeling is that the

kinetic isotope effects associated with the initial C–H bond activations are surprisingly

small.

However, the C3/C2 ratio shows pronounced, apparently random variations when

comparing the different kinds of experiments performed. Far beyond the experimental

Theoretical exploration of the valeramide potential-energy surface 23

error margins, the C3/C2 ratios range from almost 1 for the metastable ions formed upon EI

in the sector instrument to about 4 for the metastable ions in the TPEPICO experiments.24

The mechanistic analysis of both the sector-field experiments and the photoionization

studies suggests that this behavior is associated with the uncoupling of these two routes.

3.3. Computational Methods

In order to obtain the actual energetics of the above mentioned competing

processes, a theoretical insight into the behavior of ionized valeramide was desirable.

Most calculations were performed with the GAUSSIAN 98 suite of programs.25

The use of density functional theory (DFT) was a natural choice because of the balance

between accuracy and computational costs.26 The B3LYP functional, which is a HF/DFT

hybrid combining Becke’s three-parameter semiempirical exchange functional (B3)27 with

the Lee-Yang-Parr correlation functional (LYP)28, was used throughout. Geometry

optimizations were performed with Pople’s polarized double-ζ 6-31G* basis set.

In order to characterize the optimized structures, frequency analysis has been

performed at the same level of theory. Minima were characterized by the absence of

imaginary vibrational modes, while the transition structures involved one imaginary

frequency. Reaction pathways have been followed by the intrinsic reaction coordinate

(IRC) calculations at the same level of theory. Because the B3LYP/6-31G* calculations

overestimate force constants, the zero-point energies (ZPEs) obtained at this level were

scaled by 0.9805, which is the average of the factors proposed by Scott/Radom29 and

Wong.30 The scaled ZPEs were used for the conversion of electronic energies to relative

energies at 0 K. In order to get more reliable energetic profiles of the reactions in question,

single point calculations using triple-ζ basis sets with diffuse functions included (6-

311++G**) were performed, and relative energies of the stationary points were calculated

at the B3LYP/6-311++G**//B3LYP/6-31G* level of theory, where the ZPEs calculated

with B3LYP/6-31G* were used in the conversion to relative energies at 0 K.

Further, an initial screening of the conformational space of valeramide was

performed with the MM2 method implemented in the Spartan program.31

24 Theoretical exploration of the valeramide potential-energy surface

3.4. Computational Accuracy

As far as a viable computational approach to the potential-energy surface (PES) of

ionized valeramide is concerned a reasonable compromise has to be reached. Valeramide is

already quite a large molecule for advanced ab initio methods, and moreover, for a proper

description of the distonic ions formed as reaction intermediates the electron correlation

has to be taken into account. Further, valeramide, being neutral or charged, is a rather

flexible system for which a large number of energetically low-lying conformers may

contribute to the chemistry observed at room temperature.

Superimposed to these more general aspect is a specific problem of amides which

concerns the rotation around the C–N bond. Therefore, a brief survey about previous

theoretical studies of amides is warranted. Formamide, the smallest amide, has been widely

studied both experimentally and theoretically. The main interest has been focused on the

planarity of the NH2 group.32 The microwave spectrum of formamide33 is consistent with

an inversion potential for the NH2 group with a very shallow minimum for a non-planar

structure. However, earlier experimental investigations have suggested the presence of a

planar amide unit both in the gas phase and in the solid state of formamide as well as

substituted amides.34 While a large number of theoretical calculations has been carried out

on model amides, the results are controversial.35 Moreover, the solvents present in

biological systems may substantially influence the abundance of non-planar (chiral)

amides.36 Contradictory results have been published for the conformational minima of

acetamide, which can essentially assume three different types of conformations: syn,

perpendicular, and anti, where the terminology proposed by Samdal37 is used. B3LYP/6-

311++G** and B3LYP/cc-pVTZ calculations suggest that the anti-conformer is most

stable. Helgaker et al.38 have tested several computational methods with different basis sets

for the equilibrium structures of small organic molecules. In these tests, the MP2/cc-pVTZ

level of theory gave a very good agreement with the experimentally obtained equilibrium

geometries. However, there is still an open question whether those methods can predict

correct conformational minima and barrier heights as well. Thus, in the case of acetamide

MP2/cc-pVTZ calculations predict a second stable conformational minimum, which is of a

perpendicular form with the torsional angle of 30°. The energy difference between the anti

and perpendicular structures amounts to only 3 cal/mol. Samdal tried and failed to locate

the transition structure (TS) connecting these two conformers with conventional methods

Theoretical exploration of the valeramide potential-energy surface 25

of geometry optimization. For this reason, a calculation at a fixed geometry (torsional

angle of 45°) mimicking the transition structure has been performed and the barrier has

been estimated at about 4 cal/mol. In a conformational study on acetamide, Wong and

Wiberg found the perpendicular conformation to be the most stable one when MP2 and

CISD methods were used.39 In summary, the methods employed so far cannot give a clear

answer whether the anti or perpendicular conformation is the most stable one.

For an extensive ab initio study, valeramide is a relatively large molecule, thereby

imposing some restrictions to the computational approach applicable. Moreover, several

conformers have to be considered, of which each might give rise to particularly favorable

pathways. An appropriate computational description of ionized valeramide and its

rearrangement reactions requires, however, a reasonably solid quantum chemical approach,

which is able to adequately describe closed- and open-shell species, electron

delocalization, hydrogen bonding, and transition structures in particular. In these respects,

density functional theory (DFT) is successful in predicting physical properties of molecular

systems, including hydrogen-bonded species, with an accuracy equal or even better than

obtained by MP2 calculations,40,41 but at much lower computational costs than those for

higher levels of theory.42 The present choice of B3LYP/6-311++G**//B3LYP/6-31G* is

therefore considered as a proper level of theory to gain reliable potential-energy surfaces.

In turn the computations at this level of theory are already quite demanding such that the

potential-energy surface of ionized valeramide cannot be explored exhaustively. Therefore,

the theoretical examination was primarily guided by the mechanistic implications derived

from the experimental studies in conjunction with chemical intuition and plausibility

considerations as far as the choice of low-lying conformations is concerned. Concerning a

description of the distonic ion intermediates, the B3LYP/6-31G* geometries appear to

suffice, since complete geometry optimizations of a few key species at the B3LYP/6-

311++G** level of theory did not show large differences between the two methods neither

in geometrical parameters nor in energetics (see below). Accordingly, full geometry

optimizations of all species were not performed at this level of theory because the quality

of the results would not change while the computational costs would increase considerably.

The computational approach chosen does not ensure that all relevant conformers were

covered; nevertheless, the reasonable agreement between theory and experiment obtained

after all justifies the pragmatic choice of the theoretical approach used herein.

26 Theoretical exploration of the valeramide potential-energy surface

3.5. Conformational Analysis of Neutral and Ionized Valeramide

HH'

H' R

HH'

perpendicular

yn anti

Figure 3-1. Newman projections along the C(1)–C(2) bond of valeramide showing the possible

conformations of the amide group (R = n-C3H7).

As one can infer from the work done so far on formamide and acetamide,

conformational analysis can be quite demanding even for smallest amides. Turning back to

valeramide as the subject of this study, it is clear that here the situation is even more

complex. By analogy to the three leading conformers proposed for acetamide, one can

postulate the existence of seven conformational minima for valeramide (Figure 3-1), which

differ with respect to the orientations of the substitutents at C(1) and C(2). In addition, the

alkyl chain of valeramide may adopt several conformations. In combination with the

different orientations of the amide group, a considerable number of energetically low-lying

conformers evolves. For an initial screening, conformational analysis of valeramide was

performed with the conformational search algorithm of the MM2 force field. More than 70

conformers were obtained within an energy range of only 3 kcal/mol. Accordingly, a

manifold of conformers is expected to be sampled in experimental studies conducted at or

above room temperature. For such a large number of possible conformers, an explicit

consideration of all MM2 structures on the B3LYP level of theory is not practical. Because

of a particular interest in different orientations of the functional group in respect to the rest

of the carbone backbone, only those conformers depicted in Figure 3-1 were fully

optimized at the B3LYP level of theory, while the alkyl backbone was confined to an all-

anti conformation. Interestingly, the most stable conformer obtained in the MM2

calculations (similar to 15) does not even exist on the B3LYP potential energy surface,

which can be attributed to the failure of molecular mechanics to describe hydrogen- and

Theoretical exploration of the valeramide potential-energy surface 27

weak-bond interactions properly. On the B3LYP level of theory, only two different

conformations, 11 and 12 (the perpendicular conformation) were located; the latter is less

stable due to steric repulsion between R and the amino group. Geometry optimizations for

all the other possibilities ended in structure 11, suggesting this conformer as the global

conformational minimum. The failure to locate the other conformations does not explicitly

indicate that these conformers do not exist as minima on the PES of valeramide. Therefore,

a PES scan was performed keeping the dihedral angle

CCCO fixed while freely optimizing

all other parameters. The results of the scan are consistent with structure 11 as the global

minimum (Table 3-1). The energy increase that accompanies the changes in the dihedral

angle can be explained by contributions of at least two factors: (i) steric repulsion between

the alkyl unit R and the amino group (basically hydrogen repulsions), and (ii) stabilization

caused by the interaction of one of the C(2) hydrogens with the pπ-orbital on C(1), which

compensates the positive charge emerging from the polarized bonds to the heteroatom

substituents of C(1). The latter is

most pronounced in the

perpendicular conformations, in

which the interacting hydrogen

atom forms a dihedral angle

HCCO

of ca. 90°, thereby maximizing

orbital overlap. The energetic

preference of this interaction also

explains why only the

perpendicular conformers 11 and

12 exist as minima at the B3LYP

level of theory.

Table 3-1. Energetics derived from a scan of the dihedral

angle

CCCO in neutral valeramidea,b (B3LYP/6-31G*).

Conformerc

CCCObEtotdErele

14 0 -327.15421 0.11

11 30 -327.15439 0.00

16 60 -327.15393 0.29

13 90 -327.15302 0.86

15120 -327.15246 1.21

12150 -327.15224 1.35

17180 -327.15222 1.36

a In these calculations,

CCCO was kept fixed, while all other parameters

were fully optimized. b Specifically, this is the dihedral angle spanned

by the atoms O, C(1), C(2), and C(3). c See Figure 3-1. d Total energies

in Hartree; 1 H = 627.51 kcal/mol. e Energies (in kcal/mol) relative to

the most stable conformer 11.

3.6. Adiabatic and Vertical Ionization of Valeramide

Adiabatic and vertical ionization energies (IEa and IEv) were calculated for the

conformers 11 and 12 of neutral valeramide (Table 3-2). However, geometry optimizations

28 Theoretical exploration of the valeramide potential-energy surface

on the cation-radical PES leads to same cation structure 11+• for both conformers (note that

the indices used for the conformations of neutral and ionized valeramide do not coincide).

The difference between vertical and adiabatic ionization (

∆

IEv/a) is 0.36 eV for conformer

11 and 0.28 eV for conformer 12, indicating that the structural changes upon ionization are

slightly more pronounced in the former. With regard to the experimentally obtained

ionization energy (IE = 9.40 ± 0.03 eV),22,43 the relatively small

∆

IEv/a implies that the

onset for photoionization of valeramide corresponds to adiabatic ionization. Further, the

energy difference of the conformers 11 and 12 is small, such that mixtures of at least these

two conformers are likely to be sampled in the experiments. The calculated energetic

difference of ~1 kcal/mol suggests a ca. 5 : 1 ratio of 11 and 12 at 298 K. Relative to

experiment, one notes a slight underestimation of the adiabatic IEs, which may be

attributed to a general trend of the B3LYP approach in predicting IEs of closed-shell

organic molecules.44,45

Table 3-2. Relative stabilities (Erel in kcal/mol) of valeramide conformers, adiabatic and vertical

ionization energies (IEa and IEv, respectively, in eV)a and their difference

∆

IEv/a (in eV).

Conformer Method Erel IEaIEv

∆

IEv/a

11B3LYP/6-31G*//B3LYP/6-31G* 0.0 8.88 9.24 0.36

B3LYP/6-311++G**//B3LYP/6-31G* 0.0 9.19 9.55 0.36

12B3LYP/6-31G*//B3LYP/6-31G* 1.4 8.82 9.10 0.28

B3LYP/6-311++G**//B3LYP/6-31G* 1.0 9.15 9.43 0.28

a Note that adiabatic ionization of both conformers of neutral valeramide leads to the same structure for the ion, see text.

Upon ionization, geometry changes from the perpendicular into the distorted anti-

conformation (Figure 3-2), which is similar to conformer 15 of neutral valeramide, with the

dihedral angles

RCCO = 46.3° and

HCCO = 13.2°. In the cation radical, the electron

deficient oxygen atom orientates in such a manner that stabilization through bond

delocalization from the neighboring NH2- and CH2- groups can occur, which is reflected in

the changes of the charge distributions for neutral and ionized valeramide. Consideration

of the molecular orbitals supports this picture in that the cationic species bears orbitals,

which are delocalized across the C–H and N–H bonds and the carbonyl group. The

changes in dihedral angles are the main cause of the difference between adiabatic and

vertical ionization, while bond angles and bond lengths experience only minor variations.

Theoretical exploration of the valeramide potential-energy surface 29

The elongation of the C(1)-C(2) bond, for example, is rather small with rCC = 1.529 Å in

the neutral compared to rCC = 1.554 Å in the cation radical. Concerning the planarity of

amino group, the already almost planar arrangement in the neutral (the sum of the angles

around nitrogen is 358°) becomes perfect in the cation radical 11+• due to a better overlap

between orbitals including the N–H bonds and the oxygen atom.

1.222

1.371

1.009

1.529

1.100

1.011

(+ 0.297)

(+ 0.237)

(- 0.352)

(+ 0.094)

(- 0.344)

(+ 0.123)

(+ 0.180)

(- 0.265)

(+ 0.034)

1.247

(+ 0.155)

1.315

1.016

(+ 0.367)

(+ 0.295)

1.013

(- 0.261)

1.554

(- 0.465)

(+ 0.236)

(+ 0.271)

1.093

1.099

2.373

H' R

Figure 3-2. Optimized structures of neutral and ionized valeramide at the B3LYP/6-31G* level of

theory. Bond lengths (in Å) are given in bold, Mulliken charges in parentheses.

3.7. Unimolecular Dissociations of Ionized Valeramide

Detailed reaction pathways have been calculated for the five fragmentation

channels of ionized valeramide deduced from the experimental studies (Scheme 3-1). The

C3-route corresponds to the McLafferty rearrangement, which is initiated by a 1,5-H

transfer and followed by C–C bond cleavage and formation of propene and the enol cation

4+•. The C2-route comprises three channels. Two of these have an initial 1,6-H transfer in

common, i.e., the loss of C2H4 to afford the β-distonic ion 6+• and the elimination of C2H5•

to form protonated acrylamide 8+ in a more complex process. The direct loss of the

terminal ethyl group contributes to the C2-route as well. Based on the experimental

findings, the C1-route is assigned to an initial 1,4-H transfer followed by loss of CH3•

30 Theoretical exploration of the valeramide potential-energy surface

concomitant with formation of protonated vinylacetamide 12+. Finally, even though the

occurrence of a 1,3-H transfer, via keto/enol tautomerization, has not been inferred from

experiment, it was investigated theoretically.

In perfect agreement with the interpretation of the experimental data, the barriers

associated with the various hydrogen migrations in the cation radical are rather small (see

below). Therefore, internal rotations around the C–C bonds play an important role in that

adequate conformers need to be accessed before a particular rearrangement can occur. In

fact, C–C bond rotations may contribute to or even constitute the rate-determining steps.

The structural flexibility of valeramide and its cation radical makes the mechanistic study

rather demanding because the rearrangements could arise from many different conformers.

As a compromise between insight gained and computational resources available, the role

of internal rotations prior to hydrogen migration was only investigated explicitly for the

C2- and C3-routes.

3.7.1.

-C–H Bond Activation (C3-route)

In the energetically lowest-lying conformer 11+•, the distances between the oxygen

atom of the carbonyl group and the hydrogens at C(4) are much too large for hydrogen

migration to occur. Rotation around the C(2)–C(3) bond leads to conformer 13+•, which is

1.5 kcal/mol higher in energy than 11+• (Table 3-3).

Although the absence of imaginary modes characterizes 13+• as a real minimum at

the B3LYP/6-31G* level of theory, all attempts failed to locate a barrier associated with

hydrogen migration to the distonic ion 2+• (Figure 3-3). Moreover, all computed points of a

continuous scan from 13+• to 2+•, i.e., decreasing rOH while optimizing all other parameters,

were lower in energy than the starting point 13+•. Accordingly, the barrier associated with

1,5-H migration is rather small, if not spurious. Inspection of the computed vibrational

frequencies reveals a low-lying mode at 89 cm-1 of 13+• that reflects the structural changes

associated with γ-C–H bond activation.46 Further refinement might certainly be achieved

with larger basis sets in the geometry optimization combined with the application of tighter

convergence criteria. However, the barrier (if existing at all) would lie low in energy.

Theoretical exploration of the valeramide potential-energy surface 31

Table 3-3. Electronic energies (Etot, in Hartree), zero-point energies (ZPE, in Hartree), and relative

energies (Erel, in kcal/mol)a of the stationary points on the potential-energy surface of ionized valeramide.

B3LYP/6-31G*//B3LYP/6-31G* B3LYP/6-311++G**//B3LYP/6-

31G*

Etot ZPE Erelab Etot Erela-c

11+• -326.827971 0.158796 0.0 -326.923706d0.0

11+•/12+• -326.823143 0.158583 2.9 -326.919235 2.7

12+• -326.826593 0.158765 0.9 -326.922514 0.8

11+•/13+• -326.821654 0.158462 3.8 -326.917911 3.5

13+• -326.825397 0.158764 1.6 -326.921404 1.5

12+•/14+• -326.821097 0.158601 4.2 -326.917217 4.0

14+• -326.824067 0.158917 2.6 -326.919870 2.5

2+• -326.851066 0.159234 -14.2 -326.952177 -17.6

14+•/51+• -326.821475 0.158147 3.7 -326.917193 3.7

51+• -326.843174 0.159341 -9.2 -326.944120d-12.4

52+• -326.831062 0.159672 -1.4 -326.933011 -5.3

53+• -326.829377 0.158749 -0.9 -326.932492 -5.5

54+• -326.827160 0.158382 0.3 -326.930411 -4.4

51+•/c-5+• -326.819366 0.159789 6.0 -326.920266 2.8

c-5+• -326.821732 0.159752 4.5 -326.922196 1.6

51+•/6+•e-326.795501 0.155755 18.5 -326.899203 13.5

53+•/71+• -326.809434 0.155427 9.6 -326.912865 4.8

71+•f-326.851625 0.159665 -14.3 -326.954016 -18.5

52+•/72+• -326.805264 0.155389 12.2 -326.908727 7.3

72+• -326.849834 0.159679 -13.1 -326.952205 -17.3

11+•/73+• -326.782132 0.154218 26.0 -326.882266 23.2

73+• -326.854846 0.159999 -16.1 -326.957217 -20.3

11+•/11+• -326.819324 0.154831 3.0 -326.916779 1.9

11+• -326.843288 0.159169 -9.4 -326.945129 -13.2

11+•/12+e-326.793115 0.155093 19.6 -326.897284 14.3

a The lowest-lying conformer 11+• of the cation radical is used as the reference point. b ZPEs included with a scaling factor of

0.9805. c ZPEs taken from the B3LYP/6-31G*//B3LYP/6-31G* calculations. d Energies at B3LYP/6-311++G**//B3LYP/6-

311++G**: 1+•, -326.923857 H, and 51+•, -326.9442407 H. e Barrier in the exit channel, see text. f Computed energies of neutral 7:

Etot(B3LYP/6-31G*) = -327.106796 H, ZPE = 0.159554 H, Etot(B3LYP/6-311++G**//B3LYP/6-31G*) = -327.221313 H.

32 Theoretical exploration of the valeramide potential-energy surface

With regard to the interpretation of the experimental data, it is entirely sufficient

that the conformational barrier associated with the formation of 13+• is predicted to exceed

the kinetic restriction imposed by hydrogen migration. Hence, not C–H bond activation,

but access to the appropriate conformation of 1+• is rate-determining for the McLafferty

rearrangement. This conclusion also provides an explanation for the negligible kinetic

isotope effect (KIE) in the McLafferty route as derived from the analysis of the

experimental data. The distonic ion 2+• is 17.6 kcal/mol more stable than the lowest-lying

conformer of the reactant, 11+•. Bond lengths and angles characterize structure 2+• as a

genuine γ-distonic ion, rather than a loose ion/dipole complex (3+•) of the ionized

acetamide enol interacting electrostatically with neutral propene. For example, the

C(2)/C(3) and C(3)/C(4) bonds in 2+• (1.540 and 1.506 Å) almost match those in 11+•

(1.530 and 1.555 Å).

While numerous indications for the existence of ion/dipole complexes exist in the

chemistry of organic cation radicals,47 all extensive attempts failed to locate a genuine

minimum for 3+•, but instead always converged to 2+•. While this result should by no

means dispute the possible existence of 3+•, it is entirely sufficient for the present purpose

to state that structure 2+• obviously is more stable than 3+•. Dissociation of 2+• to the final

-24

-16

-8

[

]

rel

Relaxed PES scan

(difficult to locate

the 1 /2 TS)

3.5

24.2

Figure 3-3. Potential-energy surface for the loss of C3H6 from ionized valeramide (C3-route) according to

B3LYP6-311++G**//B3LYP6-31G* calculations.

Theoretical exploration of the valeramide potential-energy surface 33

products 4+• + C3H6 requires 24.2 kcal/mol at the B3LYP/6-311++G**//B3LYP/6-31G*

level of theory, corresponding to an overall endothermicity of 6.6 kcal/mol for the reaction

11+• → 4+• + C3H6 at 0 K. A more detailed consideration of the exit channels is postponed

to a separate section further below.

3.7.2.

-C–H Bond Activation (C2-route)

Figure 3-4. Conformational changes of 1+• required as a prerequisite for the access to the C2-route

according to B3LYP6-311++G**//B3LYP6-31G* calculations.

-24

-16

-8

[

]

rel

1/1

2.7 3.2

While a single C–C bond rotation is sufficient to achieve a reactive conformation

for the McLafferty rearrangement, two sequential rotations 11+• → 12+• → 14+• (Figure 3-4)

are required for δ-C–H bond activation which initiates the C2-route. Similar to the

McLafferty rearrangement, the barrier associated with hydrogen migration is rather low,

and the transition structure (TS) 14+•/51+• is only 1.2 kcal/mol above 14+• (Figure 3-5).

Again, the barrier for C–C bond rotation exceeds that associated with hydrogen migration;

the difference is considerably smaller for activation of the δ-C–H bonds, which is

consistent with the small, but non-negligible KIEs found upon deuteration at C(5) in the

experimental studies. Similar to the C3-route, the δ-distonic ion 51+• is 12.4 kcal/mol more

stable than 11+•. In order to investigate, whether or not this effect is due to an interaction

between the charge and the spin centers in 51+•, other conformers were considered as well,

34 Theoretical exploration of the valeramide potential-energy surface

including the seemingly ideal all-anti orientation of the C–C bonds. In the resulting all-anti

conformer 54+•, the O-C(5) distance amounts to 6.225 Å compared to only 2.807 Å in 51+•.

Though less strained, conformer 54+• is ca. 8 kcal/mol less stable than 51+•. A value of this

magnitude is best rationalized by involving hydrogen bonding between the radical center

and the hydroxy group, as also implied by the almost linear arrangement of the atoms

involved (

C(5)HO = 171.8°) together with rC(5)H = 1.806 Å. In comparison, hydrogen

bonding involving the amino group is energetically disfavored (conformer 52+•).

-24

-16

-8

E / [kcal/

ol]

rel

5/c-5

c-5

5/c-5

5/6

1.2

15.2

1.2

25.9

Figure 3-5. Potential-energy surface for the loss of C2H4 from ionized valeramide (C2-route) according

to B3LYP6-311++G**//B3LYP6-31G* calculations.

Any conformer of 5+• can undergo C(3)–C(4) bond cleavage to afford the cation

radical 6+• concomitant with neutral ethene. At the B3LYP/6-311++G**//B3LYP/6-31G*

level of theory, an overall endothermicity of 11.8 kcal/mol is predicted for the reaction 11+•

→ 6+• + C2H4 at 0 K. Similar to the δ-distonic ion 51+•, the β-distonic ion 6+• seems to

experience stabilization by intramolecular hydrogen bonding because in the most stable

conformer found the hydroxy group is oriented towards the radical site at C(3) with rC(3)O =

2.812 Å and

C(3)HO = 113.6°; however, rC(3)H(O) = 2.269 Å indicates that hydrogen bonding

is less efficient than in 51+•. A conformer in which the OH group points away from the

backbone (rC(3)O = 3.019 Å) is 4.3 kcal/mol less stable than 6+• at the B3LYP/6-

311++G**//B3LYP/6-31G* level of theory. In competition with dissociation, 51+• can

Theoretical exploration of the valeramide potential-energy surface 35

isomerize to the cyclic structure c-5+• where the associated TS 51+•/c-51+• is energetically

close to c-51+• (Table 3-3). The relatively low energy demand of this degenerate

rearrangement is in perfect agreement with the pairwise equilibration of the C(2)/C(3) and

C(4)/C(5) positions as inferred from the experimental studies.

For the isomerization of the δ-distonic ion 5+• to the ionized enol 7+• via a 1,4-

hydrogen migration (Figure 3-6), a conformational change is required first. Thus, the most

stable conformer 51+• must trade-off hydrogen bonding, giving rise to a conformer 53+• in

which one of the hydrogens at C(2) can interact with the radical site at C(5). While the

barrier associated with hydrogen migration via TS 53+•/71+• is not very large (10.3 kcal/mol

relative to 53+•), the resulting energy demand in conjunction with the required

conformational changes locate TS 53+•/71+• at a relative energy of 4.8 kcal/mol above 11+•.

Conformer 71+• is 18.5 kcal/mol more stable than 11+•; conformer 72+• and the associated

TS 52+•/72+• are close in energy and primarily differ in the orientation of the functional

group relative to the backbone. Any conformer of 7+• could undergo C(3)–C(4) bond

scission to yield 8+ + C2H5•, which requires 27.8 kcal/mol for conformer 71+•,

corresponding to an overall endothermicity of 9.3 kcal/mol relative to 11+• at the B3LYP/6-

311++G**//B3LYP/6-31G* level of theory at 0 K.

-24

-16

-8

5/7

E / [kcal/mol]

rel

1.2

10.3

27.8

Figure 3-6. Potential-energy surface for the indirect loss of C2H5• from ionized valeramide (C2-route)

according to B3LYP6-311++G**//B3LYP6-31G* calculations.

36 Theoretical exploration of the valeramide potential-energy surface

7.2.3.

-C–H Bond Activation (C1-route)

-24

-16

-8

11 /

[

]

rel

1.9 27.5

Figure 3-7. Potential-energy surface for the loss of CH3• from ionized valeramide (C1-route) according to

B3LYP6-311++G**//B3LYP6-31G* calculations.

The 1,4-hydrogen transfer can directly proceed from conformer 11+•, and the

associated TS 11+•/11+• requires only 1.9 kcal/mol (Figure 3-7). This facile hydrogen

migration, besides the low barrier, can be attributed to the fact that the resulting β-distonic

ion 11+• is 13.2 kcal/mol more stable than 11+•. Once more, the distonic ion formed seems

to experience stabilization via hydrogen bonding, because in the computed minimum, the

hydroxy group points towards the radical site with rC(3)H(O) = 2.190 Å, rC(3)O = 2.190 Å, and

C(3)HO = 116.4°. Interestingly, the subsequent C(4)–C(5) bond cleavage of 11+• is

associated with a significant barrier in the exit channel, TS 11+•/12+. For the final products

12+ + CH3•, an endothermicity of 8.4 kcal/mol relative to 11+• is predicted at the B3LYP/6-

311++G**//B3LYP/6-31G* level of theory at 0 K.

7.2.4.

-C–H Bond Activation (Keto/Enol Tautomerism)

Even though the all-anti conformer of the ionized enol 73+• (Erel = -20.3 kcal/mol)

most likely corresponds to the global minimum of all cationic species examined here, the

computed energy demand of 23.2 kcal/mol (Table 3-3) associated with intramolecular

Theoretical exploration of the valeramide potential-energy surface 37

keto/enol tautomerism proceeding through a 1,3-hydrogen transfer via TS 11+•/73+• is much

higher than those of all other hydrogen migrations investigated. This result is not at all

unexpected, since previous studies have amply demonstrated that the facile keto/enol

tautomerism known from the condensed phase occurs intermolecularly, whereas

intramolecular keto/enol tautomerism via 1,3-hydrogen migration is associated with

considerable barriers for neutral as well as cationic carbonyl compounds.48 In the present

case, formation of the ionized enol is indeed more likely to occur via a much more

complicated, multi-step sequence 11+• → 12+• → 14+• → 51+• → 53+• → 71+• → 73+•

described in the context of the C2-route (see above). Consequently, the direct keto/enol

tautomerism will not contribute to the dissociation behavior of ionized valeramide. The

ionized enol might be involved if some neutral 7 were present in the precursor, because

ionization of the enol is much easier than that of the keto isomer (IEa(7) = 7.19 eV vs

IEa(1) = 9.19 eV; B3LYP/6-311++G**//B3LYP/6-31G*). However, at the same level of

theory the neutral enol 7 is computed to be 24.9 kcal/mol less stable than neutral

valeramide (11), such that contributions from the enol form can be excluded rigorously at

298 K. The similar stability differences have been predicted for the keto/enol tautomers of

neutral acetamide.49

7.2.5. Exit Channels

With respect to the products formed upon dissociation of ionized valeramide, two

general and one specific point need to be addressed. The first general concern is the choice

of the basis sets in the computational study. Upon inspection of the data compiled in Table

3-4, it becomes obvious that the dissociation enthalpies relative to 11+• show a pronounced

basis set effect. The general tendency for decreasing endothermicities with increasing the

size of the basis set can be attributed to a basis set superposition error. The deviations of

∆

Erel are not at all uniform and most likely seem to reflect the role of electron correlation

in the various fragments. For example,

∆

Erel is small for the saturated, cyclic species 10+

and 13+ and large for unsaturated fragments such as 4+•, 6+•, 8+, and 12+. Irrespective of the

precise origin of these effects, these trends indicate that even the larger basis set used

might not suffice to describe the exit channels within a few kcal/mol. This has to be kept in

mind as a note of caution for the entire PES of ionized valeramide, even though the

computed data compare quite favorably with experimental data available. Nevertheless, the

38 Theoretical exploration of the valeramide potential-energy surface

use of B3LYP/6-31G* geometries appears adequate, because exploratory geometry

optimizations of 1+•, 4+•, and 51+• at the B3LYP/6-311++G** level of theory led to

differences of maximal 0.01 Å in bond lengths and maximal 0.1 kcal/mol in the relative

energetics.

Table 3-4. Electronic energies (Etot, in Hartree), zero-point energies (ZPE, in Hartree), and relative energies

(Erel, in kcal/mol)a of the dissociation products of ionized valeramide.

B3LYP/6-31G*//B3LYP/6-31G* B3LYP/6-311++G**//

B3LYP/6-31G*

Etot ZPE Erela,b Etot Erela-c

∆

Ereld

4+• -208.892507 0.073921 -208.962891e

C3H6-117.907562 0.080097 -117.945597e

4+• + C3H6-326.800069 0.154018 14.6 326.908488 6.6 8.0

6+• -248.203109 0.101795 -248.283773

C2H4-78.587457 0.051208 -78.615509

6+• + C2H4-326.790566 0.153003 19.9 -326.899282 11.8 8.1

8+-247.637169 0.092884 -247.717762

C2H5•-79.157868 0.059651 -79.185027

8+ + C2H5•-326.795037 0.152535 16.8 -326.902789 9.3 7.5

9+-247.630846 0.094573 -247.702183

9+ + C2H5•-326.788714 0.154224 21.8 -326.887210 20.1 1.7

10+-247.517747 0.087524 -247.591683

10+ + C2H5•-326.675615 0.147175 88.3 -326.776710 84.9 3.4

13+f-247.617520 0.093827 -247.689936

13+ + C2H5•-326.775388 0.153478 29.7 -326.874963 27.3 2.4

14+g-247.577271 0.088982 -247.655572

14+ + C2H5•-326.735139 0.148633 52.0 -326.840599 45.9 6.1

12+-286.956919 0.121632 -287.048005

CH3•-39.838292 0.029832 -39.855179

12+ + CH3•-326.795211 0.151464 16.1 -326.903184 8.4 7.7

a Relative energies can only be given for the sums of fragments having the same elemental composition as valeramide, where the lowest-

lying conformer 11+• of the cation radical is used as the reference point. b ZPEs included with a scaling factor of 0.9805. c ZPEs taken from

the B3LYP/6-31G* calculations. d Defined as

∆

Erel = Erel(B3LYP/6-31G*) - Erel(B3LYP/6-311++G**).

e Energies at B3LYP/6-311++G**//B3LYP/6-311++G**: 4+•, -208.9629654 H, C3H6, -117.9456353.f This structure corresponds to N-

protonated β-propiolactame. g This structure is best described as a complex of a OCNH2+ cation with ethene.

Theoretical exploration of the valeramide potential-energy surface 39

The second general aspect concerns thermal contributions. In the mass

spectrometric experiments, the valeramide samples were evaporated at room temperature.

Therefore, the relative energies computed for 0 K and 298 K are compared with each other,

where the difference

∆

Ethermal represents a measure for the importance of thermal

contributions (Table 3-5). While thermal effects hardly change the energetics associated

with the intramolecular rearrangements of ionized valeramide, all free energies of the exit

channels are lowered by about 10 kcal/mol relative to 11+•, mostly because of entropy since

two particles are formed from one. Therefore, the slightly endothermic expulsion of

propene via the McLafferty route (E0 = 6.6 kcal/mol at 0 K) becomes exoergic at room

temperature (E0 = -4.1 kcal/mol). Thermal contributions can thereby explain the

observation of the enol fragment 4+• due to the McLafferty rearrangement right at the onset

of photoionization. Moreover, while

at 0 K the indirect loss of C2H5• as

well as the McLafferty reaction are

subject to thermodynamic control due

to the exit channels, both become

kinetically controlled at 298 K.

The more specific aspect is

related to the nature of the ionic

fragment generated in the direct loss

of C2H5•. The indirect route leads to

protonated acrylamide 8+, which

appears to be the global minimum of

the [C3,H5,N,O]+ surface.50 At the

employed level of theory, the

corresponding exit channel 8+ + C2H5•

is situated at Erel = 9.2 and -1.8

kcal/mol at 0 and 298 K, respectively,

and the 0 K value is used as a

reference for the other options for

C2H5• expulsions. Four different

structures directly accessible from

ionized valeramide were studied

Table 3-5. Relative energies (Erel, Grel in kcal/mol with

11+• as the reference) of several points of the potential-

energy surface of ionized valeramide and some the

relevant dissociation channels at 0 and 298 K,

respectively, and the resulting thermal contributions

(

∆

Ethermal in kcal/mol) derived from the B3LYP/6-

311++G**//B3LYP/6-31G* calculations.a

Erel,0bGrel,298c

∆

Ethermald

11+•/13+• 3.4 4.0 0.6

21+• -17.6 -16.6 1.0

4+• + C3H66.6 -4.1 -10.7

51+• -12.5 -11.2 1.3

51+•/6+• 13.5 14.3 0.8

53+•/71+• 4.7 6.2 1.5

6+• + C2H411.7 1.8 -9.9

73+• -20.3 -20.1 0.2

8+ + C2H5•9.2 -1.8 -11.0

9+ + C2H5•20.0 9.6 -10.4

11+• -13.2 -13.1 0.1

11+•/12+14.3 14.6 0.3

12+ + C2H5•8.3 -0.3 -8.6

a Unscaled frequencies used. b Relative energy at 0 K. c Relative energy at

298 K including enthalpic and entropic effects. d Defined as

∆

Ethermal =

Grel,298 - Erel,0.

40 Theoretical exploration of the valeramide potential-energy surface

theoretically. The energetically most stable of these direct products is 9+ (Scheme 3-2), in

which the C–C bond cleavage is assisted by simultaneous C–O bond formation. The

generation of 9+ is energetically more demanding than that of 8+ by 10.8 kcal/mol. In

contrast, direct C–C bond cleavage without formation of a new bond leads to the high-

energy isomer 10+ located 75.8 kcal/mol above 8+. Alternatively to assisting C–O bond

formation, C–N bond formation might lead to 13+, i.e., N-protonated propiolactame (also

known as 2-acetidinone). Isomer 13+ is, however, 7.2 kcal/mol less stable than 9+ and 18.0

kcal/mol disfavored compared to 8+. Finally, the computational search also revealed a

minimum 14+ which is best described as a complex of a OCNH2+ cation with neutral

ethene.

NH2

- C2H5

NH2

914

Scheme 3-2. Possible products of the direct ethyl loss from 1+•.

3.8. Comparison with Literature Thermochemistry

Using thermochemical data bases51 in combination with selected isodesmic

reactions,52 the heat of formation of gaseous valeramide can be estimated as

∆

fH°(1) = -

71.3 ± 0.9 kcal/mol. Combination with IE(1) = 9.40 ± 0.03 eV, derived from the

photoionization experiments, leads to

∆

fH°(1+•) = 145.5 ± 1.4 kcal/mol. Next, the heat of

formation of acetamide (-57.0 ± 0.2 kcal/mol) combined with its IE (9.69 ± 0.07 eV) and

the stability difference of 18.9 kcal/mol in favor of the ionized enol, predicted by G2

calculations,53 suggest

∆

fH°(4+•) = 147.6 ± 2.5 kcal/mol.54 In conjunction with

∆

fH°(C3H6)

= 4.9 kcal/mol for propene, fragmentation of 1+• via the C3-route is therefore predicted to

be endothermic by 7.0 ± 2.9 kcal/mol. This value compares nicely with the computed

reaction enthalpy of 6.6 kcal/mol (Table 3-4).55 Further, the heat of formation of

Theoretical exploration of the valeramide potential-energy surface 41

acrylamide,56 its proton affinity,57 and the heat of formation of ethyl radical58 predict an

endothermicity of 10.0 ± 1.6 kcal/mol for the indirect loss of C2H5• via the C2-route which

fits well to the computed 9.3 kcal/mol. Literature values further suggest an endothermicity

of about 10 kcal/mol59 for the loss of CH3• via the C1-route compared to a computed value

of 8.4 kcal/mol for 12+ + CH3•. Finally, the relative energetics of the [C2,H5,N,O]+ isomers

8+, 9+, and 13+ are qualitatively consistent with earlier computations at the HF level.

3.9. Implications for the Fragmentation Behavior of Ionized

Valeramide

Comparing the theoretical studies with the results of the mass spectrometric

experiments leads to a consistent description of the dissociation behavior of ionized

valeramide. Thus, despite of the limitations of the computational approach used, the

B3LYP/6-311++G**//B3LYP/6-31G* level of theory appears to describe the energetics of

ionized valeramide and its rearrangement reasonably well. Moreover, the energetic order

of the fragmentation channels is the same for both approaches: loss of propene is most

facile and the multistep elimination of C2H5• can occur at slightly higher energies, while

losses of CH3• and C2H4 as well as the direct elimination of C2H5• require elevated

energies. For a quantitative comparison, the point of highest energy demand in each route

has to be considered. At room temperature, the C3-route is kinetically controlled via TS

11+•/13+• in which the access to that pathway is determined by conformational changes of

the cation radical 1+•. This situation is consistent with the negligible kinetic isotope effect

upon deuteration of the C(4) position derived from experiment (KIE(γ-CH) = 1.01). In

contrast, the indirect loss of C2H5• via the C2-route is controlled by three barriers of similar

energy demands relative to 11+•: TS 12+•/14+• (4.0 kcal/mol), TS 14+•/51+• (3.7 kcal/mol), and

TS 53+•/71+• (4.8 kcal/mol) of which the first is a conformational barrier while the two latter

are associated with hydrogen migrations. Involvement of all three TSs in the overall

reaction is consistent with the more pronounced KIEs in this route for both, the C(2) and

the C(5) positions as derived from the kinetic modeling (KIE(δ-CH) = 1.32). The slightly

larger barriers of this route compared to the McLafferty rearrangement and the lower

overall exoergicity of the C2-route also agree favorably with the strong preference of the

C3-route in the photoionization studies. According to the calculated energy profiles, loss of

42 Theoretical exploration of the valeramide potential-energy surface

C2H4 is thermodynamically controlled by the height of the exit channel, which lies ca. 6

kcal/mol above the energy demand for loss of propene. The computations predict loss of

CH3• (C1-route) to be subject to kinetic control due to TS 11+•/12+ (Erel = 14.3 kcal/mol)

operative in the exit channel. This energy demand is much larger than those of the

competing channels, which is in agreement with the low abundance of CH3• elimination in

the various kinds of mass spectrometric experiments. Finally, the theoretical data shed

some light on the structure of the fragment ion formed via the direct loss of C2H5•.

Experimentally, the direct route becomes populated at about 1 eV above photoionization

threshold. This amount of excess energy is clearly insufficient for the formation of 10+ as

well as 14+ in the direct route, and it is therefore concluded that C–C bond cleavage is

accompanied by C–O and/or C–N bond formation to yield 9+ and/or 13+, respectively.

While all these results agree pretty well, the presented theoretical results provide no

indication for the variations in the C3/C2 branching observed in various experiments. In

fact, irrespective of basis set, temperature etc., the C3-route is always clearly preferred over

the C2-route. Accordingly, the static picture of the calculated PES of ionized valeramide in

terms of minima and transition structures does not provide a rationale for the ca. 1 : 1 ratio

of the C2- and C3-channels observed in the metastable ion studies conducted in the sector

experiment. In order to bring more insight in this aspect, some molecular dynamics studies

had to be performed (see Chapter 4).

3.10. Conclusions

The theoretical study of ionized valeramide using B3LYP leads to the construction

of a potential-energy surface for the dissociation behavior of the radical cation, which is

consistent with many results of the mass spectrometric studies. The calculated PES agrees

with respect to the energetic ordering of the fragmentation channels observed and confirms

the mechanistic schemes derived from analysis of the labeling data. In fact, even subtle

details of the proposed fragmentation schemes, e.g. the pairwise equilibration of C(2)/C(3)

with C(4)/C(5), as well as kinetic isotope effects are qualitatively confirmed by theory. As

far as competition between the different fragmentation channels is concerned, the

computed results agree qualitatively with the branching ratios obtained in the

photoionization studies. Thus, the McLafferty rearrangement (C3-route) has the lowest

Theoretical exploration of the valeramide potential-energy surface 43

energy demand, while the computed pathways for losses of CH3•, C2H4, and “indirect”

C2H5•, respectively, are somewhat higher in energy, but of comparable magnitude. Quite

remarkable is the effect of thermal contribution on the dissociation behavior, in that at 0 K

all fragmentations are thermodynamically controlled by the high-energy demand of the exit

channels, whereas kinetic control due to intermediate barriers is most important at 298 K

or higher temperatures. The missing link between experiment and theory concerns the

unusual variations in the C3/C2 ratios observed in some of the experiments. While the

theoretical results support the idea that the experimentally observed routes are uncoupled

from each other, i.e., the H-migrations from various positions occur quasi-irreversibly,

none of the computed properties can explain, why the C3/C2 ratio of about 1 is observed for

metastable 1+• in the sector-field instrument.

In a more general sense, the computational exploration of the potential-energy

surface of the molecular ion of valeramide suggests that various kinds of C–H bond

activations are possible for ionized carbonyl compounds. Instead of a kinetic control by the

barrier associated with hydrogen migration, the regioselectivity of C–H bond activation

seems to be determined by the accessibility of the appropriate conformations in the parent

ion as well as the energetics of the associated exit channels. In fact, the present results

suggest that the prevalence of the McLafferty rearrangement in the mass spectrometric

fragmentation of carbonyl compounds is not primarily due to a particular preference of 1,5-

hydrogen transfer, but results from the favorable energy demand of the dissociation

products.

44 Temperature effect on the dissociation pattern of ionized valeramide

4. Temperature Effect on the Dissociation Pattern of

Ionized Valeramide∗

4.1. An Unprecedented Temperature Effect on the C3/C2 Branching

Ratio

The metastable ion studies performed in the four-sector instrument yield C3/C2

ratios close to unity. A C3/C2 ratio of about 3 ± 1 is derived as a mean for the metastable

traces in the threshold photoelectron-photoion coincidence (TPEPICO) data between 9.8

and 10.5 eV, and for dissociative photoionization the C3/C2 ratios range from ca. 5 at

photon energies above 12 eV to C3/C2 > 100 close to the ionization threshold of

valeramide. While refined insight in most of the mechanistic details is achieved, the gross

product distribution is not understood. Out of quite a few effects of various experimental

parameters on the C3/C2 ratio, the temperature of the ion source (Ts) was the only

difference between the two machines. The ion source of CERISES60 is operated at room

temperature, whereas conventional EI sources, such as the one installed in the sector

instrument,22,23 are usually maintained at elevated temperature (typically 200 °C) in order

to reduce memory effects and to avoid temperature drifts caused by the glowing filament

which effectively acts as a heater. While the temperature of the ion source is known to

affect EI mass spectra61,62 as well as the fragmentation patterns upon collisional

activation,63,64 temperature effects on intensity ratios in metastable ion spectra are usually

small. Recently, a thorough study of Norrman and McMahon further corroborated these

ideas.65 In fact, these authors even concluded that the internal energy of metastable ions

(proton-bound dimers were studied) decreases with increasing Ts. Thus, the product

branching ratios typically increased by about 50 % in favor of the thermodynamically

favored product when increasing Ts from 50 to 300 °C. Because a similar, or even

negligible temperature behavior was also expected for ionized valeramide, a pronounced,

however, reversed effect of the source temperature on the C3/C2 ratios in the MI spectra of

1+• came at a great surprise (Figure 4-1).

∗ Results discussed in this chapter have been published in: (a) Schröder, D.; Loos, J.; Semialjac, M.; Weiske,

T.; Schwarz, H.; Höhne, G.; Thissen, R.; Dutuit, O. Int. J. Mass Spectrom. 2002, 214, 155. (b) Semialjac, M.;

Schröder, D.; Schwarz, H. Chem. Eur. J. 2003, 9, 4396.

Temperature effect on the dissociation pattern of ionized valeramide 45

0 100 200 300

Figure 4-1. C3/C2 ratios in the MI spectra of mass-selected 1+• as a function of the temperature of the ion

source.

All experiments with the sector instrument22,23 were performed at Ts = 200 °C at

which C3/C2 ratios of about 1 ± 0.1 were obtained in all kinds of experiments conducted

with metastable 1+•. Upon lowering Ts, however, the C3/C2 ratios increases notably and in

fact reaches a value of ca. 3 at the lowest temperature achieved. Hence, after all it is

effectively the source temperature which gives rise to the variations in the C3/C2 ratios in

the two kinds of instruments. So far no similar effect of this magnitude has been observed

in previous metastable ion studies.66 Compared to the results of Norrman and McMahon,

the effect is much more pronounced and works in the opposite direction, i.e., the high-

energy channels are favored at higher source temperatures.

For a carbonyl compound, an obvious explanation of the temperature effect is

provided by invoking the involvement of keto/enol tautomerization of the neutral

precursor. In fact, temperature effects have been observed in the metastable mass spectra

of ionized 1,3-diones which easily undergo enolization.67 For the case of valeramide, this

would imply that increasing temperatures favor formation of the neutral enol 7 which is, in

turn, much easier to ionize than 1 (see Chapter 3). Hence, the C3/C2 ratio of about 1 at 200

°C might be explained by involving the formation of a mixture of 1+• and 7+• upon

ionization, because the former contributes to both routes while the latter decays via the C2-

channel almost exclusively. Moreover, the enol has a significantly lower ionization energy

than the keto and the corresponding cation radical 7+• resides in a much deeper well than

46 Temperature effect on the dissociation pattern of ionized valeramide

1+•. Accordingly, an enrichment of the enol cation in the mass-selected ion beam is to be

expected. Therefore, keto/enol tautomerization of the neutral would provide an intuitive

and straightforward explanation for the observed temperature dependence of the MI

spectra. However, the computed stability difference of ca. 25 kcal/mol in favor of 168

disputes involvement of neutral 7. Even if keto/enol tautomerism is effectively catalyzed

by termolecular or surface reactions, the computed energy differences suggest a keto/enol

ratio of about 1018 at room temperature, and still about 1011 at 200 °C. These ratios appear

much too large, and therefore this explanation is highly unlikely.

Three further possible mechanistic scenarios have been proposed to account for this

surprising effect:

Figure 4-2. Simplified potential-energy surface for the competitive dissociation of 1+• via the C2- and C3-

routes.

(I) Because the regioselectivities of the initial C–H bond activations are primarily

determined by the accessibility of the appropriate conformations, it is conceivable that the

population of the neutral conformers required for access to the C2 route increases at

elevated temperatures. A comprehensive description of such a scenario must also account

for the different trajectories involved in γ-C–H and δ-C–H bond activations by means of

dynamic considerations.

(II) Uncoupling of the distonic intermediates 2+• and 5+• is expected not to affect the

C3/C2 ratio in metastable ion dissociations in any but unusual situations. In the present

case, the appearance energy of the C3-route is very close to the ionization threshold of 1,

Temperature effect on the dissociation pattern of ionized valeramide 47

indicating rather low thermochemical and kinetic restrictions of this particular

fragmentation (Figure 4-2). Consequently, it is conceivable that the population of

intermediate 2+• is effectively depleted at elevated temperatures in that a significant

fraction of 2+• formed upon ionization of 1 already dissociates before time delayed mass-

selection is achieved. Thus, the unexpectedly low C3/C2 ratio of about 1 in the experiments

with metastable ions (lifetimes around few µs) conducted at a source temperature of 500 K

could be explained through an enrichment of 5+• relative to 2+•.

(III) The third hypothesis is similar to scenario (II) but involves an enhanced

propensity for the formation of long-lived 1+• upon ionization of neutral valeramide at low

temperatures. Contribution of some amount of genuine 1+• to the mass-selected ion beam

would result in a preference for the energetically favored C3 route. Thus, the C3/C2 ratio

would increase relatively to that observed at higher temperatures and this scenario can

thereby account for the observed temperature behavior as well.

The above mentioned scenarios were taken into account and investigated further

theoretically. However, yet another scenario might contribute to the temperature effect on

the dissociation pattern of the ionized valeramide as well, i.e. the difference of the cross-

sections for ionization of different valeramide conformers. In such a scenario depending on

temperature some of the valeramide conformers could be easier ionized than the others and

could give rise only to a particular rearrangement type. In order to test this scenario the

whole conformational space of the neutral and ionized valeramide should be considered

and such computations would be extremely time-consuming. Because of the limited

computational resources available, unfortunately, this aspect could not be addressed

computationally. Nevertheless, the results obtained by the Car-Parrinello molecular

dynamics provided rationals for the unusual temperature effect. However, it should be kept

in mind that the cross section might also contribute to the temperature effect.

4.2. Rationalization of the Temperature Effect on the Dissociation

Pattern: Car – Parrinello Molecular Dynamics Study

As a natural choice for testing the above mentioned hypotheses by computational

means, studies employing some of the current molecular dynamics (MD) methods are

indicated. Since the electronic effects in radical cation systems most probable play a

crucial role on rearrangement pathways, an ab initio MD method is deemed the only

48 Temperature effect on the dissociation pattern of ionized valeramide

acceptable choice for obtaining any significant results. The Car-Parrinello molecular

dynamics (CPMD)69 approach is the most appealing procedure because of its superb

performance in chemistry and material sciences.70 CPMD combines classical molecular

dynamics with quantum mechanical computations of the electronic structure (ab initio

part). The forces on the nuclei are obtained from the electronic ground state energy using

the Hellmann-Feynman theorem, rather than from an empirical force field as common for

the non-ab initio based MD methods. The Car-Parrinello procedure differs from the Born-

Oppenheimer MD technique in using a dynamical optimization scheme known as

simulated annealing for electronic wave function degrees of freedom, which can be treated

simultaneously with Newtonian nuclear dynamics. As the parameter of inertia, called

“fictitious electronic mass”, is much smaller than the nuclei masses, the wave function

adapts instantaneously to the moving nuclei and keeps the electrons sufficiently close to

the correct ground state (within the Born-Oppenheimer approximation).

4.3. Computational Methods

The Car-Parrinello molecular dynamics69 simulations were performed with the

CPMD program71 using a plane wave basis and a spin polarized semi-local BLYP

functional.27,28 The wave function was expanded at the Γ-point in a plane wave basis set

with the kinetic energy cutoff of 70 Ry and a cuboid box (dimensions [11.007 x 8.805 x

8.805] Å) was used under the periodic boundary conditions. The form of the non-local

pseudo-potential according to Kleinman and Bylander was employed,72 and the core

electrons were described by the pseudopotentials of Trouiller and Martins.73 Simulations

on positively charged species were performed with the corresponding negative charge

distributed uniformly in the cell.74 The time step (given in a.u.; 1 a.u. ~ 0.0241888 fs) for

the numerical integration of the equations of motions,75 according to the velocity Verlet

algorithm, was adjusted to a particular system under investigation; for the neutral

valeramide a time step of 4 a.u. was employed, while for the radical cation the time step

equals to 3 a.u.

Some of the optimized geometries obtained in the previous theoretical study68 were

used as initial structures for the CPMD runs. These geometry optimizations were

Temperature effect on the dissociation pattern of ionized valeramide 49

performed with the GAUSSIAN 98 suite of programs employing the B3LYP

functional27,28 and the 6-31G* basis set.76

In case of the CPMD simulations, the labels do not only represent one particular

structure (conformer) as was the case for the non-dynamical computations;68 rather, it

comprises the whole conformational subspace, although in the accompanying figures often

only one representative is depicted.

In order to test the reproducibility and compare the results obtained in the previous

study68 (B3LYP/6-311++G**//B3LYP/6-31G*) with those computed with the CPMD

(BLYP and cutoff of 70 Ry), one of the crucial transition barriers for the conformational

change in valeramide radical cation has been singled out. For the conformational change

11+• → 13+•, the barrier equals to 3.5 kcal/mol at the B3LYP/6-311++G**//B3LYP/6-31G*

level of theory, while it amounts to 4.0 kcal/mol (0 K) when computed with the BLYP

functional as implemented in the CPMD program. Thus, an overall good agreement

between the results obtained with the two computational methods is expected.

4.4. Neutral Valeramide

McLafferty rearrangement

route)

-H transfer

route)

EI EI

Scheme 4-1. Conformational changes from the conformation with a relaxed carbon backbone 11 into

folded ones, that upon ionization may lead eventually to the McLafferty or the δ-H transfer

rearrangements.

A CPMD study of neutral valeramide 1 is used to address hypothesis (I), i.e. that

the population of the neutral conformers required to access the C2-route increases at

elevated temperatures. Therefore, CPMD simulations at an average temperature of 519 K

were performed.77 As an initial geometry conformer 11 was used (Scheme 4-1), which was

obtained as the (global) minimum in the previous study.68 Monitoring the dihedral angle

50 Temperature effect on the dissociation pattern of ionized valeramide

C(1)-C(2)-C(3)-C(4) during the CPMD simulation (Figure 4-3) should indicate

conformational changes of the fully extended carbon-chain conformation into folded

conformers that might serve as precursors for the intramolecular H-transfers. However,

during the MD simulation, which lasted for 6250 fs, no relevant conformational changes of

1 were observed (the dihedral angle C(1)-C(2)-C(3)-C(4) remains practically constant).

The parameter that fluctuates most is the dihedral angle N-C(1)-C(2)-C(3) (Figure 4-3),

which is associated with an internal rotation of the amide group. However, as the results of

such simulations depend heavily on the initial conditions (e.g. choice of the starting

conformer) and a possibility of insufficient sampling time, a note of caution is warranted.

There are two ways to address the problem: either to perform a great number of MD

simulations with different initial conformers, or to compute the free activation energy

associated with the conformational changes crucial for the eventual hydrogen transfers.

Since for valeramide more than 200 different conformers were indicated to exist,68 it seems

rather impractical to perform as many MD runs commencing from those conformers.

Instead, the barriers associated with the conformational change starting from a

conformation with the totally relaxed carbon-backbone (Scheme 4-1: encircled) into the

folded ones, i.e. 12 and 13 were computed.

/ °

t / fs

(C -C -C -C )

1234

(N-C -C -C )

123

0 1000 2000 3000 4000 5000 6000

100

150

200

Figure 4-3. Changes in the dihedral angles of neutral valeramide 1 during the CPMD simulation; average

temperature 519 K; trajectory sampled for 6250 fs.

The free energy profiles associated with both conformational changes were

computed at approximately 500 K; in these computations the distances between the oxygen

atom and a hydrogen atom attached to C(4) (crucial for the McLafferty rearrangement) or

to C(5) (crucial for the δ-H shift) were varied by performing a series of short CPMD

simulations at different, fixed O-H distances (constraint parameter). For the purpose of

driving the system along the reaction path it is not necessary that the constraint degree of

freedom is identical with the true reaction coordinate. Rather, it suffices that the constraint

Temperature effect on the dissociation pattern of ionized valeramide 51

variable approximately points in the direction of the tangent of the reaction path.78 The free

energy profile can be determined by integrating the mean averaged force with respect to

the constraint coordinate.79 Therefore, short CPMD simulations (ca. 0.5 ps) were

performed for a constraint O-H distance with an increment of 0.2 Å.80 The free activation

energy (

∆

G‡) associated with the conformational change from the completely relaxed

carbon chain (11)81 into the folded conformer that after ionization could lead to the

McLafferty rearrangement (12) amounts to 3.5 kcal/mol (Figure 4-4), while

∆

G‡ for the

change into a conformer, from which the δ-H shift might commence (13), equals to 5.9

kcal/mol (Figure 4-5). At average temperatures82 of the simulations, the thermal energy

available in the direction of the reaction coordinate equals to 0.5 kcal/mol. Thus, the

conformational barriers in these endergonic reactions cannot be overcome just by thermal

motion. Moreover, taking into account relative stabilities using the Boltzmann equation,

one obtains an approximate composition of the conformational populations assuming that

the ensemble contains only the fully relaxed carbon chain conformation (11) and the two

folded ones (12 and 13). This estimation results in a composition of 96.4 % 11, 3.3 % 12,

and 0.3 % 13. Therefore, the first hypothesis can be ruled out since the conformational

population of neutral valeramide at ca. 500 K consists mostly of a conformation with a

fully relaxed carbon backbone 11. Folded conformations cannot explain the observed

d(O-H ) /

C(4)

Figure 4-4. The free energy profile at an average temperature of 521 K for the conformational

change 11 → 12; from the latter, upon ionization, the McLafferty rearrangement

could commence. For the CPMD simulations the distances between the oxygen

atom and a hydrogen at the C(4) center were constrained.

52 Temperature effect on the dissociation pattern of ionized valeramide

temperature effect on the dissociation pattern because they are not populated in sufficient

amount due to the conformational barriers that cannot be surmounted by thermal motion.

Thus, an explanation of the anomalous temperature effect has to be sought on the potential

energy surface of the valeramide radical cation 1+•.

d(O-H ) /

C(5)

Figure 4-5. The free energy profile at an average temperature of 523 K for the conformational change 11

→ 13; from the latter, upon ionization the δ-H transfer could commence. For the CPMD

simulations the distances between the oxygen atom and a hydrogen at the C(5) center were

constrained.

4.5. Valeramide Radical Cation

4.5.1. Simulations at 300 K

As initial geometries for the CPMD simulations at ca. 300 K, three different

conformers of the valeramide radical cation (11+•, 13+• and 14+•)83 were used. Conformer

11+•, which contains a fully relaxed carbon backbone, corresponds to the global

minimum,68 and conformers 13+• and 14+• were identified as those from which the

McLafferty and the δ-H shift rearrangements commence. When 11+• is used as the initial

geometry for the CPMD simulation, an intramolecular hydrogen transfer was not observed

even after 7257 fs (see inset in Figure 4-6). Further, the dihedral angle C(1)-C(2)-C(3)-

C(4) that could indicate a reaction does not change significantly during the simulations,

neither does the distance between the oxygen atom and a hydrogen from the C(4)

Temperature effect on the dissociation pattern of ionized valeramide 53

position.84 However, if the initial geometry contains already a folded carbon backbone, the

McLafferty rearrangement is completed after only 392 or 1925 fs, depending whether the

initial geometry for the CPMD simulation was 13+• or 14+•, respectively.

0250 500 750 1000

0500 1000 1500 2000 2500

t / fs

d(O-H ) /

C(4)

Åd(O-H ) /

C(4)

d(O-H ) /

C(4)

t / fs

0 2000 4000 6000 8000

Figure 4-6. The CPMD simulations of 1+• at 300 K. The reaction (γ-H shifts) constitutes the initial phase

of the McLafferty rearrangement. Two different conformers of the valeramide radical cation

were used as starting geometries: A) 13+• and B) 14+•. In the inset, the CPMD simulation at

300 K is shown for the conformer 11+• as initial geometry; trajectory sampled for 7257 fs

during which no reaction is observed.

The progress of the McLafferty reaction can be followed by monitoring the distance

between the oxygen and a hydrogen atom bonded to the C(4) center (Figure 4-6). In

conformer 13+• the oxygen-hydrogen distance is already relatively short (3.023 Å), thus

facilitating the H-transfer reaction (completed within 392 fs). Even though in the non-

dynamical computations conformer 14+• was identified as the one from which the δ-H shift

commences,68 the dynamical simulation (Figure 4-6B) indicates that the McLafferty

rearrangement is easily accessible from that conformation as well. Accordingly, the

54 Temperature effect on the dissociation pattern of ionized valeramide

McLafferty rearrangement seems more probable than the δ-hydrogen shift. However, in

order to substantiate this assumption, the

∆

G‡ changes associated with both rearrangements

had to be computed. Therefore, constraint molecular-dynamics simulations were

performed at ca. 300 K for both rearrangements.85 In order to trigger the McLafferty

rearrangement, the distance between the oxygen and a hydrogen atom bonded to C(4) atom

was constrained (Figure 4-7), and the competing δ-H shift was monitored by confining the

distance between the oxygen and a hydrogen at the C(5) atom (Figure 4-8).

d(O-H ) /

C(4)

=4.5kcal

mol

Figure 4-7. The free energy profile for the McLafferty rearrangement at an average temperature of 299

K, as obtained from the series of constraint CPMD simulations. The distances between the

oxygen atom and a hydrogen at the C(4) center were constrained.

The activation free energy associated with the McLafferty rearrangement 1+• → 2+•

amounts to 4.5 kcal/mol. As can be seen in Figure 4-7, the major amount of the activation

energy is used for the conformational change (the O-H distance varies from 3 - 5 Å), while

the actual hydrogen transfer does not seem to be rate determining; this scenario was

already suggested in the previous experimental and theoretical studies.22,68 As soon as the

“correct” conformer is formed, the hydrogen transfer proceeds without any barrier to form

Temperature effect on the dissociation pattern of ionized valeramide 55

the distonic ion 2+• in an exergonic reaction (-7.8 kcal/mol). This ion serves as an

intermediate in the pathway in which propene (C3-channel) is formed in an entropy-driven

reaction.

The δ-H shift is more complex due to the conformational changes that 1+• has to

overcome in order to populate a conformer from which the H transfer can proceed. Several

conformational steps are indicated (see Figure 4-8) and the total activation energy prior to

the H-shift activation amounts to 5.0 kcal/mol, while the free energy activation for the final

step, i.e. the δ-H transfer, equals to 2.0 kcal/mol. Thus, these CPMD computations are as

well in good agreement with experimental and theoretical studies,22,68 according to which

the conformational changes are energetically more demanding than the actual H-transfers

themselves for both competing processes. In addition, the observation that the C3 route is

associated with a negligible kinetic isotope effect for hydrogen versus deuterium migration

(KIE = 1.03 ), whereas the C2 route bears a small, but yet significantly larger effect (KIE =

1.32)22 is in accord with the present CPMD results.

(

O-H

)

C(5)

= 7.0 kcal

mol

Figure 4-8. The free energy profile for the δ-H transfer at an average temperature of 301 K, as obtained

from the series of constraint CPMD simulations. The distances between the oxygen atom

and a hydrogen at the C(5) center were constrained.

56 Temperature effect on the dissociation pattern of ionized valeramide

Comparison of the total

∆

G‡ changes (Table 4-1) for both rearrangements reveals

that the McLafferty rearrangement (4.5 kcal/mol) is energetically less demanding than the

δ-H shift (7.0 kcal/mol). Moreover, the PES associated with the McLafferty rearrangement

is less complicated and the distonic ion 2+• can immediately dissociate upon its formation

thus increasing the entropy of the reaction; in contrast, the distonic ion 5+• can enter either

directly or through yet another H-shift the dissociation channel (C2-route; see Figure 4-2).

Thus, the McLafferty rearrangement seems more probable at 300 K than the δ-hydrogen

transfer. However, this does not yet explain the observed temperature effect on the

dissociation pattern. Therefore, CPMD simulations at 500 K had to be performed.

Nevertheless, at this point a brief comment on the third hypothesis, i.e. the role of long-

lived 1+•, is warranted. Because the conformational changes are energetically more

demanding than the corresponding hydrogen transfers, conformer 1+• is trapped by

conformational barriers and can be postulated to be long-lived at ca. 300 K. In fact, no H-

transfer was observed when the fully relaxed carbon backbone conformation 1+• was taken

as the initial geometry (see inset in Figure 4-6). This finding strongly suggests that in the

experiments performed at lower temperatures (ca. 320 K) a larger population of 1+• is

mass-selected than at elevated temperatures, which eventually undergoes more readily the

McLafferty rearrangement (C3-route), thus increasing (relatively to the results at higher

temperatures) the C3/C2 ratio to approximately 3. Nevertheless, this explanation does not

exclude the possibility that at higher temperatures the population of intermediate 2+• is

effectively depleted so that a significant fraction of 2+•, formed upon ionization of 1,

already dissociates before mass-selection.

Table 4-1. Comparison between energy demands (in kcal/mol) for processes relevant for the valeramide

radical cation 1+• dissociation obtained with a non-dynamical method (B3LYP/6-311++G**//B3LYP/6-

31G*) and the CPMD method.

Non-Dynamical

MethodaCPMD method

0 K 300 K 500 K

Activation McLafferty

-H

shift

McLafferty

-H

shift

McLafferty

-H

shift

Conformational 3.5b4.0 4.5 5.0 2.5 3.6

H-transfer n/ac3.7 0.0 2.0 0.0 2.0

Total 3.5 4.0 4.5 7.0 2.5 4.4

Values taken from ref. 68; they correspond to the most stable conformer of the particular structure. The values given present

relative enthalpies at 0 K. b The BLYP as implemented in CPMD results in a barrier of 4.0 kcal/mol at 0 K. c The transition

structure associated with the H-transfer could not be located.

Temperature effect on the dissociation pattern of ionized valeramide 57

4.5.2. Simulations at 500 K

d(O-H ) /

C(4)

Θ (

C-C-C-C) / °

1234

t / fs

0500 1000 1500 200

100

150

200

Figure 4-9. The CPMD simulation at an average temperature of 535 K. The reaction observed corresponds to

the McLafferty rearrangement. The conformer 11+• was used as initial geometry.

As the initial geometry for the CPMD simulation at ca. 500 K, conformer 11+• was

employed and the McLafferty rearrangement was completed already after 1444 fs (Figure

4-9). The reaction evolution can be monitored as well by following the change in the

dihedral angle C(1)-C(2)-C(3)-C(4) that accompanies the H-transfer. Prior to the

McLafferty rearrangement a conformational change had to occur; this is achieved within

1200 fs (see the change in the dihedral angle in Figure 4-9). Simultaneously with the

hydrogen transfer, a further conformational change takes place in which the dihedral angel

decreases below 25°. After the H-transfer has been completed, a new distonic ion is formed

where the oxygen atom is protonated and the radical center is located at C(4); the resulting

distonic ion undergoes yet another conformational change in order to escape from its

staggered conformation.

58 Temperature effect on the dissociation pattern of ionized valeramide

d(O-H ) /

C(4)

=2.5kcal

mol

Figures 4-10. The free energy profile for the McLafferty rearrangement at an average temperature of 486

K, as obtained from the series of constraint CPMD simulations. The distances between the

oxygen atom and a hydrogen at the C(4) center were constrained.

In line with conclusions derived in the previous chapters, also at higher

temperatures the McLafferty rearrangement seems again more probable than the δ-H shift

counterpart. Nevertheless, to be on the safe side, the free activation energy associated with

both H-transfer processes has been computed. Therefore, constraint CPMD simulations85

were performed at ca. 500 K with 1+• as the initial geometry for both reaction coordinate

calculations. The

∆

G‡ for both rearrangements are, as expected, lower at 500 K than at 300

K. In the case of the McLafferty rearrangement (Figure 4-10), the total free activation

energy equals to 2.5 kcal/mol, while the δ-H shift is again energetically more demanding

(4.4 kcal/mol; Figure 4-11). In both cases, conformational changes need to occur prior to

the H-transfer. In the McLafferty rearrangement, the actual H-transfer proceeds barrierless,

and the reaction takes place as soon as the right conformer is formed. Prior to the δ-H

transfer, at least two conformational barriers have to be overcome (Figure 4-11), and the

activation energy associated with these steps equals to 3.6 kcal/mol, being again higher

Temperature effect on the dissociation pattern of ionized valeramide 59

than

∆

G‡ for the H-transfer (2.0 kcal/mol) itself. Thus, the conformational changes that

enable H-transfers are again rate-determining for both rearrangements.

Comparing the total free activation energies associated with the two hydrogen

transfers, it is clear that the McLafferty rearrangement is more probable. Moreover, such a

low activation energy for the McLafferty rearrangement is expected to be easily overcome

under mass-spectrometric conditions, where the appearance energy of the C3 route is very

close to the ionization threshold of 1 (Figure 4-2). Therefore, it is quite likely that at

elevated temperatures a significant fraction of 2+• formed upon ionization of 1 already

dissociates before mass-selection is achieved; as a consequence, the actual C3/C2 ratio

drops in the experiments conducted at a source temperature of 500 K. In the mass-

spectrometric experiments, the time window between the ionization and the mass-selection

(some µs) is sufficiently large to induce the γ-hydrogen transfer and the dissociation of the

distonic ion 2+•.22,23 According to the CPMD simulation (Figure 4-9) the rearrangement is

d(O-H ) /

C(5)

= 3.6 kcal/mol

= 2.4 kcal/mol

= 3.6 kcal/mol

= 4.4 kcal/mol

Figure 4-11. The free energy profile for the δ-H transfer at an average temperature of 483 K, as obtained

from the series of constraint CPMD simulations. The distances between the oxygen atom

and a hydrogen at the C(5) center were constrained.

60 Temperature effect on the dissociation pattern of ionized valeramide

completed after only 1444 fs. Since the subsequent dissociation of 2+• is barrierless,68 it is

likely to happen immediately after the H-transfer has been completed.

4.6. Conclusions

CPMD studies of neutral and ionized valeramide provide a rational for the unusual

temperature effects on the C3/C2 branching ratio as observed in mass spectrometric

experiments. According to the CPMD calculations, even at elevated temperatures, a

conformation with the fully relaxed carbon backbone predominates (96 %) the population

of the neutral valeramide. The

∆

G‡ values associated with folding of the carbon backbone

into conformers from which the desired H-transfers can commence, amount to 3.5 or 5.9

kcal/mol. However, these barriers cannot be surmounted just by thermal motion.

The CPMD simulations performed at ca. 300 K on the ionized valeramide reveal a

substantial stability of a conformation in which the carbon backbone is fully relaxed; no

reaction was observed for the trajectory that was sampled for more than 7 ps. However,

when conformers with the folded carbon backbone are used as initial geometries, the

McLafferty rearrangement is completed within 2 ps. Therefore, the McLafferty

rearrangement seems to be more probable and is associated with a total free activation

energy of 4.5 kcal/mol, while the δ-H shift is energetically more demanding being equal to

7.0 kcal/mol.

At elevated temperature (500 K), the observed reaction (within 1.4 ps) corresponds

to the McLafferty rearrangement. The estimated free activation energy associated with this

process amounts to 2.5 kcal/mol, while the total free activation energy for the δ-H transfer

equals to 4.4 kcal/mol.

In accordance with the experimental22,23 and theoretical studies performed on

valeramide, the CPMD computations provide a rational for the observed temperature effect

on the dissociation pattern of ionized valeramide. Finally, it can be concluded that the

unusually low branching ratio between the two dissociation channels observed in the

experiments conducted at the source temperature of ca. 500 K is most likely due to two

factors:

(i) The relatively low free activation energy of the McLafferty rearrangement cause

the dissociation of a substantial fraction of 1+• or its distonic ion 2+• prior to the time-

Temperature effect on the dissociation pattern of ionized valeramide 61

delayed mass selection; this reduces the C3/C2 ratio relatively to the one observed at lower

temperatures.

(ii) Since the barriers associated with conformational changes were shown to be

energetically more demanding than the corresponding hydrogen transfers, 1+•, being

trapped by conformational barriers, is believed to be long-lived at lower temperatures. This

might indicate that in the experiments performed at room temperature a greater population

of 1+• is mass-selected, which then enters easier the McLafferty rearrangement (C3-route)

increasing (relative to ratios at higher temperatures) the C3/C2 ratio.

II. PART

VITAMIN B12 DEPENDENT ETHANOLAMINE AMMONIA LYASE

Rearrangement of aminoethanol as catalysed by ethanolamine ammonia lyase 65

5. Rearrangement of Aminoethanol as Catalyzed by

the Vitamin B12-dependent Ethanolamine Ammonia

Lyase∗

5.1. Migration vs. Elimination of the (Protonated) Amino Group

The vitamin B12 coenzyme-dependent enzymes catalyze homolytic cleavage of the

C-H bond,86,87 and it is generally believed that in the subsequent 1,2-migration of

hydrogen, alkyl, carbonyl, hydroxyl, or amide groups radical intermediates are involved.88

Ethanolamine ammonia lyase89 from bacteria metabolizes the substrate 2-aminoethanol,90

1, to ethanal, 11, and ammonia (Scheme 5-1).91 Even though the best substrate for this

reaction is 1, the enzyme can utilize a number of other 2-aminoalcohols as well. The

ethanolamine ammonia lyase requires the presence of the vitamin B12 coenzyme for its

catalytic activity. A central part of the catalytic role of vitamin B12 stems from the relative

weakness of its cobalt-carbon bond with a dissociation energy less than 30 kcal/mol.92 It is

assumed that the energy required for that homolysis could be delivered by a

conformational change in the protein induced by binding of the substrate, and homolysis of

the Co-C bond is accelerated up to a factor of 1012 in the presence of an enzyme.93 In the

first step of the reaction, the homolytic cleavage of the C-Co(III) bond in the vitamin B12

coenzyme is assumed to generate the low-spin Cob(II)alamin and the 5’-deoxyadenosyl

radical, and it is the latter radical that has been proposed to abstract a hydrogen atom from

aminoethanol (Scheme 5-1: 1 → 2).94 There are some indications that the protein-

associated radical could participate in that step as well (see Chapter 7).95 As for the initially

formed intermediates involved in the subsequent rearrangement of 2, ambiguities still

exist. From experiments two basic pathways have been proposed (Scheme 5-1):96 an

amine-migration pathway (2 → 4) and an amine-dissociation pathway (2 → 10). Both

routes yield eventually the same final products, i. e. ethanal, 11, and ammonia; 11 itself is

formed by reabstraction of a hydrogen atom from 5’-deoxyadenosine, thus regenerating the

adenosyl-Cob(III)alamin and closing the catalytic cycle. As far as the rearrangement of 2 is

∗ Results discussed in this chapter have been published in: Semialjac, M.; Schwarz, H. J. Am. Chem. Soc.

2002, 124, 8974.

66 Rearrangement of aminoethanol as catalysed by ethanolamine ammonia lyase

concerned, despite elegant EPR experiments97 and circumstantial evidence, the detailed

mechanistic picture of this and related B12 catalyzed transformations is the least understood

aspect in the bound free-radical hypothesis.

CHOH

CHO

Ad-CH

-Co

(III)

Ad-CH

+ Co

(II)

Ad-CH

-Co

(III)

Ad-CH

+ Co

(II)

CHO

amine-migration

pathway

amine-dissociation

pathway

Scheme 5-1. Possible rearrangement paths in the deamination of aminoethanol, 1, by ethanolamine

ammonia lyase.

The mechanistic dichotomy depicted in Scheme 5-1 seems to exist for other

systems as well, and under particular conditions radical-mediated rearrangements were

shown to be facile compared to those with closed-shell species. Often, the energy barriers

for a carbon-heteroatom bond cleavage, caused by a neighboring radical center, decrease to

half of the value for rearrangement barriers proceeding through closed-shell

intermediates.98 As far as gas-phase studies of aminoalkanes are concerned, for the

protonated ethylamine it was shown that the ammonium ion elimination is the energetically

preferred path.99

Recently, quite a few quantum-mechanical studies have been reported on B12-

mediated rearrangements, and noteworthy are the following cases: methylmalonyl-CoA,100

1,2-diols,101, ,102 103 2-methyleneglutarate,104 and the aminomutase catalyzed 1,2-amino

shifts in amino acids.105 The 1,2-amino migrations catalyzed by aminomutases differ from

the formally related 1,2-amino shift catalyzed by ethanolamine ammonia lyase due to the

fact that the former depends on the interaction of the substrate (amino acid) with another

vitamin (i. e. vitamin B6) while the latter rearrangement proceeds by cooperative action of

the enzyme and vitamin B12 only. The intriguing concept of a partially protonated

migrating group suggested by Smith, Golding, and Radom100,101,103,104 seems to play an

important role in the enzyme activity. Due to partial protonation, the energy barriers of the

corresponding rearrangements are lowered to the extent that they get close to the energetics

pertinent to enzyme catalysis.

Rearrangement of aminoethanol as catalysed by ethanolamine ammonia lyase 67

In this chapter, several mechanistic scenarios are addressed including the concept of

(partial) protonation of the substrate. The latter mode of operation is supported by the

finding that in several B12-dependent enzymes the amino-acid sequence of the enzyme

active site contains Asp and His residues,106 which might serve as proton donors. In the

case of methylmalonyl-CoA mutase catalyzed rearrangement it was concluded that His

plays a role of a proton donor.107 From the aminoethanol acidity (pKa = 9.45 for the

conjugate acid of 1), one can expect partial, if not complete protonation of the

aminoethanol substrate embedded in the enzyme’s active site. However, first only the

influence of the full protonation on the rearrangement mechanisms will be investigated,

while the more realistic scenario of partial protonation is being addressed in Chapter 6.

5.2. Computational Methods

All calculations were performed with the GAUSSIAN 98 suite of programs using

the DFT and QCISD approaches. The use of the DFT formalism was a natural choice

because of the balance between accuracy and computational time required by the

calculations. The B3LYP functional was used.27,28 It should be mentioned that in related

studies108 B3LYP calculations have provided good agreement with the experimental data

as well as the data obtained with the high-level theoretical methods.

Geometry optimizations were performed with Pople’s polarized double-ζ 6-31G*

basis set. In order to characterize the optimized structures, frequency analysis has been

performed at the same level of theory. Minima were characterized by the absence of

imaginary vibrational frequencies, while transition structures exhibited one imaginary

frequency. Computations of reaction pathways (IRC, relax PES scans) were carried out at

the same level of theory.

Since the B3LYP method occasionally performs quite unsatisfactory in the case of

the reaction enthalpy evaluations,109 geometry reoptimizations were performed at the

QCISD level of theory using Dunning’s correlation-consistent double-ζ basis set cc-

pVDZ110 in order to obtain more accurate energetic profiles of the reactions in question, as

well as the geometries of the stationary points. The CBS-RAD (QCISD, B3LYP)

method111 has not been applied since the computational cost would be even higher, and the

energetic picture of the overall rearrangement pathways would not change dramatically. A

68 Rearrangement of aminoethanol as catalysed by ethanolamine ammonia lyase

uniformed scaling factor of 0.9806 was used for the zero-point energy (ZPE) corrections

obtained at the B3LYP level of theory. The relative energies in the text (given in kcal/mol)

correspond to the enthalpies at 298 K obtained at the QCISD level of theory, unless

specified otherwise. The electronic energies, ZPEs, and the enthalpies of stationary points

can be found in the Appendix I of the Supporting Material.

Inclusion of solvent, e. g. water molecules, in the calculations is not indicated on

the ground that hydrogen exchange has not been observed in vitamin B12-dependent

rearrangements.87c While the amino-acid sequence of the enzyme has been determined,112

the X-ray structure of the enzyme is not yet known. Consequently, no information is

available on how the amino acids relevant for a protonation of 1 are positioned in the

active site. Therefore, for the time being a comprehensive computational analysis of the

isolated substrate seems to be useful of providing insight into the energetically most

feasible mechanistic scenarios operating in the actual rearrangement of 2 (Scheme 5-1).

In the computations, various rearrangement possibilities of the neutral

aminoethanol radical 2, and its N-protonated counterpart 6 (Schemes 5-2, 5-4) were

considered. The structure labels in Schemes 5-2 and 5-4 comprise the whole

conformational space to which a structure in question belongs, while in the text, when

discussing the mechanisms, a particular computationally characterized conformer is

addressed. When more than one conformer was obtained during the calculations, the

subscript of the label points to a specific conformer. The relative enthalpies at 298 K of the

stationary points are presented in Tables 5-1 and 5-2, and the optimized geometries of

minima in Figure 5-1; geometrical parameters of transition structures can be found in

Figure 5-2. Comparing the radical geometries obtained at both levels of theory (Figures 5-

1, 5-2), the most pronounced bond-length differences exist in the transition structures. The

QCISD method is believed to provide a more accurate description of the actual

geometries.113 As expected, for the closed-shell species both methods give nearly identical

results (Figure 5-1). As to the energetics, all B3LYP barriers are lower than the ones

obtained at the QCISD level of theory; this confirms the well-known B3LYP

underestimation of transition barriers for radical-mediated rearrangements.114,115

Rearrangement of aminoethanol as catalysed by ethanolamine ammonia lyase 69

1.496

1.378

1.485

1.499 1.373

0.971

1.464

1.499

1.364

0.983

1.478

2.068

5’

CCO

2.767

1.382

1.506

1.483

0.967

1.377

1.505

1.468

0.976

1.370

1.508

1.478

2.074

1.489

1.419

1.474

1.470 1.410

1.503

1.495 1.431

1.464

1.465

1.423

1.509

1.493

1.433

1.458

1.461

1.424

1.505

1.334

0.972

0.968

1.347

1.363

1.366

1.491

1.448

1.455

1.486

1.487

1.495

1.392

1.413

0.984

0.981

1.426

1.289

1.286

1.425

1.446

1.239

1.236

CCCC

1.634

1.455

1.344

0.974

1.548 0.971

1.362

1.491

1.676

1.341

0.976

1.577

0.971

1.353

1.477

1.496 1.591

1.476

1.336

1.501

1.484

1.349

1.550

· NH

1.478

1.621

1.371

1.422

1.606

1.251

1.074

1.025

1.062

1.027

1.247

1.625

1.441

1.525

1.494

12 13

1.453

1.521

1.211

1.459

1.215

1.525

1.510

1.535

1.210

1.510

1.210

1.535

1.530

1.412

2.175

1.472

2.179

1.413

1.530

1.475

0.977

0.971

Figure 5-1. Optimized geometries of minima relevant for the rearrangements of 2 and 6; bond lengths

are given in Å (B3LYP results in roman and QCISD in italics).

5.3. Aminoethanol

The conformational analysis of aminoethanol 1 was the subject of several

theoretical studies so far.116,117 Out of a total of 27 conformers, a pronounced hydrogen

bond bridging the two functional groups can be found in several of them. The most stable

70 Rearrangement of aminoethanol as catalysed by ethanolamine ammonia lyase

conformer,118 1 (Figure 5-1), exhibits the strongest stabilization due to a hydrogen bond

between the nitrogen atom and the hydrogen from the OH group (dNH = 2.179 Å).

Concerning the radical

2, several conformers were considered for the reaction

pathway calculations. The hydrogen bond is again an important factor for the structure

stabilization. In the 21 conformer (Figure 5-1) a H-bond exists between a hydrogen atom

from the NH2 group and oxygen (dHO = 2.767 Å); this conformer corresponds to the third

stable structure of aminoethanol. The conformer 22 is structurally related to the global

minimum 1; in 22 the N-H distance of 2.074 Å is even shorter than in 1 (2.179 Å), thus the

H-bond is even stronger in the radical. The third conformer of the aminoethanol radical,

i.e. 23 (Figure 5-1), does not exhibit any stabilization through a H-bond; it is energetically

less stable than the two counterparts mentioned above (by 5.2 kcal/mol relative to 22).

While the most stable conformer 22 may serve as a good candidate for the direct loss of

ammonia (see further in text), this conformer is not likely to play a role in the amino-group

migration towards the electron deficient carbon atom. For this particular rearrangement,

conformers 21 and 23 are better candidates.

6/8

9’/8

6/10

CCCCCC

OOO

1.460

1.693

1.343

1.817

1.402

2.321

1.294

2.745 0.986

2.723 2.521

2.608 2.648

1.297

1.409

1.555

1.662

1.536

1.349

1.469

1.838

2.569

0.980

1.290

1.417

2.701

2/3

3/4

2/4

OCC

1.358

1.362

2.211

2.115

1.369

1.377

1.372 1.359

2.124

2.070

1.366

1.386

1.476

1.389

1.458

1.461

1.388

1.483

1.699

1.713

1.507

1.493

1.455 1.367

2.030

2.031

1.376

1.470

1.996

2.024

2/10

1.638

1.463

1.638

1.733

1.466

1.704

1.29

1.292

1.094

1.067

1.026

1.024

6/13

2/12

3/11

1.411

1.285

1.522

1.291

1.271

1.284

1.429

1.510

1.513 1.244

1.456

1.514

1.451

1.255

1.517

1.461

1.524

1.238

1.514

1.616

1.523

1.249

1.528

1.507

Figure 5-2. Optimized geometries of the transition structures involved in the rearrangements of 2 and 6;

bond lengths are given in Å (B3LYP results in roman and QCISD in italics).

Rearrangement of aminoethanol as catalysed by ethanolamine ammonia lyase 71

5.4. Intramolecular Migration

A) NH

CHOH CH

CHOH

234

B) NH

CHOH CH

CHOH

C) NH

CHOH CH

CHOH

D) NH

CHOH CH

CHOH

678

E) NH

CHOH CH

CHOH

698

F) NH

CHOH CH

CHOH

2/3

CHOH

3/4

CHOH

2/5 5/4

CHOH

2/4

CHOH CH

CHOH

6/7 7/8

CHOH

6/9 9/8

6/8

Scheme 5-2. NHx (x = 2, 3) migration pathways of 2 and 6 resulting in the formation of 1-aminoethanol

radical, 4, and the N-protonated counterpart, 8. The encircled rearrangement 6 → 8

corresponds to the energetically preferred path.

72 Rearrangement of aminoethanol as catalysed by ethanolamine ammonia lyase

5.4.1. Dissociation-association Mechanism (Schemes 5-2A and 5-2D)

The activation enthalpy for the dissociation of the aminoethanol radical 21 into

ethenol, 3, and NH2 equals 24.1 kcal/mol; this barrier is somewhat higher than the one for

the C-N bond cleavage of the aminoethyl radical. IRC calculations from the 21/3 transition

structure in the direction of the reactant resulted in the 21 conformer. The optimization of

the IRC structure in the product direction (3 and NH2) did not indicate the existence of a

complex between the two species. Instead, the structure breaks into two separate species;

thus, convergence could not be achieved. Therefore, the combined energy of the products

was obtained by calculating the energies of the separately optimized geometries of 3 and

the NH2 radical. A further possibility of the cleavage of 21 has been considered as well:

however, even permitted extensive solvation of the charged species the formation of a

radical-cation 7 and an NH2 anion can be excluded since the energy sum relative to 21

equals 248.7 kcal/mol. With regard to the final rearrangement product, 41, the transition

structure 3/41 has been located. In analogy with the 21/3 transition structure, the

optimization of the IRC structure in a direction of the reactant could not converge.

Assuming that the reaction proceeds indeed via 3 and the NH2 radical, the energy required

to overcome the 3/41 transition state barrier equals 25.6 kcal/mol relative to 21. Obviously,

path 2A is energetically too demanding to account for the enzyme-mediated rearrangement

of 2, since it is necessary for an enzymatic reaction that the energy demand for the rate-

determining step falls below 20 kcal/mol.102,108

For the related reactions of the protonated radical 6 (Scheme 5-2D), the transition

structures 6/7 and 7/8 were not located. Nevertheless, the combined energy of the

intermediate enol radical cation 7 and ammonia (Table 5-2) is already too high to make

this route a likely pathway in the rearrangement of the protonated radical 61. While the

energy sum of the products 7 and NH3 of the first rearrangement step equals 29.2 kcal/mol,

relative to 61, this situation gets worse energetically if ethenol 3 and the radical cation

NH3+• are considered as a possible pair of products; the combined energy of 3 and NH3+•,

relative to 61, amounts to 47.0 kcal/mol. Clearly, this pathway is energetically not

accessible for a fast enzymatic reaction, even if the enzyme might stabilize the transition

states of the dissociation/association pathways 2A and 2D substantially.

Rearrangement of aminoethanol as catalysed by ethanolamine ammonia lyase 73

5.4.2. Sequential Intramolecular Isomerizations (Schemes 5-2B and 5-2E)

All attempts to locate the cyclic structure 5 as a minimum on the PES failed.

During geometry optimization, one of the hydrogen atoms dissociates from the NH2 group,

forming the closed-shell cyclic structure 5’ (see Scheme 5-3A). The final product 43 (a

conformer of 4 obtained with the IRC calculation from the corresponding TS 5’/43), can be

formed through the transition structure 5’/43, which is associated with re-addition of the

hydrogen atom (the activation enthalpy relative to 21 equals 58.1 kcal/mol). Again, and in

line with findings on related processes, the energies of all species characteristic for the

sequence depicted in Scheme 5-3A are much too high to play a role in an enzymatic

reaction.

A nonclassical structure proposed by George et al.102 in the related isomerization of

1,2-ethanediol, where a hydrogen atom from an OH group bridges the C-C bond, could not

be found as a stationary point of any kind for the isomerization of 2. Similarly, in that

study102 a classical structure where oxygen, rather than NH2, is the bridging group could

not be located either.

Some of the problems encountered in the reaction pathway calculation discussed

above were faced in the case of the protonated radical 6 as well. Instead of locating the

cyclic protonated radical 9 (Scheme 5-2E), the closed-shell cyclic cation 9’ was obtained

upon geometry optimization of 9. The transition structure 9’/8 involved in the formation of

8 was found to lie 72.7 kcal/mol above 61 (Scheme 5-3B), thus discarding this route in the

isomerization of 6.

CHOH CH

CHOH

5' 4

CHOH

5'/4

CHOH CH

CHOH

9' 8

CHOH

9'/8

Scheme 5-3. NHx (x = 2, 3) migration accompanied by hydrogen atom dissociation/association.

74 Rearrangement of aminoethanol as catalysed by ethanolamine ammonia lyase

5.4.3. One-step Migration of NH2/NH3 (Schemes 5-2C and 5-2F)

All stationary points of interest have been located on the respective PESs. The IRC

calculations performed from the transition structure 23/42 lead to the conformers 23 and 42.

The barrier for a direct migration of a NH2 group amounts to 78.2 kcal/mol, and this

pathway is therefore not expected to play role in the enzymatic reaction.

In contrast to the radical 2, the activation enthalpy for the intramolecular transfer of

the NH3 group starting from 61 equals to only 10.4 kcal/mol, thus clearly falling into the

energy range typical for enzyme-catalyzed reactions. The analogous barrier in the case of

ammonium-ethyl radical was calculated to be 25.0 kcal/mol for the investigation of a 1,2-

amino shift catalyzed by aminomutases. Obviously, the presence of the OH group at the

radical terminus dramatically influences the transition state in such a way that the

rearrangement is feasible even without the action of an additional cofactor, e.g. B6, as in

the case of the 1,2-amino shift catalyzed by aminomutases. Apparently, the spin

delocalization through an additional heteroatom makes the migration more feasible.

The origin for the huge difference in the activation enthalpies between the

migration of a neutral versus a charged group is most likely due to the bond redistribution

in the two transition structures. In the case of a protonated group migration, TS 61/8

corresponds closely to 7 and NH3, which can be inferred from the C-N bond lengths (see

Figures 5-1 and 5-2). The enol radical cation 7 is more stable than its keto counterpart due

to a better spin delocalization in the C-C-O backbone;119 such a spin delocalization

stabilizes the transition structure as well. The slightly preferred interaction of NH3 with the

C(1) center, on which the positive charge emerges, is reflected in a shorter N-C(1) distance

with respect to the second C(2)-N bond. As further suggested by the calculations, the spin

density at C(2) exceeds that of C(1). In contrast, in the 23/42 transition structure a three-

center three-electron bond is present through a delocalization of electrons between nitrogen

and two carbon atoms. Any significant delocalization of the spin density between C(1) and

C(2), which would correspond to a partial CC double-bond formation, can be neglected

due to the fact that the C-C bond in 23/42 is actually elongated if compared to 23 (see

Figures 5-1 and 5-2). The two C-N bonds of 23/42 are much shorter than in the related 61/8

transition structure, showing a strong interaction between the NH2 group and the C2

backbone. The formation of such a strained structure with an extra electron in a high-lying

orbital is obviously energetically more demanding than the corresponding 61/8 transition

structure.

Rearrangement of aminoethanol as catalysed by ethanolamine ammonia lyase 75

5.5. Dissociation Pathways

Concerning the role of stepwise NHx (x = 2, 3) dissociation reactions, two

mechanisms were considered, which differ in the details of the initial step. The reaction

can commence either by the cleavage of the C-N bond (elimination of NH2 or NH3) or via

hydrogen atom elimination from the OH group.

CHOH CH

CHO NH

210

2/10

CHOH CH

CHO NH

610

CCH

6/10

CHOH H

CCHOH

CHOH

2/3

CCH

CHO

CHO NH

CHOH

22/12

CHO

CHOH CH

CHOH

6/7

CHO

CHOH

66/13

CHO

3/11 +

Scheme 5-4. Dissociation pathways for the formation of the 2-ethanal radical, 10. The encircled

rearrangement 6 → 10 corresponds to the energetically preferred path.

76 Rearrangement of aminoethanol as catalysed by ethanolamine ammonia lyase

5.5.1. Elimination of the NHx (x = 2, 3) Group as the Initial Step (Schemes 5-4A

and 5-4D)

These two initial steps have already been discussed in the context of dissociation-

association mechanisms (see Schemes 5-2A and 5-2D), and therefore need not to be

analyzed any further.

From the enol 3, ethanal, 11, could be formed directly through keto-enol

tautomerization. The corresponding transition structure 3/11 for the unimolecular 1,3-H

migration120 lies 56.6 kcal/mol above 3; thus, this symmetry-forbidden route can be

discarded due to its high-energy demand. Besides, for that mechanistic proposal, the NH2

radical formed in the step 21 → 3 should then be capable of abstracting a hydrogen atom

from 5’-deoxyadenosine; however, according to EPR experiments a hydrogen atom is

abstracted by either 1-aminoethanol (8) or ethanal (10) radicals.121 Formation of 10

through the homolytic bond cleavages of the O-H bond in 3 or a C-H in 11 is compatible

with the expected high-energy demands, i.e. 76.9 and 90.5 kcal/mol, respectively. If one

assumes that the 3 → 10 transformation is supported by the NH2 radical formed in the

previous step, then the reaction becomes exothermic (-21.1 kcal/mol relative to 3 + NH2•).

Even though the overall reaction energetics starting from 21 turns out to be almost thermo-

neutral (3.0 kcal/mol; taking into account the energy-demanding first step and energy-

releasing second one), the stepwise elimination mechanism starting with an amino-group

elimination is highly unlikely as the initial step 21 → 3 is energetically not accessible.

If a homolytic O-H bond cleavage was to take place in structure 7 (Scheme 5-4D), a

hydrogen radical and the acetyl cation122,123 would be formed, and the combined energy

relative to 7 equals 21.1 kcal/mol. A heterolytic O-H bond cleavage of 7 to produce 10 and

a proton would be even more demanding (187.2 kcal/mol relative to 7). In contrast,

formation of an ammonium ion and 10 makes the latter reaction quite exothermic (-22.8

kcal/mol). However, once more this pathway is not very probable to play a role in the

enzymatic reaction since the initial step, with an activation enthalpy higher than 29.2

kcal/mol, poses a too high barrier.

Rearrangement of aminoethanol as catalysed by ethanolamine ammonia lyase 77

5.5.2. O-H Bond Cleavage as the Initial Step (Schemes 5-4B and 5-4E)

From 21, the homolytic O-H bond cleavage occurs through the transition structure

21/12. The related energy demand equals 33.9 kcal/mol, and it is unlikely that the enzyme

could reduce such a high-energy barrier to make this step feasible. Nevertheless, for the

sake of completeness, the whole reaction profile was investigated. The energy sum of the

products, hydrogen and aminoethanal, 12, lies 20.4 kcal/mol above the reactant structure

21. If a heterolytic O-H bond cleavage of 21 were to take place, the energy of the

aminoethanal radical-anion124 would be, as expected, even higher (371.0 kcal/mol above

21). The energy demand for the homolytic C-N bond cleavage in 12 equals 73.2 kcal/mol.

If this cleavage is coupled with ammonia formation the reaction enthalpy drops to -24.7

kcal/mol (relative to 12 + H•). A heterolytic C-N bond cleavage of 12 can be discarded

since the energy sum of the products, NH2 anion and acetyl cation,122,123 lies 249.3

kcal/mol above 12. In any case, since the first step of the reaction, the hydrogen-

abstraction, is energetically quite demanding (33.9 kcal/mol), it is very unlikely that this

mechanistic scenario plays a role in the enzymatic catalysis.

A homolytic O-H bond cleavage125 in 61 proceeding through the transition structure

61/13 would require 38.1 kcal/mol, again too high for an enzymatic reaction. Consequently,

the PES involving 13 needs no further detailed discussion. Rather briefly, a heterolytic C-

N bond cleavage in 13 yields ammonia and the acetyl cation122,123 as the products, with a

combined energy of 25.3 kcal/mol relative to 13. A homolytic C-N bond cleavage in 13 is

energetically even more demanding, being equal to 98.8 kcal/mol. Even if the latter

cleavage is accompanied by the N-H bond formation to generate the ammonium ion in a

process that is overall exothermic (-18.6 kcal/mol relative to 13 + H•), that route can also

be excluded as the barrier for the initial step 61 → 13 cannot be overcome.

5.5.3. Direct Ammonia/Ammonium Eliminations (Schemes 5-4C and 5-4F)

In the

22 conformer an intramolecular nitrogen-hydrogen interaction renders the

direct elimination of NH3 quite attractive. The transition structure for this path 22/10 lies

29.6 kcal/mol above 22; this barrier originates from the cleavage of a strong O-H bond

accompanied by the formation of a weaker N-H bond, thus resulting in a relatively high

activation enthalpy of the late transition structure 22/10 in which the N-H bond is formed

78 Rearrangement of aminoethanol as catalysed by ethanolamine ammonia lyase

while O-H is almost completely broken (see Figure 5-2). While a complex between

ammonia and the ethanal radical, 10, has not been located on the PES, it can be postulated

to exist (see next paragraph). However, once more the high activation energy makes the

direct loss of ammonia not a very probable rearrangement pathway even if the barrier

could become lowered somehow by enzyme catalysis.

The activation

enthalpy for the direct

elimination of an

ammonium ion starting

from 62 via TS 62/10126

equals only 10.6

kcal/mol. The transition

structure 62/10 can be

discussed in terms of an

interaction of NH3 with

the stable enol radical-

cation 7 (e.g. compare

the bond lengths of

62/10 and 7; Figures 5-

1 and 5-2), where a H-

bond between the

nitrogen atom and the

hydrogen from the OH

group exist (dNH =

2.569 Å). Further, as

already mentioned, a

spin delocalization

through the C-C-O backbone in 62/10 stabilizes the transition structure in contrast to 22/10

where the spin delocalization through three centers is not achievable. A complex between

the ethanal radical, 10, and NH4+ has been located with a stabilization energy of 17.6

kcal/mol below 62. The energy requirement for a complete separation of the two building

blocks amounts to 22.4 kcal/mol, indicating a strong electrostatic interaction between NH4+

and the carbonyl group. However, in an enzymatic environment interaction of NH4+ with

a For electronic energies, ZPEs, and enthalpies see Table AI-1 in the Appendix I.

Table 5-1. Relative enthalpiesa (in kcal/mol) at 0 K (Hrel, 0 K), and 298 K

(Hrel, 298 K) of the stationary points on the aminoethanol radical PES.

B3LYP/6-31G* QCISD/cc-pVDZ

Hrel, 0 K Hrel, 298 K Hrel, 0 K Hrel, 298 K

210.0 0.0 0.0 0.0

22-4.1 -4.4 -4.1 -4.4

231.0 1.1 0.8 0.8

413.7 3.6 -0.8 -0.9

423.2 3.6 1.5 1.9

43-0.2 -0.1 -1.6 -1.6

21/3 20.4 20.6 23.9 24.1

3/4123.0 23.2 25.5 25.6

5’/4354.7 54.4 58.6 58.1

23/4272.5 72.4 79.1 79.0

22/10 16.9 16.4 25.7 25.2

21/12 28.0 28.2 33.7 33.9

5’ + H•44.6 45.4 43.2 43.9

3 + NH2•18.1 19.4 15.6 16.8

7 + NH2-241.4 242.8 247.5 248.7

10 + NH3-6.8 -5.5 -5.4 -4.3

12 + H•21.0 22.0 19.4 20.4

Rearrangement of aminoethanol as catalysed by ethanolamine ammonia lyase 79

negatively charged

amino acid residues

may help to pull out

NH4+ from the active

site; in this case the

overall rearrangement

costs only 10.6

kcal/mol.

13 + H•27.7 28.4 24.3 25.0

a For electronic energies, ZPEs, and enthalpies see Table AI-2 in the Appendix I.

10 + NH4+6.7 7.7 5.4 6.4

29.2 29.3 30.4 28.2 7 + NH3

46.0 47.0 52.2 53.3 3 + NH3+•

620.4 0.6 1.5 1.6

8 2.9 3.0 -0.3 -0.1

61/8 4.7 4.9 10.2 10.4

62/10 8.8 9.1 12.0 12.2

9’/8 69.1 68.7 73.3 72.7

10 · NH4+-17.9 -17.1 -16.7 -16.0

61/13 33.8 33.5 38.4 38.1

9’ + H•48.9 49.5 46.5 47.0

610.0 0.0 0.0 0.0

Hrel, 298 K

Hrel, 0 K Hrel, 298 K Hrel, 0 K

B3LYP/6-31G* QCISD/cc-pVDZ

Table 5-2. Relative enthalpiesa (in kcal/mol) at 0 K (Hrel, 0 K), and 298 K

(Hrel, 298 K) of the stationary points on the protonated aminoethanol radical

PES.

5.6. Formation of Ethanal

Any acceptable mechanism for ethanal formation, in the context of the

ethanolamine ammonia lyase reaction, must be compatible with the rate constant for the

product formation. In an ideal case of complete enzyme saturation, one could approximate

kcat with the rate constant of the product formation. In a realistic case, the rate of the

product formation would be lower, and thus the activation enthalpy higher. Taking the

value of kcat = 55 s-1 for the ethanolamine ammonia lyase at 295 K,127 the activation

enthalpy for the rate determining step can be derived from the Eyring equation. Assuming

a reasonable range of activation entropy of 0 - 10 cal/mol·K, the activation enthalpy falls

into the range 14.9 - 17.8 kcal/mol, respectively; thus any process with an activation

enthalpy higher than ca. 16 kcal/mol can be discarded as a potential step in the deamination

of aminoethanol catalyzed by the enzyme. Therefore, 4 can not serve as an intermediate in

the rearrangement of 1 → 11, since all the investigated reactions, in which 4 is involved

80 Rearrangement of aminoethanol as catalysed by ethanolamine ammonia lyase

(Schemes 5-2 and 5-3), have activation enthalpies of their rate determining steps highly

exceeding 16 kcal/mol.

CHOH

CHO

- NH

5.8

CHO

CHOH

- NH

14.5

CHOH

-H

+ H

96.7 -220.7

-0.1

4.8

- NH

-98.5

-90.5

96.9

-220.9

Scheme 5-5. Conceivable pathways for the conversion of aminoethanol, 1, into ethanal, 11. The numbers

in italics correspond to the reaction enthalpies in kcal/mol at 298 K of the corresponding

reactions (a: number corresponds to a reaction in which conformer 61 is involved; b: number

corresponds to a reaction in which conformer 62 is involved).

Possible steps for the formation of ethanal 11 from intermediates involved in these

reactions, which obey the transition barrier criterion stated above, are summarized in

Scheme 5-5; energies of the relevant closed-shell species are presented in Table AI-3 in the

Appendix I. For example, intermediate 10 is accessible via direct loss of NH4+ from the

protonated radical precursor 62 (see Scheme 5-4F); here the corresponding activation

enthalpy equals only 10.6 kcal/mol. Considering the energy barrier, this elimination has a

high probability to occur even if full protonation of 2 in the enzymatic process has not yet

been demonstrated to take place. Nevertheless, as already shown also partial protonation

can result in a substantial stabilization of the transition structure thus bringing the energy

demand in a region accessible to the enzymatic reaction. From 10, ethanal, 11, could be

formed by interaction with the 5’-deoxyadenosine, while at the same time, the active form

of the vitamin B12 is regenerated.

Intermediate

8 can be formed either by a dissociation-association mechanism

(Scheme 5-2D), or via direct migration of NH3 group (Scheme 5-2F). The former path can

be ruled out due to the energy barrier involved in the rearrangement (higher than 16

kcal/mol). In contrast, the latter route 61 → 8 with an activation enthalpy of only 10.4

kcal/mol has the lowest energy barrier of all investigated rearrangement possibilities. From

8, ethanal can be formed either by loss of an ammonium ion resulting in 10, or by

hydrogen addition from the 5’-deoxyadenosine followed by loss of an ammonium ion.

Rearrangement of aminoethanol as catalysed by ethanolamine ammonia lyase 81

The proposal for an intramolecular NH3 migration 6 → 8 (Scheme 5-2F) is in line

with computational findings of quite similar rearrangements catalyzed by diol

dehydrase,101-103,108 while a dissociation pathway related to 6 → 10 (Scheme 5-4F) is

supported by solution experiments.128 However, the EPR spectra do not allow to

distinguish between intermediates of the rearrangements, thus leaving the question of the

actual rearrangement pathway still unanswered. While the calculations slightly favor the

NH3 migration pathway, with an activation-enthalpy difference between the direct NH3

migration and the NH4+ elimination of only 0.2 kcal/mol, a definitive answer cannot be

given. From the deuterium kinetic isotope effects, it was concluded, that the rate

determining step in the overall reaction sequence corresponds to the hydrogen abstraction

from the 5’-deoxyadenosine by the product radical.129 The estimated energy barrier

associated with that reaction step equals 15 kcal/mol at 298 K;130 thus, both scenarios

suggested by the computational work could well take place in the real enzymatic reaction.

All other investigated pathways can be ruled out on energetic grounds.

5.7. Reaction Enthalpies – a Comparison of Calculated and

Experimental Values

The reaction enthalpies for the transformation of aminoethanol radical, 21, into

ethanal radical, 10, and ammonia have been calculated at both levels of theory (Table 5-3).

In order to obtain even more accurate reaction enthalpies, a frequency analysis of the

structures in question was performed at the QCISD/cc-pVDZ level of theory as well. As

the experimentally derived data for the enthalpy of the aminoethanol radical formation do

not seem to exist in the literature, this figure was estimated from other data available.131

Since the reliability of some of the numbers presented in thermochemical tables can be

questioned, where available, the revised enthalpies132 were used. For protonated

aminoethanol 6 and its rearrangement into ethanal radical 10 and ammonium ion, no

sufficient experimental data could be found in order to calculate the corresponding

experimental enthalpy, thus only the computed values are given. The reaction enthalpies

calculated at both levels of theory fall into the range of the enthalpy predicted from the

experimentally available data. The uncertainty of experimentally derived enthalpies is

82 Rearrangement of aminoethanol as catalysed by ethanolamine ammonia lyase

quite pronounced, and one can safely assume that the computationally determined values,

especially at the QCISD level of theory, are even more reliable in this particular case.

Table 5-3. Comparison between the computed and experimentally derived reaction enthalpies (in

kcal/mol).

B3LYP/6-31G*

aQCISD/cc-pVDZa,b

∆

rH (0 K)

∆

rH (298 K)

∆

rH (0 K)

∆

rH (298 K)

∆

rHexp

21→ 10 + NH3-6.8 -5.5 -6.1 -4.8 -4.6 ± 3.2

61→ 10 + NH4+6.7 11.9 4.4 5.6

a ZPE correction has been taken into account.

b Enthalpies obtained by performing the frequency calculations for reactants and products at the QCISD/cc-pVDZ level of theory.

5.7. Summary and Conclusions

The computational study of the aminoethanol rearrangement clearly discriminates

between various mechanistic scenarios, thus adding in the elucidation of the actual

mechanism of this important enzymatic reaction.

Due to their high activation enthalpies (more than 23 kcal/mol), and reaction

mechanisms involving complete detachment of the NH2/NH3 groups (dissociation-

association mechanisms) can be ruled out. Further, isomerization pathways proceeding

through cyclic intermediates are unrealistic as well due to the fact that such cyclic

structures have not been obtained as minima on the PES neither for the protonated nor the

unprotonated radical. Also, mechanisms involving a stepwise elimination of the NH3/NH4+

species are highly unlikely to play a role in the actual rearrangement routes due to high

energy barriers involved in these pathways.

Concerning the direct transfer of the NH2 group in the aminoethanol radical, that

pathway can be definitively ruled out due to the exceeding high energy demand (more than

70 kcal/mol). It is inconceivable that any enzyme could reduce such a barrier for this

rearrangement to become feasible. On the other hand, the activation enthalpy for a direct

transfer of the NH3 group in the protonated aminoethanol radical is computed to be the

lowest (10.4 kcal/mol) of all rearrangement barriers investigated in this study, thus making

that pathway the most probable rearrangement mechanism of the enzyme catalysis. Indeed,

Rearrangement of aminoethanol as catalysed by ethanolamine ammonia lyase 83

this finding confirms the earlier hypothesis100,101,108 that (partial) protonation of the

migrating group reduces significantly the energy barrier.

The direct NH3 elimination in aminoethanol radical is not expected to be the actual

rearrangement because of an energetically quite demanding barrier. On the other hand, for

the protonated form of aminoethanol radical the activation enthalpy for a direct NH4+

elimination falls into the range of enzyme catalysis (10.6 kcal/mol). However, the possible

complex formation between an NH4+ ion and the ethanal radical could present a bottleneck

for that particular mechanistic route due to the high-energy demand for dissociation of the

complex (22.4 kcal/mol). Nevertheless, as mentioned the enzyme surrounding could help

in abstracting the NH4+ ion from the active site, thus preventing a complex formation.

Clearly, an X-ray structure of the ethanolamine ammonia lyase or further

computational investigations (see next chapter) could help in resolving the mechanistic

dichotomy in distinguishing between the two mechanistic pathways (i.e. direct NH3

migration 6 → 8 vs. NH4+ elimination 6 → 10) predicted by the present model calculations

as the two most probable rearrangements of aminoethanol in enzymatic reactions.

84 His and Asp/Glu acting simultaneously as catalytic auxiliaries

6. His and Asp/Glu Acting Simultaneously as Catalytic

Auxiliaries∗

The further computational investigation aimed firstly at distinguishing between the

two mechanistic scenarios identified as the most probable rearrangement pathways133

discussed in the previous chapter, and will continue with a refinement of the mechanistic

picture of the reaction. To this end, the more realistic concept of partial protonation of a

migrating group introduced earlier by Smith, Golding, and Radom100,101,103,104 has been

applied. Further, since a push-pull mechanism as proposed by Radom and co-workers in

the case of diol dehydrase134 and employed in the study of ethanolamine rearrangement

catalyzed by ethanolamine ammonia lyase as well,135 seems to play a crucial role in the

catalytic activity of ethanolamine ammonia lyase, this mechanistic variant was also taken

into account. However, in contrast to the previous work,135 a model that is more

appropriate for mimicking the actual amino acids has been chosen. A difference between

the ethanolamine ammonia lyase and the related diol dehydrase catalysis is that for the

latter system K+ ions were shown to play a crucial role in reducing the reaction barrier due

to its interaction with the migrating group.134,136

While for the fully protonated substrate 6 the activation enthalpy difference for the

two competing reactions as depicted in Scheme 6-1 (without X) is rather small (0.2

kcal/mol) in contrast to those involving uncharged 2, it can be expected that partial

protonation is likely to discriminate between the two pathways. Again, as stated earlier,

inclusion of solvent, e. g. water molecules, in the calculations is not warranted on the

ground that hydrogen exchange has not been observed in vitamin B12-dependent

rearrangements.87c Thus, any continuum solvent model is not likely to provide more

reliable data than the gas-phase calculations presented herein since the choice of dielectric

constant needed for such calculations is ambiguous. As well, it was shown that the

dielectric constant and the physical environment of an enzyme’s active site are often closer

to those in the gas phase than in bulk solution,137 and furthermore, it was demonstrated that

the protein backbone can substantially influence a local pH.138 In several B12-dependent

enzymes the amino-acid sequence of the enzyme’s active site were found to contain Asp

and His residues, which might serve as proton donors. In the case of the related

∗ Results discussed in this chapter have been published in: Semialjac, M.; Schwarz, H. J. Org. Chem. 2003,

68, 6967.

His and Asp/Glu acting simultaneously as catalytic auxiliaries 85

methylmalonyl-CoA mutase catalyzed rearrangement it was concluded, based on

mutagenesis studies, that His-244 acts as a Brønsted acid.139 For example, mutation of His-

244 from the wild type enzyme into Gly-244 in the mutant led to ca. 300-fold lowering in

the catalytic efficiency of the enzyme. In addition, the crystal structure of methylmalonyl-

CoA mutase indicated that His-244 is within hydrogen-bonding distance to the carbonyl

oxygen of the carbonyl-CoA moiety.140,141 Interestingly, computational studies by

Wetmore et al. confirmed the experimental findings that His most likely partially

protonates the substrate. However, recent QM/MM studies indicated that besides His-244,

two additional amino acids (i.e. Gln-197, Tyr-89) might contribute as well in reducing the

activation barrier.142 In the case of glutamate mutase it was shown by mutagenesis studies

that Glu-171 plays a role of a catalytic auxiliary,143 which was confirmed later as well by

theoretical studies.144 While the amino-acid sequence of the ethanolamine ammonia lyase

has been determined, the X-ray structure of the enzyme is not yet known, and

consequently, no information is available which particular amino acids are relevant for a

protonation of 1 (or 2) and how precisely they are positioned in the active site. Therefore,

several catalytic auxiliaries were considered (Scheme 6-1), including some model systems

for His (X = CH2NH, imidazole) and Asp/Glu (X = HCOOH, CH3COOH). Further, the

questions of the catalytic auxiliary(ies) that interact synergistically with the substrate in the

enzyme’s active site were addressed as well.

CHOH CH

CHOH

X6 X8

CHOH

X6/8

CHO NH

X6 10

CCH

X6/10

CHOH

Scheme 6-1. Partially protonated aminoethanol radical 6 serving as a precursor for: A) NH3 migration, B)

NH4+ elimination (X stands for different interacting groups).

86 His and Asp/Glu acting simultaneously as catalytic auxiliaries

6.1. Computational Methods

All calculations were performed with the GAUSSIAN 98 suite of programs using

the DFT and QCISD approaches. The B3LYP functional was employed.27,28 Geometry

optimizations were performed with Pople’s polarized double-ζ 6-31G* basis set. In order

to characterize the optimized structures, frequency analysis has been performed at the same

level of theory. Computations of reaction pathways, i.e. intrinsic reaction coordinate (IRC)

calculations and relaxed scans of the potential energy surface (PES) were carried out at the

same level of theory.

Because the B3LYP method occasionally performs quite unsatisfactorily in the case

of the reaction enthalpy evaluations, single point calculations and in some cases even

geometry reoptimizations were performed at the QCISD level of theory using Dunning’s

correlation-consistent double-ζ basis set cc-pVDZ in order to obtain more accurate

energetic profiles of the reactions in question. Relative energies (given in kcal/mol)

discussed in the text correspond to the enthalpies at 298 K obtained at the QCISD level of

theory (SP calculations),145 unless specified otherwise. Electronic energies, ZPEs, and the

enthalpies of stationary points are quoted in the Appendix II.

The structure labeling code employed in the previous chapter for the direct

migration of an NH3 group (e.g. TS label: 6/8) and the elimination of NH4+ (e.g. TS label:

6/10) was employed herein with a difference that the structures of analogous

rearrangement types (migration vs. elimination) for different protonating groups HX+ are

described by similar labels distinguished only in the prefix X (more on structure labeling in

the Appendix III of the Supporting Material). As to the formal description of the reactions

depicted in Scheme 6-1, partial protonation and its consequences for the two competing

processes can be viewed as a reaction of 2 with a Brønsted acid HX+ in which, after

formation of 6 the conjugated base X remains interacting with 6 throughout the whole

reaction; alternatively, one may describe the rearrangement in terms of a reaction in which

2 is “sharing” a proton with HXP

+. In the computations reported next the former formalism

has been employed, i.e. the rearrangement commences with 6 that itself remains interacting

via sharing its proton with X.

His and Asp/Glu acting simultaneously as catalytic auxiliaries 87

6.2. Migration vs. Elimination

6.2.1. Hydroxonium and Ammonium Ions as Protonating Groups

As the amino acids Asp, Glu and His contain in their proton donor part either an

oxygen or a nitrogen atom, the protonation of 2 and the ensuing rearrangements of 6 using

NH4+ and H3O+ as Brønsted acids were investigated first.

Table 6-1. Relative enthalpiesa (in kcal/mol) at 0 K (Hrel, 0 K), and 298 K (Hrel, 298 K) of the stationary

points on the PES of 6 interacting with NH3.

B3LYP/6-31G* QCISD/cc-pVDZ//

B3LYP/6-31G*

QCISD/cc-pVDZc

Hrel, 0 K Hrel, 298 K Hrel, 0 K Hrel, 298 K Hrel, 0 K Hrel, 298 K

N610.0 0.0 0.0 0.0 0.0 0.0

N61/8 12.8 13.1 19.9 20.2 20.2 20.5

N8 2.0 2.0 -1.0 -1.0 -0.6 -0.6

N62-0.4 -0.7 -0.9 -1.2

N62/10 17.3 17.5 23.1 23.3

N6’ b-5.5 -5.3 -5.5 -5.3

N6’/8’ b12.6 12.8

N8’ b3.0 3.2

a For electronic energies, ZPEs, and enthalpies, see Table AII-1 in the Appendix II.

b Structures contain an OH group orientation pointing away from the NH3 group (see Scheme 6-3); thus, elimination of NH4+ is not

possible for these conformers.

c Data to be discussed in the paragraph “Influence of the OH Group Conformation on the Migration”.

As expected, with NH4P

+ both transition structures, N6 /8 and N6 /10, are

energetically more demanding than when the stronger Brønsted acid H O

1 2

3+ serves as a

proton donor (Tables 6-1 and 6-2). Comparing structural details of the transition structures

for the reactions with the two protonating groups (see Figure 6-1), it is obvious that in the

TSs proton transfer from H O

3+ is more advanced in comparison to the analogous structures

with NH4+ (see, e.g. the H···X distances in N6 /8 and O6 /8 correspond to 1.831 Å vs.

1.898 Å). Correspondingly, the N···H distance is larger for N···H···X when X = NH (1.055

Å) than for X = H O (1.030 Å).

1 1

88 His and Asp/Glu acting simultaneously as catalytic auxiliaries

Table 6-2. Relative enthalpiesa (in kcal/mol) at 0 K (Hrel, 0 K), and 298 K (Hrel, 298 K) of the stationary

points on the PES of 6 interacting with H2O.

B3LYP/6-31G* QCISD/cc-pVDZ//

B3LYP/6-31G*

QCISD/cc-pVDZ c

Hrel, 0 K Hrel, 298 K Hrel, 0 K Hrel, 298 K Hrel, 0 K Hrel, 298 K

O610.0 0.0 0.0 0.0 0.0 0.0

O61/8 9.9 10.0 16.6 16.7 16.9 16.9

O8 2.8 2.7 -0.1 -0.2 0.4 0.3

O620.2 0.3 0.2 0.3

O62/10 14.6 14.7 18.7 18.8

10·NH4+·H2O -17.1 -16.7 -15.9 -15.4

10 + NH4+·H2O 1.9 2.7 1.4 2.2

O6’ b-4.9 -4.8 -5.0 -4.8

O6’/8’ b9.6 9.7

O8’ b2.6 2.7

a For electronic energies, ZPEs, and enthalpies, see Table AII-2 in the Appendix II.

b Structures contain an OH group orientation pointing away from the NH3 group (see Scheme 6-3); thus, elimination of NH4+ is not

possible for these conformers.

c Data to be discussed in the paragraph “Influence of the OH Group Conformation on the Migration”.

Common to both Brønsted acids is that the transition structures N61/8 and O61/8 for

a migration of the protonated amino group are energetically less demanding than for the

elimination of NH4+ via N62/10 and O62/10. The activation enthalpy difference between

these two transition structures X61/8 and X62/10 varies slightly: it is smaller in the case of

H3O+ (2.1 kcal/mol) than for NH4+ (3.1 kcal/mol). Even though the differences in

activation enthalpy between these two reactions are still rather small, they are more

pronounced than in the case of the full protonation of the amino group (0.2 kcal/mol.

Further, in the H3O+ initiated reaction, a complex between the emerging ethanal radical,

10, NH4+ and H2O was found to exist on the potential energy surface (PES; see Figure 6-

1B). The energy requirement for its dissociation to liberate a free intermediate 10 equals to

17.6 kcal/mol, thus making this pathway even less probable. However, formation of such a

product complex can be by-passed since the enzyme could pull out NH4+ upon its

formation. In any case, the computational data obtained for the rearrangements of 2 with

the crude model systems NH4+ and H3O+ clearly indicate that partial protonation of the

substrate results in an energetic discrimination between the two competing rearrangements.

His and Asp/Glu acting simultaneously as catalytic auxiliaries 89

Whether this encouraging trend continues will be tested next by employing improved

amino acid-model systems.

1.356

1.681

1.557

1.360

1.645

1.553

1.40

1.614

1.525

1.317

1.831

2.437

2.687

1.299

1.844

2.105

2.661

N6 /8

N6 /10

1.367

1.699

1.525

1.403

1.641

1.512

1.309

1.915

2.509

2.520

1.084

1.099

1.046

1.055

1.057

1.117

1.106

1.097

OCC

1.470

1.573

1.706

1.354

1.471

1.572

1.707

1.356

1.388

2.655

1.898

2.502

1.297

2.012 2.275

1.423

1.743

1.654

1.484

1.716

1.566

O6 /8

O6 /10

·NH ·H O

1.495

1.532

1.367

1.403

2.536

2.046

2.600

1.496

1.720

1.539

1.051

1.028

1.051

1.055

1.054

1.030

1.025

1.050

1.065

1.055

1.704

Figure 6-1. Optimized geometries of stationary points relevant for the rearrangements of partially

protonated aminoethanol radical 6 interacting with: A) NH3; B) H2O (bond lengths are given

in Å; B3LYP results in roman and QCISD in italics).

90 His and Asp/Glu acting simultaneously as catalytic auxiliaries

6.2.2. Active Site – What is the Most Probable pH?

The precise pH of a reaction environment around an enzyme’s active site is difficult

if not impossible to predict,146 even if the X-ray structure of the enzyme were known.

Nevertheless, depending on the nature of the amino acids present in the active site the pH

can be approximated provided the effective dielectric constant is known. As mentioned,

deuterium labeling experiments suggest that solvent molecules do not have access to the

active site; consequently, the effective dielectric constant depends mostly on the amino

acids. However, as acidity is also affected by the molecular architecture of the actual

environment (orientations of the amino acids, the protein’s permanent and induced

dipoles),147 due to the absence of an X-ray structure, an accurate prediction of the local pH

is not possible in the present case. Therefore, the discussion will be limited to several

assumed pH ranges, determined by the acidity of the substrate and the amino acids Asp,

Glu and His (Scheme 6-2). Aminoethanol 1 behaves as a base having a pKa of 9.45 for its

conjugated acid. For the radical 2 a similar pKa can be reasonably assumed, as

substantiated by high level ab initio calculations for the proton affinities of aminoethanol 1

and its radical 2, which are identical. If the pH in the active site approximates the one

prevailing under physiological conditions (pH ~ 7.5), 96,97,148 most of the substrate 2 exists

in its fully protonated form. However, partial rather than full protonation might well result

through the interaction of the 2/6 couple with amino acid residues, which can serve as

proton donors or as buffer reagents. As a result, substrate 2 captured in the active site

would not be completely “free” but would interact with the protein backbone; clearly, such

a refined picture resembles more closely enzyme-catalyzed reactions, where an enzyme

through interaction with a substrate lowers the transition structure energy and thus serves

as a catalyst.149

Asp/Glu as protonating agents (Scheme 6-2A): Assuming the amino acids Asp or

Glu to act as proton donors, the pH regimes can be meaningfully divided in three regions,

which are determined by the pKa values of the Asp/Glu side chains150,151 and the pKa of the

substrate. In the case of related glutamate mutase it was confirmed that Glu-171 acts as a

catalytic auxiliary.143,144

At pH < 4, amino acids exist in their non-dissociated form (RCOOH), while

substrate 2 is protonated. Nevertheless, an interaction between the amino acid and the

substrate is possible through a H-bond between the basic carbonyl oxygen of the COOH

His and Asp/Glu acting simultaneously as catalytic auxiliaries 91

group and a proton from the NH3+ group. While that kind of interaction is expected to

stabilize the structure due to a better redistribution of charge, such a low pH in the active

site is not common for enzymes; however, as it cannot be discarded a priori, this scenario

was investigated by computational means.

In the pH regime 4 < pH < 9.5, both amino acids Asp/Glu exist in their carboxylate

forms (RCOO¯) while the substrate is still protonated. Therefore, a “salt bridge”-like

interaction exists between the two charged species. As a consequence, the migrating NH2

group of 2 is only weakly protonated and that results in a destabilization of the

corresponding transition structures. However, as this pH range is common for biological

systems it presents a realistic pH scenario in the active site of the enzyme in question.

At pH > 9.5, the substrate is not protonated and the amino acids exist in their

dissociated forms. An interaction between the two basic sites certainly would not

contribute to a stabilization of the transition structure. As any process involving neutral 2

requires unrealistically high activation enthalpies, a further investigation of such an

interaction was not taken into account. However, interactions of basic auxiliaries with the

OH group of 2 will be addressed later.

A) Asp

Glu

B) His

pH < 4 4 < pH < 9.5 pH > 9.5

pH < 6 6 < pH < 9.5 pH > 9.5

Ostrong attraction

attraction

NH2

CH2CHOH

no interaction

NH3

CH2CHOH H3N

CH2CHOH

attraction

no interaction

NH2

CH2CHOH

repulsion

H2C

CH2

H3N

CH2CHOH

O O

HCH2CHOH

O O

CH2

Scheme 6-2. Different interaction modes between the amino acid and the substrate depending on assumed

pH values in the active site: A) Asp/Glu; B) His.

92 His and Asp/Glu acting simultaneously as catalytic auxiliaries

His as a protonating agent (Scheme 6-2B): His is a common amino acid, which

serves as a proton buffering agent in numerous biological systems because of its pKa value

of 6, which is close to a physiological pH. For example, in the case of the methylmalonyl-

CoA mutase catalyzed rearrangement it was concluded that His-244 is the very amino acid

that partially protonates a substrate and, therefore, lowers the transition barrier.139-141,144

If pH < 6, His and aminoethanol radical 2 are in their N-protonated forms, and

consequently, repulsion is expected as a net effect. Clearly, such a scenario needs not to be

addressed further.

In the pH regime 6 < pH < 9.5, the N(3) atom of His is not protonated, while

substrate 2 is expected to be protonated. Here, a H-bond between N(3) of His and a proton

from the NH3 group of 6 is likely to stabilize a transition structure via charge

delocalization. As mentioned, this particular pH range is common for biological systems

and a computational investigation of this scenario was undertaken.

At pH > 9.5, both the substrate and His are not protonated. Since no stabilization occurs

and all barriers involving 2 are high, a further investigation was not pursued.

6.2.3. His Serving as a Proton Donor

For the interaction of the substrate with His first the most simple imine

(methanimine, CH2=NH) was used as a model system. Despite its limitations, methanimine

is structurally closer to His than NH3 (e.g. the hybridization of the basic nitrogen atoms

that is crucial for the reaction). However, the proton affinity (PA) of methanimine (203.8

kcal/mol) is similar to the PA of ammonia (204.0 kcal/mol), and both differ considerably

from the PA of His (236.0 kcal/mol); consequently, an even closer model system for His

had to be introduced (see further below).

As discussed above, only a pH range 6 – 9.5 needs to be taken into consideration.

In this pH regime the strongest attraction between the substrate and His is expected to exist

between the protonated amino group from the substrate and the imidazole sp2-hybridized

nitrogen atom from His (see Scheme 6-2B).

His and Asp/Glu acting simultaneously as catalytic auxiliaries 93

1.316

1.873

2.459

2.667

1.273

1.296

1.876

2.057

2.678

1.273

1.367

1.694

1.525

1.286

1.404

1.652

1.511

1.286

Mi-6

Mi-6 /8

Mi-6 /10

Mi-8

1.080

1.356

1.703

1.559

1.274

1.086

1.356

1.702

1.559

1.274

1.086

1.406

1.652

1.526

1.274

1.090

1.099

1.046

1.308

1.939

2.519

2.511

1.286

1.041

Figure 6-2. Optimized geometries of stationary points relevant for the rearrangements of partially

protonated aminoethanol radical 6 interacting with CH2=NH which serves as a His model

system (bond lengths are given in Å; B3LYP results in roman and QCISD in italics).

In fact, the trends already observed with the most simple protonating groups (H3O+,

NH4+) exist in the case of the His model methanimine (Mi) as well: migration of a partially

protonated amino group is energetically less demanding than elimination of the ammonium

ion. According to the calculations, the transition structure Mi-61/8 is 2.5 kcal/mol lower in

energy than its Mi-62/10 counterpart (Table 6-3). The stabilization of the former transition

structure is most probably achieved through the formation of a relatively stable planar enol

radical cation moiety.152 In contrast, in the Mi-62/10 transition structure, the enol is

distorted from planarity (Figure 6-2), and already shows a trend of ethanal radical

formation; for example, the C-O bond is shorter, while the C-C bond of Mi-62/10 is longer

than corresponding bonds in Mi-61/8.

Here, a brief comment on the computed values for the activation enthalpies seems

warranted: for the migration of a partially protonated amino group in the system

6/CH2=NH this barrier height amounts to 20.0 kcal/mol, exceeding the upper limit value

(ca. 15 kcal/mol). However, a final answer whether an interaction of His with the substrate

is of any relevance on the migration pathway can be given only after an even more reliable

94 His and Asp/Glu acting simultaneously as catalytic auxiliaries

model system for His has been considered (see further in the text). Nevertheless, the

migration of a partially protonated amino group is once more favored as compared to the

elimination of NH4+.

Table 6-3. Relative enthalpiesa (in kcal/mol) at 0 K (Hrel, 0 K), and 298 K (Hrel, 298 K) of the stationary

points on the PES of 6 interacting with CH2=NH (Mi) which serves as the simplest His model system.

B3LYP/6-31G* QCISD/cc-pVDZ//

B3LYP/6-31G*

QCISD/cc-pVDZ c

Hrel, 0 K Hrel, 298 K Hrel, 0 K Hrel, 298 K Hrel, 0 K Hrel, 298 K

Mi-610.0 0.0 0.0 0.0 0.0 0.0

Mi-61/8 12.4 12.6 19.8 20.0 20.0 20.3

Mi-8 2.1 2.2 -0.8 -0.8 -0.4 -0.4

Mi-620.0 0.0 0.0 0.0

Mi-62/10 16.8 17.0 22.3 22.5

Mi-6’ b-5.4 -5.2 -5.5 -5.2

Mi-6’/8’ b12.1 12.4

Mi-8’ b2.9 3.1

a For electronic energies, ZPEs, and enthalpies see Table AII-3 in the Appendix II.

b Structures contain an OH group orientation pointing away from the NH3 group (see Scheme 6-3); thus, elimination of NH4+ is not

possible for these conformers.

c Data to be discussed in the paragraph “Influence of the OH Group Conformation on the Migration”.

6.2.4. Asp/Glu serving as Proton Donors

Since both amino acids Asp and Glu have similar structures and comparable

acidities formic acid (Fo) was used as a rather crude model to represent both of them

(Figure 6-3). For the sake of shortness, in the text it will be referred only to Asp. Two pH

ranges will be discussed in some detail.

At pH < 4 Asp exists in its non-dissociated form and the substrate 2 is protonated.

Again, the activation enthalpy for the migration involving Fo-61/8 is 2.4 kcal/mol lower

than for the elimination proceeding through the Fo-62/10 transition structure (Table 6-4).

While the activation enthalpy for the migration of a protonated amino group with 16.2

kcal/mol falls into the range of required activation enthalpies (ca. 15 kcal/mol), the

assumed pH < 4 is not common for biological systems.

His and Asp/Glu acting simultaneously as catalytic auxiliaries 95

1.379

1.723

1.563

1.217

1.327

1.355

1.721

1.571

1.216

1.328

1.314

1.930

2.433

1.213

1.330

2.702

1.370

2.333

1.475

1.746

1.015

1.327

1.217

1.368

1.713

2.073

1.973

1.020

1.326 1.218

1.427

1.470

1.751

1.015

1.328

1.216

)

1.297

2.003

2.648

2.250

Fo-6

Fo-6 /8

Fo-6 /10

Fo-8

Fo¯-6

Fo¯-6/8

Fo¯-8

1.218

1.325

1.354

1.719 1.574

1.224

1.317

2.149

2.440

1.053

1.027

1.053

1.024

1.054

1.382

1.713

1.537

1.218

1.329

1.052

1.368

1.709

1.531

1.218

1.329

1.052

1.303

2.088

2.550

1.214

1.334

2.562

1.027

Figure 6-3. Optimized geometries of stationary points relevant for the rearrangements of partially

protonated aminoethanol radicals 6 interacting with Asp/Glu model systems: A) HCOOH

acid, B) HCOO¯ (bond lengths are given in Å; B3LYP results in roman and QCISD in

italics).

In a pH regime of 4 – 9.5 Asp is deprotonated while the substrate still prefers the

protonated form. Since solvent molecules do not have access to the active site of

ethanolamine ammonia lyase,87c the overall “neutral” H-bonded complexes, which can be

96 His and Asp/Glu acting simultaneously as catalytic auxiliaries

viewed as structural analogues of “salt bridges”, obtained as the stationary points on the

PES are believed to be more stable in the gas phase. In fact, computational studies on

similar “salt bridge” complexes in biological systems showed that neutral complexes with

double H-bonds between the two charged building blocks are more stable in the gas phase

than their zwitter-ionic counterparts; however, the latter are clearly favored in an aqueous

environment.153

Table 6-4. Relative enthalpiesa (in kcal/mol) at 0 K (Hrel, 0 K), and 298 K (Hrel, 298 K) of the stationary

points on the PES of 6 interacting with HCO2H (Fo) serving as the simplest Asp/Glu model system.

B3LYP/6-31G* QCISD/cc-pVDZ//

B3LYP/6-31G*

QCISD/cc-pVDZ c

Hrel, 0 K Hrel, 298 K Hrel, 0 K Hrel, 298 K Hrel, 0 K Hrel, 298 K

Fo-610.0 0.0 0.0 0.0 0.0 0.0

Fo-61/8 9.6 9.8 16.0 16.2 16.3 16.5

Fo-8 2.5 2.5 -0.3 -0.4 0.1 0.1

Fo-62-0.6 -0.5 -0.5 -0.4

Fo-62/10 14.6 14.9 18.3 18.6

Fo-6’ b-4.8 -4.8 -4.9 -4.8

Fo-6’/8’ b9.9 10.1

Fo-8’ b2.5 2.6

a For electronic energies, ZPEs, and enthalpies, see Table AII-4 in the Appendix II.

b Structures contain an OH group orientation pointing away from the NH3 group (see Scheme 6-3); thus, elimination of NH4+ is not

possible for these conformers.

c Data to be discussed in the paragraph “Influence of the OH Group Conformation on the Migration”.

Here, the

Fo¯-61 structure can be interpreted as 2 interacting with the formic acid;

thus in the transition structure Fo¯-61/8 a required protonation of the migrating group NH2

cannot occur and therefore, no stabilization of TS will take place. Further, the migrating

group does not have a net charge and is no longer a good leaving group either (for

example, the C-N bonds of Fo¯-61/8 are shorter than in the analogous Fo-61/8 transition

structure; Figure 6-3); thus, the transition structure Fo¯-61/8 is energetically extremely

unfavored (Table 6-5: 80.2 kcal/mol) making this reaction highly improbable. Finally, the

Fo¯-61/8 transition structure can be described in terms of a migration of the amino group in

aminoethanol radical 2 only weakly interacting with the HCOOH moiety. However, as

His and Asp/Glu acting simultaneously as catalytic auxiliaries 97

already shown, rearrangement of unprotonated aminoethanol radical 2 is extremely

demanding energetically and, consequently, the new findings do not come as any surprise.

Table 6-5. Relative enthalpiesa (in kcal/mol) at 0 K (Hrel, 0 K), and 298 K (Hrel, 298 K) of the stationary

points on the PES of 6 interacting with HCO2¯ (Fo¯)as a dissociated Asp/Glu model system.

B3LYP/6-31G* QCISD/cc-pVDZ// B3LYP/6-31G*

Hrel, 0 K Hrel, 298 K Hrel, 0 K Hrel, 298 K

Fo¯-610.0 0.0 0.0 0.0

Fo¯-61/8 72.8 72.7 80.3 80.2

Fo¯-8 -0.4 -0.4 -2.3 -2.2

a For electronic energies, ZPEs, and enthalpies, see Table AII-5 in the Appendix II.

6.2.5. Résumé

This computational study of the aminoethanol rearrangement, including different

models for a partial substrate protonation, clearly discriminates between the two most

likely mechanisms (Scheme 6-1: direct NH3 migration, 6 → 8, vs. NH4+ elimination, 6 →

10). As a result, migration of the partially protonated amino group is shown to be

energetically less demanding in all investigated cases in comparison to the elimination

process.

In a recently published paper, Radom and co-workers arrived at the same

conclusion. Employing isodesmic reactions for the hydrogen abstraction from the 5’-

deoxyadenosine model system by the putative product radicals 8 and 10, the authors

concluded that the migration 6 → 8 constitutes a more favorable scenario since hydrogen

abstraction from 5’-deoxyadenosine by 8 is calculated to be exothermic (-1.2 kcal/mol),

while the same reaction, where 10 abstracts a hydrogen atom, is quite endothermic (6.2

kcal/mol). Possible barriers associated with both process have not been reported.

98 His and Asp/Glu acting simultaneously as catalytic auxiliaries

6.3. Influence of the OH Group Conformation on the Migratory

Aptitude

A realistic activation enthalpy for the migration process can be estimated only if the

most stable conformer of the reactant is identified. For the migration 6 → 8 different

conformations of the OH group are conceivable, out of which two extreme cases will be

discussed in more detail (Scheme 6-3). One of the conformations might be crucial since the

(partially) protonated aminoethanol radical 6 can be stabilized through an intramolecular

H-bond interaction with the lone-electron pair of the OH group (Scheme 6-3B).

Interestingly, in the analogous case of non-protonated aminoethanol 2, the orientation of

the OH group towards the NH2 group was found to be the most stable conformation due to

the strong H-bonding between the hydrogen from OH and a nitrogen from the NH2-group.

In the case of a H-bonding between the oxygen from the OH-group and a hydrogen atom

from the NH3 group (Scheme 6-3B), one can expect that the stability of the OH group

conformation will be dictated by the strength of the proton-donating group X. Therefore,

the influence of an OH group conformation on the barrier for the migration employing

different protonating groups has been explored.154 Structures corresponding to the OH

group oriented away from the NH3 group are denoted by a prime, e.g. 6’, 8’ etc.

Table 6-6. Relative enthalpiesa (in kcal/mol) at 0 K (Hrel, 0 K), and 298 K (Hrel, 298 K) of the stationary

points on the PES of protonated aminoethanol radicals; comparison between the energetics of the

migration pathways for two different orientations of the OH group in 6.

B3LYP/6-31G* QCISD/cc-pVDZ

Hrel, 0 K Hrel, 298 K Hrel, 0 K Hrel, 298 K

61 a0.0 0.0 0.0 0.0

61/8 a4.7 4.9 10.2 10.4

8 a2.9 3.0 -0.3 -0.1

6’ b-5.6 -5.6 -6.6 -6.6

6’/8’ b4.2 4.4 9.5 9.7

8’ b2.8 2.8 0.5 0.5

a Energies taken from ref. 133.

b Structures contain an OH group orientation pointing away from the NH3 group (see Scheme 6-3). For electronic energies, ZPEs,

and enthalpies, see Table AII-6 in the Appendix II.

His and Asp/Glu acting simultaneously as catalytic auxiliaries 99

In order to obtain even more reliable activation enthalpies for the migration

rearrangements, the reoptimizations of X61, X61/8 and X8 were performed at the

QCISD/cc-pVDZ level of theory.

X6 X8

X6/8

H H

X6' X8'

X6'/8'

H H

HOH

Scheme 6-3. Different OH group orientations in the (partially) protonated aminoethanol radical 6 and

their influence on the migration pathway.

Firstly, the rearrangement of the fully protonated aminoethanol radical 6 will be

addressed (Scheme 6-3 but without X); here the influence of the OH conformation should

be most pronounced. According to the data in Table 6-6, conformer 6’ corresponds to the

(global) minimum on the PES; this is due to a quite strong H-bond between the oxygen

lone pair and a hydrogen atom from the NH3 group (2.281 Å, QCISD geometry; Figure 6-

4). The H-bond stabilization amounts to 6.6 kcal/mol. However, in line with the Curtin-

Hammett principle155 it is irrelevant energetically whether the migration proceeds directly

through 6’/8’ (16.3 kcal/mol) or sequentially 6’ → 61 (6.6 kcal/mol) and 61/8 (10.4

kcal/mol). The resulting overall activation energy as well as the product energies are

almost identical (Table 6-6).

100 His and Asp/Glu acting simultaneously as catalytic auxiliaries

Since for the migration processes discussed previously transition structures were

located commencing from a conformer in which a H-bond between the NH2-H and OH

groups does not exist, in order to estimate the energy demand for the overall migration

process, the transition structures X6’/8’ as well as the minima connected by the

corresponding TSs for different protonating groups (X = H2O, NH3, CH2NH, HCO2H)

were located at the B3LYP/6-31G* level of theory. Next, the geometry reoptimizations of

the X6’ structures were performed at the QCISD/cc-pVDZ level of theory in order to

estimate the overall migration enthalpy as stated above.

Comparing the energies of the conformers X61 and X6’, it can be seen that the

stabilization gained through the H-bond interaction in the conformer X6’ amounts to ca. 5

kcal/mol (Tables 6-1 – 6-4; QCISD/cc-pVDZ method), which implies that the overall

migration pathways are ~ 5 kcal/mol more demanding than previously stated. More

precisely, for X = H2O, the overall activation enthalpy for the migration equals to 21.7

kcal/mol and for X = NH3 it amounts to 25.8 kcal/mol. In case of the small amino-acid

model systems the overall activation enthalpies change to 21.3 kcal/mol (X = HCOOH)

and 25.5 kcal/mol (X = CH2NH).

1.359

1.733

1.215

1.330

2.567

1.368

1.723

1.527

1.217

1.331

2.384

6’

Fo-6’

N6’ O6’

Mi-6’

1.352

2.651

1.367

1.523

2.281

2.572

1.691

1.367

2.392

1.522

1.712

1.358

1.558

1.713

1.367

2.370

1.714

1.359

2.575

1.547

1.274

1.716

1.367

2.393

1.521

1.286

1.710

Figure 6-4. Optimized geometries of stationary points relevant for the rearrangements of (partially)

protonated aminoethanol radicals 6’ with H-bond interaction (bond lengths are given in Å;

B3LYP results in roman and QCISD in italics).

His and Asp/Glu acting simultaneously as catalytic auxiliaries 101

Not surprisingly, the activation enthalpy is lowest in the case of full protonation of

2; as soon as deprotonation comes into play, the activation barrier increases substantially.

However, even partial protonation renders the migration more favorable since the

corresponding barriers for all investigated protonating groups are lower than for a

completely deprotonated precursor 2. At first sight, this statement is in disagreement with

the conclusion derived by Radom and co-workers, who concluded that partial

deprotonation has an anticatalytic effect based on the activation energy comparison with

the rearrangement of non-protonated aminoethanol radical, 2 (23.6 kcal/mol; fragmentation

– recombination mechanism156). However, for their particular case, the TS located does not

commence from the most stable aminoethanol radical structure. However, the global

minimum has been previously located (see Chapter 5; the structure denoted as 22), which is

4.4 kcal/mol more stable than the aminoethanol radical conformer located by Radom and

co-workers. Keeping this in mind, the energy requirement for the rearrangement of the

aminoethanol radical 2 amounts to 28 kcal/mol,157 thus being higher than for any of the

partially protonated precursors X6.

However, even if the partial protonation reduces the activation enthalpy compared

to the non-protonated case, all estimated migration enthalpies still exceed the activation-

enthalpy upper limit determined experimentally as acceptable for an enzymatic catalysis

(ca. 15 kcal/mol). One of the possible explanations could be related to the inaccuracy of

the computational method chosen. However, concerning that topic a comparison with the

data reported by Radom and co-workers is warranted. The latter estimated the transition

barrier 6’ → 8’ to be 15.7 kcal/mol (0 K) at the G3(MP2)-RAD(p) level of theory; this

agrees pleasingly with the result derived in this study (16.1 kcal/mol at 0 K). Therefore,

this computational method employed herein produces data comparable in its quality to

those obtained from the computationally more demanding G3 method. Further, it is worth

noting that single point calculations at the QCISD/cc-pVDZ level of theory on the B3LYP

optimized geometries provide very similar relative enthalpies as the data obtained by

computationally more demanding geometry reoptimizations at the QCISD level of theory

(see Tables 6-1 - 6-4). Clearly, for the cases that follow it is sufficient to perform only

single-point calculations at the QCISD/cc-pVDZ level of theory since these data are of the

same accuracy as those that would be obtained by the geometry reoptimizations at the

same level of theory.

As the method chosen cannot be the cause for an overestimation of the activation

barriers, a partial protonation alone does not sufficiently reduce the activation enthalpy;

102 His and Asp/Glu acting simultaneously as catalytic auxiliaries

thus, some more refined mechanistic scenarios for the migration rearrangement have to be

considered. However, before discussing some of these mechanistic variants, the migration

pathways were computed using some more appropriate models for the amino acids in order

to eliminate a possible overestimation of the activation enthalpy caused by employing

unrealistic model systems. Thus, the migration pathway was calculated employing acetic

acid (rather than formic acid) as a model system for Asp/Glu and imidazole (rather than

methanimine) as a model system for His.

6.4. Acetic acid and Imidazole – More Reliable Model Systems for

Asp/Glu and His

1.360

1.693

1.223

1.344

2.561

Im-6’

Ac-8’

Im-6’/8’ Im-8’

Ac-6’

1.360

2.579

1.539

1.325 1.622

Ac-6’/8’

1.505

1.383

1.379

1.368

1.353

1.200

2.494

2.630

1.356

1.836

1.383

1.369

1.323

1.378

1.049

1.105

1.386

1.551

1.368

1.616

1.325

1.353

1.384

1.379

1.109

1.059

1.317

1.030

1.220

1.508 2.535

1.344

1.890

1.382

1.689

1.224

1.504

1.341

1.060

Figure 6-5. Optimized geometries of stationary points relevant for the rearrangements of partially protonated

aminoethanol radical 6 interacting with more realistic model systems for amino acids: A) imidazole

as His model system, B) acetic acid as Asp/Glu model system (bond lengths are given in Å;

B3LYP results).

His and Asp/Glu acting simultaneously as catalytic auxiliaries 103

For both model systems, the rearrangement commences from a conformer in which

an intramolecular H-bond exists (Figure 6-5); thus, the computed activation enthalpy

corresponds to the final energy demand for the migration pathway. His is expected to

catalytically interact with the substrate radical in the pH regime 6 – 9.5, while for Asp

model system only interactions in the pH < 4 were taken into account. When imidazole

interacts with the NH3 group of 6, the activation enthalpy is quite high and equals to 27.4

kcal/mol due to a higher degree of deprotonation in Im-6’/8’ as compared to the analogous

TS Ac-6’/8’ (Figure 6-5). In case of acetic acid the activation enthalpy is somewhat lower

being 24.2 kcal/mol (Table 6-7). While both models are structurally closer to the amino

acids than the previously employed systems, and further, have proton affinities comparable

to those of the amino acids,158 the computed barriers, nevertheless, are too high to be

acceptable for the enzymatic reaction. Even though partial protonation helps to lower the

barrier for the rearrangement 6 → 8, the amount gained is not sufficiently large to bring

about acceleration of the enzymatic process. Clearly, in reality a more complex situation

must prevail.

Table 6-7. Relative enthalpiesa (in kcal/mol) at 0 K (Hrel, 0 K), and 298 K (Hrel, 298 K) of the stationary

points on the PES of 6 interacting with imidazole (Im) as a His model system and acetic acid (Ac) as

Asp/Glu model system.

B3LYP/6-31G* QCISD/cc-pVDZ//B3LYP/6-31G*

Hrel, 0 K Hrel, 298 K Hrel, 0 K Hrel, 298 K

Im-6’ b0.0 0.0 0.0 0.0

Im-6’/8’ b 19.1 19.3 27.2 27.4

Im-8’ b 7.8 7.8 5.3 5.3

Ac-6’ c 0.0 0.0 0.0 0.0

Ac-6’/8’ c 15.5 15.8 24.2 24.2

Ac-8’ c 7.2 7.2 5.8 5.9

a For electronic energies, ZPEs, and enthalpies, see Table AII-7 in Appendix II.

b Im-6’ structure taken as a reference point.

c Ac-6’ structure taken as a reference point.

104 His and Asp/Glu acting simultaneously as catalytic auxiliaries

6.5. Pull Mechanism

Since

2 contains two functional groups, it is conceivable that the OH-group as well

interacts with some amino acid from the active site, and by partial deprotonation of the OH

group the barrier is lowered. For the non-protonated form of substrate 2 it was shown in

Chapter 5 that a dissociation-association pathway is energetically least demanding; thus,

this scenario was investigated for the partial deprotonation as well (Scheme 6-4). Only the

first reaction step (dissociation of the NH2 group) was computed for different

deprotonating groups Y, rather than computing the whole reaction profile that includes

association as well. Clearly, if dissociation of the NH2-group exceeds the activation

enthalpy upper limit value, the pull mechanism alone will not play a role in the enzymatic

catalysis.

2/3-Y

H H

HOH

2-Y 4-Y

H H

2/3-Y

HOH

3-Y

Scheme 6-4. Pull mechanism for the dissociation-association pathway.

First the rather small OH¯ ion was used as a deprotonating agent. Even though the

activation enthalpy for the dissociation process (15.2 kcal/mol, Table 6-8) falls into the

range acceptable for the enzymatic catalysis, bare OH¯ as a model system for Asp/Glu is

quite inappropriate. Thus, the interaction at the OH-site in 2 was computed employing

better model systems for the amino acids.

If the pH in the active site is higher than 4, Asp and Glu exist in their dissociated

forms; thus, a carboxylate ion can partially deprotonate the OH group in 2. The model

systems employed in order to mimic these interactions were formate and acetate (see

Figure 6-6). For the interaction of HCOO¯ with the OH group, the activation enthalpy for

the dissociation of NH2 equals to 19.7 kcal/mol. When acetate as model system for

Asp/Glu was employed, the activation enthalpy is somewhat higher being equal to 20.2

kcal/mol (Table 6-8).

His and Asp/Glu acting simultaneously as catalytic auxiliaries 105

1.461

1.284

1.241

2-Fo¯

3-A

2/3-Fo¯3-Fo¯ ·

2-Ac

2/3-A

1.350

1.058

1.081

1.319

1.225

1.531

1.296

1.402

1.456

1.286

1.240

1.551

1.331 1.057

1.470

1.280

1.237

1.350

1.055

1.330

1.288

1.231

1.317

1.115

1.352

1.287

1.232

1.348

1.331

1.104

Figure 6-6. Pull mechanism; optimized geometries of stationary points relevant for the rearrangements

of partially deprotonated aminoethanol radical 2 interacting with two His model systems:

A) CH2NH, B) imidazole (bond lengths are given in Å; B3LYP results).

Table 6-8. Pull mechanism; relative enthalpiesa (in kcal/mol) at 0 K (Hrel, 0 K), and 298 K (Hrel, 298 K) of the

stationary points on the PES of 2 interacting with OH¯ (O¯), HCO2¯ (Fo¯) and CH3CO2¯ (Ac¯) which

serve as dissociated Asp/Glu model systems.

B3LYP/6-31G* QCISD/cc-pVDZ//B3LYP/6-31G*

Hrel, 0 K Hrel, 298 K Hrel, 0 K Hrel, 298 K

2O¯ b0.0 0.0 0.0 0.0

2/3O¯ b8.7 8.9 15.1 15.2

3O¯ · NH2• b 7.7 8.6 12.8 13.7

2-Fo¯ c0.0 0.0 0.0 0.0

2/3-Fo¯ c14.7 14.9 19.5 19.7

3-Fo¯ · NH2• c 11.3 12.4 8.6 9.7

2-Ac¯ d0.0 0.0 0.0 0.0

2/3-Ac¯ d 14.6 14.8 20.0 20.2

3-Ac¯ +NH2• d 19.8 21.0 17.1 18.3

a For electronic energies, ZPEs, and enthalpies, see Table AII-8 in the Appendix II.

b 2O¯ structure taken as a reference point.

c 2-Fo¯ structure taken as a reference point.

d 2-Ac¯ structure taken as a reference point.

106 His and Asp/Glu acting simultaneously as catalytic auxiliaries

His can act as a proton acceptor if the pH in the active site is higher than 6. When

the smaller model system CH2NH is used to partially deprotonate 2, the computed

activation enthalpy amounts to 24.1 kcal/mol. In the case of a more realistic model system,

i.e. imidazole (Figure 6-7), the activation enthalpy is somewhat lower being equal to 23.8

kcal/mol (Table 6-9).

In general, partial deprotonation at the OH group of 2 acts catalytically as well,

since in all investigated cases the activation enthalpy obtained is lower than for a non-

deprotonated radical 2 (28.0 kcal/mol). However, the computed activation enthalpies for

the dissociation of NH2 group still exceed the upper limit value determined from the

experimental studies (ca. 15 kcal/mol); thus, the association of the NH2 radical with 3-Y

(Scheme 6-4) was not deemed necessary to be investigated computationally. Clearly, a

partial deprotonation at the OH-group in 2 (pull mechanism) alone cannot sufficiently

decrease the activation enthalpy. More likely, only when both interactions, i.e. partial

deprotonation of the OH and partial protonation of the NH2 group, occur simultaneously,

the activation enthalpy might fall below 15 kcal/mol.

2-Mi

3-Im

2/3-Mi 3-Mi

2-Im

1.361

2/3-Im

1.381

1.379

1.370

1.318

NCC

1.368

1.489 0.985 1.270

1.352

2.260

0.987 1.271 1.357

0.984

1.271

1.367

1.490 0.988 1.360

1.381

1.379

1.370

1.318

1.350

2.261

0.991

1.361

1.381

1.378 1.370

1.318

1.355 0.987

Figure 6-7. Pull mechanism; optimized geometries of stationary points relevant for the rearrangements of partially

deprotonated aminoethanol radical 2 interacting with two His model systems: A) CH2NH, B)

imidazole (bond lengths are given in Å; B3LYP results).

His and Asp/Glu acting simultaneously as catalytic auxiliaries 107

Tables 6-9. Pull mechanism; relative enthalpiesa (in kcal/mol) at 0 K (Hrel, 0 K), and 298 K (Hrel, 298 K) of

the stationary points on the PES of 2 interacting with CH2NH (Mi) and imidazole (Im) as His model

systems.

B3LYP/6-31G* QCISD/cc-pVDZ//B3LYP/6-31G*

Hrel, 0 K Hrel, 298 K Hrel, 0 K Hrel, 298 K

2-Mi b0.0 0.0 0.0 0.0

2/3-Mi b 20.9 21.1 24.0 24.1

3-Mi + NH2• b 20.1 21.2 17.4 18.5

2-Im c0.0 0.0 0.0 0.0

2/3-Im c20.4 20.7 23.6 23.8

3-Im +NH2• c 19.9 21.1 17.2 18.4

a For electronic energies, ZPEs, and enthalpies, see Table AII-9 in the Appendix II.

b 2-Mi structure taken as a reference point.

c 2-Im structure taken as a reference point.

6.6. Synergistic Action of Two Catalytic Auxiliaries

One of the options by which the enzyme can reduce the activation enthalpy for the

rearrangement process is the so-called push-pull mechanism proposed by Radom and co-

workers in the case of diol dehydrase134 and employed as well in the study of ethanolamine

rearrangement catalyzed by ethanolamine ammonia lyase. Since substrate 2 exhibits acidic

(OH group) and basic (NH2 group) features, both sites might interact with different amino

acid residues of the enzyme as depicted in Scheme 6-5. Depending on the actual pH in the

enzyme’s active site, interaction is possible separately at the NH2 or OH group, or both

sites of substrate 2 are simultaneously interacting with appropriate catalytic auxiliaries of

the enzyme.

As already demonstrated by Radom and co-workers, a push-pull mechanism

(Scheme 6-5) might serve as the best model for the rearrangement of aminoethanol

catalyzed by ethanolamine ammonia lyase. Even though the rearrangement barriers were

calculated to be lower than the upper limit value acceptable for the enzymatic reaction, one

should be aware of the rather crude model systems (e.g. NH3, H2O) employed in the latter

study. Therefore, the activation enthalpies were computed using rather some more realistic

model systems for those amino acids that might act as catalytic auxiliaries. Clearly, these

data are not only likely to result in more reliable activation enthalpies, but as well, and

108 His and Asp/Glu acting simultaneously as catalytic auxiliaries

perhaps even more importantly, they might help to provide a realistic picture of possible

interactions in the enzyme’s active site.

X-6/8-Y

H H

HOH

Scheme 6-5. Push-pull mechanism for a migration pathway of 6 involving a partial protonation of the

NH2 group and a partial deprotonation of the OH group of the substrate.

The elucidation of the question which amino acid acts as a catalytic auxiliary at the

hydroxyl and which at the amino group of 2 is related to the possible pH prevailing in the

active site. Having in mind pKa values of the potential amino acid candidates (Asp, Glu,

His) and the pKa of aminoethanol, it is clear that in the pH regime 6 - 9.5 a synergistic

interaction can take place. In this pH range, Asp/Glu exist as carboxylate, His is non-

protonated and the substrate 2 is protonated. In the section where aspects of partial

protonation were discussed in detail, it was concluded that interaction of carboxylate with

the NH3 group in 6 substantially increases the activation enthalpy and is definitely not

catalytic. Thus, only His is an acceptable candidate for the interaction with the NH3 group

of 6. However, both His and Asp/Glu in this particular pH range might partially

deprotonate the OH group of 6. When discussing the pull-mechanism, it was shown that

the activation enthalpy is lower when model systems for Asp/Glu were employed in

comparison with model systems for His. Thus, Asp/Glu were assumed to serve as better

catalytic auxiliaries at the OH-site in 6.

His and Asp/Glu acting simultaneously as catalytic auxiliaries 109

In order to elucidate the push-pull mechanism in more detail two different systems

were employed. First a set of smaller models for the above mentioned amino acids was

employed (CH2NH for His and HCOO¯ for Asp/Glu; Figure 6-8A). The computed

activation enthalpy amounts to 11.6 kcal/mol (Table 6-10) being lower than the upper limit

value derived from the experiment. When a more realistic model for the amino acids was

used (imidazole for His and CH3COO¯ for Asp/Glu; Figure 6-8B), the activation enthalpy

is slightly higher being equal to 13.7 kcal/mol. The analysis of the structural details (Figure

6-8) reveals that the low activation enthalpies are due to both reactant destabilization and

transition structure stabilization. For example, in both structures Mi-6-Fo¯ and Im-6-Ac¯

the C(2)-N bonds are extremely prolonged when compared to the ones in Mi-61 (Figure 6-

2) or Im-6 (Figure 6-5). At the same time, interaction of the carboxylate with the OH

group of 6 results in a lengthening of the O-H bond; as a consequence, the system develops

features of an ethanal structure (e.g. compare the C-C and C-O bond lengths given in

Figure 6-8). The emerging radical center on C(2) is stabilized by delocalization through the

developing ethanal structure. It is this subtle interplay of the two catalytic auxiliaries that

makes the migration energetically less demanding than when compared to situations where

Mi-6-Fo¯

Im-8-Ac

Mi-6/8-Fo¯Mi-8-Fo¯

Im-6-A

Im-6/8-Ac

1.648

1.323

1.259

1.407

1.012

1.274

2.108

1.025

1.209

1.307

1.469

1.224

1.276

1.865

1.048

1.791

0.987

1.294

1.484 1.871

1.276

1.860

1.005

1.534

1.706

1.222

1.256

1.411 1.003

2.030

1.031

1.377

1.380

1.356

1.323

1.373

1.226

1.230

1.474 1.204

1.031

1.308

1.359

1.370

1.380

1.381

1.8311.324

0.989

1.238

1.484 1.844

1.053

1.386

1.360

1.370

1.380

1.381

1.837

1.323

Figure 6-8. Push-pull mechanism; optimized geometries of stationary points relevant for the

rearrangements of 6 interacting with His and Asp/Glu model systems: A) CH2NH and

formate, B) imidazole and acetate (bond lengths are given in Å; B3LYP results).

110 His and Asp/Glu acting simultaneously as catalytic auxiliaries

only one of the catalytic auxiliaries is in action (e.g. Im-6/8 or 2/3-Ac¯). As a result, the

activation enthalpy for the migration costs only 13.7 kcal/mol, which is lower than the

upper limit value determined from the experiment (ca. 15 kcal/mol).

Table 6-10. Push-pull mechanism; relative enthalpiesa (in kcal/mol) at 0 K (Hrel, 0 K), and 298 K

(Hrel, 298 K) of the stationary points on the PES of 6 interacting with model systems for His and

Asp/Glu (CH2NH with HCOO¯ and imidazole with CH3COO¯).

B3LYP/6-31G* QCISD/cc-pVDZ//B3LYP/6-31G*

Hrel, 0 K Hrel, 298 K Hrel, 0 K Hrel, 298 K

Mi-6-Fo¯ b0.0 0.0 0.0 0.0

Mi-6/8-Fo¯ b13.8 12.8 12.6 11.6

Mi-8-Fo¯ b9.3 8.3 5.3 4.3

Im-6-Ac¯ c0.0 0.0 0.0 0.0

Im-6/8-Ac¯ c16.9 15.7 14.9 13.7

Im-8-Ac¯ c13.0 11.9 8.7 7.6

a For electronic energies, ZPEs, and enthalpies, see Table AII-10 in the Appendix II.

b Mi-6-Fo¯ structure taken as a reference point.

c Im-6-Ac¯ structure taken as a reference point.

6.7. Summary and Conclusions

The computational study of the aminoethanol rearrangement, including different

models for a partial substrate protonation, clearly discriminates between the two

mechanisms (direct NH3 migration, 6 → 8, vs. NH4+ elimination, 6 → 10) which were

identified as the most likely routes in Chapter 5. As a result, migration of the partially

protonated amino group is shown to be energetically less demanding in all investigated

cases in comparison to the elimination process.

However, even if realistic model systems for the amino acids His, Asp and Glu, that

can act as catalytic auxiliaries and partially protonate the substrate, are employed, the

computed activation enthalpies exceed the upper limit value (ca. 15 kcal/mol) determined

by kinetic studies as acceptable for enzymatic catalysis. For example, when imidazole is

employed as a model system for His to interact with the NH3 group of substrate 6, the

activation enthalpy for the migration process amounts to 27.4 kcal/mol. If acetic acid is

employed to mimic Asp or Glu interacting with NH3 in 6, the activation enthalpy is

His and Asp/Glu acting simultaneously as catalytic auxiliaries 111

somewhat lower, being equal to 24.2 kcal/mol. Thus, partial protonation of the amino

group in the substrate alone does not sufficiently reduce the activation enthalpy for this

pathway to be feasible under enzymatic conditions. However, partial protonation of the

amino group still acts catalytically since all computed activation enthalpies are lower than

when compared to a rearrangement of the non-protonated substrate radical 2 (28 kcal/mol).

In the case of a partial deprotonation of the substrate 2 at the OH group, the

rearrangement mechanism consists of a dissociation of the NH2 radical from C(2) and its

association at the C(1) atom. For all investigated proton acceptors (OH¯, HCOO¯,

CH3COO¯, CH2NH, imidazole), the activation enthalpy for the dissociation step exceeds

the limit value. Typical data are 20.2 kcal/mol for acetate and 23.8 kcal/mol for imidazole

interacting with the OH group of 2; thus, Asp or Glu present better candidates than His to

pull a proton from the OH group of the substrate. As in the case of partial protonation of

the NH2 group, the partial deprotonation of the OH group acts catalytically in that it

reduces the activation enthalpy, though, not sufficiently.

Obviously, a synergistic action (Scheme 6-5) of two catalytic auxiliaries in the

enzyme’s active site is necessary to result in a sufficient reduction of the activation

enthalpy. Elucidation of the question which amino acid acts as a catalytic auxiliary at the

OH (partial deprotonation) and which at the NH2 group (partial protonation) of 2 depends

on the possible pH in the active site. Only in a pH regime 6 - 9.5 the synergistic interaction

can take place; in this pH range Asp/Glu exist as carboxylates and His is non-protonated,

while the substrate is still protonated. Thus, His is a better candidate for an interaction with

the NH3 group in substrate 6. However, in this particular pH range both His and Asp/Glu

might partially deprotonate the OH-group in 6. Since it was shown for the pull-mechanism

(Scheme 6-4) that the activation enthalpy is lowest when model systems for Asp/Glu were

employed in comparison with model systems for His, in the deprotonation step either Asp

or Glu are predicted to be involved.

Details of the push-pull mechanism were calculated employing two different

systems (Figure 6-8). When the smaller models for the catalytic auxiliaries His and

Asp/Glu (i.e. CH2NH and HCOO¯) were used, the computed activation enthalpy amounts

to 11.6 kcal/mol being lower than the upper limit value determined from the experiment.

For more realistic models (i.e. imidazole and CH3COO¯), the activation enthalpy is

slightly higher (13.7 kcal/mol), but still lower than the upper limit value determined

experimentally (ca. 15 kcal/mol). Further, this activation enthalpy is lower than the barrier

associated with hydrogen abstraction from the 5’-deoxyadenosine by the product radical;

112 His and Asp/Glu acting simultaneously as catalytic auxiliaries

this process was shown to be the rate determining step in the overall reaction sequence. In

addition, the synergistic interaction of His and Asp/Glu is operative only in the pH regime

of 6 - 9.5; this pH range is common in many biologically active systems.159

Finally, these computational data do not only provide reliable activation enthalpies,

more importantly, they produce quite a realistic picture of possible interactions in the

enzyme’s active site. These findings may prove helpful in the on-going experimental

attempts to structurally characterize ethanolamine ammonia lyase.

Hydrogen abstraction from 2-aminoethanol by a model system for the 5’-deoxyadenosyl radical 113

7. Hydrogen Abstraction from 2-Aminoethanol by a

Model System for the 5’-Deoxyadenosyl Radical∗

Important questions that remained unresolved for ethanolamine ammonia lyase, as

well as other coenzyme B12-dependent enzymes, concern details by which these enzymes

bring about the homolytic C-H bond activation and how they catalyze the cleavage of the

Co-C bond; for the latter, bond homolysis is accelerated up to a factor of 1012 in the

presence of an enzyme. Quite a few different mechanisms have been proposed that could

account for this enormous rate acceleration, i.e. enzyme induced distortion of the corrin

ring to sterically labilize the Co-C bond,160 enzymatic compression of the axial Co-N bond

causing a weakening of the trans-located Co-C bond,160c,161 corrin ring distortion by

twisting the axial Co-N bond to rotate the 5,6-dimethylbenzimidazole,162 direct bending of

the Co-C bond by interaction of the adenosyl ligand with the protein,160b,d,163 or, as

indicated by early studies, that the substrate itself might induce weakening of the Co-C

bond because in the absence of the substrate, Cob(II)alamin was not formed in significant

quantity.164 Direct evidence that a substrate promotes the Co-C bond homolysis has been

provided for methylmalonyl-CoA mutase where it was shown that the rate of Co-C bond

catalysis is sensitive on isotopic substitution in the substrate.165

In order to computationally investigate the effects that could promote the Co-C

bond homolysis the whole coenzyme should be taken into account; because of the

computationally extremely demanding coenzyme B12 and limited computer resources that

were available, this topic, unfortunately, could not be addressed. However, another

intriguing aspect that is easier to tackle computationally concerns the mechanistic details

by which the 5’-deoxyadenosyl radical abstracts a hydrogen atom from the substrate. In the

case of ethanolamine ammonia lyase, both steady state hydrogen isotope exchange studies

and EPR spectroscopy of trapped radical intermediates suggested the involvement of two

different species, i.e. the 5’-deoxyadenosyl radical itself and a protein radical formed in the

reaction with the former.166,167 Evidence for the direct interaction of the 5’-deoxyadenosyl

radical with substrate was provided by isotope exchange experiments, where the

incorporation of tritium from 1-[3H]-aminoethanol into the coenzyme was demonstrated as

well as the release of tritium from 5’-[3H]-adenosylcobalamin to the product radical.168

∗ Results discussed in this chapter are in press: Semialjac, M.; Schwarz, H. Chem. Eur. J.

114 Hydrogen abstraction from 2-aminoethanol by a model system for the 5’-deoxyadenosyl radical

Recently, several different experiments, in particular the exchange of deuterium between

the 5’-deoxyadenosyl radical and the enzyme’s deactivator, electron nuclear double

resonance studies and electron spin-echo envelope modulation spectroscopy provided

additional support for this mechanism. However, the isotope effect observed for the

incorporation of tritium from 5’-[3H]-deoxyadenosylcobalamin into ethanal was

contradictory to the conclusion that the three hydrogen atoms at the C5’-position in 5’-

deoxyadenosine (the one abstracted from the substrate and the two from the intact

coenzyme) were equivalent with respect to the probability of incorporation into the product

ethanal. Similar observations were made for the related diol-dehydrase.169 The anomalous

tritium isotope effects observed for both enzymes have been rationalized by a model that

rests on the assumption the possibility that two radical species, the 5’-deoxyadenosyl

radical itself and a protein radical, interact with the substrate.170 In this “two-radicals”

model the major part of hydrogen exchange proceeds through a protein radical, while only

in ca. 11% of cases the 5’-deoxyadenosyl radical abstracts directly a hydrogen atom from

the substrate. Even though the substrate and the product radicals for the ethanolamine

ammonia lyase catalyzed reaction have been detected by EPR spectroscopy, a possible

candidate for a protein radical has not yet been identified, in contrast to the related B12

dependent ribonucleotide triphosphate reductase for which the protein radical has been

characterized as a cysteine thiyl radical.171 However, for the base-off B12 dependent

enzymes (class I) methylmalonyl-CoA mutase and glutamate mutase, the 5’-

deoxyadenosyl radical appears to react directly with the substrate.

In the present chapter the focus

will be on the “non-protein radical

hypothesis”, i.e. assuming that the

initially formed C-centered 5’-

deoxyadenosyl radical acts as a

hydrogen atom abstractor from

substrate 1 (Scheme 7-1). In addition,

the following question will be

addressed: whether the substrate is

“free” in the active site prior to the

hydrogen abstraction or its position is

fixed and the C-H bond homolysis

DMB

H2NCH2

H H

Scheme 7-1. Abstraction of a hydrogen atom by the

5’-deoxyadenosyl radical from substrate

interacting with two amino acids X and

Y in the active site of ethanolamine

ammonia lyase.

Hydrogen abstraction from 2-aminoethanol by a model system for the 5’-deoxyadenosyl radical 115

facilitated by interaction with some amino acids from the enzyme’s active site, a scenario

which seems more appropriate for an enzymatic catalysis (residue X and Y, as depicted in

Scheme 7-1). The insight derived from this computational model study could be useful in a

further clarification of those factors which affect the hydrogen abstraction reactions in

coenzyme B12 dependent enzymes.

7.1. Computational Methods

All calculations were performed with the GAUSSIAN 98 suite of programs using

both density functional theory (DFT) and an ab initio approach. The use of the DFT

formalism was a natural choice because of the balance between accuracy and

computational time required by the calculations, and the B3LYP functional was

employed.27,28 Geometry optimizations were performed with Pople’s polarized double-ζ 6-

31G* basis set. In order to characterize the optimized structures, frequency analysis has

been performed at the same level of theory. Minima were characterized by the absence of

imaginary vibrational frequencies, while transition structures exhibited one imaginary

frequency. A uniform scaling factor of 0.9806 was used for the zero-point energy (ZPE)

corrections calculated at the B3LYP level of theory. Computations of reaction pathways,

i.e. intrinsic reaction coordinate (IRC) calculations were carried out at the same level of

theory.

In order to obtain more reliable energetic profiles of the reactions in question,

single point calculations using triple-ζ basis sets with diffuse functions (6-311++G**)

were performed employing ab initio theory (MP2). The relative energies of the stationary

points were calculated at the MP2/6-311++G**//B3LYP/6-31G* level of theory, where the

ZPEs calculated with B3LYP/6-31G* were used in the conversion to relative energies at 0

K. Due to the size of the system under investigation, it had to be refrained from performing

single point calculations at some more accurate level of theory, as in the studies discussed

in previous chapters on related problems (i.e. QCISD).133,172 However, as reported by

Morokuma and co-workers,173 even for the hydrogen bonding energies in the 5’-

deoxyadenosyl radical the B3LYP and MP2 results are of sufficient accuracy and therefore

these methods are helpful in answering the questions addressed in the present chapter.

116 Hydrogen abstraction from 2-aminoethanol by a model system for the 5’-deoxyadenosyl radical

Relative energies (given in kcal/mol) discussed in the text correspond to the

enthalpies at 298 K obtained at the MP2 level of theory (single-point calculations),174

unless specified otherwise.

7.2. Hydrogen Abstraction Scenarios from Aminoethanol by 1,5-

Dideoxyribose-5-yl Radical

As already mentioned, while the amino-acid sequence of the ethanolamine

ammonia lyase has been determined, the X-ray structure of the enzyme is not yet known.

However, as the active sites of several coenzyme B12 dependent enzymes were shown to

exhibit high similarities, pertinent results obtained from the X-ray structure of B12-

dependent glutamate mutase175 will be used. In the active site of this enzyme two different

conformers of the 5’-deoxyadenosyl moiety have been observed and the major

conformational difference concerns the backbone of the ribose part. While a C2’-endo

conformation is adapted by the 5’-deoxyadenosyl radical formed shortly after homolysis of

the Co-C bond, a C3’-endo conformer is favored by the 5’-deoxyadenosine precursor.

'Base

C2'-endo

'Base

C3'-endo

H H

HO OH

Scheme 7-2. A) 5’-deoxyadenosyl moiety, B) different ribose conformations, C) 1,5-dideoxyribose

employed as a model system for the 5’-deoxyadenosyl moiety.

Theory has characterized no less than 34 conformers of the 5’-deoxyadenosly

radical. As to the global minimum, the solid state structure176 of the 5’-deoxyadenosyl

moiety does not correspond to the one obtained by the computational studies. In the latter

the global minimum of the free radical contains a hydrogen bond between the C2’

hydroxyl group and the N3-atom from adenine. Even though the X-ray structure of the

enzyme does not reveal this particular hydrogen bonding there are two water molecules

situated suitably to form H-bonds with the N3-atom from adenine and the OH-group at the

C2’ center of ribose via a network of water molecules. Concerning the relative orientation

Hydrogen abstraction from 2-aminoethanol by a model system for the 5’-deoxyadenosyl radical 117

of the ribose and adenine moieties, the X-ray structure points to an arrangement that is

disfavored by the computational work. It has been concluded that this particular

orientation of the ribose and adenine ring in the solid state is a result of several stabilizing

interactions between the 5’-deoxyadenosyl moiety, additional water molecules and the

corrin ring. Moreover, the computationally preferred C2’-endo conformation of the ribose

ring in the “liberated” 5’-deoxyadenosyl radical is triggered exactly by the H-bond

interaction between the C2’ hydroxyl-group and the N3-atom from adenine. In view of

these conflicting results, the focus will be on calculating the energetics of the hydrogen

abstraction step by employing a more simplified model system for the 5’-deoxyadenosyl

radical. Clearly, QM/MM studies would represent an attractive alternative for obtaining

more accurate computational results. However, as long as the X-ray structure of

ethanolamine ammonia lyase remains unknown, one has to refrain from such an approach.

Ayl

CCC

)

1.541

1.433

1.516

2.052

1.434

1.540

1.542

1.545

1.448

1.522

2.076

1.422

1.534

1.540

1.563

1.434

1.477

2.059

1.433

1.536

1.540

1.558

1.446

1.485

2.094

1.422

1.533

1.537

Figure 7-1. Optimized geometries (B3LYP/6-31G*) of A) 1,5-dideoxyribose (C3- and C2-endo

conformers), B) 1,5-dideoxyribose-5-yl radical (C3- and C2-endo conformers; bond

lengths in Å).

118 Hydrogen abstraction from 2-aminoethanol by a model system for the 5’-deoxyadenosyl radical

Mi-TS

H-TS

Mi-TS -Fo

1.540

1.431

1.542

2.036

1.404

1.497

1.553

1.476

1.390

1.306

1.426

1.534

1.443

1.543

2.036

1.397

1.497

1.553

1.522

1.404

1.339

1.383

1.274

1.742

1.073

1.533

1.445

1.544

2.073

1.396

1.497

1.555

1.542

1.406

1.345

1.376

1.537

1.432

1.542

2.061

1.403

1.496

1.550

1.504

1.375

1.310

1.416

1.269

2.019

1.037

1.665

1.003

Figure 7-2. Optimized geometries (B3LYP/6-31G*) of transition structures for hydrogen abstraction

reaction by C3-endo conformers of 1,5-dideoxyribose-5-yl radical (bond lengths in Å).

The model chosen, i.e. 1,5-dideoxyribose177 (see Scheme 7-2C), is reduced to the

ribose part of 5’-deoxyadenine; the adenine fragment has not been included on the ground

that its presence is not likely to affect energetically the hydrogen abstraction from substrate

Hydrogen abstraction from 2-aminoethanol by a model system for the 5’-deoxyadenosyl radical 119

1 by the C5’-centered radical. For the 1,5-dideoxyribose a conformation that contains one

intramolecular H-bond (Scheme 7-2C) was taken into account, and in the computations

two different conformations of the “ribose” ring (C3-endo and C2-endo) were considered;

structural details can be found in Figure 7-1.

Further, in view of the findings135,172 that the energetics of the rearrangement 2 → 4

(Scheme 5-1, Chapter 5) is crucially dependent on the simultaneous operation of partially

protonating and deprotonating auxiliaries X and Y, it is investigated as well whether the

barrier of the hydrogen abstraction from substrate aminoethanol (1) is also affected by the

presence or absence of amino acid residues. To this end four different scenarios have been

studied: i.e. the hydrogen abstraction from the “free” substrate 1 (Scheme 7-1, without X

and Y), from a fully protonated substrate (Scheme 7-1, X = H+ and without Y), from a

substrate interacting with a His equivalent (Scheme 7-1, X = His and without Y), and

finally from a substrate interacting simultaneously with His and Asp models (Scheme 7-1,

X = His and Y = Asp).

According to the computations, the C3-endo conformer of 1,5-dideoxyribose is

slightly more stable (by 0.9 kcal/mol) than the C2-endo counterpart, and this difference

gets even smaller (0.6 kcal/mol) for the corresponding radicals. Concerning the labeling of

the stationary points, all structures having a C3-endo conformation are labeled with the

subscript 1 (e.g. for 1,5-dideoxyribose A1 and its radical Ayl1) in contrast to the C2-endo

conformers, which carry a subscript 2 (e.g. for 1,5-dideoxyribose A2 and its radical Ayl2).

7.2.1.Non-protonated Substrate

When a hydrogen atom is abstracted from the non-protonated substrate 1 by the two

conformers Ayl1 and Ayl2, the corresponding transition structures TS1 and TS2,

respectively, are energetically almost equivalent (17.3 and 16.7 kcal/mol). Commencing

from the corresponding TSs, intrinsic reaction coordinate (IRC) computations in the

direction of reactants converged into complexes between the C5-radical and 1 (1*Ayl1 and

1*Ayl2), which are slightly less stable than the reactants, i.e. 0.9 kcal/mol for 1*Ayl1 and

1.8 kcal/mol for 1*Ayl2 (Table 7-1).178,179 Irrespective of the conformation of the C5-

radical, the energy demands to overcome the hydrogen abstraction barrier exceed the

activation enthalpy (15 kcal/mol) of the rate determining step in the whole catalytic

sequence. Therefore, hydrogen abstraction from a non-protonated substrate is quite

120 Hydrogen abstraction from 2-aminoethanol by a model system for the 5’-deoxyadenosyl radical

unlikely to occur. Moreover, the pKa value for the conjugated acid of 1 equals to 9.45 and

consequently, it is reasonable to assume that 1 is (partially) protonated by some of the

amino acids present in the enzyme’s active site. Therefore, hydrogen abstraction from both

fully and partially protonated substrates 1 will be considered next.

Table 7-1. Relative enthalpies (in kcal/mol) at 0 K (Hrel, 0 K), and 298 K (Hrel, 298 K) of the stationary

points relevant for the hydrogen abstraction reaction from substrate 1.

B3LYP/6-31G* MP2/6-311++G**//

B3LYP/6-31G*

Hrel, 0 K Hrel, 298 K Hrel, 0 K Hrel, 298 K

1 + Ayl10.0 0.0 0.0 0.0

1*Ayl1-2.8 1.5 -4.4 0.9

TS110.1 13.6 15.1 17.3

2*A1-10.7 -6.2 -10.0 -4.5

2 + A1-10.2 -6.8 -9.1 -4.7

1 + Ayl20.9 1.0 0.6 0.6

1*Ayl2-1.6 2.6 -3.4 1.8

TS29.7 13.0 14.4 16.7

2*A2-10.1 -5.8 -9.3 -3.6

2 + A2-10.1 -5.8 -8.3 -3.8

7.2.2. Fully Protonated Substrate

For both conformers of the 1,5-dideoxyribose-5-yl radical, transition structures for

the hydrogen abstraction from the fully protonated substrate (H-1) were located. When

compared to the separate reactants, both TSs lie very low in energy (see Table 7-2) with H-

TS1 only 2.2 kcal/mol and H-TS2 3.7 kcal/mol above the reactant pair H-1/Ayl1. However,

from the corresponding TSs in the direction of reactants, the IRC computations converged

in complexes of H-1 with Ayl1 or Ayl2. Assuming that these complexes are present in the

active site, the actual activation barriers for the hydrogen abstraction amount to 13.1

kcal/mol when the Ayl1 radical is involved and 13.8 kcal/mol for the Ayl2 counterpart.

Hydrogen abstraction from 2-aminoethanol by a model system for the 5’-deoxyadenosyl radical 121

When compared to the hydrogen abstraction from the non-protonated substrate 1,

the decreased activation enthalpy is quite likely a result of the stabilization of the emerging

radical, where in the TSs the radical center is better delocalized through the C-C bond by

the presence of the electron withdrawing NH3-group. This is already indicated in some of

the structural features of TS1 versus H-TS1 (Fig. 7-2). In the latter, the relevant C-C bond

is shorter (1.503 Å) when compared to TS1 (1.526 Å), while the C-N bond is elongated,

i.e.1.542 Å vs. 1.476 Å. For H-TS1 the IRC computations in the direction of a product

converged into a complex 6*A1 between the protonated product radical (6) and A1.180 This

complex is much more stable (21.7 kcal/mol) than the separate species 6 and A1 and

extensive charge delocalization can be hold responsible for this effect.

Even though hydrogen atom abstraction from a fully protonated substrate is feasible

from an energetic point of view it is quite unrealistic to expect that 1 will exist as a “free”,

fully protonated species 6 in the active site. More likely is a scenario in which the substrate

is captured in the enzyme’s active site and its position fixed by interaction with some

amino acids that may result in partial protonation of the NH2 group and, depending on

structural details, partial deprotonation of the OH group as well. The implications of these

features for the energetics of the C-H bond homolysis will be considered next.

Table 7-2. Relative enthalpies (in kcal/mol) at 0 K (Hrel, 0 K), and 298 K (Hrel, 298 K) of the stationary points

relevant for the hydrogen abstraction reaction from the fully protonated substrate H-1.

B3LYP/6-31G* MP2/6-311++G**//

B3LYP/6-31G*

Hrel, 0 K Hrel, 298 K Hrel, 0 K Hrel, 298 K

H-1 + Ayl10.0 0.0 0.0 0.0

H-1*Ayl1-10.2 -10.2 -11.8 -10.9

H-TS1-0.6 -0.9 3.9 2.2

6*A1-30.0 -29.5 -28.8 -27.4

6 + A1-9.6 -9.4 -5.9 -5.7

H-1 + Ayl20.9 1.0 0.6 0.6

H-1*Ayl2-9.0 -9.1 -11.0 -10.1

H-TS20.9 0.5 5.3 3.7

6 + A2-8.4 -8.3 -5.1 -4.8

122 Hydrogen abstraction from 2-aminoethanol by a model system for the 5’-deoxyadenosyl radical

7.3. Partially Protonated Substrate

As already mentioned, the concept of partial protonation of a migrating group was

shown to play an important role for several coenzyme B12 dependent enzymes because it

lowers the barriers for the substrate rearrangement. As a model for an amino acid that

might partially protonate 1 a quite simple imine (methanimine, CH2=NH) was used to

mimic His, as one of the natural choices to interact with the substrate. As shown in the

previous chapter, the energetics of the reaction 2 → 4 for partially protonated 2 were

almost identical for different His models employed, and to save computational time the

structurally most simple system CH2NH was used here.

Table 7-3. Relative enthalpies (in kcal/mol) at 0 K (Hrel, 0 K), and 298 K (Hrel, 298 K) of the stationary points

relevant for the hydrogen abstraction reaction from substrate Mi-1 interacting with a His model system.

B3LYP/6-31G* MP2/6-311++G**//

B3LYP/6-31G*

Hrel, 0 K Hrel, 298 K Hrel, 0 K Hrel, 298 K

Mi-1 + Ayl10.0 0.0 0.0 0.0

Mi-1*Ayl1-8.8 -8.1 -10.8 -9.1

Mi-TS12.0 1.9 6.0 4.5

Mi-6*A1-8.6 -15.8 -16.5 -14.7

Mi-6 + A1-9.0 -8.7 -6.0 -5.7

Mi-1 + Ayl20.9 1.0 0.6 0.6

Mi-1*Ayl2-8.1 -8.1 -10.0 -9.0

Mi-TS23.2 3.0 7.2 5.8

Mi-6 + A2-7.8 -7.6 -5.1 -4.8

If the

Ayl1 radical abstracts the hydrogen atom from Mi-1, the corresponding TS

(Mi-TS1) lies 4.5 kcal/mol above the separate reactants, i.e. Ayl1 radical (C3-endo

conformer) and Mi-1. Mi-TS2 is slightly less stable lying 5.8 kcal/mol above reactants.

This small difference in the stability of the two TSs Mi-TS1 and Mi-TS2 reflects the

energetic difference that already exists for the 1,5-dideoxyribose, where the C3-endo form

was found to be 0.9 kcal/mol more stable. Taking into account the existence of complexes

Mi-1*Ayl1 and Mi-1*Ayl2, that were obtained in the IRC computations from the

Hydrogen abstraction from 2-aminoethanol by a model system for the 5’-deoxyadenosyl radical 123

corresponding TSs in the direction of the reactants, the activation enthalpy for the

hydrogen abstraction from Mi-1 by Ayl1 amounts to 13.6 kcal/mol and for Ayl2 to 14.8

kcal/mol; this is only slightly higher than for the analogous reaction in which the substrate

is fully protonated (13.1 kcal/mol), but still below the limiting value of 15 kcal/mol. The

IRC calculations from Mi-TS1 in the direction of a product led to a complex between Mi-6

and A1;181 the formation of this complex is highly exothermic (-14.7 kcal/mol) and the

complex itself is 9.0 kcal/mol more stable than the separate constituents Mi-6 and A1.

As to the role of substrate protonation on the activation enthalpy for the C-H bond

homolysis of 1, the computational findings clearly point to the operation of a catalytic

effect. However, in view of previous findings,135,172 that the synergistic operation of a

simultaneous partial protonation of the NH2 and a partial deprotonation of the OH group of

1 brings about a dramatic acceleration of the intramolecular rearrangement 2 → 4, it is

interesting to explore if this effect also holds true for the C-H bond activation step 1 → 2

as well.

7.4. Substrate Captured by Two Amino Acids from the Active Site

In addition to His partially protonating the NH2 group of 1, Asp (in its carboxylate

form) is assumed to partially deprotonate the OH group of the substrate; this kind of

synergistic interaction of the two amino acids can take place in a physiologically realistic

pH regime of 6 – 9.5 (discussed in details in Chapter 6). As a model system for Asp

formate was employed, which was shown to serve well for the computational investigation

of the rearrangement reactions. The TS involving the C3-endo conformation of the 1,5-

dideoxyribose-5-yl moiety (Mi-TS1-Fo; 12.4 kcal/mol) is energetically 0.8 kcal/mol less

demanding than the one involving the C2-endo conformer (Mi-TS2-Fo; 13.2 kcal/mol).

While IRC computations from the TSs in the direction of reactants did not converge to the

expected complexes between the reactant species, by means of exhaustive geometry

optimization two relevant complexes between the reactants have been located. The

complex Mi-1-Fo*Ayl1 lies 13.2 kcal/mol below the separate reactants, while Mi-1-

Fo*Ayl2 is 7.7 kcal/mol more stable then the noninteracting reactants. Assuming that such

complexes can be formed in the active site, the activation enthalpy for the hydrogen

abstraction would amount to 25.6 kcal/mol, thus clearly exceeding the upper limit of 15

kcal/mol. Such a high activation enthalpy presumably is the result of an unfavorable

124 Hydrogen abstraction from 2-aminoethanol by a model system for the 5’-deoxyadenosyl radical

delocalization of the emerging radical center at C(1) in the presence of the partially

developing negative charge on the adjacent oxygen from the OH group. A comparison of

the relevant C-O and C-C bond lengths of the substrates (Mi-1 and Mi-1-Fo) in the

transition structures Mi-TS1 and Mi-TS1-Fo (Fig. 7-2) lends qualitative support to this

suggestion. Consequently, for the C-H bond activation step, the synergistic interaction of 1

does not lower the barrier; rather, the effect of only one partially protonating amino acid

suffices.

IRC computations in the direction of the products result in quite stable complexes

between the radical Mi-6-Fo and 1,5-dideoxyribose (A1 and A2); assuming the existence of

such complexes, hydrogen abstraction from 1 becomes highly exothermic, especially in the

case of Mi-6-Fo*A1 which is 21.5 kcal/mol more stable than the separate products Mi-6-

Fo and A1 (Table 7-4). If this product complex is really formed in the active site, the A1

moiety being kept close to the radical 2 in the course of the subsequent amino-group

migration 2 → 4 could immediately deliver a hydrogen atom back to 4 thus regenerating

the 5’-deoxyadenosyl radical and closing the catalytic cycle.

Table 7-4. Relative enthalpies (in kcal/mol) at 0 K (Hrel, 0 K), and 298 K (Hrel, 298 K) of the stationary points

relevant for the hydrogen abstraction reaction from substrate Mi-1-Fo interacting synergistically with the

His and Asp model systems.

B3LYP/6-31G* MP2/6-311++G**//

B3LYP/6-31G*

Hrel, 0 K Hrel, 298 K Hrel, 0 K Hrel, 298 K

Mi-1-Fo + Ayl10.0 0.0 0.0 0.0

Mi-1-Fo*Ayl1-12.7 -12.8 -16.1 -13.2

Mi-TS1-Fo 9.1 8.6 14.0 12.4

Mi-6-Fo*A1-23.7 -24.2 -25.3 -22.1

Mi-6-Fo + A1-11.4 -10.8 -0.3 -0.6

Mi-1-Fo + Ayl20.9 1.0 0.6 0.6

Mi-1-Fo*Ayl2-6.3 -6.2 -10.0 -7.7

Mi-TS2-Fo 9.6 9.0 14.7 13.2

Mi-6-Fo*A2-14.3 -14.4 -15.6 -13.0

Mi-6-Fo + A2-10.3 -9.6 0.5 0.3

Hydrogen abstraction from 2-aminoethanol by a model system for the 5’-deoxyadenosyl radical 125

7.3. Conclusions

According to the computations, the TSs in which the C3-endo conformer of 1,5-

dideoxyadenosyl radical is involved are only slightly energetically less demanding than

those which involve the C2-counterpart, and the energy differences in the transition

structures reflect to a large extent those that already exist for the free conformers Ayl1 and

Ayl2. Further, since the transition structures for both 1,5-dideoxyribose-5-yl conformers in

all cases investigated are energetically and structurally quite similar it is difficult (if not

impossible) to decide definitively which of the C5-radical conformers actually attacks the

substrate.

As to the energetics, homolysis of the C-H bond from the non-protonated substrate

requires for both conformers of the model radical activation enthalpies > 16.7 kcal/mol. In

contrast, all computed activation enthalpies for the hydrogen abstraction from a partially or

fully protonated substrate 1 are energetically less demanding than the value associated with

the rate determining step that has been experimentally derived (15 kcal/mol), i.e. the

hydrogen abstraction from 5’-deoxyadenosine by the product radical. As it is realistic to

assume that the quite basic 2-aminoethanol substrate is at least partially protonated in the

active site, we conclude that from an energetic point of view the initially formed 5’-

deoxyadenosyl radical can abstract a hydrogen atom directly from an appropriately

“activated” substrate. Consequently, it does not seem necessary to invoke the role of a

protein radical (“two-radicals hypothesis”).

Interestingly, in case of a synergistic interaction, when substrate 1 is captured by

two amino acids (e.g. His and Asp), the activation enthalpy for the hydrogen abstraction

exceeds 25 kcal/mol. Therefore, it is likely that in the homolysis, in distinct contrast to the

rearrangement step 2 → 4, a synergistic interaction of 1 with two activating auxiliaries is

not essential; rather partial protonation suffices.

Conclusions and outlook 127

8. Conclusions and Outlook

In this thesis computational methods were used in order to investigate

rearrangement reactions that occur in same systems of biological relevance. The insight

gained by theory was shown to be useful in answering some of the crucial questions, where

the experimental methods could not provide a complete mechanistic picture of the

processes under investigation. Rather, it is the synergy between theory and experiment

makes it possible to elucidate complex (bio)chemical processes at the molecular level.

In the first part of this thesis the rearrangement reactions of ionized valeramide are

computationally investigated in order to bring insight into the mechanistic pathways

derived from mass-spectrometric experiments; in these experiments it was observed that

the major dissociation processes correspond to competing losses of neutral propene,

formed via the McLafferty rearrangement, and an ethyl radical to presumably afford

protonated acrylamide; formations of a methyl radical as well as ethene occur as side

reactions. According to the theoretical investigations (Chapter 3), the valeramide radical

cation bears several low-lying routes for unimolecular rearrangements. The energetically

preferred route involves initial γ-C–H bond activation according to the well-known

McLafferty rearrangement. Other low-lying channels proceed via β-C–H and δ-C–H bond

activations, respectively, leading to specific fragmentation reactions as observed in the

experiments. The theoretical results are in agreement with the experimental data as far as

the relative energetic ordering of the fragmentation channels, isotope effects, and the

occurrence of H/D equilibration are concerned. However, the non-dynamical calculations

cannot provide a straightforward mechanistic rational for the pronounced temperature

effect on the C3/C2 branching ratios observed in the metastable ion spectra of ionized

valeramide; at elevated temperatures the energetically more demanding C2-route becomes

actually as populated as the less complicated and energetically less demanding McLafferty

channel (C3-route). In order to explain this puzzling result, Car-Parrinello molecular

dynamics studies of neutral and ionized valeramide were performed (Chapter 4). These

dynamical computations provided two rationals for the unusually low C3/C2 branching

ratio observed in the experiments conducted at elevated temperatures: (i) The relatively

low free activation energy of the McLafferty rearrangement causes the dissociation of a

substantial fraction of the parent ion or its distonic counterpart at elevated temperatures.

128 Conclusions and outlook

Therefore, the McLafferty rearrangement occurs prior to the time-delayed mass selection

and consequently, the C3/C2 ratio observed at elevated temperatures is formally reduced.

(ii) Since the barriers associated with conformational changes were shown to be

energetically more demanding than the corresponding hydrogen transfers themselves,

which initiate further rearrangement reactions, the parent ion is trapped by conformational

barriers and is therefore, long-lived at lower temperatures. This indicates that in the

experiments performed at room temperature a greater population of parent ion is mass-

selected, which then enters easier the McLafferty rearrangement (C3-route), thereby

increasing (relative to higher temperatures) the C3/C2 ratio.

The detailed insight in the mechanism of the valeramide radical-cation

rearrangement holds the promise of helping to understand the rearrangement pathways of

biologically important compounds containing an amide functional group upon free radical

attacks. As a further research direction the combined experimental and theoretical

investigations of amides with even bigger side chains or with unsaturated alkyl parts are

warranted. The latter studies would be particularly interesting because a large number of

the biologically active amides contain a double bond in their alkyl chain. Since many

severe and yet incurable diseases are likely to be triggered by the action of free radicals,

the information obtained in such studies could aid in fighting the causes of the human-cell

damage induced by these diseases.

The subject of the second part of this Thesis concerns the catalytic activity of

ethanolamine ammonia lyase, the coenzyme B12 dependent enzyme. First, the

rearrangement of 2-aminoethanol into ethanal and ammonia is investigated (Chapter 5),

where several possible mechanisms involving free radical intermediates as well as their

protonated forms are considered. Two major types of rearrangements are discussed in

detail, namely intramolecular migration and dissociation of the amine/ammonia groups, for

both of which several scenarios are considered. The complete dissociation of the migrating

group and its subsequent association constitute an unlikely route for both the protonated

and the unprotonated reactant due to the high-energy barriers involved in these steps.

Direct migration of the protonated amine group is far more favorable, and therefore

presents the most likely candidate for the actual enzymatic reaction. The calculations

further imply that the direct loss of an ammonium cation also represents a feasible

pathway. Comparing the rearrangements for the aminoethanol radical and its protonated

counterpart, migration of a protonated group is in general associated with lower energy

Conclusions and outlook 129

barriers, suggesting that the actual enzyme substrate quite likely corresponds to (partially)

protonated aminoethanol. As the extent of the substrate protonation/deprotonation by the

active site of the enzyme may vary, the actual energy barriers are expected to range

between the values calculated for the two extreme cases of a substrate, i. e. the

aminoethanol radical, and its fully protonated form. Further, in order to distinguish

between the two most likely mechanisms, i.e. the direct intramolecular migration of the

partially protonated NH2 group vs. elimination of NH4+, the influence of the enzyme’s

active site has been taken into account (Chapter 6). Three scenarios were explored, in

which some of the conceivable amino acids (e.g. Asp/Glu or His) from the active site may

act as catalytic auxiliaries and interact with the substrate: (i) Irrespective of the nature of

the protonating species intramolecular migration of the NH3 group is energetically less

demanding than elimination of NH4+. However, all computed activation enthalpies exceed

the experimentally derived activation enthalpy associated with the rate determining step,

i.e. the hydrogen abstraction from the 5’-deoxyadenosine by the product radical. (ii) For a

partial deprotonation of the substrate at the OH group, the rearrangement mechanism

consists of the dissociation of an NH2 radical from C(2) and its association at C(1) atom.

For all investigated proton acceptors, the activation enthalpy for the dissociation step also

exceeds experimentally determined limit. (iii) Only in a synergistic action of partial

protonation of the NH2 group and partial deprotonation of the OH group by the two

conceivable catalytic auxiliaries Asp/Glu and His, the activation enthalpy computed is

compatible with the experimental data. Therefore this kind of “push-pull” mechanism

presents most like a way of 2-aminoethanol rearrangement in the active site of the enzyme.

This synergistic action is expected to take place in a physiologically realistic pH range of 6

– 9.5. In contrast to the rearrangement reactions, the energetics of the initial hydrogen

abstraction from 2-aminoethanol by the 5’-deoxyadenosyl radical are lowered only by an

interaction of the substrate with a protonating auxiliary (Chapter 7); the synergistic

interaction does not seem necessary.

These computational findings, besides bringing an insight in the rearrangement of

aminoethanol, may as well help to further characterize the yet unknown structural details

of the ethanolamine ammonia lyase’s active site. As a further direction of experimental

research the most appealing seems the elucidation of the enzyme’s X-ray structure. With

this information further theoretical insight could be gained from the QM/MM studies,

which would make possible to model the whole active site and all relevant interactions

between the substrate, the enzyme and the coenzyme B12. Since all coenzyme B12

130 Conclusions and outlook

dependent enzymes are structurally and functionally similar, insight gained by a detailed

study of ethanolamine ammonia lyase would definitively be useful in understanding the

whole class of the B12 dependent enzymes that catalyze extremely important rearrangement

reactions in living systems.

Supporting material 131

9. Supporting Material

Appendix I

Table AI-1. Electronic energies (Eel, in Eh), zero-point energies (ZPE, in Eh), and enthalpies (H at 298 K, in

Eh) of the stationary points on the aminoethanol radical PES.

B3LYP/6-31G* QCISD/cc-pVDZ

Eel ZPE H298K Eel H298K a

21-209.716125 0.084738 -209.625158 -209.159075 -209.068109

22-209.723439 0.085503 -209.632144 -209.166357 -209.075062

23-209.714085 0.084362 -209.623459 -209.157382 -209.066757

41-209.708955 0.083412 -209.619355 -209.159075 -209.069475

42-209.708382 0.082104 -209.619381 -209.154141 -209.065140

43-209.714833 0.083203 -209.625342 -209.160143 -209.070652

21/3 -209.678946 0.080010 -209.592344 -209.116344 -209.029742

3/41-209.674367 0.079665 -209.588212 -209.113413 -209.027258

5’/43-209.620566 0.076322 -209.538534 -209.057488 -208.975456

23/42-209.595700 0.079801 -209.509721 -209.028252 -208.942273

22/10 -209.686613 0.082093 -209.599064 -209.115554 -209.028006

21/12 -209.661970 0.074995 -209.580200 -209.095786 -209.014015

NH2•-55.872619 0.018974 -55.849865 -55.730422 -55.707668

NH2--55.840835 0.017657 -55.819398 -55.680568 -55.659131

NH3-56.547948 0.034531 -56.509614 -56.398982 -56.360648

3 -153.805680 0.056746 -153.744385 -153.394950 -153.333655

5’ -209.134693 0.074645 -209.054871 -208.581116 -208.501294

7 -153.479948 0.056466 -153.418883 -153.073673 -153.012608

10 -153.171537 0.042733 -153.124344 -152.761437 -152.714244

3/11 -153.714173 0.050441 -153.659457 -153.298195 -153.243479

12 -209.171954 0.074025 -209.092116 -208.618444 -208.538607

5’ + H• -209.552783 -208.998212

3 + NH2• -209.594250 -209.041323

7 + NH2- -209.238281 -208.671739

10 + NH3 -209.633958 -209.074892

12 + H• -209.590028 -209.035524

a Enthalpy was calculated as a sum of enthalpy at 0 K obtained at the QCISD level of theory and the difference between enthalpies

obtained at the B3LYP level of theory at 298 K and 0 K. Enthalpies at 0 K correspond to a sum of Eel and ZPE scaled by 0.9806.

132 Supporting material

Table AI-2. Electronic energies (Eel, in Eh), zero-point energies (ZPE, in Eh), and enthalpies (H at 298 K, in

Eh) of the stationary points on the protonated aminoethanol radical PES.

B3LYP/6-31G* QCISD/cc-pVDZ

Eel ZPE H298K Eel H298K a

61-210.081847 0.098289 -209.976902 -209.524736 -209.419791

62-210.080807 0.097919 -209.976025 -209.522010 -209.417228

8 -210.075658 0.096659 -209.972070 -209.523602 -209.420014

61/8 -210.070428 0.094324 -209.969125 -209.504595 -209.403292

62/10 -210.063741 0.094230 -209.962428 -209.501626 -209.400313

9’/8 -209.962510 0.089116 -209.867410 -209.398995 -209.303895

10 · NH4+-210.106891 0.094873 -210.004133 -209.548043 -209.445286

61/13 -210.020164 0.090317 -209.923442 -209.455758 -209.359037

NH3+• -56.184377 0.032875 -56.147657 -56.048011 -56.011291

NH4+-56.893889 0.049860 -56.840235 -56.749059 -56.695405

9’ -209.493824 0.088388 -209.400089 -208.941701 -208.847965

13 -209.528423 0.089082 -209.433695 -208.977700 -208.882972

9’ + H• -209.898001 -209.344883

3b +NH3+• -209.892042 -209.344947

7b + NH3b -209.928497 -209.373256

10b + NH4+ -209.964579 -209.409649

13 + H• -209.931607 -209.379890

a Enthalpy was calculated as a sum of enthalpy at 0 K obtained at the QCISD level of theory and the difference between enthalpies

obtained at the B3LYP level of theory at 298 K and 0 K. Enthalpies at 0 K correspond to a sum of Eel and ZPE scaled by 0.9806.

b Energy of species in Table AI-1.

Table AI-3. Electronic energies (Eel, in Eh), zero-point energies (ZPE, in Eh), and enthalpies (H at 298 K, in

Eh) of the closed-shell stationary points on the aminoethanol PES and its protonated counterpart.

B3LYP/6-31G* QCISD/cc-pVDZ

el ZPE H298K Eel H298K a

1 -210.379581 0.099062 -210.280519 -209.818276 -209.719214

11 -153.830122 0.055825 -153.769456 -153.416121 -153.355455

14 -210.749742 0.113617 -210.629987 -210.190933 -210.071178

15 -210.751489 0.112017 -210.633042 -210.192425 -210.073978

a Enthalpy was calculated as a sum of enthalpy at 0 K obtained at the QCISD level of theory and the difference between enthalpies

obtained at the B3LYP level of theory at 298 K and 0 K. Enthalpies at 0 K correspond to a sum of Eel and ZPE scaled by 0.9806.

Supporting material 133

134 Supporting material

Supporting material 135

136 Supporting material

Supporting material 137

Table AII-5. Electronic energies (Eel, in Eh), zero-point energies (ZPE, in Eh), and enthalpies (H at 298 K, in

Eh) of the stationary points on the PES of 6 interacting with HCO2¯ (Fo¯)as a dissociated Asp/Glu model

system.

B3LYP/6-31G* QCISD/cc-pVDZb

Eel ZPE H298K Eel H298K a

Fo¯-61-399.4924380 0.120882 -399.361071 -398.4731622 -398.341795

Fo¯-61/8 -399.3712215 0.115572 -399.245262 -398.3399231 -398.213964

Fo¯-8 -399.4915734 0.119326 -399.361648 -398.4752482 -398.345323

HCO2¯ -189.1775625 0.020267 -189.153385 -188.7049686 -188.680791

a Enthalpy was calculated as a sum of enthalpy at 0 K obtained at the QCISD level of theory and the difference between enthalpies

obtained at the B3LYP level of theory at 298 K and 0 K. Enthalpies at 0 K correspond to a sum of Eel and ZPE scaled by 0.9806.

b The method used corresponds to QCISD/cc-pVDZ// B3LYP/6-31G*.

Table AII-6. Electronic energies (Eel, in Eh), zero-point energies (ZPE, in Eh), and enthalpies (H at 298 K, in

Eh) of the stationary points on the PES of protonated aminoethanol.

B3LYP/6-31G* QCISD/cc-pVDZ

Eel ZPE H298K Eel H298K a

6’ -210.0910820 0.098553 -209.985841 -209.5355139 -209.430273

6’/8’ -210.0712105 0.094212 -209.969925 -209.5055545 -209.404269

8’ -210.0757860 0.096585 -209.972412 -209.5223363 -209.148962

a Enthalpy was calculated as a sum of enthalpy at 0 K obtained at the QCISD level of theory and the difference between enthalpies

obtained at the B3LYP level of theory at 298 K and 0 K. Enthalpies at 0 K correspond to a sum of Eel and ZPE scaled by 0.9806.

Table AII-7. Electronic energies (Eel, in Eh), zero-point energies (ZPE, in Eh), and enthalpies (H at 298 K, in

Eh) of the stationary points on the PES of 6 interacting with imidazole (Im) as a His model system and acetic

acid (Ac) as Asp/Glu model system.

B3LYP/6-31G* QCISD/cc-pVDZb

Eel ZPE H298K Eel H298K a

Im-6’ -436.3542789 0.170813 -436.171692 -435.1645897 -434.982003

Im-6’/8’ -436.3203434 0.167314 -436.140979 -435.1177574 -434.973576

Im-8’ -436.3399806 0.168842 -436.159338 -435.1542189 -434.938393

Ac-6’ -439.2049031 0.162167 -439.030120 -438.0652833 -438.891948

Ac-6’/8’ -439.1758942 0.157994 -439.004960 -438.0242586 -437.853324

Ac-8’ -439.1914252 0.160093 -439.018576 -438.0553887 -437.882540

a Enthalpy was calculated as a sum of enthalpy at 0 K obtained at the QCISD level of theory and the difference between enthalpies

obtained at the B3LYP level of theory at 298 K and 0 K. Enthalpies at 0 K correspond to a sum of Eel and ZPE scaled by 0.9806.

b The method used corresponds to QCISD/cc-pVDZ// B3LYP/6-31G*.

138 Supporting material

Table AII-8. Pull Mechanism; electronic energies (Eel, in Eh), zero-point energies (ZPE, in Eh), and

enthalpies (H at 298 K, in Eh) of the stationary points on the PES of 2 interacting with OH¯ (O¯) , HCO2¯

(Fo¯) and CH3CO2¯ (Ac¯) as dissociated Asp/Glu model systems.

B3LYP/6-31G* QCISD/cc-pVDZ//

B3LYP/6-31G*

Eel ZPE H298K Eel H298K a

2O¯ -285.5653046 0.095182 -285.461225 -284.8252480 -284.721168

2/3O¯ -285.5476777 0.091426 -285.447071 -284.7975310 -284.696924

3O¯·NH2•-285.5483634 0.090373 -285.447592 -284.8001656 -284.699394

2-Fo¯ -398.9451197 0.106247 -398.828651 -397.9145418 -397.798073

2/3-Fo¯ -398.9155533 0.100064 -398.804904 -397.8773851 -397.766736

3-Fo¯·NH2•-398.9195809 0.098596 -398.808942 -397.8932858 -397.782647

2-Ac¯ -438.2652801 0.134256 -438.119360 -437.1150659 -436.969146

2/3-Ac¯ -438.2366910 0.128771 -438.095839 -437.0778451 -436.936993

3-Ac¯ -382.3520146 0.106042 -382.235957 -381.3483441 -381.232287

NH2•-55.8726187 0.018974 -55.849865 -55.7304220 -55.707668

a Enthalpy was calculated as a sum of enthalpy at 0 K obtained at the QCISD level of theory and the difference between enthalpies

obtained at the B3LYP level of theory at 298 K and 0 K. Enthalpies at 0 K correspond to a sum of Eel and ZPE scaled by 0.9806.

Table AII-9. Pull Mechanism; electronic energies (Eel, in Eh), zero-point energies (ZPE, in Eh), and

enthalpies (H at 298 K, in Eh) of the stationary points on the PES of 2 interacting with CH2NH (Mi) and

imidazole (Im) as His model systems.

B3LYP/6-31G* QCISD/cc-pVDZ//

B3LYP/6-31G*

Eel ZPE H298K Eel H298K a

2-Mi -304.3592351 0.126995 -304.221727 -303.5393790 -303.401871

2/3-Mi -304.3211060 0.122086 -304.188119 -303.4963838 -303.363397

3-Mi -248.4458248 0.09912 -248.338054 -247.7725158 -247.664745

2-Im -435.9491077 0.157914 -435.779537 -434.7587607 -434.589190

2/3-Im -435.9116164 0.152875 -435.746627 -434.7162543 -434.551265

3-Im -380.0358069 0.129769 -379.896045 -378.9919651 -378.852203

a Enthalpy was calculated as a sum of enthalpy at 0 K obtained at the QCISD level of theory and the difference between enthalpies

obtained at the B3LYP level of theory at 298 K and 0 K. Enthalpies at 0 K correspond to a sum of Eel and ZPE scaled by 0.9806.

Supporting material 139

Table AII-10. Push-Pull Mechanism; electronic energies (Eel, in Eh), zero-point energies (ZPE, in Eh), and

enthalpies (H at 298 K, in Eh) of the stationary points on the PES of 6 interacting with model systems for His

and Asp/Glu (CH2NH and HCOO¯; imidazole and CH3COO¯).

B3LYP/6-31G* QCISD/cc-pVDZ

Eel ZPE H298K Eel H298K a

Mi-6-Fo¯ -494.1428962 0.160288 -493.967221 -492.8509360 -492.6752608

Mi-6/8-Fo¯ -494.1177935 0.157081 -493.946857 -492.8276672 -492.6567307

Mi-8-Fo¯ -494.1288556 0.161039 -493.953942 -492.8432684 -492.6683548

Im-6-Ac¯ -665.0634295 0.218483 -664.826266 -663.2805179 -663.0433544

Im-6/8-Ac¯ -665.0337881 0.215666 -664.801311 -663.2539381 -663.0214611

Im-8-Ac¯ -665.0437142 0.219521 -664.807268 -663.2676321 -663.0311859

a Enthalpy was calculated as a sum of enthalpy at 0 K obtained at the QCISD level of theory and the difference between enthalpies

obtained at the B3LYP level of theory at 298 K and 0 K. Enthalpies at 0 K correspond to a sum of Eel and ZPE scaled by 0.9806.

140 Supporting material

Appendix III

Structure labeling code

Labels of different rearrangement types:

I ) Migration of NH3 group: 6 → 8; corresponding TS 6/8.

II) Elimination of NH3 group: 6 → 10; corresponding TS 6/10.

- different conformers of the same structure type differ only in suffix number (e.g. 61,

62). In case of different OH group conformation, a prime sign is used (e.g. 6’).

III) Dissociation – association of NH2 group: 2 → 3 + NH2• → 4; corresponding TS 2/3

and 3/4

Interaction at the NH3- group in 6:

Depending on the interacting agent, different prefix is used:

- for NH3 label N (where NH3 interacts with proton from NH3 group)

- for H2O label O (where H2O interacts with proton from NH3 group)

- for CH2NH label Mi (where methanimine interacts with proton from NH3 group)

- for HCOOH label Fo (where formic acid interacts with proton from NH3 group)

- for HCOO¯ label Fo¯ (where formate interacts with proton from NH3 group)

- for imidazole label Im (where imidazole interacts with proton from NH3 group)

- for CH3COOH label Asp (where acetic acid interacts with proton from NH3 group)

Interaction at the OH- group in 2:

Depending on the interacting agent, different sufix is used:

- for OH¯ label O¯

- for HCOO¯ label Fo¯

- for CH3COO¯ label Ac¯

- for CH2NH label Mi

- for imidazole label Im

Interactions at NH3 and OH groups:

The above code is employed simultaneously, where the prefix points to the agent

interacting with the NH3 group and the suffix refers to the deprotonating agent at the

OH group in 6.

References and notes 141

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46 The absence of imaginary modes in 13+• may also result as an artifact of the limited

size of the grid used in the B3LYP calculations.

47 (a) Frisch, M. J.; Raghavachari, K.; Pople, J.A.; Bouma, W.J.; Radom, L. Chem.

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144 References and notes

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48 (a) Bouma, W. J.; Radom, L. Aust. J. Chem. 1978, 31, 1167. (b) Heinrich, N.

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(d) Mourgues, P. Chamot-Rooke, J. van der Rest, G. Nedev, H. Audier H.E.,

McMahon, T.B. Int. J. Mass Spectrom. 2001, 210/211, 429. (e)Turecek, F. J. Am.

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49 (a) Wu, C.-C.; Lien, M.H. J. Phys. Chem. 1996, 100, 594. (b) Sung, K.; Tidwell,

T.T. J. Am. Chem. Soc. 1998, 120, 3043. (c) Sklenak, S.; Apeloig, Y.; Rappoport,

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1998, 63, 9669.

50 Lin, C.K.; Chen, S.Y.; Lien, M.H. J. Phys. Chem. 1995, 99, 1454.

51 (a) Lias, S.G.; Bartmess, J.E.; Liebman, J.F.; Holmes, J.L.; Levin, R.D.; Mallard,

W.G. J. Phys. Chem. Ref. Data 1988, 17 Suppl. 1. (b) NIST Chemistry WebBook,

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20899, USA (http://webbook.nist.gov).

52 In the isodesmic reactions, processes such as RCONH2 + n-C4H9COOH →

RCOOH + n-C4H9CONH2 were assumed be thermoneutral.

53 Mourgues, P.; Chamot-Rooke, J.; Nedev, H.; Audier H.-E. J. Mass Spectrom. 2001,

36, 102.

54 An average error of ± 2 kcal/mol is assigned to the G2 calculations and used in the

error estimation.

55 Since the relative enthalpies computed at 0 K and 298 K do not differ significantly,

the computed values at 0 K (Table 3-4) can be compared with the experimental

values derived at the standard conditions.

56 Taken from ref. 51b.

57 Hunter, E.P.L.; Lias, S.G. J. Phys. Ref. Data 1998, 27, 413.

58 Berkowitz, J. Ellison, G.B. Gutman, D. J. Phys. Chem. 1994, 98, 2744.

References and notes 145

59 No error bar is given because the estimation of the unknown proton affinity of

vinylacetamide is ambiguous. Here, PA(vinylacetamide) = PA(acrylamide) = 208

kcal/mol was used.

60 Dutuit, O. Alcaraz, C. Gerlich, D. Guyon, P.M. Hepburn, J.W. Metayer-Zeitoun, C.

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61 Abebe, M.; Maccoll, A.; Bowen, R.D. Eur. Mass Spectrom. 1997, 3, 197.

62 Vékey, K. J. Mass Spectrom. 1996, 31, 445.

63 Mason, R.S.; Milton, D.; Harris, F. J. Chem. Soc. Chem. Commun. 1987, 1453.

64 Mason, R.S.; Williams, C.M.; Anderson, P.D.J. J. Chem. Soc. Chem. Commun.

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65 Norrman, K.; McMahon, T.B. Int. J. Mass Spectrom. 1998, 176, 87.

66 Medved, M.; Cooks, R.G.; Beynon, J.H. Int. J. Mass Spectrom. Ion Phys. 1976, 19,

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67 Rennekamp, M.E.; Paukstelis, J.V.; Cooks, R.G. Tetrahedron 1971, 27, 4407.

68 Semialjac, M.; Loos, J.; Schröder, D.; Schwarz, H. Int. J. Mass Spectrom. 2002,

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69 Car, R.; Parrinello, M. Phys. Rev. Lett. 1985, 55, 2471.

70 (a) Haase, F.; Sauer, J. J. Am. Chem. Soc. 1998, 120, 13503. (b) Rovira, C.;

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71 Hutter, J.; Alavi, A.; Deutsch, T.; Bernasconi, M.; Goedecker, S.; Marx, D.;

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72 Kleinman, L.; Bylander, D. Phys. Rev. Lett. 1982, 48, 1425.

73 Troullier, N., Martins, J. L. Phy. Rev. B 1991, 43, 1993.

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146 References and notes

75 (a) Tuckerman M. E., Parrinello M. J. Chem. Phys. 1994, 101, 1302.

(b) Tuckerman M.E., Parrinello M. J. Chem. Phys. 1994, 101, 1316.

76 Hehre, W. J.; Ditchfield, R.; Pople, J. A. J. Chem. Phys. 1972, 56, 2257.

77 The temperature was obtained as an average during the CPMD run. Instead of using

a thermostat, another common method of adjusting the system to a desired

temperature is to use, as the initial temperature for the CPMD simulation, a

temperature which is approximately 2 times higher than the desired one. With time

evolution the system adjusts to the desired temperature and fluctuates around an

average value, which in the present case equals to 519 K.

78 Sprik, M. Chem. Phys. 2000, 258, 139.

79 Sprik, M.; Ciccotti, G. J. Chem. Phys. 1998, 109, 7737.

80 The system was adjusted to the particular constraint value within 1000 steps of the

simulation. Therefore, the first ca. 1000 steps were not taken into account for an

estimation of the average force (average Lagrangian) acting on the system as a

result of the constraint introduced in the system. After 1000 steps of the simulation,

the average value of the Lagrangian fluctuates around some mean value that is

taken for the estimation of the free energy through the integration scheme (for

technical details see ref. 78, 79).

81 One particular structure cannot be addressed since the picture obtained from the

MD simulation is dynamical; even though in the constrained CPMD one

geometrical parameter is kept fixed, many different conformers are available due to

internal rotations. Since these conformers have similar structures, they can be

represented by one structure that corresponds to the whole conformational subspace

(e.g. for the conformation with fully relaxed carbon backbone a structure with the

label 11 was used).

82 Average temperatures of 521 K and 523 K as obtained during the CPMD

trajectories.

83 For details of the labeling code, see Chapter 3. Superscripts in the labeling scheme

point to one specific conformer although in the case of the CPMD studies it is

refrained from addressing a particular conformer because of the dynamical picture.

Therefore, labeled structures without a superscript represent a conformational

subspace.

References and notes 147

84 A change in only one O-H distance is depicted in the inset in Figure 4-6. The

distance between the other hydrogen atom attached to C(4) and oxygen was

monitored resulting as well in a picture comparable to the one depicted in the inset

in Figure 4-6.

85 The short CPMD simulations for a particular value of the constrained parameter

lasted for at least 0.9 ps. The system was adjusted to the particular constraint value

within ca. 3000 steps of the simulation. Therefore, the first 3000 steps were not

taken into account for an estimation of the average force acting on the system as a

result of the constraint introduced in the system.

86 (a) Frey, P. Chem. Rev. 1990, 90, 1343. (b) Kräutler, B.; Arigoni, D., Golding, B.

T. Vitamin B12 and B12-Proteins, Wiley-VCH,: Weinheim, 1998.

87 (a) Buckel, W.; Golding, B. T. Chem. Soc. Rev. 1996, 26, 329. (b) Golding, B. T.;

Buckel, W. Comprehensive Biological Catalysis, Sinnott, M. L., Ed.; Academic

Press, London, 1997, Vol. 3, p 239. (c) Banerjee, R. Biochemistry 2001, 40, 6191.

88 (a) Eggerer, H.; Stadtman, E. R.; Overath, P.; Lynen, F. Biochem Z. 1960, 333, 1.

(b) Finke, R. G.; Schiraldi, D. A.; Mayer, B. J. Coord. Chem. Rev. 1984, 54, 1. (c)

Wollowitz, S.; Halpern, J. J. Am. Chem. Soc. 1984, 106, 8319. (d) Halpern, J.

Science 1985, 227, 869. (e) Golding, B. T. Chem. Br. 1990, 26, 950. (f) Rétey J.

Angew. Chem. Int. Ed. Eng. 1990, 29, 355. (g) Ludwig, M. L.; Matthews, R. G.

Ann. Rev. Biochem. 1997, 66, 269.

89 The original name of the enzyme was ethanol deaminase (see ref. 91) but later it

was changed to ethanolamine ammonia lyase (EC 4.3.1.7).

90 While the actual substrate is 2-aminoethanol, for the sake of shortness, it is

abbreviated in the text as aminoethanol.

91 Bradbeer, C. J. Biol. Chem. 1965, 240, 4669.

92 Halpern, J.; Kim, S.-H.; Leung, T. W. J. Am. Chem. Soc. 1984, 106, 8317.

93 Hay, B. P.; Finke, R. G. J. Am. Chem. Soc. 1987, 109, 8012.

94 LoBrutto, R.; Bandarian, V.; Magnusson, O., Th.; Chen, X.; Schramm, V., L.;

Reed, G. H. Biochemistry 2001, 40, 9., and references cited therein.

95 O’Brien, R. J.; Fox, J. A.; Kopczynski, M. G.; Babior, B. M. J. Biol. Chem. 1985,

260, 16131.

96 Warncke, K.; Ke, S.-C., J. Am. Chem. Soc. 1999, 121, 9922.

148 References and notes

97 Warncke, K.; Schmidt, J. C.; Ke, S.-C., J. Am. Chem. Soc. 1999, 121, 10522.

98 Zipse, H. Acc. Chem. Res. 1999, 32, 571.

99 Bouchoux, G.; Djazi, F.; Hguyen, M. T.; Tortajada, J. J. Phys. Chem. 1996, 100,

3552.

100 (a) Smith, D. M.; Golding, B. T.; Radom, L. J. Am. Chem. Soc. 1999, 121, 1383.

(b) Smith, D. M.; Golding, B. T.; Radom, L. J. Am. Chem. Soc. 1999, 121, 9388.

101 Smith, D. M.; Golding, B. T.; Radom, L. J. Am. Chem. Soc. 2001, 123, 5700.

102 George, P.; Glusker, J. P.; Bock, Ch. W., J. Am. Chem. Soc. 1997, 119, 7065.

103 Smith, D. M.; Golding, B. T.; Radom, L. J. Am. Chem. Soc. 1999, 121, 1664.

104 Smith, D. M.; Golding, B. T.; Radom, L. J. Am. Chem. Soc. 1999, 121, 1037.

105 Wetmore, S. D.; Smith, D. M.; Radom, L. J. Am. Chem. Soc. 2001, 123, 8678.

106 Banerjee, R. Chem. Biol. 1997, 4, 175.

107 Wetmore, S. D.; Smith, D. M.; Radom, L. ChemBioChem. 2001, 2, 919.

108 Smith, D. M.; Wetmore, S. D.; Radom, L. in Eriksson, L. A. (Ed.), Theoretical

Biochemistry – Processes and Properties of Biological Systems, Elsevier Science,

Amsterdam, 2001, Chapter 5.

109 Henry, D. J.; Radom, L., in Cioslowski, J. (Ed.), Quantum-Mechanical Prediction

of Thermochemical Data, Kluwer Academic Publishers, Dordrecht, 2001, Chapter

110 Woon, D. E.; Dunning, Jr., T. H. J. Chem. Phys. 1993, 98, 1358.

111 Mayer, P. M.; Parkinson, C. J.; Smith, D. M.; Radom, L. J. Chem. Phys. 1998, 108,

604.

112 Faust, L. P.; Connor, J. A.; Roof, D. M.; Hoch, J. A.; Babior, B. M. J. Biol. Chem.

1990, 265, 12462.

113 Lynch, B. J.; Truhlar, D. G. J. Phys. Chem. A 2001, 105, 2936.

114 Nguyen, M. T.; Creve, S.; Van Quickenborne, L. G. J. Phys. Chem. 1996, 100,

18422.

115 Thümmel, H. T.; Bauschlicher, Jr., C. W. J. Phys. Chem. A 1997, 101, 1188.

116 Chang, Y.-P.; Su, T.-M-; Li, T.-W.; Chaou, I. J. Phys. Chem. A 1997, 101, 6107.

117 Silva, C. F. P.; Duarte, M. L. T. S.; Fausto, R. J. Mol. Struct. 1999, 482-483, 591.

118 The g’Gg’ structure, as defined in ref. 117.

References and notes 149

119 (a) Smit, B. J.; Nguyen, M. T.; Bouma, W. J.; Radom, L. J. Am. Chem. Soc. 1991,

113, 6452. (b) Turecek, F.; Cramer, C. J. J. Am. Chem. Soc. 1995, 117, 12243. (c)

Rodríguez-Santiago, L.; Vendrell, O.; Tejero, I.; Sodupe, M.; Bertran, J. Chem.

Phys. Lett. 2001, 334, 112.

120 Since an isotope exchange has not been observed between the substrate and the

solvent in the vitamin B12-dependent rearrangements, the variant of an

intermolecular keto-enol tautomerization, catalyzed by an acid or a base, need not

to be considered.

121 According to the IUPAC rules more appropriate names for these radicals are 2-

amino-2-oxoethyl and 2-oxoethyl radicals.

122 The n-CH2CHO+ cation does not exist as a minimum on the PES. As already shown

(see ref. 123), the global minimum on the C2H3O+ PES corresponds to the acetyl

cation (CH3CO+); thus, its formation was assumed in our investigation as well. At

the B3LYP/6-31G* level of theory the electronic energy of the acetyl cation equals

–152.923534 Eh with a ZPE of 0.044775 Eh and the enthalpy of –152.874253 Eh at

298 K. The electronic energy obtained by a geometry reoptimizations at the

QCISD/cc-pVDZ level of theory amounts to –152.531426 Eh.

123 (a) Nobes, R. H.; Bouma, W. J.; Radom, L. J. Am. Chem. Soc. 1983, 105, 309. (b)

Egsgaard, H.; Carlsen, L. Chem. Phys. Lett. 1995, 236, 78.

124 For NH2CH2CHO-• the electronic energy at the B3LYP/6-31G* level of theory

equals -209.120158 Eh with a ZPE of 0.070674 Eh and the enthalpy of –209.043794

Eh at 298 K. At the QCISD/cc-pVDZ level of theory the electronic energy amounts

to –208.553294 Eh.

125 The alternative, heterolytic O-H bond cleavage of 61 can be discarded, since the

energy of hypervalent aminoethanal radical (NH3-CH2-CH=O•; the electronic

energy on the B3LYP/6-31G* level of theory equals -209.723439 Eh with a ZPE

correction of 0.085502 Eh and the enthalpy of –209.632144 Eh at 298 K; at the

QCISD/cc-pVDZ level of theory the electronic energy equals –209.166357 Eh) lies

216.3 kcal/mol above 61.

126 The optimization of the IRC structure in the direction of product could not

converge because of the formation of two separate species. Thus, the energy of the

150 References and notes

product structure was obtained by combining the energies of the separately

optimized structures 10 and NH4+.

127 Faust, L. P.; Babior, B. M. Arch. Biochem. Biophys. 1992, 294, 50.

128 Walling, C.; Johnson, R. A. J. Am. Chem. Soc. 1975, 97, 2405.

129 Weisblat, D. A.; Babior, B. M. J. Biol. Chem. 1971, 246, 6064.

130 Babior, B. M. in Dolphin, D., (Ed.), B12, Wiley, New York, 1982; Vol. 2, Chapter

10.

131 For NH2CH2CH2OH, an experimentally determined enthalpy of formation does not

seem to have been reported. In order to obtain the enthalpy of the corresponding

radical, the following reaction was used: NH2CH2CH2OH → NH2CH2CHOH• + H•,

where all other values are available except for the enthalpy of the C-H bond

cleavage; the latter was approximated as the reaction enthalpy of the following

reaction: CH3OH → CH2OH• + H•.

132 Cioslowski, J.; Schimeczek, M.; Liu, G.; Stoyanov, V. J. Chem. Phys. 2000, 113,

9377.

133 Semialjac, M.; Schwarz, H. J. Am. Chem. Soc. 2002, 124, 8974.

134 Smith, D. M.; Golding, B. T.; Radom, L. J. Am. Chem. Soc. 2001, 123, 1664.

135 Wetmore, S. D.; Smith, D. M.; Bennett, J. T.; Radom, L. J. Am. Chem. Soc., 2002,

124, 14054.

136 (a) Toraya, T.; Yoshizawa, K.; Eda, M.; Yamabe, T. J. Biochem. 1999, 126, 650.

(b) Toraya, T.; Eda, M.; Kamachi, T.; Yoshizawa, K. J. Biochem. 2001, 130, 865.

75, 1469.

137 (a) Simons, T.; Archontis, G.; Karplus, M. J. Phys. Chem. B 1999, 103, 6142. (b)

Czerwinski, R. M.; Harris, T. K.; Massiah, M. A.; Mildvan, A. S.; Whiteman, C. P.

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1768.

138 Petersson, E. J.; Choi, A.; Dahan, D. S.; Lester, H. A.; Dougherty, D. A. J. Am.

Chem. Soc. 2002, 124, 12662.

139 Maiti, N.; Widjaja, L.; Banarjee, R. J. Biol. Chem. 1999, 274, 32733.

140 Mancia, F.; Keep, N. H.; Nakagawa, A.; Leadlay, P. F.; McSweeney, S.;

Rasmussen, B.; Bosecke, P.; Diat, O.; Evans, P. R. Structure 1996, 4, 339.

References and notes 151

141 Mancia, F., Evans, P. R. Structure with Folding & Design 1998, 6, 711.

142 Loferer, M. J.; Webb, B. M.; Grant, G. H.; Lied, K. R. J. Am. Chem. Soc., 2003,

125, 1072.

143 Madhavapeddi, P.; Marsh, E. N. G. Chem. Biol. 2001, 8, 1143.

144 Wetmore, S. D.; Smith, D. M.; Golding, B. T.; Radom, L. J. Am. Chem. Soc., 2001,

123, 7964.

145 The QCISD enthalpies at 298 K were computed as fallows: ∆H (QCISD; 298 K) =

∆H (QCISD; 0 K) + ∆H (B3LYP; 298K) – ∆H (B3LYP; 0K), where enthalpies at 0

K include the sum of the electronic energy and ZPE corrections scaled by 0.9806.

146 For the sake of shortness, it is the pH of the reaction environment around the

enzyme’s active site which is meant when the phrase “pH in the active site” is used.

For a superb discussion of this and related aspects, see: Barril, X.; Alemán, C.;

Orozco, M.; Luque, F. J. Proteins 1998, 32, 67.

147 Warshel, A. Biochemistry 1981, 20, 3167.

148 Bandarian, V.; Reed, G. H. Biochemistry 1999, 38, 12394.

149 (a) Pauling, L. Chem. Eng. News 1946, 24, 1375. (b) Pauling, L. Am. Sci. 1948, 36,

51.

150 (a) Dawson, R. M. C.; Elliott, D. C.; Elliott, W. H.; Jones, K. M.; Data for

Biochemical Research, Oxford, Oxford Science Publication, 3rd Ed., 1986 (b)

Perrin, D. D., Dempsey, B.; Serjeant, E. P. pKa Prediction for Organic Acids and

Bases, London, Chapman and Hall Publishers, 1981.

151 pKa (Asp) = 3.9, pKa (Glu) = 4.1, taken from ref. 150.

152 (a) Smith, B. J.; Tho, N. M.; Bouma, W. J.; Radom, L. J. Am. Chem. Soc. 1991,

113, 6452. (b) Turecek, F; Cramer, C. J. J. Am. Chem. Soc. 1995, 117, 12243.

153 (a) Campbell, S.; Rodgers, M. T.; Marzluff, E. M.; Beauchamp, J. L. J. Am. Chem.

Soc. 1995, 117, 12840. (b) Zheng, Y-J.; Ornstein, R. L. J. Am. Chem. Soc. 1996,

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154 Conformational aspects for the interaction of 6’ with HCOO¯ will not be included

due to the very high activation enthalpy associated with the migration pathway.

152 References and notes

155 (a) Curtin, D. Y. Rec. Chem. Prog. 1954, 15, 111. (b) (b) Winstein, S.; Holness, N.

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156 In Chapter 5 this type of rearrangement was described as “dissociation - association

mechanism”.

157 The barrier for the NH2 dissociation process can be either estimated by locating a

transition structure commencing from the (most) stable conformer 22, or

equivalently, calculating the activation enthalpy for the dissociation starting from

the conformer in which the H-bond interaction does not exist and adding the energy

difference between the two reactant conformers. Here, the latter method was used.

158 PA(Asp) = 217.2 kcal/mol and PA(Glu) = 218.2 kcal/mol vs. PA(CH3COOH) =

187.3 kcal/mol, PA(HCOOH) = 177.3 kcal/mol), PA(H2O) = 165.0 kcal/mol;

PA(His) vs. PA (imidazole) = 225.3 kcal/mol, PA(CH2NH) = 203.8 kcal/mol,

PA(NH3) = 204.0 kcal/mol. All data taken from ref. 51b.

159 For example, the optimal pH for catalytic activity of related glutamate mutase falls

into the range 7.5 – 8; see ref. 143.

160 (a) Halpern, J. Pure Appl. Chem. 1983, 55, 1059. (b) Toraya, T.; Ishida, A.

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162 Bresciani-Pahor, N.; Forcolin, M.; Marzilli, L. G.; Randaccio, L.; Summers, M. F.;

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163 Zhu, L.; Kostic, N. M. Inorg. Chem. 1987, 26, 4194.

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165 Padmakumar, R.; Padmakumar, R.; Banerjee, R. Biochemistry 1997, 36, 3713.

166 Stubbe, J.; van der Donk, W. A. Chem. Rev. 1998, 98, 705.

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168 (a) Carty, T. J.; Babior, B. M.; Abeles, R. H. J. Biol. Chem. 1971, 246, 6313. (b)

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169 (a) Frey, P. A.; Essenberg, M. K.; Abeles, R. H. J. Biol. Chem. 1967, 242, 5369. (b)

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170 Cleland, W. W. Crit. Rev. Biochem. 1982, 13, 385.

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172 Semialjac, M.; Schwarz, H. J. Org. Chem. 2003, 68, 6967.

173 Khoroshun, D. V.; Warncke, K.; Ke, S.-C.; Musaev, D. G.; Morokuma, K. J. Am.

Chem. Soc. 2003, 125, 570.

174 The enthalpies at 298 K were computed as follows: ∆H (MP2/6-311++G**; 298 K)

= ∆H (MP2/6-311++G**; 0 K) + ∆H (B3LYP/6-31G*; 298K) – ∆H (B3LYP/6-

31G*; 0K), where enthalpies at 0 K include the sum of the electronic energy and

ZPE corrections scaled by 0.9806.

175 (a) Reitzer, R.; Gruber, K.; Jogl, J.; Wagner, U. G.; Bothe, H.; Buckel, W.; Kratky,

C. Structure 1999, 7, 891. (b) Gruber, K.; Reitzer, R.; Kratky, C. Angew. Chem.,

Int. Ed. Engl. 2001, 40, 3377. (c) Gruber, K.; Kratky, C. Curr. Opin. Chem. Biol.

2002, 6, 598.

176 Savage, H. F. J.; Lindley, P.F.; Finney, J. L.; Timmins, P. A. Acta Crystallogr.

1987, B43, 280.

177 While the correct name for the model employed is (2S,3R,4S)-2-methyl-3,4-

dihydroxytetrahydrofurane, an abbreviated version derived from the structurally

related ribose, i.e. 1,5-dideoxyribose will be used. For details concerning the

configurations at the C2, C3 and C4 centers (as well as the numbering of the atoms)

and the nature of the intramolecular H-bond between the two OH-groups, see

Scheme 7-2C.

178 Similarly, IRC computations from the TSs in the direction of a product led to

complexes between 2 and 1,5-dideoxyribose (2*A1 and 2*A2; Table 7-1); these are

154 References and notes

slightly less stable (each 0.2 kcal/mol) than the separate species 2 and 1,5-

dideoxyribose (C3- or C2-endo conformers).

179 Because of the pronounced structural similarities of the TSs for the reactions with

the C3- and C2-endo conformers, only those involving the C3-endo conformer of

the 1,5-dideoxyribose are depicted in Figure 7-2.

180 IRC computations commencing from H-TS2 in the direction of a product did not

converged into a complex, but because of otherwise strong similarities between the

two conformers involved in this reaction, it might be postulated to exist. Since the

main interest concerns the barriers of the hydrogen abstractions, it has been

refrained from an exhausting search for this kind of a product complex.

181 Commencing from Mi-TS2 in the direction of a product, the IRC computations did

not converged into a complex. See ref. 180.

155

Publication Index

1. Semialjac, M.; Loos, J.; Schröder, D.; Schwarz, H. Int. J. Mass Spectrom. 2002,

214,129.

Dissociation behavior of ionized valeramide. Part II: Theoretical exploration of the

potential-energy surface

2. Schröder, D.; Loos, J.; Semialjac, M.; Weiske, T.; Schwarz, H.; Höhne, G.;

Thissen, R.; Dutuit, O. Int. J. Mass Spectrom. 2002, 214, 155.

Dissociation behavior of ionized valeramide. Part III: An unprecedented

temperature effect on the C3/C2 branching ratio and its implications for metastable

ion dissociations

3. Semialjac, M.; Schwarz, H. J. Am. Chem. Soc. 2002, 124, 8974.

Computational exploration of rearrangements related to the vitamin B12-dependent

ethanolamine ammonia lyase catalyzed transformation

4. Schröder, D.; Soldi-Lose, H.; Semialjac, M.; Loos, J.; Schwarz, H.; Eerdekens, G.;

Arnold, F. Int. J. Mass Spectrom. 2003, 228, 35.

On gaseous C4H6O2 compounds in the Earth atmosphere: New insights from

collision experiments of the protonated molecules in the laboratory and on aircraft

5. Schröder, D.; Semialjac, M.; Schwarz, H. Eur. J. Mass Spectrom. 2003, 9, 287.

Potential role of methyl-radical adducts with carbon dioxide in the Martian

atmosphere

6. Semialjac, M.; Schwarz, H. J. Org. Chem. 2003, 68, 6967.

Computational study on mechanistic details of the aminoethanol rearrangement

catalyzed by the vitamin B12-dependent ethanolamine ammonia lyase: His and

Asp/Glu acting simultaneously as catalytic auxiliaries

7. Semialjac, M.; Schröder, D.; Schwarz, H. Chem. Eur. J. 2003, 9, 4396.

Car-Parrinello molecular dynamics study of the rearrangement of the valeramide

radical-cation

8. Schröder, D.; Semialjac, M.; Schwarz, H. Int. J. Mass Spectrom., in press.

Secondary kinetic isotope effects in cation-bound dimers of acetone

(C3H6O)M(C3D6O)+ with M = H, Li, Na, K, Rb, Ag, and Cs

9. Semialjac, M.; Schwarz, H. Chem. Eur. J., in press.

Computational investigation on the hydrogen abstraction from 2-aminoethanol by

1,5-dideoxyribose-5-yl radical: A model study of a reaction occurring in the

active site of ethanolamine ammonia lyase

157

Curriculum Vitae

Marija Semialjac

born on March 8th 1977 in Varaždin, Croatia

Croatian, single

Educational Background and Previous Position

from 02/2001

Ph.D. student at the Technische Universität Berlin, Institut für Chemie, in the

group of Prof. Dr. Helmut Schwarz:

Ph.D. Thesis: “Computational Studies on the Rearrangement Reactions of

Some Biologically Relevant Radicals”

04/2002 Research stay in the group of Prof. Dr. Michele Parrinello, Swiss Center for

Scientific Computing (Lugano, Switzerland)

10/1999 - 02/2001

Research Assistant at the University of Zagreb, Faculty of Science,

Chemistry Department (Zagreb, Croatia)

10/1995 - 09/1999 Chemistry Studies at the University of Zagreb, Faculty of Science (Zagreb,

Croatia)

Diploma Thesis: “7-Norbornanone-oxime Rearrangement in Superacids”

09/1991 - 06/1995 Secondary chemical school (Varaždin, Croatia)

09/1983 - 07/1991 Primary school (Varaždin, Croatia)

Fellowships/Awards

2002 - 2003 Ph.D. Fellowship of the Schering Research Foundation

1999 The University of Zagreb Rector’s Award for the best student’s research

project

1998, 1999 The Dean’s Award for the best chemistry student at the Faculty of Science

1998 - 1999 The fellowship of the City of Zagreb for the state’s best students

Professional Skills

Languages: English (fluent), German (very good), Croatian (mother-thong)

Computer-operating Systems: Windows, Macintosh, Linux, Unix

Programming: Fortran

Chemical Software: Gaussian, Gamess, CPMD

Personal Interests

literature, classical music, dancing (salsa, tango argentino), travelling