quantum mechanics methods for molecular biophysics

7/29/2019 Quantum Mechanics Methods for Molecular Biophysics

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Part One

Quantum Mechanics Methods

for Molecular Biophysics and

Electronic Structure

Calculations of Biomolecules

Handbook of Molecular Biophysics. Methods and Applications . Edited by Henrik G. Bohr.Copyright 2009 WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimISBN: 978-3-527-40702-6


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1

Quantum Molecular Biological

Methods Using Density

Functional Theory

Karl James Jalkanen, Sandor Suhai, and Henrik G. Bohr

1.1 Introduction 9

1.2 Introduction to Density Functional Theory methods 221.3 Calculating Vibrational Absorption and Vibrational Circular

Dichroism Spectra 281.3.1 Vibrational Absorption (VA) or Infrared (IR) Absorption and

Vibrational Circular Dichroism 281.4 Calculating Raman Scattering and Raman Optical Activity Spectra 301.4.1 Raman Scattering 301.4.2 Raman Optical Activity 321.5 Classifying Conformational States and Structures based on VA, VCD,

Raman, and ROA Spectra 351.5.1 Experimental Vibrational Frequencies for N-Methylacetamide,

NALANMA, Peptides, and Proteins 351.5.2 Results for the DFT Calculations 351.5.2.1 L-Alanine 351.5.2.2 N-Acetyl L-Alanine N

-Methylamide 391.5.2.3 L-Alanyl L-Alanine 431.5.2.4 L-Histidine 491.5.2.5 N-Acetyl L-Histidine N

-Methylamide 511.5.2.6 N-Acetyl L-Alanine L-Proline L-Tyrosine N

-Methylamide 531.5.3 Future Perspectives and Applications for DFT-based Simulations 551.5.4 Future Perspectives of the Multidisciplinary

Fields of Molecular Biophysics, Molecular Biology, SystemsBiology, and Molecular Medicine and Molecular Psychiatry 56

Acknowledgments 60References 60

Handbook of Molecular Biophysics. Methods and Applications . Edited by Henrik G. Bohr.Copyright 2009 WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimISBN: 978-3-527-40702-6


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1.1Introduction

Toward the end of last century, whenclassical molecular dynamics (MD) be-came a very sought after technique forstudying structure and conformations oflarge biomolecules, it was not an ap-propriate quest to employ and utilizequantum mechanical methods for study-ing dynamics of biomolecules (Warsheland Levitt, 1976; van Gunsteren et al.,1983; Kollman, 1992). Initially, the po-

tential energy surfaces were determinedby fitting to experimental observed spec-tra (Colwell and Percival, 1983a,b), butlater, also by parameterization/fittingto a combination of both experimen-tal and theoretical data (Brooks et al.,1983; Weiner et al., 1984, 1986; Floriset al., 1992; Brooks and Case, 1993; Cor-nell et al., 1995; Dudek and Ponder,1995; Maple et al., 1998; MacKerell et al.,1998). Owing to a limited amount ofexperimental data many assumptions

and approximations needed to be made.These assumptions and approximationsgained credence and support by beingable to reproduce the (limited amountof)data.This hasalso created subsequentproblems, as many of the assumptionsand approximations involved throwingaway/neglecting fundamental physics,

which has subsequently been shown tobe important and is essential to predictsome experimental observables. In manycases,the acceptance andwidespread useof simplified models and theories haveprevented researchers from further de-veloping and extending the models andtheories, as it has been hard to get fund-ing to further develop and extend meth-ods when the general consensus in theapplication field is that the methodsare already of a sufficient level to warrant

general use in applications. This has sub-sequently immensely slowed down thedevelopment of methods, as the fundinghas focused on applications to the detri-ment of further developing the methods.The black box approach to theory be-comes prevelantand then researchersarelimited to what is available in the pack-ages like Gaussian, Amsterdam DensityFunctional (ADF), Dalton, QChem, Tur-bomole, Cambridge Analytical Deriva-tives Package (CADPAC), Spanish Ini-

tiative for Electronic Simulations withThousands of Atoms (SIESTA), ViennaAb-initio Simulation Package (VASP),and so on. The development and refine-mentofthemethodsisthenlefttoasmallnumber of researchers who all have theirso-called development versions of thesecodes/packages.More recently, there has

Handbook of Molecular Biophysics. Methods and Applications. Edited by Henrik G. Bohr.Copyright 2009 WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimISBN: 978-3-527-40702-6


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10 1 Quantum Molecular Biological Methods Using Density Functional Theory

been a call for more open-source codes,such as ABINIT, and forthe National Sci-ence Foundation USA (NSF), AustralianResearch Council (ARC), National In-stitutes of Health (NIH), EuropeanUnion (EU), and the National Healthand Medical Research Council Australia(NHMRC) to continue to fund the devel-opment of methods for use in quantumnanobiology and molecular biology andfor a core of young researchers to be sup-ported to learn these methods by sum-

mer schools, North Atlantic Treaty Orga-nization (NATO) workshops, and so on.This is clearly a high priority if the field isto continue to thrive and flourish and forthe methods to continually be extendedand developed, as problems are identi-fied by theso-calledusers of theacademicand commercial codes. The time lagbetween identifying the problems andimplementing the changes/new devel-opments needs to be reduced.

Basically, the overall goal of utilizingwave function and density functional the-

ory based quantum mechanical methodsfor biomolecules is to derive from firstprinciples functional and spectroscopicdata. Here one calculates the struc-tures, electric and magnetic properties,and vibrational, nuclear magnetic reso-nance (NMR), electron spin resonance(ESR), and electronic spectra of iso-lated molecules, aggregates, and molec-ular complexes in various environmentswhere measurements have been made(nonpolar solvents, embedded within

membranes, in solvents of varying po-larity and ionic strengths, and finally inmixed environments, the most complexbeing proteins and glycoproteins thathave part outside the membrane, partwithin the membrane, and part insidethe membrane). Here one realizes thatthe structure, function, and properties

of these complex machines are lostwhen the machine (molecular complex)is broken down into its various parts (in-dividual species). Here the combinationof theory and experiment has a lot tooffer, as either on its own is less useful.

Within the current set of assumptionsand approximations, many physicallymeasurable properties are predicted tobe zero, which clearly shows that thereare occasions and phenomena whichcannot be treated by making the simpli-

fying assumptions and approximations.The most commonly used ones be-ing the so-called Born Oppenheimer(BO) approximation and the harmonicapproximation (both mechanical (for vi-brational frequencies) and electronic (forinfrared/vibrational intensities)). Actu-ally, the concept of the potential energysurface which one parameterizes to gen-erate a molecular mechanics force fieldis based on the validity of the BO ap-proximation, which as we shall see laterbreaks down for some very interest-

ing phenomena, the so-called non-BOproperties. Many of these properties in-volve electric currents, magnetic fields,and angular momenta. The develop-ment/parameterization of classical me-chanical force fields(and othermolecularproperty surfaces which depend onlyon the nuclear positions of the atoms)is a field within itself, and the inter-ested are encouraged to read specialitypapers on this (Maple et al., 1998; MacK-erell et al., 1998). The point here is that

even though these molecular mechan-ics force fields are commonly used inmolecular biology, they should be usedonly in specific cases where the assump-tions and approximations made are valid.Clearly, for the case of quantum molec-ular biology, where a biological processis initiated by the absorption of a photon


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1.1 Introduction 11

of light, followed by subsequent elec-tron and energy transfer, one must gobeyond the use of molecular mechan-ics methods. Here, one can turn toeither semiempirical-based methods orfirst principles/ab initio-based methods.

The field of developing and parameter-izing molecular mechanical force fields(and property surfaces) has itself bene-fited immensely from both wave func-tion quantum mechanics (WFQM)- anddensity functional theory (DFT)-based

methods, as has the field of developingsemiempirical-based methods, whicharebased on WFQM (Klopman, 1964a,b;Dewar et al., 1985; Stewart, 1989, 2007)and DFT (Elstner et al., 1998; Bohr et al.,1999; Frimand and Jalkanen, 2002). Inaddition, as more accurate and completeexperimental data becomes available,these data can be used both in the param-eterization and testing/verifying stages.This is especially important for more ex-otic molecules and molecular complexes

and assemblies (nanoparticles and pro-tein ligand complexes to name two),which have not been included in thedata sets used for parameterizing and/ortesting. In many cases, for example innon ab initio DFT methods, this newdata provides a wealth of data to test thenewly developed force fields, semiem-pirical methods, and new exchange andcorrelation (XC) functionals.

Since the beginning of this century,it has seemed much more appropri-ate to study, mainly, the electronicstructure of large molecules with thehelp of quantum mechanical methods,with WFQM, DFT, and Greens func-tions being the three most commonlyused. This is because the electronicstructures and properties are necessaryfor deriving the spectroscopic data and

for understanding experimental observ-ables (electric and magnetic properties)for the structures of molecules andmolecular complexes/aggregates (Farid,2002; Onida, Reining and Rubio, 2002;Amos, Jalkanen and Stephens, 1988;Amos et al., 1987; Amos, 1982, 1986,1984, 1987; Buckingham, 1967). Addi-tionally, the electronic structures andproperties are important for understand-ing the reactivity and functionality ofbiomolecules and biomolecular com-

plexes (Deslongchamps, 1983; Hanes-sian, 1983). Hence one must extend themethods of classical MD simulations,where only one calculates the energyand gradients, to include the calculationof the various electronic and magneticproperties at each step of the MD sim-ulation. Here, one has various ways toproceed. One can parameterize molecu-lar property surfaces, similar to potentialenergy surfaces (force fields). For someproperties, the property may depend onthe momenta of the particles in ad-

dition to the positions (Buckingham,1967; Amos, 1982, 1987; Buckingham,Fowler and Galwas, 1987; Lee, Colwelland Handy, 1994; Ioannnou, Colwell andAmos, 1997; Hornicek, Kapralova andBour,2008). The properties(observables)that depend on the momenta, in additionto the positions, are the so-called non-BOproperty surfaces. In some cases, thereareequivalentexpressionsintermsofpo-sitions, momenta, and torque, which intheory should give the same results, but

in practice for a variety of reasons do not(Stephens et al., 1990; Amos, Jalkanenand Stephens, 1988).

Hence, the methodology and tech-niques which have been developed toparameterize potential energy functionscan and have been extended to pa-rameterize molecular property surfaces


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(Amos, 1987). By calculating the proper-ties at each step of the MD simulation,in addition to the energy, one can thensimulate various measured propertiesand other experimental observables thatdepend on these molecular propertiesand how they change as a function ofboth positions/displacements and mo-menta. In addition, one would like toperturb the system and observe the sys-tem evolve back to equilibrium, ifindeed this occurs. In some cases, the

perturbation may induce conformationalchanges and even chemical reactions.For example, the absorption of ultravio-let (UV) radiation by DNA or RNA ofteninvolves the formation of either cyclobu-tane or oxetane rings,damaging theDNAor RNA. One can determine the corre-lated changes that occur between variousquantities as the molecules and molec-ular complexes not only change theirpositions but also change their linearand angular momenta. Many of thesequantities also change and are correlated

with each other (this occurs due to sol-vation, hydration, desolvation and ligandbinding, and the presence of spectatormolecules like the chaperon proteins).Here, one has the ability to do correctaveraging (in principle), which is harderto do when one calculates only a finitenumber of local minima.

Depending on the barriers between thelocal minima, experimental conditionssuch as temperature, pressure, andpresence of chaperon proteins, and/or

other species, which may reduce thebarriers, the species and conformerspresent may vary (Ertl, 2008). Oneassumes in many cases that the systemis in thermal equilibrium and thatsmall fluctuations do not perturb thesystem. In some cases, the completephase space available to the molecule

or molecular complex is sampled duringthe experiment (assuming the barriersare low enough). Here, one assumes thatthe system is in thermal equilibrium andthat small fluctuations do not perturbthe system, and so we do not needto take them, that is, the fluctuationsin temperature (pressure), into account.In other cases, one may be trappedin a local minimum as the other localminima and even the global minimumare not accessible due to larger barriers.

Hence one can measure the spectraand properties of a metastable state andthink that one is in the global minimumdue to the stability of the spectra andhence structure which give the uniqueand high resolution spectra. When onethen perturbs the system and gives itenough energy to surmount the largebarrier, the properties can then changedrastically, which is thought to be thecase for instance of the prion proteins.In this case, the global minimum of theindividual molecules and the complexes

(dimers, trimers, etc.) are not the same.For example, on dimerization fibrilsform. The vibrational circular dichroism(VCD) and Raman optical activity (ROA)spectra of fibrils have been shown toreflect a large change from the nonfibrilstate. These spectroscopic techniquescan hence be used to monitor suchprocesses.

In some cases, one measures a su-perposition of the spectra of speciespresent weighted by their Boltzmann

populations, and in other cases, one ac-tually measures an average spectrum,which may not even represent a realspecies/structure, but a sort of aver-age structure. Hence, it is important toknow both what one is measuring andone is simulating, and how to connectthe two experiments, one in solution


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1.1 Introduction 13

and one in silico. One would like todetermine the structure of the speciespresent and also conformers in the caseof flexible molecules from just vibra-tional spectral measurements, similarto what one now does with the X-rayand NMR methods. Many proteins andother molecules, molecular complexes,and molecular assemblies have escapedX-ray and NMR structure determinationand it would be remarkable if vibrationalstructure determination were developed.

To date, one can determine the per-centage of secondary structure elementspresent and the side chain torsion an-gles for specific residues, but not thecomplete three-dimensional structure ofa protein. What one would really like isto determine the side chain and back-bone torsion angles for each residue.One promising extension of normal vi-brational spectroscopy includes isotopicsubstitution at each residue in the pro-tein to shift the modes and hence makethem separate from those for the other

N 1 residues in the protein. This al-lows one in many cases to assign thebackbone and side chain angles for onlythis specific residue, but not for theother N 1 residues in the protein,which makes this impractical as a generalmethod.

Finally, in addition to the ground statepotential energy and property surfaces,one is interested in various excited stateenergy and property surfaces, and ofcourse, the transition rates and probabili-

ties to jump from one surface to anotherand back, not only in the absence ofradiation but also in the presence of co-herent and incoherent electromagneticradiation (Onida, Reining and Rubio,2002; Farid, 2002; Farid, 1999). There aremany cases in biological systems wherea photon (quanta) of light is necessary

to initiate a/the process, hence the termquantum nanobiology. One example is therepair of damaged DNA (due to UV radi-ation) in the presence of the photolyaseprotein and blue light (Jalkanen et al.,2006a; Bohr, Jalkanen and Malik, 2005).

In this review, we present some ofour contributions to the field of quan-tum nanobiology and also some maincontributions from other researchers tothis newly developing field and the out-standing problems that are yet to be

addressed to make these simulationstransparent and routine. This is donemodestly by complete ab initio calcula-tions of small biomolecules in variousenvironments so as to derive structures,electronic and magnetic properties, andthe various spectra of these molecules,aggregates, and molecular complexes.Hence, this area of research and study isa work in progress and each year moreand more work is contributing to thefields development and evolution. Thedevelopment of multidimensional in-

frared (IR) and Raman experiments, theanalogs of two- and three-dimensionalNMR, have recently been proposed (Cho,2008; Scott, 2003; Jung, 2000; Mukamel,1995), both of which in theory give morestructural information than the simpleone-dimensional spectra. What has lim-ited the development and subsequentuse of these techniques has been thedevelopment of a rigorous theory. Thetheories used to date involve many as-sumptions that have not been adequately

tested, verified, and substantiated (Cho,2008).Hencethereisaneedforthedevel-opment of a rigorous high-level first prin-ciples theory and implementation, whichcanbeusedtotestandbenchmarktheap-proximate classical, semiempirical, DFT,and ab initio methods. This is similarto the development of commercial VCD


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and ROA instruments. Until rigoroustheories were developed, the commer-cial companies were unwilling to investin commercializing instrumentation forwhich the analysis of the spectra wasnot considered rigorous and transparent.In addition, pattern recognition methodsshould be developed which can be usedto go directly from the measured spectrato structure or possible structures andnot to have to do a complete MD, BOMD(Born Oppenheimer Molecular Dynam-

ics) or even non-BOMD simulation foreach system studied. Hence the termvibrational structure determination like X-ray and NMR structure determination.

In the following, we describe andsummarize several applications of quan-tum mechanics to small biomolecules.We review our own and other groupsrestricted Hartree Fock (RHF) andDFT studies for hydrated L-alanine(LA) (Jalkanen, Bohr and Suhai, 1997;Tajkhorshid, Jalkanen and Suhai, 1998;Frimand et al., 2000; Jalkanen et al.,

2001, 2008a; Thar, Zhan and Kirch-ner, 2008), L-alanyl-L-alanine (LALA)(Knapp-Mohammady et al., 1999; Jalka-nen et al., 2003), N-acetyl L-alanineN-methylamide (NALANMA) (Jalkanenand Suhai, 1996; Deng et al., 1996; Hanet al., 1998; Bohr et al., 1999; Pohl et al.,2007; Jalkanen et al., 2008a), L-histidine(LH) (Bohr and Jalkanen, 2005; Jalkanenet al., 2006a; Deplazes et al., 2008), N-acetyl L-histidine N-methylamide (NAL-HNMA) (Bohr and Jalkanen, 2005; Jalka-

nen et al., 2006a), L-tryptophan (LW)(Jalkanen et al., 2006a; Bombasaro, Ro-driquez and Enriz, 2005), and cappedL-alanine L-proline L-tyrosine (APY) [N-acetyl L-alanine L-proline L-tyrosine N-methylamide (NALALPLYNMA) (Nardi,1999; Nardi et al., 2000; Jalkanen et al.,2009c)] and examine the effects of

water hydration on the structures, thevibrational frequencies, vibrational ab-sorption (VA),VCD, Raman scattering,and ROA intensities. The large changesthat hydration has on the structures,relative stability of conformers, and onthe VA, VCD, Raman, and ROA spectraobserved experimentally are qualitativelyreproduced by our DFT calculationswhen one adequately treats the environ-ment, which to date has been neglectedin the literature where one has mostly

tried to correlate features in the vibra-tional spectra of proteins and peptideswith known X-ray or NMR structures(Zhu et al., 2005; Barron et al., 2000).The goal has been to decompose theVA, VCD, Raman, and ROA spectra intotheir principle components, so that theseprinciple components are the character-istic spectra of either local minima orparts of the structures of local minima,which together make up the measuredspectra. This is the premise in the at-tempts to deconvolute or partition the

measured spectra into their principlecomponents (Kubelka, Pancoska andKeiderling, 1999; Baello, Pancoska andKeiderling, 1997; Baumruk, Pancoskaand Keiderling, 1996; Keiderling, 1996).

In the past, theoreticians have ne-glected to properly take into accountthe effects of the environment on sta-bilizing structures that were thought tobe stable without environmental influ-ences (Jalkanen, Bohr and Suhai, 1997;Tajkhorshid, Jalkanen and Suhai, 1998;

Han et al., 1998; Han et al., 2000; Elstneret al., 2000, 2001). Many of the routinelyused molecular mechanics force fieldshave parameterized in local minima inthe absence of solvent, where these localminima are only stable in the presenceof the solvent (Jalkanen et al., 2008a;Han et al., 1998). Hence one must be


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1.1 Introduction 15

careful in using molecular mechanicsforce fields; cases still exist where the var-ious force fields give different results. Tobe fair though, this is also the case withmany of the routinely used generalizedgradient approximation (GGA) and hy-brid exchange correlation functionals.The methods, which have been shownto be systematically correct, are the veryexpensive and rigorous ab initio DFT andcoupled-cluster methods of the Bartlettgroup. The methods have been used to

benchmark the more approximate andcomputationally faster methods: GGAs,hybrid XC functionals and, of course,the SCC-DFTB (Self Consistent Charge-Density Functional Tight Binding) andPM6 (Parametric Method 6) semiempir-ical DFT and WFQM methods.

In addition to the work on hydrationof amino acids, peptides, and proteinsvia vibrational spectroscopy, there isa large body of related work on gashydrates, both experimental and theo-retical (van Klaveren et al., 2001). The

formation of gas hydrates in natural gaspipelines initiated a lot of fundamentalwork on characterizing and understand-ing the process of hydrate formation(Hammerschmidt, 1934). Furthermore,calorimetric methods have been used todetermine the compositions, heat capac-ities, and enthalpies of dissociation fora number of hydrates (Handa, 1986a,b).MD simulation of N2 and O2 hydrateshave been used to interpret the dou-ble maximum in large clathrate cages

and single maxima in small clathratecages for N2 and double maximum inboth cages for O2 (Horikawa et al., 1997).Here, one is able to use MD simulationsto interpret the experimentally observedspectra of gases isolated in various cagesof water molecules. Similar types of ex-periments and MD simulations can be

used to understand the hydration ofamino acids, peptides, and proteins.

Neutron and X-ray diffraction ex-periments have shown that the watermolecules encapsulating peptides andproteins are different from bulk water(Sauter et al., 2001). The question ofthe encapsulation of polar and nonpo-lar groups in amino acids, peptides, andproteins and the effects of hydration onthe vibrational spectra, both frequenciesand VA, VCD, Raman, and ROA inten-

sities are very much related. To date,very little work has been done on ana-lyzing the changes of VA, VCD, Raman,and ROA intensities due to the envi-ronment. This is due to the fact thatlarge changes are observed because ofconformational changes induced by thechanging environment. Here, the twoeffects may not be able to be distin-guished. Indeed, the work of Han et al.(1998) on NALANMA has shown that thespecies of interest maynot be the isolatedmolecule, as it is in nonpolar solvents,

in the gas phase or at low temperaturein inert gas matrices, but the moleculeand its bound water/solvent molecules, amolecular complex. The topology of thepotential energy surface of the moleculeappears to be very solvent/environmentdependent, a fact that hasnot been appre-ciated in the past. Much of the complexitythat appears in the gas phase appears togo away in strongly interacting polar me-dia like water. But then the question ishow does one determine the species of

interest/study? This is especially impor-tant and relevant when one wishes totreat the systems in layers using variouslevels of theory, that is, different modelsfor each layers.

The assumption that the properties ofthe molecular complex are a simple su-perposition or sum of the properties of


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the individual molecules (parts) may bein gross error. Hence the continued de-velopment of fields of complex systemsand systems biology. Chaos theory isanother example of a theory being devel-oped which describes phenomena whichcannot be explained using the standardmodel.

Finally, the treatment of solvent ef-fects on crystallization and predictingthe morphology of the crystals formedhas recently been addressed by Gale

and Rohl (2007). They have extendedthe COSMO (Conductor-Like ScreeningModel) model to treat solute moleculesin solution to deal with solute moleculesin a mother liquor at the crystal sur-face. Here they calculate both the sur-face energy and attachment energy inthe presence of implicit solvent (Gayand Rohl, 1995). Previous work calcu-lated these energies from the gas phase,which, though important, are not consis-tent with the media from which manycrystals are grown. The molecules in the

mother liquor can either adsorb on var-ious crystal faces or desorb and go backinto solution. MD simulations of thisprocess are very time consuming andGale and Rohl have developed a methodthat is highly efficient and uses classicalpotentials. The method can be extendedto ab initio and DFT methods, but to datethis has not been done.

In addition to changes in the vibra-tional spectra, the thermal conductivityof gas hydrates changes; it is much

lower than that of ice and has been as-signed due to coupling between the guestmolecules and the water framework (Tseet al., 2001; Inoue, Tanaka and Nakan-ishi, 1996). Changes in the vibrationalspectra were also simulated and are fur-ther evidence for the coupling of themodes of the crystalline water cages and

the embedded guest molecules. The lowfrequency modes have been observed inthe incoherent inelastic neutron scatter-ing (IINS) spectra, at frequencies whichare very hard to observe in the IR and Ra-man spectra (Gutt et al., 2002). Hence itis very usefulto measure the IINS spectrafor molecular hydrates and complexes,in addition to the VA, VCD, Raman, andROA spectra (Oyama et al., 2003; Subra-manian and Sloan, 2002).

The IINS spectra for amides have

also recently been analyzed with MDsimulations (Itoh et al., 2003). Earlysimulations of the IINS spectra for N-methylacetamide (NMA) using simplemodels have been shown to be in error(Fillaux et al., 1993), even though theywere consistent with the experimentaldata (Fillaux, 1999, 2004; Kearley et al.,1994, 2001; Fillaux et al., 1998; Kearley,1986, 1995; Kearley, Tomkinson andPenfold, 1987). The models for theIINS reassigned the so-called amideA NH stretch mode in NMA to be

approximately half the value found inthe isolated state in nonpolar solventsand in low temperature matrices. In thesolid state, the NH hydrogen is hydrogenbonded with another C=O oxygen ofan adjacent NMA molecule. The modelused was a double-well potential andthe model fit consistently all of theIINS data, so the work was acceptedand caused quite a controversy in theconventional vibrational spectroscopyfield, both experimental and theoretical.

Subsequent work using a more rigorousab initio model has shown that theinitial assignment was right and theproposed new model, although able toreproduce the experimental data, was inerror (Kearley et al., 1994). This was dueto the approximations and assumptionsbeing made that are not strictly valid.


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1.1 Introduction 17

This emphasizes the fact that justbecause a simple model is able toreproduce a limited amount of experi-mental data does not mean it is correct.Hence the use of Ockhams razor doesnot always apply (it states that essen-tially one should use and accept thesimplest possible explanation and/ormodel and/or theory). In this case, themore sophisticated model was necessaryto get the physics correct . In some cases,one is happy to use a nonphysical model,

as is quite often used in classical molec-ular mechanics and MD simulationsthat use harmonic potentials for bondstretches. But if one wants to make pre-dictions and understand the physics ofthe phenomena, then one should striveto use models and theories which in-clude the basic physics of the problem.Hence the term ab initio or first principlestheories. But in many cases even the so-called first principles or ab initio theoriesinvolve approximations, the one mostcommonly made, but not explicitly stated

being the BO approximation. There aremany phenomena that cannot be de-scribed within the BO approximation,for example, the electronic contributionto the atomic axial tensors (AATs), whichare needed to predict/simulate the VCDintensities.

Hence it is very important that themodel is used to simulate as much of theavailable experimental data (Serdyuk,Za-ccai and Zaccai, 2007). MD simulationshave recently been extended to grow

methyl hydrate sII from a supersaturatedaqueous methane solution (Vatamanuand Kusalik, 2008). The next applicationis to develop inhibitors, as hydrate for-mation in natural gas pipelines is veryproblematic and much research has beenundertaken to understand and to preventit from occurring, including the use of

proteins (Zeng et al., 2003; Moon, Taylorand Rodger, 2003). Here the two fieldsmerge. The multidisciplinary nature ofmany problems is finally being appre-ciated. Here researchers can really gainfrom working together and getting freshnew ideas and perspectiveson their prob-lems from researchers in other fields. Inmany cases, having to rigorously defendones methods and approaches, and in-herent assumptions, results in onesfinding some of the weaknesses that do

not get noticed when one just turns thecrank. It is good every once in a whileto analyze the gears and mechanism thatgo along with the crank.

Matrix isolation (Whittle, Dows andPimentel, 1955; Pimentel, 1975), X-raydiffraction, and solid-state vibrationalstudies have been undertaken to try todetermine relationships between struc-tural parameters (both intermolecular,intramolecular, and intermolecular hy-drogen bonding) and vibrational fre-quencies (VA, VCD, Raman, and ROA

intensities) (Charles and Lee, 1965; Pi-mentel and Charles, 1963; Pimenteland Sederholm, 1956). Early Ramanstudies on lysozyme, ribonuclease, and-chymotrypsin documented that vibra-tional studies could also contribute infor-mation to help understand the complexi-ties of biomolecules in aqueous solution(Lord and Yu, 1970a,b).

In addition, one has also constructedsoftware systems such as artificial neuralnetworks to solve the inverse scattering

problem of retrieving structural infor-mation of the biomolecule from spectro-scopic data, that is, vibrational frequen-cies as well as VA and VCD intensitiesof isolated NALANMA (Bohr et al., 2001;Ramnarayan, Bohr and Jalkanen, 2008).

Two possible routes have been consid-ered to predict the structure of our test


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molecule from the spectroscopic data.One route is to use DFT to calculate allthe possible structures/conformers andtheir corresponding frequencies, VA,VCD, Raman and ROA intensities andthen compare them to the experimentaldata. The other is to train expert systems,for example, neural networks on a largecombination of calculated and experi-mental spectra with known structures,either determined experimentally fromX-ray or neutron diffraction or NMR.

Then correlations and/or componentspectra are used to infer or extrapo-late new results, that is, to predict thestructures, fold classes, and percentageof secondary structural elements presentfrom only the measured VA, VCD, Ra-man, and ROA spectra.

In case of large biomolecules, one candetermine whether there are correlationsbetween the best-predicted structural de-tails from spectroscopic data and thedata connected to secondary structurestability and the structures predicted

from neural network programs, whichare based on only sequence and struc-tural correlations. The main problemthat prevented a complete protein struc-ture to be determined from thecombinedVA, VCD, Raman, and ROA spectra hasbeen to determine which spectroscopicdata are the most important determin-ers of secondary structures, so that suchinformation can be used to predict sec-ondary structural elements, and thensubsequently how these secondary ele-

ments fold up to form their tertiary andfinally even quaternary structure. Oneas-sumes that the information is containedin the combined VA, VCD, Raman, andROA spectra: frequencies, line widths,and integrated intensities; polarizationproperties of the intensities; and finallythe frequency dependence of the Raman

and ROA intensities. To date the meth-ods are only able to predict percentagesof various secondary structural elements,but not to assign the secondary structuralelements to each and every residue in theprotein.

Finally, in addition to the secondarystructural element (i and i angles) foreach residue, one needs to determine theside chain torsion angles {ij} and anydisulfide or salt bridges connecting twononadjacent residues (giving extra sta-

bility to this structure). In many cases,the protein folds up to its native stateand is then posttranscriptionally modi-fied/cleaved by an enzyme to achieve itsfunctional state. Insulin is formed fromthe larger proinsulin by such a process.Hence, in many cases, the functionallyactive state of a protein does not corre-spond to any one gene or protein, butto a set of proteins/genes working ina concerted manner. Hence the termsystems biology. One cannot really un-derstand biological function by studying

individual molecules or even individualmolecules in their native environment.Once must know how the molecules in-teract with other molecules to do so.In the case of insulin, the ligand bindsto the transmembrane insulin receptorextracellularly, which triggers dimeriza-tion and then a subsequent activationof intracellular tyrosine kinase activity,the so-called signal transduction process.This is as complex as its get, and onewould like to be able to use spectroscopy

to follow each and every step of this verycomplex process.What has made this problem more

difficult for biomolecules is the absorp-tion of radiation by the environment,water being a strong absorber in the IR,and the strong interaction between thewater molecules and the biomolecules


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1.1 Introduction 19

via hydrogen bonding. Hence one mustconsider in their native environment,the biomolecules that interact with otherbiomolecules, counterions, cations, an-ions, and finally prosthetic groups andbound ligands, which in many casesare necessary for the biomolecules tofunction.On ligand binding, for so-calledinduced fit binding, both the proteinand ligand can undergo conformationalchanges (Keskin et al., 2008). Many ofthe current docking algorithms assume

a lock- and key-type interaction, andhence fail to predict the binding of lig-ands via induced fit, and hence attemptshave been made to improve and extendthe current docking models (Bohm andKlebe, 1996; Davis and Teague, 1999;Cavasotto and Abagyan, 2004; Oliveiraet al., 2006).

The use of VA, VCD, Raman, and ROAspectroscopy are ideal tools to monitorsuch conformational changes in both theligand and the protein on ligand binding.In addition, VCD and optical rotation

have been shown to be sensitive enoughto be able to observe the induced chiralityin achiral solvent molecules and ligandson binding or even interacting with a chi-ral environment (Losada and Xu, 2007;Jalkanen et al., 2008a; Mukhopadhyayet al., 2007; Losada, Tran and Xu, 2008).The sesquiterpene moleculeshave multi-ple chiral centres and in many cases flex-ible side chains, which though achiral,have induced chirality due to the interac-tions with chiral cyclic system (Jalkanen

et al., 2008c; Kulcitki et al., 2005; Wey-erstahl et al., 1995; Ayafor et al., 1994;Newman, 1972).

The larger goal is to find/develop/derive ways to determine structuralminima, not only for the individualmolecules but also when they interactto form ligandprotein complexes. In

addition, in many cases there are otherparticipants in the stable and functionalbiological unit, a metal center, boundsolvent molecules, prosthetic groupslike the porphyrin ring in myoglobinand hemoglobin, and finally, cations oranions (Sauter et al., 2001). For theseminimum energy stable complexes, VA,VCD, Raman, and ROA intensities arecalculated by DFT in order to producetraining data, that is,sets of spectroscopicdata correlated with angles and

other structural determiners for thenetwork. Other methods such as X-raycrystallography and NMR have only beenutilized to determine the native statesof proteins. The VA, VCD, Raman, andROA spectra for proteins and peptideswith known structures should also beadded and be part of the training set.By using DFT methods, the VA, VCD,Raman, and ROA spectra of the so-called denatured states of proteins andpeptides can also be added to the trainingset. Many of the so-called random coil

and denatured states have been shownto have a lot of secondary structurein the CD, VCD, and ROA spectra.All that one can say for sure is thatthese structures are different from theso-called minimum energy structuresunder physiological conditions. In somecases, these structures may even beglobal minima and the structures whichare biologically active may actually be inmetastable states. For example, the prionproteinsmay belower inenergyin the so-

called denatured state, thereby makingattempts to refold the prion proteins verydifficult. In addition, it has recently beenproposed that the functional states ofsome proteins are only present when theligand is bound and the so-called nativeisolated protein is not one conformer(global deep minimum energy state), but


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an ensemble of structures (Keskin et al.,2008; Sauter et al., 2001). Only on ligandbinding or in complex with anotherprotein, does a single unique functionalconformer arise. This could account forthe failure of X-ray and NMR techniquesin determining the unbound state(s)andstructure(s) of this class of proteins.

One of the main problems is to de-termine the structures from the VA,VCD, Raman, and ROA spectra of thedenatured states of proteins. Keiderling

and coworkers have utilized neural net-work methodology to find correlationsof electronic absorption (EA), electroniccircular dichroism (ECD), VA, and VCDspectra with the native states of proteinsby utilizing the known NMR and X-raycrystallographic structures (Pancoska,Yasui and Keiderling, 1989, 1991; Pan-coska, Blazek and Keiderling, 1992; Pan-coska et al., 1994, 1995; Pancoska, Janotaand Keiderling, 1996; Baumruk, Pan-coska and Keiderling, 1996; Baello, Pan-coska and Keiderling, 1997; Pancoska,

Kubelka and Keiderling, 1999; Kubelka,Pancoska and Keiderling, 1999). Ourwork compliments their work in pro-viding correlations of VA, VCD, Raman,and ROA spectra and the higher energydenatured states of peptides and pro-teins. These denatured states can beproduced under various experimentalconditions, that is, in aqueous solution,for example, under various pHs and saltconditions and by the presence of ureaand other denaturing conditions.

In that sense one should be able topredict higher level intermediate en-ergy states during folding processes ofbiomolecules with the help of expert soft-ware systems such as artificialneural net-works and principle component analysesthat have to be trained on known datain order to predict structural data novel

to the networks. Once they are trainedon known sets of intermediate energystates, that is, the set of structural datawe present to the network they shouldbe able to extrapolate to new relationsbetween spectrum and structure. Theadvantage of utilizing software systemssuch as neural network techniques andprinciple component analyses for theinverse scattering problem of derivingstructural information from scatteringdata is that they go hand in hand with

experiments and DFT calculations in thesense that one of the tools can supportthe other when it fails or is impractical.The big endeavor is to produce detailedstructural data of proteins and peptides,both in the isolated state and in com-plex with each other and other proteins,and either measure the experimentalVA,VCD, Raman, and ROA spectra and/orsimulate them with DFT calculations. Inmany cases the spectra and structures ofproteins can be assembled from the prin-ciple components, that is, small peptides

that constitute the whole protein.In many cases, the diverse confor-

mational spectrum of small peptides isgreatly reduced when they form part ofa protein. Hence one may not need todetermine the structures and spectra forall possible conformers of small pep-tides, which itself is a very challengingproblem. But like the protein not sam-pling all possible conformational states,peptides may and probably do not sam-ple all possible states either. This has

also been confirmed via MD simulations.Hence the many groups and researchersworking on methods to sample the com-plete conformational space for proteinsand peptides, though interesting froman academic point of view, may not re-ally be necessary. This may be necessaryto do once for each amino acid and


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1.1 Introduction 21

then for sequence of dipeptide, tripep-tide, and so on, but is really a wasteof time and resources to do again andagain for each protein and/or for eachnew study/simulation. What is requiredis to assemble/collect the results fromvarious laboratories and annotate andverify the data before making it avail-able to the research community. This issimilar to what has been done for bothexperimental X-ray and NMR structures.What is needed is a similar database

for theoretically determined structures.In addition, what is important for themolecular biophysicists, molecular biol-ogists, and quantum nanobiologists tounderstand are the biophysical forcesand interactions that are responsiblefor not only stabilizing the conformers,structures, and assemblies but also thebiophysical processes and events whichare responsible for function, and dynam-ics. In the opinion of these authors, toomuch emphasis has been put on staticstructures and not enough on dynamics

and function. In many cases, the dynam-ical fluctuations and function go handin hand. Vibrational spectroscopies areideal techniques to study and investigateboth dynamics and function.

If biomolecules and biomolecularcomplexes only sample a small part ofthe total available phase and confor-mational space possible, then this iswhat one would like to simulate, andnot large portions of phase space whichare not sampled and/or relevant for the

experiments being studied. Part of thisquestion can be addressed with, for ex-ample, neural network and principlecomponent analyses tools determiningthe dihedral angles in the protein thatareactuallypopulated from the VA,VCD,Raman, and ROA data for each subunit.If one is able to achieve this goal, then the

combination of VA, VCD, Raman, andROA spectroscopy will take a seat alongwith X-ray and neutron diffraction andNMR spectroscopies as standard toolsfor structure determination of proteinsand peptides.

A library of various conformersfor each amino acid along with itscorresponding properties as a func-tion of various environments (aqueous,nonpolar membrane, or mixed) wouldbe very beneficial, similar to the cur-

rent protein data base (PDB) for X-rayand NMR-determined structures andthe Cambridge crystallographic databasefor small molecules and ligands. Ofcourse, along with amino acids, itscorresponding capped amino acid, andsequences of dipeptides, tripeptides,and so on, data of dipeptides, tripep-tides, and so on should also be col-lected/assembled and most certainlyannotated. Many experiments and the-oretical simulations have not been ableto be reproduced (a fundamental part

of good science) due to the lack of be-ing adequately annotated/documented.A simple case is of whether one useddistilled water or distilled anddeionizedwater and whether one carefully con-trolled the pH with a buffer solutionand then, which buffer, HEPES (N-2-Hydroxyethyl-piperazine-N1-2-Ethane-sulfonic Acid), phosphate, and so on.Some effects due to different bufferingsolutions have even been observed. Theregrettable fact is that, in many experi-

ments, everything seems to matter, andhence needs to be properly documentedand controlled.

This large (and ever increasing)amount of data could then be usedeither in the parameterization and/ortesting of new molecular mechanics andsemiempirical methods, and even newly


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developed XC functionals. It is impor-tant to continually test and retest and,if necessary, reparameterize and furtherdevelop and extend methods as prob-lems and/or disagreements arise and arefound. A classical example has been theso-called standard hybrid XC functional,the B3LYP, now being replaced by avariety of more accurate and general XCfunctionals,one such being the B3PW91.

In the next sections, we present ourtheoretical approach to simulate the VA,

VCD, Raman, and ROA spectra of pro-teins and peptides. First, we present anintroduction to DFT methods. Then apresentation is given on how one cal-culates/simulates VA and VCD spectrafollowed by the same for Raman andROA spectra. The last section coversthe use of VA/VCD/Raman/ROA exper-imental and theoretical spectroscopy inmolecular biophysics, molecular biology,and quantum nanobiology.

1.2Introduction to Density FunctionalTheory methods

DFT is in principle an ab initio methodthat allows one to calculate the struc-tures and properties of single isolatedmolecules and various aggregated com-plexes (Hohenberg andKohn,1964; Mer-min, 1965; Kohn and Sham, 1965; Pople,1999; Kohn, 1999; Bartlett et al., 2005;Bartlett, Lotrich and Schwiegert, 2005).

It is more complete than HartreeFockmethodology in that it includes electroncorrelation and is better than other cor-related methods because it requires lesscomputational resources (disk, memory,and CPU time) than otherwise, for thesame computational complexity. DFTformulates the energy of the system

in terms of the electron density andelectron current density instead of thewave function. The trade-off is that onemust determine the various terms inthe Hamiltonian for the total energy ofthe system, the kinetic energy (nuclearand electron) and Coulomb energy(nuclear nuclear, nuclear electron, andelectronelectron)in terms of the elec-tron density, current density, and per-haps the gradients and higher orderspatial derivatives of these so-called ob-

servables. Since these quantities arethemselves functions of functions, theyare called functionals. Various local andnonlocal electron density functionals andlocal electron current density function-als have been determined and tested intheir ability to determine structures, rel-ative energies, binding energies, dipolemoments, polarizabilities, hyperpolar-izabilities, dipole moment derivatives,NMR shielding tensors, and variousother molecular and aggregate prop-erties (Ma and Brueckner, 1968; Ra-

jagopal and Callaway, 1973; Perdew andLevy, 1983; Sham and Schluter, 1985;Lannoo, Schluter and Sham, 1985; Vi-gnale and Rasolt, 1987, 1988; Godby,Schluter and Sham, 1988; Becke, 1988a,1993a; Lee, Yang and Parr, 1988; Levineand Allan, 1989; Papai et al., 1990;Perdew and Wang, 1992; Malkin, Malk-ina and Salahub, 1993a,b; Komornickiand Fitzgerald, 1993; Colwell et al., 1993;Lee and Sosa, 1994; Johnson and Frisch,1994; Schreckenback and Ziegler, 1995;

Malkin et al., 1995; Wilson, Amos andHandy, 1999; Wolff, 2005; Kongsted andRuud, 2008).

The first HohenbergKohn theoremshowed that the electron density deter-mines the energy and hence reformu-lated the basic equation to solve as one inwhich one has to determine the electron


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1.2 Introduction to Density Functional Theory methods 23

density rather than the wave function(Hohenberg and Kohn, 1964). The en-ergy function can be written as

Ev [] = T[] + Vne[] + Vee[] (1)

=

(r)v(r)dr+ FHK[] (2)

where

FHK[] = T[] + Vee[] (3)

and v(r) is the external potential.

The second HohenbergKohn the-orem provides the energy variationalprinciple, which enables one to findthe density that minimizes this energyfunctional (Kohn and Sham, 1965). Theproblem is we do not know the functionalFHK[] and many functionals have beendeveloped that try to address this prob-lem. By introducing the Kohn Shamorbitals, Kohn and Sham were able toaddress the problem of not being ableto determine the electron kinetic energyfunctional in terms of only the density.

At this point, they could have also usedthe KohnSham orbitals to determinethe exchange energy functional by sim-ply substituting now the Kohn Shamorbitals within a Slater determinant. Butby doing this, they would have intro-duced a nonlocal exchange term andthe simplicity and robustness of DFTwould not have been apparent. So in-stead of taking this route, which wouldhave been to search for the correlationenergy functional also in terms of the

KohnSham orbitals, Kohn and Shamexplored using the local density approxi-mation (LDA) for both the exchange andcorrelation energy functionals. For prob-lems in solid-state physics, LDA workswell and has been used for decadesnow. Owing to problems with scalingin WFQM, quantum chemists turned

to DFT as an alternative to the WFQMsemiempirical based methods. For someproblems LDA did fine, but for complexorganic and bioorganic molecules, espe-cially those involving hydrogen bonding,one requires higher accuracy than LDAcan give. This led to the developmentof the so-called GGA functionals, wherein addition to the density, the exchangeand correlation energy functionals arefunctions of the gradient of the den-sity, in addition to the density (Perdew,

Burke and Ernyerhoh, 1996, 1997). Stillhigher accuracy was required, and to getthis higher accuracy one went to thenonlocal HartreeFock form for the ex-change energy functional, substitutingthe KohnSham orbitals into the ex-pressions instead of the HartreeFockorbitals. This led to the so-called hybridXC functionals.

Commonly used hybrid functionals,the Becke 3LYP (B3LYP) (Becke, 1988a,1993a; Lee, Yang and Parr, 1988; Perdewand Wang, 1992),

E[(x, y, z), ((x, y, z))]

= ERB + EHF ELYP (4)

and Becke 3PW91 (B3PW91)

E[(x, y, z), ((x, y, z))]

= ERB + EHF EPW91 (5)

hybrid exchange correlation functionalshave been implemented in CADPAC,Dalton, Turbomole, and Gaussian 94,

98 and 2003 (Stephens et al., 1994; Leeand Sosa, 1994; Becke, 1993a; Lee, Yangand Parr, 1988). B3LYP and B3PW91level analytical Hessian and atomicpolar tensors (APT) calculations havealso been implemented in Gaussian94, 98, 03, CADPAC, and Dalton.More recently, the AAT have been


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implemented in the ADF suite ofprograms utilizing Slater-type orbitals(STOs) (Nicu et al., 2008). Previousimplementations had all been with theGaussian-type orbitals (GTOs), whichhave been used by quantum chemists,since these allow one to analyticallyevaluate many integrals, in contrast tothe use of numerical integrations toevaluate many of the integrals whenusing STOs. But with the use ofnumerical integration to evaluate many

of the exchange and correlation integralsrequired for various XC functionals, thenecessity and advantage of using strictlyGTOs no longer exists, and hence thereturn to the use of STOs.

The B3LYP and B3PW91 level forcefields have been shown to be more ac-curate than RHF level Hessians, whichmust be scaled to get good agreementwith both experimental frequencies andVA and VCD intensities (Jalkanen andStephens, 1991; Stephens et al., 1994;

Jalkanen and Suhai, 1996; Jalkanen et al.,2008a,b; Deplazes et al., 2008). The na-ture of the normal modes have beenshown to depend very much on the scal-ing scheme one chooses to scale theHessian (Jalkanen et al., 1987, 2008b;Jalkanen and Stephens, 1991). The ad-vantage of the B3LYP and B3PW91hybrid exchange correlation functionalsis that the Hessians appear to be ac-curate enough to predict the VA andVCD intensities when coupled with ac-curate APT and distributed origin (DO)gauge and gauge invariant atomic orbital(GIAO) AAT without scaling. The num-ber of molecules for which the B3LYPand B3PW91 Hessians, APT and AAT,have been calculated and used to pre-dict and help interpret the VA and VCDspectra has been quite extensive now.

This level of field has became the stan-dard where either B3LYP or B3PW91are able to predict the correct struc-ture (conformer) and relative energies.The good agreement shown to date hasincluded only a small number of func-tional groups and the comparison hasbeen with measurements of the VA andVCD spectra of molecules in nonpolarsolvents. Recently, systematicerrors withB3LYP have been found (Matsuda, Wil-sonand Xiong,2006), andhencethe need

for a more systematic approach to de-velop XC functionals. The ab initio DFTmethod of Bartlett,which uses optimizedeffective potentials (OEPs) for both ex-change and correlation (XC), appears tobe the most promising (Bartlett et al.,2005; Bartlett, Lotrich and Schwiegert,2005). The work of Bartlett built on pre-vious works with OEPS is covered brieflyand cited in the classical quantum chem-istry text by Levine (2000).

Even though much more expensivethan the GGAs like PBE, OEPs give

the correct answer for the correct rea-sons (correct physics and chemistry),and hence the additional effort andcost is justified. Therefore, the OEP XCfunctionals of the Bartlett group havebecome the new gold standard and, allthe more, simple, approximate, and ro-bust XC functionals should be tested andbenchmarked against the Bartlett OEPs.With the work of Bartlett and coworkers,DFT has now been put on as a rigor-ous level as WFQM, with a systematic

way to improve both the XC function-als achievable, though at much highercost and complexity than originally for-mulated first by Thomas, then Thomasand Fermi, and finally by Hohenberg,Kohn, and Sham. The merging and inte-gration of the works by Kohn and Popleand many others in DFT and WFQM


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appears to have finally been achieved.Now one can use DFT and WFQM andsemiempirical methods based on eachalmost interchangeably, depending onthe focus of ones work. Each method, aswell as Greensfunctions-based methods,has its advantages and disadvantages,especially with respect to the treatmentof excited electronic states and excitedstate potential energy surfaces, whichare required for photon-induced photo-chemical reactions. Many reactions in

molecular biology and molecular bio-physics are photon initiated, so thereis plenty of work to be done to furtherdevelop and refine DFT-based methodsfor electronic excited state MD. In thisrealm, WFQM and Greens functions-based methods are more accurate andshould be used to test and bench-mark the time-dependent density func-tional theory (TD-DFT)- based methods(Onida, Reining and Rubio, 2002; Rein-ing et al., 2002; Ismail-Beigi and Louie,2003; Zhukov, Chulkov and Echenique,

2004).In this review, we summarize previous

works and present some new results onsome small peptides (LALA, NALANMA,and NALHNMA) and two amino acids(LA and LH). LA and LH are two clear ex-amples of a biological molecules whoseproperties and structures in water andgas phase are very different. We havefound that without the water being ex-plicitly or implicitly accounted for, thegas phase or isolated molecule calcula-

tions are of questionableuse in analyzingthe measurements on these moleculesin aqueous solution, though they havefound recent application in mass spec-troscopic studies (Ipolyi et al., 2006). Thezwitterionic structure of LA, the pre-dominant species in aqueous solution,is not stable in the gas phase according

to our 6-31G B3LYP ab initio calcula-tions (Jalkanen, Bohr and Suhai, 1997;Tajkhorshid, Jalkanen and Suhai, 1998).Thereforewe have explicitly included sol-vent, in this case water, to stabilize thisstructure and also to be able to com-pare to the measurements of the VA,VCD, Raman, and ROA spectra of LA inaqueous solution (Tajkhorshid, Jalkanenand Suhai, 1998; Frimand et al., 2000;Jalkanen et al., 2001, 2008a). The VA andVCD spectra of LA in aqueous solution

were initially measured by the groups ofM. Diem at Hunter College in NY, NY(Diem, 1988) and L. Nafie at SyracuseUniversity in Syracuse, NY (Freedmanet al., 1988). Raman and ROA measure-ments and calculations on LA have alsobeen reported by Barron and coworkers(Barron et al., 1991a). At our ab initio6-31G B3LYP DFT-optimized geome-tries we have calculated the vibrationalfrequencies, VA and VCD intensities.The VA and VCD spectra were calcu-

lated with the 6-31G

B3LYP force field(Hessian) and APT and the 6-31G RHFDO gauge AAT.

For LALA, three zwitterionic struc-tures were able to be stabilized with four,six, and seven water molecules, respec-tively (Jalkanen, Bohr and Suhai, 1997;Bohr and Jalkanen, 1998). The zwitteri-onic structure was not stable relative toproton transfer of one of the protons ofthe NH+3 group to the C=O group ofthe adjacent amide group, whereas theproton of the NH group was concur-rently transferred to the closest oxygenof the CO2 group. Subsequently com-pletely solvated (hydrated) structures ofthe LALA zwitterion were extracted fromMD simulations and subsequently op-timized at the B3LYP level of theory(Knapp-Mohammady et al., 1999). Here


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only the water molecules directly hydro-gen bonded with the polar groups werekept and the number of waters variedfrom 10 to 14, depending on the con-formation of the LALA zwitterion. In asubsequent study, we used one of thestructures and predicted the VA, VCD,Raman,and ROAspectra (Jalkanen et al.,2003). Here we present our new resultsfor the LALA plus 11 water clustersembedded within the polarizable con-tinuum model (PCM). We present the

VA, VCD, Raman, and ROA spectrafor the LALA zwitterion with 11 watermolecules. As one can see the waterabsorption masks many of the LALAmodes. Note that in addition to maskingthe LALA modes, the water modes cou-ple with the LALA modes and thereforethe water molecules in the first solvationshell surrounding the LALA zwitterionare different than those in bulk water.This has been documented by X-ray andneutron diffraction studies as well asfrom VCD signals due to chiral water

molecules (the chirality is due to the chi-ral environment of the LALA molecule)(Sauter et al., 2001; Losada and Xu, 2007;Losada, Tran and Xu, 2008).

The goal there was and here is todetermine the structure (a conformer)of the zwitterionic form of LALA inaqueous solution from the experimentalvibrational spectra, VA, VCD, Raman,and ROA, if possible. As shown byour calculations on the neutral species,there are many possible conformers

for this molecule and the structure(s)of this molecule in water has(have)not yet been determined, though theVA, VCD, Raman, and ROA spectrahave been measured. The goal of ourwork is to help answer the question ofthe conformation and species of LALAin aqueous solution and to develop

and document a methodology whichwill work for larger peptides and evenproteins in both native and nonnativeconditions.

We also present here optimized struc-tures of NALANMA with four watersstarting from our 6-31G B3LYP opti-mized structures. The relative energiesof these complexes are compared withthe isolated molecule values. In additionwe explore the effect of changing thehybrid exchange correlation functional,

as recently the B3LYP hybrid exchangecorrelation functional has been calledinto question. Hence we have replacedthe LYP correlation functional with thePW91 correlation functional and haveoptimized the structure of NALANMAwith the four bound waters embeddedwithin the PCM and conductor-like po-larizable continnum model (CPCM) con-tinuumsolvent models with the B3PW91hybrid exchange correlation functional(Jalkanen et al., 2008a).

The goal here has been to model

biomolecules by explicitly adding wa-ter molecules to provide calculationswhich can be used to critically evalu-ate solvent models and specific modelsdeveloped for water (liquid simula-tions) (Jorgensen, Madura and Swen-son, 1984; Jorgensen and Swenson,1985a,b; Jorgensen and Tirado-Rives,1988; Jorgensen, Maxwell and Tirado-Rives, 1996). The H-bonding propertiesas exemplified by some of the simple wa-ter models are clearly incorrect, and we

feel that conclusions based on these mod-els can be critically evaluated utilizingthe better models of water (Berendsenet al., 1981). In addition, the propertiesfor the water potentials that are usedin parameterization may not necessar-ily be those one is interested in. Formodels which do not include effects due


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to polarization, there is no change inthe electronic charge density on hydro-gen bonding, which is known to occur.Hence whenever one uses a classical po-tential, it should be benchmarked for theproperties of interest. In many cases,a more refined model must be usedfor more sophisticated and elaborate ex-periments, for example, the vibrationaland EA and CD spectra. In addition,since many models using parameters re-duce the error between measured and

simulated results, care must be takento ensure that the parameters do notappear to correct the physics and chem-istry that is lacking in the model. Forexample, to use parameters to makeharmonic frequencies anharmonic. Bydoing so, other real anharmonic effectsare lost.

Various models have been developedfor implicitly and explicitly taking intoaccount water at various levels (On-sager, 1936; Richmond, 1984; Wessonand Eisenberg, 1992; Schiffer et al., 1992;

Fortunelli and Tomasi, 1994; Schmidtand Fine, 1994; Tomasi and Persico,1994; Fortunelli, 1996; Cossi et al., 1996;Tawa et al., 1996; Osapay et al., 1996;Craw et al., 1996; Rauhut et al., 1996;Mok, Nwumann and Handy, 1996;Jalkanen and Suhai, 1996, 1998; Jor-gensen, Maxwell and Tirado-Rives, 1996;Tajkhorshid, Han et al., 1998; Knapp-Mohammady et al., 1999; Frimand et al.,2000; Jalkanen et al., 2001, 2003, 2006a;Tomasi, Mennucci and Cammi, 2005;

Mantz et al., 2006). At the molecularmechanics level, the force field canbe parameterized against experimen-tal data measured on the molecule inthe aqueous solution. The force fieldis then an effective force field in thatit is not useful for doing calculationson the molecule in the gas phase or

for other solvents, the optimized po-tentials for liquid simulation (OPLS)force field being the most specific ofthis type (Jorgensen, Madura and Swen-son, 1984; Jorgensen and Swenson,1985a,b; Jorgensen and Tirado-Rives,1988; Jorgensen, Maxwell and Tirado-Rives, 1996). Another approach to thesolvent and/or hydration problem is touse a distance-dependent dielectric orsome other perturbation to the gas phasepotential energy surface and/or inter-

actions to take into account the effectof water without actually adding ex-plicit waters. The goal here is to savecomputational time and resources be-cause the addition of explicit watermolecules adds to the length of thecalculation and the multiple minimumquestions become exponentially worsewhen one tries to find the globalminimum of the molecule solvatedby water molecules. Finally the ques-tion of temperature, and hence entropiceffects are very important when mod-

elling hydrated systems, as there aremany possible orientations of the watermolecules encapsulating and/or hydrat-ing the molecule.

The hydrated structures presentedhere for LA, NALANMA, LALA, LH, andNALHNMA can be used to test the vari-ous water models before one uses themin expensive molecular dynamic simula-tions on proteins and nucleic acids. Thework is a part of our collaborative workinvolving groups at the German Cancer

Research Center, the Technical Univer-sity of Denmark, Helsinki University ofTechnology, Curtin University of Tech-nology, and the University of Bremen tomodel proteins and nucleic acids alongwith various ligands in the presenceof water and denaturing environments.In the next sections, we present the


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methodology to simulate the vibrationalspectrum, not only the frequencies butalso the intensities, followed by the useof the spectroscopic methods in molec-ular biology, molecular biophysics, andquantum nanobiology.

1.3

Calculating Vibrational Absorption andVibrational Circular Dichroism Spectra

1.3.1

Vibrational Absorption (VA) or Infrared(IR) Absorption and Vibrational CircularDichroism

Vibrational absorption and CD spectraare related to molecular dipole androtational strengths via,

() =8 3NA

3000hc(2.303)

i

Difi(i, )

(6)

() = 323

N3000hc(2.303)

i

Rifi(i, )

where and = L R are molarextinction and differential extinction co-efficients, respectively, Di and Ri arethe dipole and rotational strengths ofthe ith transition of wavenumbers iin cm1, and f(i, ) is a normal-ized line-shape function and NA isAvogadros number. For a fundamen-tal (0 1) transition involving the ithnormal mode within the harmonic ap-

proximation

Di =

h

2i

S,iP

S,iP

(7)

Ri = h2Im

S,iP

S,iM

where hi is the energy of the ithnormal mode, the S,i matrix interre-lates normal coordinates Qi to Cartesiandisplacement coordinates X , where specifies a nucleus and = x, y,or z:

X =

i

S,iQi (8)

P and M (, = x, y, z) are the APT

and AAT of nucleus . P is defined by

P =

XG(R)|(el) )|G(R)

Ro

(9)

= 2

G(R)

X

Ro

eel G(Ro)

+ Ze

where G(R) is the electronic wavefunc-tion of the ground state G, R specifiesnuclear coordinates, Ro specifies theequilibrium geometry, el is the electricdipole moment operator, eel = e

i ri

is the electronic contribution to el, andZe is the charge on nucleus and M

is given by

M = I +

i

4hc

Ro(Ze)

I

=G(R)

XRe

G(Re, B )

B

B =0

(10)

where G(Ro, B ) is the ground stateelectronic wavefunction in the equilib-rium structure Re in the presence of the


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1.3 Calculating Vibrational Absorption and Vibrational Circular Dichroism Spectra 29

perturbation (emag) B , where emag isthe electronic contribution to the mag-netic dipole moment operator. M isorigin dependent. Its origin dependenceis given by

(M )0 = (M)

0 +i

4hc

YP

(11)

whereY isthevectorfromOtoO forthetensor of nucleus . Equation (11) per-mits alternative gauges in the calculationof the set of (M)

0 tensors. If Y = 0,and hence O = O, for all the gaugeis termed the common origin (CO) gauge.If Y = Ro, so that in the calculationof (M)

0 O is placed at the equilib-rium position of nucleus , the gauge istermed the DO gauge (Stephens, 1985,1987; Buckingham, Fowler and Galwas,1987; Amos et al., 1987; Amos, Jalkanenand Stephens, 1988).

The problem with the expressions forthe APT and AAT presented initially

is that they involved the wavefunctionand wavefunction derivatives (usuallycalculated with Coupled HartreeFocktheory). These expressions were imple-mented in CADPAC to calculate the APTat the self-consistent field (SCF) and MP2levels and the AAT at the SCF level. Thefirst rigorous VA and VCD spectral sim-ulations were performed using the Gaus-sian and CADPAC programs (Stephensand Lowe, 1985; Amos et al., 1987; Amos,Jalkanen and Stephens, 1988, 1991). The

scaled quantum mechanical (SQM) forcefields (Lowe et al., 1986; Jalkanen et al.,1987, 1988; Kawiecki et al., 1991) wereinitially scaled using the scaling meth-ods of Blom and Altona (1976) andPulay et al. (1979). Later more accurateMP2 force fields appeared to be accurateenough, when combined with MP2 APT

and RHF/SCF AAT tensors (Stephenset al., 1993). This gave qualitative accu-racy in general, and in some cases evenquantitative accuracy, though there werecases which were problematic, one beingtrans-1,2-dicyanocyclopropane, which isnow still considered problematic anda good test case for any new method(Jalkanen et al., 2008b). Subsequently,the AAT have been implemented withGIAOs at both the SCF and multicon-figuration self-consistent field (MCSCF)

levels of theory within the Dalton suite ofprograms (Bak et al., 1993, 1994, 1995).The advantages of DFT are numerous,

but the main one is to extend rigorousmethodology to the calculation of prop-erties of large biological molecules. DFTseems to provide a way to do that. Butthe expressions must be reformulated asexpressions amenable for DFT, whereone has the density expressed in termsof the so-called Kohn Sham orbitals andnot in terms of rigorous wave functions.The KohnSham orbitals are only used

to generate the density, and one must bevery careful in applying and using the or-bitals and eigenvalues outside the scopefor which they were intended.

The calculation of the DFT AATs hasbeen implemented within the coupledperturbed Kohn Sham formalism usingGTOs in CADPAC, Dalton, and Gaus-sian (Cheesman et al., 1996) and usingSTOs in the ADF program (Nicu et al.,2008; Wolff, 2005; te Velde et al., 2001).For many cases, SCF AAT appear to be

of sufficient accuracy, but with the preva-lence of implementations of DFT, DFTmethodology appears to be taking over.A comparison of rotational strengths formolecules with both RHF and DFT AATis still important, as in many cases onecan use a different method for the ten-sors required for the VA and VCD (and


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also Raman and ROA) intensities, thanone requires for the geometry optimiza-tionandsubsequentHessianandnormalmode calculation. The implementationof VA and VCD spectral simulation inGaussian, Dalton, CADPAC, and ADFall allow one to accurately predict theVA and VCD spectra for molecules innonpolar solvents, in inert low temper-ature nobel gas and N2 matrices, andin membranes where there is no stronginteraction between the solute molecule

and the solvent/environment.Recently, various continuum mod-

els have been implemented in Gaus-sian, Dalton, and ADF that allow notonly geometry optimizations but alsoanalytical derivative methods for thecalculation of the Hessian, APT andAAT, required to simulate the VA andVCD spectra. The continuum solventmodels have required continuous re-finements and extensions as one hasstarted to use them to treat biolological

systems, where many of the assump-tions inherent in the development ofthe models break down. One of theseis that there are no specific directionaleffects which must be treated. Hydro-gen bonding effects have been shownto be inadequately treated, and hybridmodels have been developed to treatthese systems (Jalkanen and Suhai,1996,1998; Jalkanen, Bohr and Suhai, 1997;Han et al., 1998; Tajkhorshid, Jalkanenand Suhai, 1998; Knapp-Mohammadyet al., 1999; Jalkanen et al., 2008a). Es-pecially when one attempts to treathydrogen-bonded systems with implicitsolvent models one must be very careful.One cannot treat an explicit directionaland specific interaction between thecharged NH+3 and CO

2 groups in an

amino acid, peptide and protein with

solvent/water molecules, cations, or an-ions with an implicit continuum solventmodel. Here we have introduced ourembedded molecular(hydrogen-bonded)complex model (Jalkanen and Suhai,1996; Jalkanen, Bohr and Suhai, 1997;Han et al., 1998; Tajkhorshid, Jalkanenand Suhai, 1998; Knapp-Mohammadyet al., 1999; Jalkanen et al., 2006a, 2008a;Jurgensen and Jalkanen,2006). Here oneneeds to identify the important solventmolecules, cations, and anions which are

(thought to be) important in stabilizingthe structure/conformation/functionalstate of the molecule/molecular com-plex/assembly/aggregate. This complex/assembly/aggregate can be embeddedwithin a solvent cavity and/or proteinactive site and/or micelle, where the cav-ity surface is treated implicitly by usinga lower level of theory (perhaps usinga molecular mechanics force field). Acomplete review of these methods is be-yond the scope of this work on the useof vibrational spectroscopic methods inquantum nanobiology, molecular biol-ogy, and molecular biophysics.

1.4

Calculating Raman Scattering and RamanOptical Activity Spectra

1.4.1

Raman Scattering

If one wishes to simulate the Raman

scattering intensities, one is requiredto calculate the electric dipoleelectricdipole polarizability derivatives. Hereone can use either the static values,as was done in most early works,or one can take into account thefrequency response, as is now routine.In most conventional Raman scattering


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1.4 Calculating Raman Scattering and Raman Optical Activity Spectra 31

experiments one uses either 488, 532, or1064 nm source, the later for moleculesfor which fluorescence is a problem.

The Raman intensity is proportional tothe Raman scattering activity, which isgiven for the jth normal mode Qj by

IRamj = gj(452

j + 72

j ) (12)

where gj is the degeneracy of the jth tran-sition, and the electric dipoleelectricdipole polarizability tensor derivativeinvariants 2j and

2j are given by

2j

=1

9

S,j

xx + S,j

yy + S,j

zz

2(13)

and

2j =1

9

(S,j

xx S,j

yy )

2

+ (S,jxx S,j

zz )

2

+ (S,jyy S,j

zz )

2

+ 6[(S,jxy )

2 + (S,jyz )

2

+ (S,jxz )

2]

(14)

respectively. The S,j matrix relates thenormal coordinates Qj to the Cartesiandisplacement coordinates X, where specifies a nucleus and = x, y, or z(Diem, 1993): as previously defined. Inaddition to normal and Cartesian coor-dinates there are symmetry coordinates

(Cotton, 1990). The advantage of usingsymmetrycoordinatesisthattheHessianwill block diagonalize, that is, the Hes-sian will be reduced to independent summatrices. Before the advent of supercom-puters, symmetry coordinates were usedfor all symmetrical molecules. They arestill used as in the IR and Raman modes

for molecules with a center of inversionare mutually exclusive. That is, modeswhich are active in the Raman and inac-tive in the IR and vice versa. Here onecan make use of character tables (Cotton,1990). In addition, some modes are notseen in either the Raman or IR,and herethe use of IINS can help. The selectionrules for IR, Raman and IINS are alldifferent, so the three experiments arecomplementary and all necessary if onewishes to get complete data for all of the

vibrational modes.The normal frequencies are the eigen-values of the Hessian matrix H (thesecond derivative of the energy with re-spectto nuclear displacements,evaluatedat the equilibrium geometry):

H, =

2E(R)

X X

R=Ro

(15)

and

C1HC= (16)

C is the eigenvector matrix, whichdefines the transformation matrix Swhich is given by

S = M1/2C (17)

where Mis the mass matrix.Therefore, through the matrix S (ob-

tained by diagonalizing the Hessianmatrix) and the polarizability derivatives(Electric Dipole-Electric Dipole Polariz-ability Derivatives EDEDPD), , one

can obtain the Raman scattering activ-ity IRamj of any normal mode Qj. The

first efficient method for determiningthe EDEDPD was implemented utilizingfinitefield perturbation theory by Komor-nicki and McIver (1979). Subsequentlythe analytical EDEDPD were derived andimplemented in CADPAC (Amos, 1986,


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1987) and Gaussian (Frish et al., 1986)at the Hartree Fock level of theory, andsubsequently at the DFT level. The ED-EDPD have also been implemented atthe DFT level and used to simulatethe Raman spectra without any solventtreatment (Johnson and Florian, 1995;Stirling, 1996; Collier, Magdo and Klots,1999; Halls and Schlegel, 1999a; vanCaillie and Amos, 2000; Jalkanen et al.,2006b) and subsequently by treating thesolvent with explicit solvent molecules,

with continuum solvent models, andfinally using hybrid models which com-bine the two (Jurgensen and Jalkanen,2006; Jalkanen et al., 2006a, 2008a; De-plazes et al., 2008). In contrast to solventsubtraction which is common in IR/VAspectroscopy, this is notalways done withRaman measurements. Investigationsof the performance of local, gradient-corrected, and hybrid density functionalmodels in predicting Raman intensitieshave shown that the hybrid functionalsare very accurate when the solvent effects

are not important (Halls and Schlegel,1999b; Jalkanen et al., 2006b).

Hence the question of whether andhow to perform a solvent subtraction forRaman measurements is a question thatwe and others have started to address(Jalkanen et al., 2001, 2003, 2008a; Hanet al., 1998; Tajkhorshid, Jalkanen andSuhai, 1998).

1.4.2

Raman Optical Activity

Finally if one wishes to simulate theROA intensities, one is required tocalculate the electric dipole magneticdipole polarizability derivatives (ED-MDPD) and the electric dipoleelectricquadrupole polarizability derivative (ED-EQPD) (Buckingham, 1967; Atkins and

Barron, 1969; Barron and Buckingham,1971, 2001; Fischer and Hache, 2005).The calculation of the EDMDP, G, havebeen implemented in CADPAC (Amos,1982). The EDMDP can be evaluated asthe second derivative of the energy withrespect to a static electric field and a timevarying magnetic field. Hence the ED-MDPD is a third derivative with respectto the nuclear displacement.

G

= 3WG(R, F , B)

X

F

B R=Ro,F =0,

B=0

=

G (R)

X

R=Ro

(18)

The electric dipole electric dipole, elec-tric dipolemagnetic dipole, and electricdipoleelectric quadrupole polarizabilitytensors can also be calculated at the fre-quency of the incident light using SCFlinear response theory. London atomicorbitals have been employed, hence theresults are gauge invariant (Helgaker

et al., 1994). In this work, the elec-tric dipolemagnetic dipole orbitals aregauge independent when using a finitebasis set due to theuse of gauge-invariantatomic orbitals as implemented in Gaus-sian 03. Previously we used conventionalbasis sets which were not gauge invari-ant, similar to the work of Polavarapuand coworkers(Polavarapu, 1990;Barronet al., 1991a,b; Deng et al., 1996) and ourprevious work on NALANMA (Han et al.,1998),where that level of theoryhad been

shown to give predicted ROA spectra ingood agreement with the experimentallyobserved spectra. We are thus confidentthat the new level of theory can be usedto answer the structural questions posedhere, realizing that the agreement inabsolute intensities could be improvedby using much larger basis sets, as we


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1.4 Calculating Raman Scattering and Raman Optical Activity Spectra 33

shall do for the NALANMA4WC, but notthe LA20WC.

2j =1

2

(S,j

xx S,j

yy )(S,jG

xx S,jG

yy ) + (S,jxx S,j

zz )

(S,jG

xx S,jG

zz ) + (S,jyy S,j

zz )(S,jG

yy S,jG

zz )

+ 3

(S,jxy )(S,jG

xy + S,jG

yx) + (S,jyz )(S,jG

yz + S,jG

zy)

+(S,jxz )(S,jG

xz + S,jG

zx)

(21)

The EDEQP, A, can be evaluated asthe second derivative of the energy withrespect to a static electric field anda static electric field gradient. Hencethe EDEQPD is a third derivative, thethird derivative being with respect to thenuclear displacement.

A, =

3WG(R, F , F

)

XF F

R=Ro,F =0,

F

=0

= A,(R)

XR=Ro

(19)

The Cartesian polarizability derivativesare required to calculate the ROAspectra. The quantities required havebeen derived by Barron and Buckingham(1971) and are jGj,

2j , and

2j (Barron,

1982, 2004; Buckingham, 1967; Barron,Bogaard and Buckingham, 1973; Hechtand Barron, 1990). The quantities arecalculated by combining the variouspolarizability derivatives with the normalmode vectors in the following equations.

jGj is given by

jGj

=1

9

S,j

xx + S,j

yy + S,j

zz

S,jG

xx + S,jG

yy + S,jG

zz

(20)

2j is given by

and 2j is given by

2j =

2

(S,j

yy S,j

xx)S,jA

z,xy

+ (S,jxx S,j

zz )S,jA

y,zx

+ (S,jzz S,j

yy )S,jA

x,yz

+ S,jxy (S,jA

y,yz S,jA

z,yy

+ S,jAz,xx S,jA

x,xz)

+ S,jxz (S,jA

y,zz S,jA

z,zy

+ S,jA

x,xy S,jA

y,xx)

+ S,jyz (S,jA

z,zx S,jA

x,zz

+ S,jAx,yy S,jA

y,yx)

(22)

The equations relating these tensorderivatives to the ROA spectra are givenby Barron (1982, 2004); Hecht, Barronand Hug (1989), and Barron et al. (1994).These references provide a good intro-duction to the theory and application ofROAspectroscopy. Here we shall give the

relevant equations for completeness. Wefollow very closely the notation of Bar-ron from his Faraday Discussions reviewarticle (Barron et al., 1994).

The commonly reported quantity fromROA measurements is the dimension-less circular intensity differential (CID)defined as


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=

IR ILIR + I

L

(23)

where IR and IL are the scattered in-

tensities with linear polarization inright- and left-circularly polarized inci-dent light. In terms of the quantities,EDEDPD, EDMDPD and EDEQPD, theCIDs for forward, backward, and polar-ized and depolarized right-angle scat-tering from an isotropic sample forincident laser light are (Barron et al.,1994):

(forward)

=

8[45G + (G)2 (A)2]

2c[452 + 7()2]

(24)

(backward)ICP

=

48[(G)2 + (1/3)(A)2]

2c[452 + 7()2]

(25)

(90

, polarized)

=

2[45G

+ 7(G

)

2

+ (A)2

]c[452 + 7()2]

(26)

(90, depolarized)

=

12[(G)2 (1/3)(A)2]

6c()2

(27)

(backward)DCPI

=

48[(G)2 + (1/3)(A)2]

2c[6()2]

(28)

where c is the speed of light and theisotropic invariants are defined as

= (1/3) (29)

and

G = (1/3)G (30)

and the anisotropic invariants as

()2 = (1/2)(3 )

(31)

(G)2 = (1/2)(3G G

)

(32)

(G)2 = (1/2)(3G G

)

(33)

(A)2 = (1/2) A (34)

Using these expressions, we can calcu-late theROA spectra withinthe harmonicapproximation for the vibrational fre-quencies and with the static field limit forthe EDEDPD, EDMDPD, and EDEQPD.In addition, one can take into accountthe frequency dependence of the Ramanand ROA intensities. A new formalismfor the Raman and ROA intensities inthe near resonance regime has recentlybeen presented by Nafie, though notyet implemented (Nafie, 2008). Finally

the analytical derivatives of the G andA tensors have recently been reportedby Cheeseman and Frisch (2008); Ruud(2008); Liegeois and Champagne (2008);Liegeois (2008). Hence the efficiency ofcalculation of Raman and ROA spectrais now the same as that for VA and VCDspectra. The availability of commercialRaman and ROA and VCD and VA spec-trometers and programs to simulate thespectra has been a major breakthroughin the use of these spectroscopies in

quantum nanobiology, molecular biol-ogy, and molecular biophysics. In thelast section, we now present some in-teresting and pioneering work on theuse of VA, VCD, Raman, and ROAspectroscopy in quantum nanobiology,molecular biology, and molecular bio-physics.


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1.5 Classifying Conformational States and Structures based on VA, VCD, Raman, and ROA Spectra 35

1.5Classifying Conformational States andStructures based on VA, VCD, Raman,and ROA Spectra

1.5.1

Experimental Vibrational Frequencies forN-Methylacetamide, NALANMA,Peptides, and Proteins

The amide modes have been determinedexperimentally from the simple amidesformamide, acetamide, and NMA. NMA

has been used as a model since its twomethyl groups can be assumed to rep-resent the two C carbons in proteins.The amide A mode is mainly a NHstretch, amide I is mainly a C=O stretch,amide II a NH bend coupled withC N stretching, amide III N-bendingand C N stretching (only in simpleamides as it has been shown to cou-ple with the CH deformations on theadjacent C carbons with C HR groups[nonglycine] (Diem, 1993; Jalkanen et al.,

2003),

quantum mechanics methods for molecular biophysics

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