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Accurate Potential Energy Surfaces and Beyond: Chemical Reactivity, Binding, Long-Range Interactions, and Spectroscopy

Bytautas, Laimutis,Bowman, Joel M.,Huang, Xinchuan,Varandas, António J. C. · 2012

Abstract

Beginning with the seminal paper of Born and Oppenheimer (BO) [1] in 1927, the concept of the potential energy surface (PES) plays a critical role in the description, simulation, and modeling of molecular systems. It provides the basis [2] for understanding the processes associated with the nuclear motions in molecules. By going beyond the characteristic stationary points and barriers, full dimensional, accurate potential energy surfaces have a very broad range of applications in many areas of physical chemistry; for example, they provide insight into structure, reactivity, and spectroscopy of molecules.While the majority of stable structures on PES are associated with the covalent or ionic bonding [3], the regions of PES dominated by van derWaals interactions are essential for low-temperature phenomena and molecular stacking which are critical for understanding biomolecular structures involving DNA and RNA molecules [4]. Furthermore, the advances in “cold chemistry” [5] make it possible to test the theoretical predictions (see, e.g., [6]) involving very small barriers of <15 K. At such low temperatures the quantum effects, for example, tunneling, play a significant role in chemical reactivity. For instance, the large de Broglie wavelength of ultracold molecules entirely changes the nature of reaction dynamics [7], and energy barriers on the PES play a different role because, in this regime, quantum tunneling becomes the dominant reaction pathway [8]. In addition, our understanding of potential energy surfaces has benefitted greatly from the ability of experimentalists to study chemical reactions and “observe” transition states in real time using the transition-state spectroscopy [9]. Due to the recent advances in ab initio method development [10] primarily focusing on the solution of the nonrelativistic Schr¨odinger equation, the theoretical data representing PESs is of higher quality and the cost and timing for such calculations is considerably improved. Furthermore, the relativistic corrections [11] can be significant and should be included if high accuracy of PESs is needed. For instance, the inclusion of the spin-orbit coupling effect (relativistic phenomenon) may turn a crossing of two potential energy curves into an avoided crossing [12]. Finally, given the raw ab initio data, efficient fitting techniques [13] are capable of generating excellent analytical representations of potential energy surfaces. One example is the functional representation of a PES using the double many-body expansion method [14]. Another important class of PESs corresponds to the ones that are constructed to be explicitly invariant with respect to all permutations of equivalent atoms [15, 16]. It is well recognized that one of the most stringent criteria of the quality of the PES is its ability to reproduce the experimental rotational-vibrational spectrum with the “near-spectroscopic” accuracy [12] of about 10cm− 1 or better [17]. Occasionally, the empirical refinements for ab initioPESs are used in order to achieve a very close agreement (<0.1 cm−1) with experiment for rovibrational transitions [18]. In many cases the BO approximation is valid to a high degree, and a single PES is sufficient to describe the motion of nuclei. However, when several electronic states get close in energy, the coupling between different potential energy surfaces becomes significant. The crossings of several PESs (e.g., conical intersections) or avoided crossings require a more refined treatment of nuclear dynamics which extends nuclear motion to more than one BO surface [19]. The conical intersections or “seams” [20, 21] play an important role in photochemistry, for example, contributing to the photostability of DNA and participating in the isomerization process of cofactor retinal that initiates visual reception.

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Accurate Potential Energy Surfaces and Beyond: Chemical Reactivity, Binding, Long-Range Interactions, and Spectroscopy

Author: Bytautas, Laimutis,Bowman, Joel M.,Huang, Xinchuan,Varandas, António J. C.
Year: 2012
DOI: 10.1155/2012/679869
Source: https://estudogeral.uc.pt/bitstream/10316/102720/1/Accurate-potential-energy-surfaces-and-beyond-Chemical-reactivity-binding-longrange-interactions-and-spectroscopyAdvances-in-Physical-Chemistry.pdf
Hindawi Publishing Co po a ion
Ad ances in Physical Chemis y
Volume 2012, A icle ID 679869, 4pages
doi:10.1155/2012/679869
Edi o ial
Accu a e Po en ial Ene gy Su aces and Beyond: Chemical
Reac i i y, Binding, Long-Range In e ac ions, and Spec oscopy
Laimu is By au as,1Joel M. Bowman,2Xinchuan Huang,3and An ´
onio J. C. Va andas4
1Depa men o Chemis y, Rice Uni e si y, Hous on, TX 77005, USA
2Che y L. Eme son Cen e o Scien i ic Compu a ion and Depa men o Chemis y, Emo y Uni e si y, A lan a, GA 30322, USA
3SETI Ins i u e and NASA Ames Resea ch Cen e , MS 245-6, Moffe Field, CA 94035, USA
4Depa amen o de Quimica, Uni e sidade de Coimb a, 3004535 Coimb a, Po ugal
Co espondence should be add essed o Laimu is By au as, laimu is.by au as@ ice.edu
Recei ed 13 Feb ua y 2012; Accep ed 13 Feb ua y 2012
Copy igh © 2012 Laimu is By au as e al. This is an open access a icle dis ibu ed unde he C ea i e Commons A ibu ion
License, which pe mi s un es ic ed use, dis ibu ion, and ep oduc ion in any medium, p o ided he o iginal wo k is p ope ly
ci ed.
1. Backg ound
Beginning wi h he seminal pape o Bo n and Oppenheime
(BO) [1] in 1927, he concep o he po en ial ene gy su ace
(PES) plays a c i ical ole in he desc ip ion, simula ion,
and modeling o molecula sys ems. I p o ides he basis [2]
o unde s anding he p ocesses associa ed wi h he nuclea
mo ions in molecules. By going beyond he cha ac e is ic
s a iona y poin s and ba ie s, ull dimensional, accu a e
po en ial ene gy su aces ha e a e y b oad ange o applica-
ions in many a eas o physical chemis y; o example, hey
p o ide insigh in o s uc u e, eac i i y, and spec oscopy o
molecules. While he majo i y o s able s uc u es on PES a e
associa ed wi h he co alen o ionic bonding [3], he egions
o PES domina ed by an de Waals in e ac ions a e essen ial
o low- empe a u e phenomena and molecula s acking
which a e c i ical o unde s anding biomolecula s uc u es
in ol ing DNA and RNA molecules [4]. Fu he mo e, he
ad ances in “cold chemis y” [5] make i possible o es he
heo e ical p edic ions (see, e.g., [6]) in ol ing e y small
ba ie s o <15 K. A such low empe a u es he quan um
effec s, o example, unneling, play a signi ican ole in
chemical eac i i y. Fo ins ance, he la ge de B oglie wa e-
leng h o ul acold molecules en i ely changes he na u e o
eac ion dynamics [7], and ene gy ba ie s on he PES play
adiffe en ole because, in his egime, quan um unneling
becomes he dominan eac ion pa hway [8]. In addi ion,
ou unde s anding o po en ial ene gy su aces has bene i ed
g ea ly om he abili y o expe imen alis s o s udy chemical
eac ions and “obse e” ansi ion s a es in eal ime using
he ansi ion-s a e spec oscopy [9].
Due o he ecen ad ances in ab ini io me hod de el-
opmen [10] p ima ily ocusing on he solu ion o he
non ela i is ic Sch ¨
odinge equa ion, he heo e ical da a
ep esen ing PESs is o highe quali y and he cos and iming
o such calcula ions is conside ably imp o ed. Fu he mo e,
he ela i is ic co ec ions [11] can be signi ican and should
be included i high accu acy o PESs is needed. Fo ins ance,
he inclusion o he spin-o bi coupling effec ( ela i is ic
phenomenon) may u n a c ossing o wo po en ial ene gy
cu es in o an a oided c ossing [12]. Finally, gi en he aw
ab ini io da a, efficien i ing echniques [13]a ecapable
o gene a ing excellen analy ical ep esen a ions o po en ial
ene gy su aces. One example is he unc ional ep esen-
a ion o a PES using he double many-body expansion
me hod [14]. Ano he impo an class o PESs co esponds
o he ones ha a e cons uc ed o be explici ly in a ian
wi h espec o all pe mu a ions o equi alen a oms [15,
16]. I is well ecognized ha one o he mos s ingen
c i e ia o he quali y o he PES is i s abili y o ep oduce
he expe imen al o a ional- ib a ional spec um wi h he
“nea -spec oscopic” accu acy [12]o abou 10cm
−1o
be e [17]. Occasionally, he empi ical e inemen s o ab
ini io PESsa eusedino de oachie ea e ycloseag eemen
(<0.1 cm−1) wi h expe imen o o ib a ional ansi ions
[18].
In many cases he BO app oxima ion is alid o a high
deg ee, and a single PES is sufficien o desc ibe he mo ion
o nuclei. Howe e , when se e al elec onic s a es ge close
in ene gy, he coupling be ween diffe en po en ial ene gy
su aces becomes signi ican . The c ossings o se e al PESs
2Ad ances in Physical Chemis y
(e.g., conical in e sec ions) o a oided c ossings equi e a
mo e e ined ea men o nuclea dynamics which ex ends
nuclea mo ion o mo e han one BO su ace [19]. The
conical in e sec ions o “seams” [20,21] play an impo an
ole in pho ochemis y, o example, con ibu ing o he
pho os abili y o DNA and pa icipa ing in he isome iza ion
p ocess o co ac o e inal ha ini ia es isual ecep ion.
2. The P esen Issue
The cu en special issue ( en pape s: six e iews and ou
esea ch a icles) ep esen s an excellen collec ion o pape s
ocusing on he a ious aspec s o po en ial ene gy su aces.
The pape “Cons uc ing po en ial ene gy su aces o
polya omic sys ems: ecen p og ess and new p oblems” by
J. Espinosa-Ga cia, M. Monge-Palacios, and J. C. Co chado
p o ides a comp ehensi e desc ip ion o diffe en me hods
o cons uc ing PESs based on elec onic s uc u e calcu-
la ions, and hei pe o mance is e alua ed by calcula ing
p ope ies associa ed wi h chemical eac ion dynamics. The
au ho s conclude ha a he p esen s age he ield o small
sys ems has become ma u e; howe e he ealm o la ge
polya omic sys ems equi es conside able imp o emen ,
especially when dealing wi h ela i is ic (e.g., spin-o bi )
effec s.
M. Ayouz and D. Babiko in hei esea ch pape “Im-
p o ed po en ial ene gy su ace o ozone cons uc ed using
he i ing by pe mu a ionally in a ian polynomial unc-
ion” illus a e he ad an ages o hei me hod by s udy-
ing he o ma ion o ozone a he mal ene gies and
i s spec oscopy nea he dissocia ion limi . The au ho s
demons a e ha he app oach o i ing he ab ini io da a
by pe mu a ionally in a ian polynomial unc ions allows
he cons uc ion o accu a e global PESs o symme ic
molecules using only ela i ely small numbe o poin s.
The esea ch pape “Ab ini io po en ial ene gy su aces
o bo h he g ound (

X1A)andexci ed(

A1A ) elec onic
s a es o HSiB and he abso p ion and emission spec a
o HSiB /DSiB ” by A. Li, S. Lin, and D. Xie illus a e he
high quali y o he PESs by calcula ing he ib a ional ene gy
le els o he g ound and exci ed s a es o hese challenging
sys ems. The la e we e ound o be in good ag eemen wi h
he a ailable expe imen al band o igins.
The su ace diffusion o adso bed a oms and molecules
plays a signi ican ole in a ious su ace dynamical p o-
cesses, e.g., in he e ogeneous chemical eac ions and o -
ma ion o sel -assembled s uc u es. N. Tsukaha a and J.
Yoshinobu in he pape “Po en ial ene gy su ace o NO
on P (997): adso bed s a es and su ace diffusion” elucida e
he PES by in es iga ing he adso p ion s a es and diffusion
p ocesses o NO on P (997) using in a ed abso p ion
spec oscopy (IRAS) and scanning unneling mic oscopy
(STM).
The classical ansi ion s a e heo y (TST) has been e y
popula o e he yea s o calcula ing he eac ion a e con-
s an s, and i has been qui e success ul in he high- em-
pe a u e egime. Howe e , a low empe a u es, especially
in ol ing ligh nuclei, he quan um effec s become signi -
ican . Quan um ins an on (QI) app oxima ion has been
in oduced as one way o quan ize he TST by na u ally
inco po a ing he quan um effec s, like, o example, unnel-
ing. Fo his eason, he quan um ins an on app oxima ion
has ecei ed much a en ion o es ima ing he chemical eac-
ion a e cons an s using ull-dimensional po en ial ene gy
su aces. The QI can be applied o qui e complex molecula
sys ems ia well-es ablished imagina y ime pa h in eg al
echniques as desc ibed by Y. Zhao and W. Wang in hei
pape “Quan um ins an on e alua ions o he he mal a e
cons an s o complex sys ems.” The au ho s demons a e
he u ili y o he QI me hod by applying i o such complex
p ocesseslikeHdiffusion on Ni(100) su ace, and su ace-
subsu ace anspo and in e io mig a ion o H/Ni.
The hyd ogen bonding plays a signi ican ole in li ing
o ganisms, o example, be ween DNA o RNA bases. The
coope a i i y o hyd ogen bonding and he subs i uen
effec s a e e y impo an in s abilizing biomolecules. In his
issue, A. Eb ahimi, S. M. Habibi-Kho assani, F. B. Akhe , and
A. Fa okhzadeh in he esea ch a icle “The N···HF in e -
ac ions in he X-py idazine···(HF)2complexes: subs i uen
effec s and ene gy componen s” in es iga e he s eng h o
he hyd ogen bonding be ween X-py idazine (N-si es) and
HF molecules depending on he subs i uen . The au ho s
ind ha in all complexes he binding ene gies (N···HF)
inc ease o elec on-dona ing subs i uen s and dec ease o
elec on-wi hd awing subs i uen s. Also a nega i e coope a-
i i y is obse ed o wo hyd ogen bond in e ac ions.
In o de o unde s and he en i e pho ochemical eac ion
p ocess o a gi en sys em, i is necessa y o explo e se e al
PESs ha ep esen g ound and exci ed s a es. Wi hin he
F anck-Condon (FC) app oxima ion, a eac ion s a s om
he FC poin on an exci ed-s a e su ace. Then, depending on
he opog aphy and he a ailable excess ene gy, he sys em
may selec ei he adiaba ic o nonadiaba ic pa hway. In he
adiaba ic case, he eac ing sys em mo es on he exci ed
PES su passing ansi ion s a e o yield p oduc s. In he
nonadiaba ic case, he sys em unde goes a nonadiaba ic an-
si ion (o se e al ansi ions cascading h ough a numbe o
PESs) and hen mo es on he PES o he lowe s a e. In he
la e case, he seams o in e sec ion be ween wo PESs play
an impo an ole. S. Maeda, K. Ohno, and K. Mo okuma
in he e iew pape “Explo ing mul iple po en ial ene gy
su aces: pho ochemis y o small ca bonyl compounds”
desc ibe he global eac ion ou e mapping (GRRM) me hod
o explo e he c i ical egions such as ansi ion s a es, conical
in e sec ions, in e sec ion seams, and minima associa ed
wi h mul iple PESs. The au ho s illus a e he efficiency o
he me hod by documen ing new nonadiaba ic pa hways in
he pho ochemis y o o maldehyde and ace one.
Enzyma ic eac ions explo ing ca aly ic p ope ies o
enzymes ep esen a e y in ense a ea o chemical esea ch.
Many species encoun e ed in enzyma ic eac ions, especially
me alloenzymes, may ha e mo e han one elec onic s a e
lying close in ene gy. I is possible ha as eac ion p og esses,
he ela i e ene gy sepa a ion be ween s a es may a y, and
in pa icula he ene ge ic o de ing o hese s a es may
change du ing he eac ion. Such mechanisms may include
Ad ances in Physical Chemis y 3
cases whe e he “swi ching” in ol es PESs o diffe en spin
mul iplici ies. The likelihood o such mul is a e eac i i y
may ha e impo an consequences in enzyma ic eac ions. E.
A. C. Bushnell, W. Huang, and J. Gauld in he pape “Ap-
plica ions o po en ial ene gy su aces in he s udy o enzy-
ma ic eac ions” explo e se e al s a es o diffe en spin mul-
iplici ies in he ca aly ic ac i a ion o O2by alpha-ke oglu-
a a e-dependen dioxygenase (AlkB).
The pho ochemical s udies whe e he me al a om is
pho oexci ed in o an uppe s a e and hen eac s wi h a
gi en molecule (e.g., me hane) a e qui e in o ma i e since
he eac ion pa hway and p obabili y s ongly depend on
he ini ial elec onic s a e o an a om. Fu he mo e, he
eac ion pa hway equen ly encoun e s se e al po en ial
ene gy su aces (wi h a ious mul iplici ies) be o e he inal
p oduc s a e o med. In his issue, O. No a o, M. del
Alba Pacheco-Blas, and J. H. Pacheco-S´
anchez in he pape
“Po en ial ene gy su aces o eac ions o X me al a oms
(X =Cu, Zn, Cd, Ga, Al, Au, o Hg) wi h YH4molecules
(Y =C, Si, o Ge) and ansi ion p obabili ies a a oided
c ossings in some cases” discuss he possible mechanisms
o he eac ion o he me al a om wi h he gas molecules.
In he cases abo e, he au ho s show ha eac ion pa hways
encoun e many su aces, and he ansi ion p obabili ies o
going om one su ace o ano he a e calcula ed using ime-
dependen Landau-Zene heo y. The esul s indica e a good
ag eemen wi h he expe imen al da a whene e hey a e
a ailable.
An example o he BO app oxima ion b eakdown is
he Renne -Telle effec which is due o he ac ha a
linea geome ies many o he elec onic s a es in molecules
a e wo old degene a e. This esul s in he coupling o he
elec onic mo ion wi h he nuclea mo ion gi ing ise o
he so-called o ib onic coupling. H. Ma, C. Zhang, Z.
Zhang, X. Liu, and W. Bian in hei esea ch a icle “New
ab ini io po en ial ene gy su aces o he Renne -Telle
coupled 11Aand 11A s a es o CH2” gene a e he analy ical
ep esen a ions o he PESs using a dual-le el ( he lowe le el
and he highe le el which also include co e and co e- alence
co ela ion effec s) s a egy wi h he inclusion o he Renne -
Telle e ms. The au ho s use hese PESs o he quan um
dynamical calcula ions and demons a e ha he calcula ed
ib onic ene gy le els o he wo single elec onic s a es a e
in excellen ag eemen wi h expe imen .
Finally, we would like o hank all he au ho s o p o-
iding he high-quali y pape s and also all he e iewe s who
dona ed hei aluable ime o his special issue.
Laimu is By au as
Joel M. Bowman
Xinchuan Huang
An ´
onio J. C. Va andas
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