new applications and challenges for computational roa spectroscopy

Review ArticleNew Applications and Challenges for Computational

ROA SpectroscopyMAGDALENA PECUL*

Faculty of Chemistry, University of Warsaw, Warszawa, Poland

Contribution to the special thematic project ‘‘Advances in Chiroptical Methods’’

ABSTRACT In this article, applications of quantum chemical methods in calcula-tions of the vibrational Raman optical activity (ROA) spectra are reviewed and newdevelopements are discussed. Modeling of ROA spectra of amino acids and peptidesand applications for establishing absolute configuration are briefly outlined. Particularattention is paid to the modeling of solvent effects on ROA spectra, anharmonicity inROA, resonance and pre-resonance ROA spectra, and ROA spectra of moleculesadsorbed on metal surfaces or metal nanoparticles (surface-enhanced Raman optical ac-tivity, SEROA). Remaining challenges in computational ROA spectroscopy are alsopointed out. Chirality 21:E98–E104, 2009. VVC 2009 Wiley-Liss, Inc.

KEY WORDS: Raman optical activity; theoretical calculations; review; solvent effects;resonance ROA; anharmonicity; SEROA

INTRODUCTION

Vibrational Raman optical activity (ROA) has long beena focus of interest for theoretical chemists. The theoreticalbackground for the ROA phenomenon was given byBarron and Buckingham in 1971,1 prior to the first indispu-table measurements by Barron et al. in 19732 and by Huget al. in 1975.3 The first complete ab initio simulation of aROA spectrum was presented in 1990 by Polavarapu,4 whoused the static approximation of Amos.5 The first corre-lated calculations using MCSCF wave functions and Lon-don atomic orbitals were carried out 4 years later,6 and fre-quency-dependent optical tensors were used. Currently,most of the computational techniques available for model-ing of ROA spectra rely on time-dependent density func-tional theory.7–9

In the last few years, the increasing activity in calcula-tions of vibrational ROA using quantum chemical methodscan be observed, reflecting the growing number of experi-mental works using ROA. In particular, ROA has becomea valuable tool in the investigation of structural types ofpeptides and proteins, mainly by using the vibrational am-ide bands I and II (Ref. 10 for the review), and many of thecomputational works are geared toward supporting thisbranch of research.

The present mini review outlines new developementsand remaining problems in computational ROA spectros-copy. We want to focus less on the applications of ROA cal-culations for standard chemical problems such as determi-nation of absolute configuration, since those have beencomprehensively reviewed for example by Polavarapu,11,12

and more on the remaining challenges in theoretical pre-diction of ROA spectra, and attempts to meet them. Thus,

we will discuss only briefly and only the most recent calcu-lations of ROA spectra geared toward establishing abso-lute configuration of natural and synthetic organic mole-cules and high-order structure of peptides and proteins.This review is focused more on modeling of solvent effectsin ROA spectra, of anharmonic effects, and of resonanceand pre-resonance ROA. Perspectives for relativistic calcu-lations of ROA spectra are also discussed. Particular atten-tion is paid to computational treatment of surfaceenhanced Raman optical activity (SEROA). Finally, someconcluding remarks are given.

THEORETICAL INTRODUCTION

The ROA effect is described by means of the absolutedifference between intensities of the scattered light withthe incident light circularly polarized left and right,IRk � ILk , where IL;Rk are the scattered intensities with lineark polarization for right- (R) and left- (L) circularly polarizedincident light, and k denotes the Cartesian component(incident circular polarization Raman optical activity, ICP-ROA). Alternatively, ROA can be measured as a small cir-cularly polarized component in the scattered light usingincident light of fixed polarization, including unpolarizedlight (scattered circular polarization Raman optical activity,

*Correspondence to: Magdalena Pecul, Faculty of Chemistry, Universityof Warsaw, Pasteura 1, Warszawa, 02-093 Poland.E-mail: [email protected]

Contract grant sponsor: Polish Ministry of science and Higher Education;Contract grant number: N204138637

Received for publication 24 April 2009; Accepted 21 July 2009DOI: 10.1002/chir.20781Published online 2 November 2009 in Wiley InterScience(www.interscience.wiley.com).

CHIRALITY 21:E98–E104 (2009)

VVC 2009 Wiley-Liss, Inc.

SCP-ROA). These two approaches are equivalent in thefar-from resonance limit. The differential scattering inten-sity between right and left circularly polarized light for theZ-polarized backward scattering is given by1,13:

IRz � ILz 180ð Þ ¼ 24bðG 0Þ2 þ 8bðAÞ2; ð1Þ

where

bðG 0Þ2 ¼ 3avkiG

0vki � av

kkG0vii

2; ð2Þ

bðAÞ2 ¼ 1

2xrada

vkiekjlA

vjli; ð3Þ

where xrad is the radiation angular frequency, ekjl is theunit third rank antisymmetric tensor, and the other quanti-ties are defined later.

Most of the computations of the ROA spectra is carriedout within the double harmonic approximation (see sec-tion ‘‘Modeling of Anharmonicity in ROA’’ for a review ofworks going beyond that). Within the double harmonicapproximation, the other quantities in eqs. 2 and 3,defined as products of vibrational transition moments, canbe described by means of geometric derivatives of opticaltensors.

avkiG

0vki ¼ h0jakij1ih1jG 0

kij0i ¼1

2x@aki

@Q

� �0

@G 0ki

@Q

� �0

; ð4Þ

avkiekjlA

vjli ¼ h0jakij1ih1jekjlAjlij0i

¼ 1

2x@aki

@Q

� �0

ekjl@Ajli

@Q

� �0

: ð5Þ

The tensors in eqs. 4 and 5 are the electric dipole–elec-tric dipole polarizability a, the imaginary part of the electricdipole–magnetic dipole polarizability G0, and the real partof the electric-dipole–electric quadrupole polarizability A.13

Q is the normal coordinate of the vibration under study.The subscript 0 indicates that the quantities are calculatedat the equilibrium geometry. The second equality in eqs. 4and 5 is valid only within the harmonic approximation.

The a, G0 and A tensors in the notation of modernresponse theory can be written as14

aabð�x;xÞ ¼ �hhla; lbiix ð6Þ

G 0abð�x;xÞ ¼ �ihhla;mbiix ð7Þ

Aa;bgð�x;xÞ ¼ hhla;Hbgiix ð8Þ

Expressions hhA;Biix in the above equations denote lin-ear response functions.

CALCULATIONS OF ROA SPECTRA OF AMINO ACIDSAND PEPTIDES

The most important field of experimental applications ofROA is structural investigation of proteins and their aggre-gates. As a result, most of the calculations of ROA spectranowadays are carried out for amino acids and peptides. Itis not our aim to review all those calculations, but to high-light some of the most interesting, from our point of view,applications published after 2004. For a review of the for-mer (pre-2004) computational investigations of ROA spec-tra of amino acids and peptides, we refer the reader to thereview by Pecul and Ruud.15 Other reviews of interest inthis topic are those by Jalkanen et al.16,17

Calculations for L-Alanine and Its Oligomers

The system for which the largest number of calculationsof ROA spectra has been carried out is L-alanine and itsoligomers. The first theoretical work on this subject waspublished as early as 1991,18 and since then there hasbeen many approaches to modeling of the ROA spectrumof the simplest chiral amino acid. Recently, vibrationalspectra of L-alanine and N-acetyl L-alanine N0-methyl amide(alanine dipeptide) in aqueous solution have been carriedout by Jalkanen et al.19 Calculations of the ROA spectra forthe same dipeptide have been presented by Mukhopad-hyay et al.20 In this case, Monte-Carlo simulations in waterenvironment have been used to obtain the structures. Inanother work of interest,21 the band shapes of ROA spec-trum of L-alanine zwitterion has been modeled. It has beenfound that that the shapes of the spectral bands are to alarge extent determined by the internal rotation of theNH1

3 , CO�2 , and CH3 groups.

ROA spectra of N-acetyl-(L)-alanine N-methyl amide, andtrialanine isomers containing L and S alanine enantiomershave been calculated by Herrmann et al.22 to clarify theproblem of relative contributions from the conformationsof amino acids side chains and peptide backbone to theROA bands of amide vibrations. ROA spectra of helicaldeca-alanine of several enantiomeric compositions hasbeen studied previously by the same group,23 and theresults for all-L deca-alanine have been compared withexperiment.

Calculations for L-Proline and Its Oligomers

Many calculations of the ROA have also been carriedout for L-proline24 and proline-containing peptides.21,25–27

These studies have been motivated by the role of proline,a cyclic amino acid, in forming important structural ele-ments (such as turns) in proteins. The ROA spectra of pro-line tripeptides with different ring conformations havebeen calculated to analyze experimental Raman and ROAspectra of polyproline.25 It has been found that two con-formers of the proline ring are almost equally populated inpolyproline, but that only one helical conformation pre-vails. This finding is of particular interest since the helicalconformation of polyproline (polyproline II, also abbrevi-ated as PPII) constitutes an important structural motif inproteins.

E99COMPUTATIONAL ROA SPECTROSCOPY

Chirality DOI 10.1002/chir

The comparison of performance of nuclear magneticresonance and ROA spectroscopy in conformational analy-sis for model proline-containing dipeptides (Pro-Gly, Gly-Pro, Pro-Ala, and Ala-Pro) has been carried out byBudes ısky et al.,26 and the calculated ROA spectra (withCOSMO model of the aqueous environment) have beencompared with experiment. The agreement was far fromperfect, but the main features of the experimental spec-trum in the 700–1600 cm21 region of Stokes shift havebeen reproduced by means of the calculations. The ROAspectra (experimental and theoretical) of the same dipepti-des have been analyzed in terms of the dependence of theline shape on the conformational dynamics.21 Furtherstudies by the same group included simulations of theROA spectrum of D-Ala-L-Pro-Gly-D-Ala peptide, focused onconformations of the Pro-Gly motif.27

Calculations for Other Amino Acids and Peptides

ROA spectra of amino acids other than alanine or pro-line (or peptides containing them) are calculated less fre-quently. Correlation of ROA intensitiy of a stretching vibra-tion of an indole ring in tryptophan with the conformationof the aromatic ring with respect to the remaining part of atryptophan-containing peptide has been investigated byJacob et al.28 by means of DFT calculations (b(G 0) deriva-tives only) for N-acetyl-(S)-tryptophan-N-methylamide.Another small peptide for which ROA spectrum has beencalculated is tri-L-serine.29 The ROA spectra have alsobeen modeled by means of DFT and HF calculations for L-serine and L-cysteine, but only for neutral gas phase-likeconformations.30 L-Histidine has also attracted attention ofcomputational chemists: vibrational spectra (IR, VCD,Raman, ROA) of its zwitterion forms have been computedby Deplazes et al.31 to compare the conformational infor-mation derived from different types of vibrational spectros-copy.

Local Versus Nonlocal Effects in ROA Spectra ofPeptides

Some of the previously mentioned works are focused onthe problem of separation of local and nonlocal structuraleffects in the ROA spectra of peptides in the amide I, IIand III regions (e.g., see Refs. 23 and 22). It has been sug-gested in Ref. 23 that the backbone conformation domi-nates the ROA patterns for delocalized backbone vibra-tions, in accordance with the findings for helical conforma-tions of synthetic polymers.32,33 However, Ref. 22 partlycontradicts it, at least for short peptides with relatively flat(nonhelical) backbone structure, pointing out to the impor-tance of side chain conformation. Similar conclusions(comparable contributions from backbone helicity andside chain conformations) have been drawn for polypro-line.25 In this context, it should be mentioned that somequalitative conclusions on the dependence of ROA bandsof amide vibrations can also be drawn from simulations ona simple system like nonplanar N-methylacetanide, asshown in Ref. 34.

To sum up this part, the number of computational simu-lations of ROA spectra of peptides is growing, as ROAspectroscopy becomes more and more widespread

method of structural investigations. It is also worth men-tioning that the calculations are not limited to quantumchemical studies of the whole molecule: the recent workby Choi and Cho35 has shown that the fragment approxi-mation method (commonly used in calculations of elec-tronic circular dichroism spectra) can also be sucessfullyapplied to simulate ROA spectra of peptides. One of thestill remaining problems in this type of calculations is tak-ing into account solvent effects, discussed in one of thenext subsections.

CALCULATIONS OF ROA SPECTRA AS A TOOL FORDETERMINATION OF ABSOLUTE CONFIGURATION

Calculations of ROA spectra for nonbiological moleculesare to a large extent devoted to the determination of abso-lute configuration. Quantum chemical prediction of ROAspectra of small systems is now reliable enough for thispurpose, especially if there are no or little solvent effectsto account for (that is, when experiment is carried out fora neat aprotic liquid) and conformational flexibility islimited. Recently, there has been several such applica-tions.36–39 We mention them only briefly and only the new-est works, since the subject has been adequately coveredrecently by Polavarapu.11

Zuber and Hug have assigned absolute configuration for(4S)-4-methylisochromane on the basis of its experimentaland calculated ROA spectra. Absolute configuration hasalso been assigned on this basis for juniouone (a naturalcyclobutane monoterpenoid).38 The study of chiral deuter-ated neopentane37 is particularly interesting, since vibra-tional optical activity has been, in this case, the only wayto determine absolute configuration: the molecule doesnot contain heavy atoms allowing for its investigation bymeans of crystaleographic methods, and its ‘‘electronic’’chirality (natural optical rotation, electronic circulardichroism) is expected to be too weak to be measured.Finally, we would like to mention the work of Gheorgheet al.39 on the assignment of absolute configuration to aquaternary ammonium salt with a chiral alkyl substituent,methyl-(R)-(1-methylpropyl)di(n-propyl)ammonium iodide.Similarly as prediction of ROA spectra for peptides, appli-cations of ROA spectroscopy for the determination of abso-lute configuration would certainly benefit from more accu-rate liquid phase models, capable of accurate rendering ofthe ROA spectra of neat liquids, including those withhydrogen bonds, and of aqueous solutions.

MODELING OF SOLVENT EFFECTS IN ROA

Modeling of solvent effects is essential for renderingrealistic ROA spectra of molecules in solution, especiallyin the case of hydrated species. There are basically threeapproaches to this problem: (a) the supermolecularapproach, in which solvent molecules are treated quantummechanically (usually at the same level of theory as thesolvated molecule); (b) a family of continuum models, inwhich the solvent is modeled as a macroscopic continuumdielectric medium (assumed homogeneous and isotropic)

E100 PECUL


characterized by a scalar dielectric constant, and the sol-ute, described at quantum mechanics level, is placed in acavity in a dielectric medium; and (c) the hybrid model,merging the other two, and treating, for example, the firstsolvation shell quantum mechanically and the remainingsolvent as polarizable continuum. The most widespreadapproaches of the family of continuum models are the Inte-gral Equation Formalism (IEF)-PCM method by Canceset al.40 which uses a molecule-shaped cavity to define theboundary between the solute and the solvent, and theCOSMO(COnductorlike Screening MOdel) method byKlamt and coworkers,41–43 in which the surroundingmedium is modeled as a conductor instead of a dielectric.Most of the calculations carried out for amino acids andpeptides outlined in the first subsection of this chapterhave been carried out with some variety of a solventmodel, so here we will concentrate only on those focusedspecifically on the developement and investigation of per-formance of the solvent models.

Extensive studies on hydration of alanine have been car-ried out by Jalkanen et al.19 by means of supermolecularcalculations and the hybrid model. The authors comparethe results obtained by means of Born-Oppenheimermolecular dynamics simulations with 20 solvating watermolecules and the rest of the solvent modeled by meansof various polarizable continuum models with the previousresults obtained by the same group with simpler aqueousenvironment models (four water molecules in Ref. 44).The authors conclude that the hybrid model is the bestapproach currently available, and advocate its use for fur-ther studies of amino acids and peptides. However, itseems that some features can be captured even by the useof polarizable continuum model alone, as indicated in thecalculations carried out by Pecul et al. (Manuscript inpreparation) for ROA spectra of hydroxyproline in zwitter-ion, anionic, and cationic conformations.

ROA spectra are sensitive to environment, and this fieldof application will certainly be growing. In particular, fur-ther applications of molecular dynamics to model the firstsolvation shell, possibly coupled with polarizable contin-uum model of the remaining solvent would be of interest.Another problem is that in most of the applications so farsolvent effect was taken into account only for geometryoptimization and in calculations of the force field, but notfor optical tensors. The information on relative role ofthese contributions is partly contradictory, and this issuerequires further investigation.

MODELING OF ANHARMONICITY IN ROA

A vast majority of the calculations of ROA spectra is car-ried out in double harmonic approximation, although thetheory13 allows for a more general approach. The onlywork going beyond the double harmonic approach we areaware of is that of Danecek et al.,24 in which ROA spectra(together with IR and Raman spectra) of alanine and pro-line zwitterions (obtained using COSMO-PCM solventmodel) have been calculated by means of vibrational selfconsistent field, vibrational configuration interactions

(VCI), and degeneracy-corrected perturbation calculations.Anharmonic effects have been evaluated both for vibra-tional frequencies and for ROA intensities. The authorsconcluded that the VCI method performs best in the caseof the ROA and Raman spectra, and that the most impor-tant corrections on intensities originate from the forcefield (third and fourth energy derivatives in their model).The anharmonic corrections on spectral intensities stem-ming from second intensity tensor derivatives, althoughmore important for Raman and ROA spectra than for IR,have been found to be relatively minor, and in most casesprobably below experimental noise.

ROA OF TRANSITION METAL COMPLEXES

Applications of ROA spectroscopy are not limited, inprinciple, to organic chemistry and biochemistry.Although, as far as we know, there are no experimentalROA spectra collected for chiral transition metal com-plexes, a computational study of them was presented byLuber and Reiher.45 The authors used nonrelativistic DFTand tested several exchange-correlation potentials.

Further developements in this area would require inclu-sion of relativistic effects, at least by quasi-relativisticmethods. There seem to be two relativistic approachescapable of handling ROA calculations. One is 4-componentDirac-Hartree-Fock and Dirac-Kohn-Sham approach imple-mented in Dirac,46 and the other is 2-component zerothorder regular approximation (ZORA) density functionaltheory approach47,48 implemented in ADF.49,50 Bothapproaches are already developed for a wide range of mag-netic and optical properties, and calculations of ROA spec-tra using either of these approaches are in principle feasi-ble, although, in the case of 4-component calculations,very expensive. It is to be hoped that at least 2-componentcalculations of the ROA spectra will become available inthe near future.

RESONANCE ROA

Performing ROA measurements at the wavelength cor-responding to electronic transition, thus using the reso-nance signal enhancement of vibrations of the groupinvolved in the electronic transition, has been considereda natural extension of ROA, allowing to increase the sensi-tivity and selectivity of the method. However, the appear-ance of the resonance ROA (RROA) spectrum is very dif-ferent than in the case of nonresonant ROA. The theory ofthe phenomenon, presented by Nafie51 in single electronicstate limit, predicts that all resonance-enhanced ROAbands should have the same sign, opposite to the sign ofthe rotatory strength of the electronic transition. This hasbeen verified experimentally for (1)-naproxen, its deu-tered methyl ester and (2)-naproxen52 and has beenshown to be indeed the case.

A more general theoretical approach to RROA has beenpresented and implemented within time-dependent densityfunctional theory approach by Jensen et al.53 The approachuses linear response theory incorporating a damping fac-



tor to account for finite lifetime of the electronic excitedstate. The authors used it to predict resonance vibrationalROA spectra of dihydrogen dioxide and (S)-methyloxirane,and they also obtained uniform sign for all vibrationaltransitions.

The lastest developement in the theory of RROA hasbeen recently presented by Nafie54 in the form of near-res-onance theory, which allows to treat the cases where far-from-resonance ROA theory breaks down and vibronicstructure of the excited states becomes important (withthe consequence of ICP and SCP forms of ROA becomingnonidentical). However, no numerical applications of thisapproach have been presented so far.

SURFACE–ENHANCED ROA

Another approach expected to enhance intensity of ROAspectra is to use the phenomenon of so-called surface-enhanced Raman scattering (SERS) effect: a very largeincrease of the Raman cross-section for molecules placedin resonators formed from some (e.g., Ag, Au, Cu) metalnanoclusters (such resonators can be found, for example,at electrochemically roughened metal electrodes or inmetal sols). The efficiency of SERS scattering can be insome cases 15 orders of magnitude higher in comparisonwith the normal Raman scattering,55 allowing for measure-ment of Raman spectra of samples at very low concentra-tions, and, in some cases, permitting the observation ofRaman spectra even of a single molecule.56–58 Unquestion-able SEROA spectra have been measured only in 200659

(the measurements of Kneipp et al.60 for achiral adenineare controversial), but a lot of attention has been devotedto the SEROA effect by theoretical chemists.

The first works on the effect a metal surface has onROA spectrum were those of Efrima61,62 on the electro-magnetic effects for subtrates fixed with respect to the lab-oratory frame. His analysis predicted significant enhance-ment of ROA intensity of metal surface, provided largelocal inhomogenity of the electric field, phase differencebetween the field gradient and the field itself, and exis-tence of imaginary part of molecular polarizability tensor.The author argued that those conditions are met in SERS-active systems. The theory of SEROA from moleculesattached to a surface fixed with respect to the laboratoryframe has been further explored by Hecht and Barron,63,64

who have shown that lack of orientational averaging leadsto an increase of ROA intensity and that the enhancementdepends on the electric dipole polarizability tensor.

The theory of electromagnetic enhancement in SEROAon freely rotating substrates (such as metal nanoparticlesin soles) has been developed by Janesco and Scuseria.65

They have found that for dipolar substrate the enhance-ment of SEROA is very weak, since the terms contributingto the first order for fixed orientation average out to zero.Larger enhancements are to be expected for quadrupolarsubstrates. They have implemented the methods forcalculating SEROA electromagnetic enhancement for mol-ecules adsorbed on substrates modeled as dipolar andquadrupolar spheres, and then carried out the calculations

for (R)-bromochlorofluoromethane. The numerical resultssupported the theoretical predictions: the SEROAenhancement on a dipolar sphere is very weak, but it islarger on a quadrupolar sphere.

The calculations for dipolar spheres have been repeatedby Bour 66 in matrix formulation. The results obtained for(R)-bromochlorofluoromethane on a single dipolar sphereare in agreement with those of Janesco and Scuseria.65

Interestingly, the spectrum has been found to change verymuch for a molecule in between two or more conductivedipolar spheres: the intensity is much larger and ROA sig-nals can even change their signs. Thus, it seemed thatSEROA spectra, similarly as SERS spectra, originatemostly from the so-called ‘‘hot spots’’ (sites with particu-larly high SERS activity) present on the metal surface, andare very sensitive to the size and shape of metal nanopar-ticles. This is consistent with experimental findings.67

It may be worth mentioning that the theoretical predic-tions about the SEROA enhancement being larger on sub-strates fixed with respect to the laboratory frame than onfreely rotating ones have been confirmed to some extentby experiment. Although the measurements in silver solsyield small surface enhancement,59,67,68 the SEROAenhancement factor has been estimated to be at least 3–4orders of magnitute for electrochemically roughened solidsilver substrate (Pecul and Kudelski, submitted).

According to our knowledge, there are no theoreticalstudies of ‘‘chemical’’ effect on SEROA spectra. Such cal-culations, involving explicit quantum mechanical treatmentof a small metal cluster and adsorbed molecule, would beof considerable interest. We refer the reader to the recentreview by Jensen et al.69 for a more complete review oftheoretical approaches to SERS, including SEROA.

CONCLUDING REMARKS

Much progress has been done recently in quantumchemical modeling of ROA spectra. On one hand, evenlarger systems are becoming accessible due to develope-ment of computational technique, in particular due tointroduction of analytical differentiation of optical tensorswith respect to nuclear coordinates.9,70 On the otherhand, new theoretical works have appeared, allowing tohandle nonstandard calculations of ROA spectra: signifi-cant advances have been made in the prediction of reso-nance and pre-resonance ROA spectra and in theory ofSEROA spectra. There are also approaches developedallowing to calculate ROA spectra beyond double har-monic approximation. What still remains a challenge isincluding relativistic effects in the calculations of ROAspectra of transition metal complexes, and there is still awide scope for improvements in the modeling of solventeffects.

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