Vibrational absorption spectra, DFT and SCC-DFTB conformational

study and analysis of [Leu]enkephalin

S. Abdali,*a T. A. Niehaus,b K. J. Jalkanen,a X. Cao,c L. A. Nafie,c Th. Frauenheim,b

S. Suhaid and H. Bohra

a Quantum Protein Centre QUP, Dept. of Physics, Bldg. 309, Technical University of Denmark,Technical University of Denmark, DK-2800, Kgs. Lyngby, Denmark. E-mail: abdali@fysik.dtu.dk

b Department of Theoretical Physics, University of Paderborn, D-33098 Paderborn, Germanyc Department of Chemistry, Syracuse University, Syracuse, New York 13244-4100, USAd Department of Molecular Biophysics, German Cancer Research Center, Im Neuenheimer Feld 280,D-69120 Heidelberg, Germany

Received 6th November 2002, Accepted 22nd January 2003First published as an Advance Article on the web 7th February 2003

The endogenous morphine-like pentapeptide, [Leu]enkephalin, which binds to the opiate receptor in the brain,spinal core and gut, is the subject of this study. Vibrational absorption (VA) measurements were carried out on[Leu]enkephalin in non-polar solvent, DMSO-D6 to stabilize the environment. Ab initio (DFT at the B3LYP/6-31G* level of theory) and semi-empirical (SCC-DFTB) with and without dispersion correction were applied tosimulate the VA spectra of [Leu]enkephalin. In these calculations structures taken from X-ray measurements fordifferent conformers of the molecule were used as initial structures for SCC-DFTB geometry optimizations,while the optimized SCC-DFTB geometries were used as initial structures for the DFT geometry optimizations.The experimental VA spectrum and the VA spectra calculated for the low energy conformers at each level oftheory are then compared for different conformers of this peptide. This comparison allowed structural study ofthis molecule as it is here presented.

I. Introduction

Enkephalin was first isolated in 19751 from a pig brain andfound to be a mixture of two pentapeptides; Tyr-Gly-Gly-Phe-Leu and Tyr-Gly-Gly-Phe-Met. Enkephalins are knownas morphine-like neurotransmitters (inhibitors) and they arefound in known nociceptive pathways in the brain, the limbicsystem and spinal cord. Today the names [Leu]enkephalin and[Met]enkephalin are normally used. Studies on these moleculeshave revealed that the ratio of the Leu to the Met in their mix-ture varied between species, e.g., the ratio Met:Leu equals 4:1in a pig brain,1 whereas it is 1:4 in a cow brain.2 Many neuro-blastoma cell lines carry only Enkephalin receptors, to whichEnkephalin and its stable analogs, e.g., Tyr-Gly-Gly-Phe, areable to bind better than morphine3 to the opiate receptor inthe brain, spinal cord and gut. The extreme flexibility of theEnkaphalins compared, for instance, to morphine, which is amore rigid molecule, necessitates both theoretical and experi-mental studies, aiming to locate the possible conformationsin order to facilitate structure activity studies. However, thereare still many confusions and contradictions regarding thestructure of this molecule.4 It might be useful to mention someof the important investigations, which have been reported onthis molecule during the last two decades.Theoretical studies carried out by Isogai et al.3 have pro-

vided conformational analysis of [Met]enkephalin, however,without including the solvent effect. DeCoen et al.5 have per-formed theoretical studies on the zwitterionic form of the samemolecule, while [Leu]enkephalin was studied by Humblet andDeCoen6 and by Premilat and Maigret.7,8 The conclusions ofthese studies are that there are various low-energy conforma-tions of Enkephalin in equilibrium.9

Experimentally, there have been different investigations onthese molecules including X-ray crystallographic studies on[Leu]enkephalin10–12 and on [Leu]- and [Met]enkephalin.13

NMR studies on both molecules have also been reported.14–17

Vibrational circular dichroism (VCD) measurements ofEnkephalin18 found a very strong peak near 3300 cm�1 inMet, whereas it was absent in Leu. This peak was attributedto the sulfur of methionine forming a seven membered ringstructure. A Raman spectroscopy conformational study wasreported on [Leu]enkephalin crystals19 and recently on [Leu]-and [Met]enkephalin in vivo,20 where the pH-value effect from1 to 13 on the conformational state was studied, and shownthat it can be used to trace the conformational state andhow this differs for [Leu]enkephalin than [Met]enkephalin.However, due to the resolution of the NIR-Raman employedin the reported study, it wasn’t possible to conclude the lowestenergy conformer was simply present.Previous studies have provided information mostly about

[Leu]enkephalin, whereas few reported on [Met]enkephalin.The above-mentioned X-ray studies have reported four differ-ent antiparallel b-sheet conformers with similar back-boneangles but all differ in their side-chain conformations. NMRstudies17 have shown concentration dependence, interpretedas evidence for a b-bend monomer, centered on Gly-Phe andan antiparallel b-sheet dimer appearing at higher concentra-tion. Raman studies17,21 in DMSO-D6 and water have sug-gested both a b-bend and an extended conformation for the[Leu]enkaphalin, while only an extended conformation wasfound for the [Met]enkaphalin.To understand a biomolecule’s function the determination

of its conformational details is very important. The X-rayand NMR structural determinations of biomolecules are, of

DOI: 10.1039/b210893c Phys. Chem. Chem. Phys., 2003, 5, 1295–1300 1295

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course, very useful, though these methods are still questionedregarding the biological relevance as the X-ray requires differ-ent environments than the natural environment of a moleculeor regarding interpretation difficulties. Therefore, combiningtheoretical calculations with spectral measurements and ana-lyses will provide the best estimation when the experimentalconditions are included in the theoretical simulations. How-ever, such studies are very expensive and time consuming.The recent development of theoretical methods and increasedcomputing power made it possible to study small peptides withab initio quantum mechanical methods, and larger polypep-tides have been studied mostly with empirical force fields, cal-culating free energy surfaces and performing moleculardynamics simulations, both in vacuo and in solvent. Smallmodel systems, e.g., N-acetyl-L-alanine N0-methylamide(NALANMA) have been studied using Hartree–Fock, Møller–Plesset perturbation theory (MP) and density functional theory(DFT).22,23 These data give a reliable basis for benchmarkingthan other approximate methods.In the last decade, empirical force fields have been refined

and are now able to reproduce the ab initio data with verygood precision.24 However, these methods are still in question,e.g., the a-helical conformation, aR , is not a minimum on thepotential energy surface (PES) of this model peptide at manyab initio levels, for example, RHF/6-31G*, MP2/6-31G*and B3LYP/6-31G* levels. Similarly, the Ceq

7 conformer isthe most stable dipeptide conformation in the model calcula-tions, whereas it is seldom found in proteins.On the other hand, the solvent has been shown to play a

crucial role for the stability of different conformations. Byapplying a quantum chemical reaction field model on theRHF/6-31G* level of the theory,22 the aR conformation isstabilized significantly with respect to the Ceq

7 conformation.Nevertheless, the conformation is still not a minimum on thePES. It has been shown that this conformer can be stabilizedonly by explicitly including water molecules.25 Free energy cal-culations with empirical force fields found also a significantstabilization of the conformers.24,26

Most of the above-mentioned methods have been applied onrather small model systems, e.g. L-alanine, NALANMA andother molecules of the same size, in that complex systems arenot trivial to calculate and although the computing ability andmachinery have gone through radical improvements, especiallywith respect to speed, it is still very expensive and time consum-ing to run these calculations. More approximate semi-empiricalmethods, e.g., AM1, PM3, SCC-DFTB have therefore beendeveloped and are compared27 and been applied to model bio-molecules28 and comparison between ab initio and semi-empirical methods has also been reported. However, it is ofa great interest to compare these methods while applying themon a bigger biologically active molecule, such as Enkephalinand its different conformers as in the present study.In this work, the semi-empirical method, self-consistent-

charge density functional based tight binding (SCC-DFTB)and DFT at the B3LYP/6-31G* level of theory were applied,and the absorptional spectra deduced from these methods werethen compared to VA measurements on this peptide inDMSO-D6 solvent. The present work is a part of an on-goingproject, in which Enkephalin is studied using classical, e.g.MD, semi-empirical, e.g., SCC-DFTB, AM1, PM3 andab initio methods.29 Experimentally, Enkephalin has earlieralso been studied in our group using Raman,20 VA, VCDand ROA.30

II. Methods

The above-mentioned methods are reported earlier in theliterature, and recently we have discussed calculated spectra

using DFT at the B3LYP/6-31G*28 on a simpler molecule;L-alanine and its isotopomers. Recently this model has beenshown by Frish and coworker at Gaussian Inc. to accuratelyreproduce gas and non-polar solution geometries, vibrationalfrequencies and intensities. This level of theory has alsorecently been applied to model structures of an aqueous solu-tion in which explicit water molecules of the first solvationshell, which interact strongly with the solute, are specificallytaken into account. The bulk water is accounted for by anOnsager continuum model.The so-called (SCC-DFTB) method31–34 is an approximate

DFT scheme, which is derived from the latter by a secondorder expansion in the electron density. The most importantdifferences to DFT are that only two-center matrix-elementsof the Kohn–Sham Hamiltonian are considered and thatself-consistency is achieved with respect to atomic charges esti-mated by a Mulliken analysis rather than the full density. Incontrast to other semi-empirical methods, all parameters arecompletely calculated within DFT and no fitting to experimen-tal data is performed. The resulting scheme is numerically effi-cient which allows one to model systems with hundreds ofatoms and at the same time the accuracy of DFT is almostretained. As an example, bond lengths for a test set of severalorganic molecules were calculated with a mean absolute devia-tion of 0.012 A.32 Vibrational frequencies are also reasonablydescribed within the SCC-DFTB. For a set of 33 molecules themean absolute deviation of 6.4% is comparable to the accuracyof DFT methods, which usually provide frequencies with anerror of 3–5%.In the last few years the SCC-DFTB method has been exten-

sively used to address problems of biological relevance (see ref.27 for a review). Here a proper description of H-bonding iscrucial and it was found that although the binding energiesof weakly bound complexes are consistently underestimatedby about 1–2 kcal mol�1, the energetical ordering of differentconformers as well as the geometrical structure are in goodagreement with MP2 and DFT calculations.35,36

For the small peptide model NALANMA vibrational fre-quencies as well as IR intensities have also been studied.37

Again the SCC-DFTB method compared satisfactorily withhigher levels of theory. For the Ceq

7 and C5 conformers thedeviation from experimental frequencies was reported to be6.7%, 4.4% and 3.0% for the SCC-DFTB, DFT/B3LYP andMP2 approaches respectively.A recent development of the method is related to inter-

actions of the van der Waals type. Here it is well known thatcommon exchange-correlation functions, e.g. B3LYP describethe long-range dispersion incorrectly. Since the SCC-DFTBscheme as an approximation to DFT shares this deficiencyan empirical correction term was added to the total energyexpression which leads to the desired R�6 dependence for longdistances. In this way the description of H-bonding and espe-cially stacking interactions was markedly improved.38

III. Experiment and theoretical modeling approach

III.1 Modeling approach

Model structures for the optimization were created by usingthe coordinates of the heavy atoms from the available threeconformational motifs: the extended (e), the single b-bend (s)and the double b-bend (d), taken from X-ray data.10,12,39,40

Since there are in general different non-equivalent moleculesin the unit cell, this resulted in:(i) 6 extended structures: two models of the extended struc-

ture are based on the reported structure of Griffin et al.,39 andthey are presented as e1 and e2 and four models for theextended structure based on the reported structure of Karleet al.,12 presented as e3–6. In the results we present only thoseof lowest energies.

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(ii) 4 single b-bend structures: models for the single b-bendstructure are based on the reported structure of Smith andGriffin,10 and they are presented as s1–4.(iii) 1 double b-bend structure: the model for the double

b-bend structure is based on the reported structure of Aubryet al.,40 and it is presented as d.As the interest in this work is to compare the calculated VA

spectra with those measured in a non-polar solvent, we mod-eled the peptide in its neutral form rather than in the zwitter-ionic configuration, as seen in Fig. 1. Using standard bondlengths and angles, hydrogens were added to the heavy atoms,where attention has been paid to the location of the hydrogensto the carboxyl and amine groups since these may participatein intramolecular hydrogen bonding.The first set of structures was generated with the carboxyl

group in anti-periplanar conformation and the two H–N1–C1

a–C1 dihedral angles set to 180 and �60�. This choice wasmade to prevent close contact between possible donors andacceptors, and in order not to bias the conformational search

towards H-bonded structures. However, from the single bendconformers using the SCC-DFTB method for optimization,only s4 did not relax to an H-bonded structure involving theN-terminus. We therefore added one trial structure s5 whichwas equivalent to s4 but with one of the amine hydrogensdirected toward the possible acceptor O4 . Since the orientationof the amine group can be expected to be of major importanceonly for the single bend conformers, a hydrogen bond betweenthe carboxyl hydrogen and O4 should be possible for all struc-tural motifs. Accordingly, we added the trial structures e7–12for the extended motif, s6–10 for the single bend and d2for the double bend. Here, the carboxyl hydrogen was broughtinto closest contact with O4 while maintaining the O5

0–Hbond length and the C5–O5

0–H angle in order to facilitateH-bonding.Additionally, using the SCC-DFTB method, we checked for

the s4 conformer, whether rotation of the amine group (insteps of 30� each) and positioning the carboxyl hydrogen onthe two oxygens in syn- and anti-periplanar conformationresult in new minima. This was not the case. The approach pre-sented here is by no means a stringent conformational search.However, we find this approach suitable as long as we areinterested in finding general differences in the energetical rela-tions between the principle motifs and their differences in thespectra.All the generated conformers were then optimized at DFT

as well as the SCC-DFTB level both with and without the dis-persion correction mentioned above, and the atomic number-ing used for the optimization is shown in Fig. 2. DFT/B3LYP calculations were performed using a 6-31G* basis setwith the Gaussian 98 suite of programs.41 For the two SCC-DFTB methods (with and without dispersion) the VA spectrawere obtained from numerical differentiation of Mullikendipole moments, whereas for DFT the atomic polar tensorsAPT were calculated analytically as implemented in theCADPAC package.42

III.2 IR-measurement

Enkephalin was purchased from Bachem and was dissolved inDMSO-D6 solvent to a concentration of 4.5 mg/100 ml. Thesample was then brought into a liquid cell from InternationalCrystal Laboratory1 with a BaF2 window of 95.3 mm pathlength. The spectra were recorded in the 2000–800 cm�1 fre-quency range and for 2 h using Bomem/BioTools Chiral-irmid-infrared Fourier Transform VA/VCD instrument.43–47

The resolution of the setup was set to 8 cm�1 because this

Fig. 1 The three optimized structures from the X-ray data for thedouble b-bend, d2, extended, e5 and single b-bend, s7, correspondingto the lowest energy found by SCC-DFTB.

Fig. 2 Naming convention for the backbone of [Leu]enkephalin.

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resolution is sufficient for VA measurement for moleculeslike [Leu]enkephalin in solution as its spectral bands arebroader than 8 cm�1. The DMSO-D6 was also measuredand the spectrum was then subtracted from the IR spectrumof Enkephalin.

IV. Results and discussion

In Table 1, the relative energies of different conformers of[Leu]enkephalin are listed. These results are calculated bySCC-DFTB, DFT based on SCC-DFTB optimized geometriesand SCC-DFTB with dispersion (SCC-DFTB-D). The lowestenergy conformer of each method has been set to 0.00 kcalmol�1.All the computational schemes agree that the extended con-

formers have higher energies than those of the single- and dou-ble b-bend. This was expected since the latter conformers arestabilized by intramolecular hydrogen bonds, and only in verypolar solvents a competition of all three motifs should beobserved. Comparing the results obtained by DFT and SCC-DFTB within the subset of single- and double b-bendstructures we find that in both methods the single b-bend con-formers are more stable than the double b-bend conformers.Although the energetical ordering is not quite the same forthese methods, e.g., the s7/s9 structures which relax to thesame minimum, are the lowest energy conformers found bySCC-DFTB, while it is the s10 found by DFT, in spite of thefact that both methods start from the same optimized structurefound by SCC-DFTB. As mentioned above both DFT andSCC-DFTB schemes do not correctly include the effect of dis-persion. This should be of special importance for the double b-bend motif where the tyrosine and phenylalanine aromaticrings are arranged in a T-stack configuration. Consequently,the dispersion corrected SCC-DFTB-D predicts a reversedordering of single and double b-bend conformers with respectto both DFT and SCC-DFTB.The lowest energy conformers presented in Table 1 were

then employed to calculate the VA spectra for each conformer.From the SCC-DFTB calculations, we found s7 and s9 areequally stable and s4 and s5 showed no recognizable differencebetween their calculated spectra. Therefore, we compare inFig. 3 only s4, s7 and s10 to the measured spectrum. DFTcalculations have shown the same stability for the same con-formers, i.e. s4, s7 and s10, when the start structure is theSCC-DFTB optimized structure. The calculated spectra arecompared to the measured spectrum in Fig. 4.The SCC-DFTB-D calculations have shown a different con-

former to be more stable than the others. However, s10, whichis found to have low energy by both DFT and SCC-DFTB, isalso of a lower energy when dispersion is included. The

SCC-DFTB-D spectra of the lowest energy conformers arecompared to the measured spectrum in Fig. 5.Considering the Amide I region, we find a peak in the

experimental spectrum with the main absorption located at1670 cm�1 and a shoulder at 1715 cm�1. This peak is alsofound in the SCC-DFTB, seen in Fig. 3, in all lower energyconformers. However, the shoulder peak in the measured spec-trum is better resolved in the calculated spectra, and in the s10conformer, this peak turns to be a doublet. Including the dis-persion, the SCC-DFTB-D spectra seen in Fig. 5, the positionof the main absorption is well described for all conformers,although especially for the single b-bend motif, i.e. s10, thebroadness is overestimated and some additional structuresare also present. The latter also holds for the DFT simulations,whereas the position of the main absorption is blue-shifted by80 cm�1. A normal mode analysis reveals that the peak ofhighest frequency in the SCC-DFTB-D spectra (i.e. the oneat 1740 cm�1 for d1), which should correspond to the men-tioned shoulder in the experimental data, originates from aC=O stretch in the carboxyl group. If the carboxyl hydrogenis in syn-periplanar position, as in s10 and d2, this peakappears at too high frequency, while the agreement with the

Table 1 Relative energies of the different conformers of [Leu]enke-

phalin for different methods described in the text. The numbers are

in kcal mol�1. Only low energy conformers are highlighted

Conformer SCC-DFTB DFT SCC-DFTB-D

s1 2.83 7.09 8.71

s2 2.20 6.22 7.64

s3 2.56 6.22 8.03

s4 0.83 0.22 1.86

s5 0.89 2.37 1.82

s7 0.00 0.99 2.84

s8 1.91 4.03 5.82

s9 0.00 0.99 6.00

s10 0.22 0.00 1.83

e5 6.85 11.36 12.51

d1 3.05 7.27 0.68

d2 1.38 6.70 0.00

Fig. 3 The measured spectrum of [Leu]enkephalin in DMSO-D6 iscompared to the calculated spectra using SCC-DFTB. The s7 relaxesat the lowest energy 0.00 kcal mol�1, s10 at 0.22 kcal mol�1 and s4at 0.83 kcal mol�1.

Fig. 4 The measured spectrum of [Leu]enkephalin in DMSO-D6 iscompared to the VA spectra calculated by using DFT at theB3LYP/6-31G* level of the theory. The s4 conformational structureand s10 are found to be at the lower energies of 0.22 and 0.00 kcalmol�1, respectively, while s7 is found just below 1 kcal mol�1.

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experiment is much better when it is in anti-periplanarconfiguration as in d1.In the Amide II region of the experimental spectrum, char-

acterized by NH bend motion, the peak absorption occurs at1515 cm�1 with a very broad high frequency shoulder extend-ing over 40 cm�1. Both SCC-DFTB and DFT schemes tend tooverestimate the frequencies in this region,37 which is partiallydue to the harmonic approximation used in the calculation.Concerning the broadness of the absorption observed in theexperiment, we find that all low energy conformers calculatedby DFT and d1 and s10 calculated by SCC-DFTB-D showsmall splitting in this region. However, d2 and s10 are in betteragreement with the experiment, although the intensity of thepeaks is not correctly reproduced.Considering the side-chain region, three important peaks

at 1450 cm�1, 1380 cm�1 and 1250 cm�1 are observed in theexperimental spectrum. The intensity of these absorptions ishighly underestimated at the SCC-DFTB-D level of theory.This is in agreement with earlier observations and was attrib-uted to the approximation of the dipole derivatives.27 A betterfit to the experiment in this region is found by the DFT calcu-lations for the s4 conformer, when a constant red shift of 50cm�1 is applied. However, in this case the peaks at 1210cm�1 and 1170 cm�1 do not have corresponding peaks in theexperimental spectrum.The d1 conformer, calculated by the SCC-DFTB-D method,

shows a good agreement in the Amide I region, whereas it hasless correlation with the experiment in the Amide II range. Forthe d2 and s10 structures the situation is reversed. Taking intoaccount the stability considerations given above, it seemsplausible that different conformers are populated at room tem-perature. However, the large variability in the VA spectra,even among structures of the same basic motif, would resultin a considerable broadening for an effective Boltzmann-weighted spectrum in the Amide I region, which is notobserved in the experiment.From the results above we speculate that only one confor-

mer, most likely the low energy double b-bend structure d1,is present in the sample. In this case the measured broadeningin the Amide II region could be due to solvent effects, whichare not taken into account in the theoretical simulation.Although DMSO is not a highly polar solvent it can act as aH-bond acceptor48 modifying the NH bend frequencies.Finally, the calculated spectra by DFT, SCC-DFTB andSCC-DFTB-D propose that [Leu]enkephalin has a single b-bend structure, e.g., s10 if the dispersion is not included in

the calculations, whereas a double b-bend structure, e.g., d1is most probable if dispersion is included. Consequently, it isimportant to extend this study to include, e.g., vibrational cir-cular dichroism (VCD) measurements,30 in that characteristicfeatures in the spectra are sensitive to conformational changes,and better determination of conformations can be achieved.Enkephalin is an on-going subject for our studies, where a ser-ies of calculations49 and measurements20 are already reported,based on MD, DFT and SCC-DFTB compared to experimen-tal measurements from Raman, VA and VCD.

V. Conclusion

We have in this work studied [Leu]enkephalin structure usingboth theoretical and experimental VA spectra in non-polar sol-vent, namely DMSO-D6. The DFT model at the B3LYP/6-31G* level of the theory was applied as well as SCC-DFTBwith and without dispersion. The non-polar study here is initself interesting as enkephalin can be functional in this solventas it is in water, which our previous study20 has shown. How-ever, due to the resolution provided by the applied instrument,i.e., NIR-Raman, the structure of the molecule was not clearlyresolved.The SCC-DFTB with dispersion correction (SCC-DFTB-D)

spectra seem to provide a better fit to the measured spectrumthan the SCC-DFTB without the dispersion correction, whenamide I and II regions are considered and when both fre-quency and intensity are taken into account. However, dueto the overestimation with this method, the calculated peaksare found around 50 wavenumbers away from the measuredpeaks.The calculated DFT spectra provide more features and bet-

ter fit when all regions of the measured spectrum are taken intoaccount. However, as the difference is not that big betweenthese methods, it is much cheaper to employ a semi-empiricalmethod such as the SCC-DFTB.Although the low energy conformers of the SCC-DFTB and

SCC-DFTB-D fit quite well with the measured spectrum in theAmide I and II regions, the features of the calculated peaksshow no splitting in these regions as it is the case in themeasured spectrum.When dispersion is included in the SCC-DFTB, the calcula-

tions suggest a double-bend structure as the best fit to themeasured spectrum. However, we find the results very impor-tant as the methods suggest exclusively one conformer, i.e.,either a single b-bend as it is the case for SCC-DFTB andDFT or a double b-bend as it is the case when dispersion isincluded in SCC-DFTB, whereas most of the previous studiessuggest different conformers in equilibrium energetical state.However, this conclusion is valid only if a shift of the fre-quency is accepted. This shift misfit was also found in a pre-vious study, when DFT was applied on a smaller moleculesuch as L-alanine.

Acknowledgements

This work is financed by Danish National Research Founda-tion. T.A.N. would like to thank Markus Elstner for fruitfuldiscussions.

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Fig. 5 The measured spectrum of [Leu]enkephalin in DMSO-D6 iscompared to the calculated SCC-DFTB with dispersion. The d1 con-formational structure and d2 are found to be at the lowest energiesof 0.68 and 0.00 kcal mol�1, respectively, and s10 at 1.83 kcal mol�1.

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