J. Phys. Chem. 1994,98, 9919-9930
9919
Vibrational Properties of the Peptide Group: Achiral and Chiral Conformers of N-Methylacetamide Prasad L. Polavarapu* and Zhengyu Deng Department of Chemistry, Vanderbilt University, Nashville, Tennessee 37235
Carl S. Ewig Biosym Technologies Inc., 9685 Scranton Road, Sun Diego, Califomia 92121 Received: April 20, 1994; In Final Form: July 6, 199@
Vibrational optical activity associated with the peptide group vibrations has been examined with Nmethylacetamide (NMA) as a model compound. In this process, the structures and vibrational infrared and Raman spectra of NMA are also examined. The a b initio Hartree-Fock investigations with the 6-31G* basis set and higher level calculations using electron correlation (MP2/6-31G*) and a larger TZP basis set indicate that the chiral structures have energies comparable to, and some times slightly lower than, the energies of the achiral structures. The predicted absorption spectra for chiral and achiral NMA conformers are similar and consistent with the corresponding experimental spectra of NMA. However, the predicted Raman spectra of the chiral and achiral conformers show significant differences. The predictions for vibrational optical activity of the chiral conformers suggest that the vibrations of carbonyl and of methyl groups are especially sensitive to the conformation of peptide groups. These investigations are expected to serve as reference points for the interpretation of the experimental vibrational optical activity spectra of peptides.
Spectral properties of the peptide group [C-C(0)-N(H)C] represent active areas of current research. Natural optical activity in vibrational transitions, referred to as vibrational optical activity (VOA), is supported by chiral molecules.' Vibrational circular dichroism (VCD) and Raman optical activity (VROA) are two phenomenologically different, yet complementary, branches of VOA s p e c t r o ~ c o p ythat ~ ~ ~ are gaining increased attention for three-dimensional structural determination of biological molecules in the solution phase. For example, the absolute configurations of chiral anesthetics were determined4 for the first time using VOA. A large body of experimental VOA data is now available on molecules containing the peptide group^,^ and some VCD calculations were undertaken recently assuming planar peptide skeleton^.^^ The interpretation of this experimental data will be facilitated by an understanding of the VOA associated with the peptide group. Since the experimental VOA measurements on NMA are not possible (because resolution of the chiral antipodes is unlikely to be achievable), theoretical investigations of VOA in chiral conformers of NMA will provide an altemative route to gain an understanding of the VOA associated with the peptide group. In order to understand the VOA properties of peptide groups in peptides and proteins, a careful and reliable analysis for molecules containing a single peptide group is useful. NMethylacetamide (NMA, CH3CONHCH3) is one of such simple model molecules. Despite widespread studies on NMA, several fundamental questions remain. The experimental data for the structure of NMA were derived from X-ray and electron diffraction studies. The X-ray diffraction results of Katz and Post6 indicated that in the crystalline phase the five heavy atoms of NMA are coplanar with a trans structure (trans- and cis-NMA refer to the trans and cis orientations of the H3C-C and N-CH3 bonds around the central C-N bond). In analyzing the electron diffraction intensity data for vapor phase NMA, Kitano et al.' @
Abstract published in Advance ACS Abstracts, September 1, 1994. 0022-3654/94/2098-99 19$04.50/0
assumed that NMA has (a) plane of symmetry, (b) trans orientation of CH3 groups around the central C-N bond, and (c) local C3"symmetry for the methyl groups. The heavy atom positions determined in the X-ray diffraction studies may have some influence from hydrogen bonding and packing effects in the crystalline phase. Such effects are not present in the vapor phase, and therefore it would have been useful if the electron diffraction data were also analyzed by eliminating the symmetry constraints to estimate the consequences resulting from such constraints. Several theoretical studies on the structures and vibrational frequencies of NMA at various levels of approximation have been reported.8-20 In the most recent ab initio theoretical studies, (a) 4-3 1G vibrational frequencies modified through nonuniform scaling were reported for the NMA conformers with C, symmetry by Williams,16 (b) 3-21G vibrational frequencies modified through nonuniform scaling were reported by Cheam17 for the same conformer (with C, symmetry) as that assumed in electron diffraction study, (c) 4-3 lG* optimized geometries and vibrational frequencies were reported by Mirkin and KIk"m5 for four conformers of trans-NMA, all with C, symmetry, (d) a preliminary 4-31G* study for the cis-NMA conformers with C, symmetry was also reported by Mirkin and Krimm,14 and (e) 6-31G* optimized geometries for trans- and cis-NMA conformers with C, symmetry were reported by Jorgenson and Gao.13 In all these studies, C,symmetry for isolated NMA has been either assumed or supported. After completion of the work reported here, we became aware of a paper by Guo and K a r p l ~ s who , ~ ~ found that the chiral conformer of trans-NMA has lower energy than those with a plane of symmetry, but the vibrational frequencies for these conformers were not investigated. In one of the early studies, the nonplanar peptide structures were investigated by Kolaskar et a1.18 using semiempirical methods, and a significant deviation from planarity of the C-C(0)-N(H)-C skeleton was predicted for different peptides. The calculations of Tvaroska et aL20 with semiempirical methods indicated that some semiempirical methods 0 1994 American Chemical Society
9920 J. Phys. Chem., Vol. 98, No. 39, 1994 predict significant nonplanarity of the skeleton, while others predict a planar skeleton. Chiral conformers of NMA can arise from nonplanarity of the peptide group, asymmetric orientations of the hydrogen atoms of the methyl groups, or both effects collectively. Except for the cited earlier, where nonplanarity of the peptide group was addressed, chiral conformers have not been investigated. Vibrational spectroscopy has also been used in the literature to characterize the structure of NMA. In particular, infrared absorption spectra of matrix-isolated NMA21-23have provided useful information for some of the vibrational properties of trans- and cis-NMA conformers. Based on the infrared absorption spectra obtained in Ar and N2 matrices at cryogenic temperatures, the possibility of a nonplanar peptide group has been suggested by Fillaux and De Loze,22 but no further discussion on this topic is available in the literature. All other spectroscopic studies have assumed C, symmetry for all NMA conformers. Resonance Raman spectroscopy of NMA has been investigated in different l a b o r a t ~ r i e s . ~ In ~ -particular, ~~ the resonance enhancement of 1385 cm-’ Raman band in trans-NMA raised some speculation as to the origin of this band.26-30 It was t h o ~ g h tthat ~ ~ the , ~ mode ~ responsible for this band, originating from a bending motion of the acetyl CH3 group, is coupled to the amide I11 vibration, and the extent of coupling diminishes from trans-H-C-C=O orientation to cis-H-C-C=O. Similarly, significant differences in the resonance enhancement of the Raman spectra of cis-NMA were s u g g e ~ t e dto~ ~originate .~~ from the uncoupling of amide I1 and I11 modes in this isomer. These interpretations were based on the mode descriptions derived from the vibrational analyses employing empirical force fields. The main goal of this paper is to investigate the VOA associated with the peptide group, although in this process the above-mentioned fundamental issues pertaining to NMA will also be addressed. First, the issue of the structures and conformers of NMA is discussed by presenting the optimized structures, energies, and vibrational frequencies for chiral as well as achiral conformers of NMA. Second, the theoretical vibrational spectra are compared to the experimental spectra to infer the presence (or absence) of these conformers in the experimental data. Also, the vibrational mode assignments for the peptide group and mode couplings derived from the present results are presented. Finally, the vibrational optical activity associated with the peptide group vibrational modes is discussed.
Polavarapu et al.
aj is the mean of polarizability derivative tensor and Pj2 is the anisotropy of that tensor given as
Similarly, the ROA intensities are calculated37with the expression
where superscripts R and L represent the right and left circular polarization states of the incident radiation; P, = (16w/c)[(45/ w)aj,.Gj (l/w)y? - (l/w)df], (960/~)[(l10)yj2_+( 1 / 3 ~ ) 6 f ] , (40~0/3~)[(9/w)ajG’j (2/w)yf], ( 4 ~ / ~ ) [ ( 4 5 / ~ ) a j G(’7j / ~ ) y f (l/w)df], (24w/c)[(l/w)yf - (1/3w)Sf] respectively for forward, 180” backward, 90” magic angle, 90” polarized, and 90” depolarized scattering geometries. In the above equations, Qj is the normal coordinate for jth vibration, % is the electric dipole-electric dipole polarizability, G’M is the electric dipolemagnetic dipole polarizability, is the electric dipoleelectric quadrupole polarizability, w is the angular frequency of the excited radiation, is the product of the mean of a%/aQj and aG’M/aQj tensors, and
+
+
+
However, since the measured Raman and ROA intensities are not absolute, it is customary to compare the normalized values, A = (p- p ) / ( p p). For the forward, 180” backward, 90” magic angle, 90” polarized, and 90” depolarized scattering geometries A are designated as Ao, A180, A*, A,, and Az and given respectively as
+
( 2 4 w / c )1[ j ?
Structural optimizations were performed with GAUSSIAN92 program31 using the 6-31G* basis set32and using the TURBOMOLE program33with TZP basis set.34 The latter program was also used for evaluating the electron correlation (MP2 method35) effects with the 6-3 1G* basis set. Vibrational frequencies, absorption, and Raman scattering parameters were determined for the fully optimized structures using the 6-31G* basis set as implemented in the CADPAC As described earlier,37 the Raman intensity for a vibrational mode j is obtained with the expression
where YO is the exciting frequency and h, c, and k are universal constants. For polarized and depolarized Raman spectra presented here S, = [45C$ 4#] and 3#, respectively, where
+
+ --62]/[45ai” 1 + 7p;], 3w
(20lc) -a.G’. [9w- J-
Computational Details
+
J
J
+ -yi” w
1
/[9a;
+ 2p;],
As seen from the above equations, Raman optical activity parameters require the polarizability derivatives aa,-&3Qj, w-l aG’,&3Qj, and aAc,B,/aQj. To obtain these derivatives, the tensors Q, o-’G’ga, and were determined in the static limit at the equilibrium geometry and at the geometries displaced by 0.005 8, along each Cartesian coordinate as described el~ewhere.~’The procedure for obtaining the w-IG‘M tensor in the static limit is due to Amos38 as implemented in the CADPAC program, which simultaneously evaluates the and AM,, tensors. From these tnsors the atomic Cartesian displacement derivatives a q a X a , w-l aG’M/aXA,and aAMy/aXAwere determined numerically and transformed to normal coordinate space, and the ROA parameters for different scattering geometries were evaluated by an ROA algorithm developed in our
J. Phys. Chem., Vol. 98,No. 39, 1994 9921
Vibrational Properties of the Peptide Group
TABLE 1: Dihedral Angles (degrees) and Relative EnergiesO of the Optimized Conformers of N-Methylacetamide trans-NMA conformers cis-NMA conformers cc
Ct
HNCH
0.0
0.0
180.0
tc 180.0
CNCH
180.0
180.0
0.0
0.0
OCNH
180.0
180.0
180.0
180.0
CCNC
180.0
180.0
180.0
180.0
HCCO
0.0
180.0
180.0
0.0
energyb*' energy'.'
0.09 0.14 0.24
0.02 0.05 -0.05
0.16 -0.02 0.27
0.22 0.07 0.50
energy','
tt
PP 20.1' 21.2c 17.7d -168.7' -168.6' -170.2d 174.66 174.0' 175.9 -175.76 -175.4' -175.5d 39.96 40.2' 41.2d 0.0 0.0 0.0
cc 0.0
tc 180.0
ct 0.0
180.0
180.0
0.0
180.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
180.0
1180.0
2.52 2.31 2.77
3.06 2.76 3.36
tt
PP 18.9b 21.7' 20.6' -172.9' -173.7' -173.1' -4.3' -6.1' -5.w 7.9' 9.9' 9.w 2.4b 1.9' 2.w
3.37 3.32 3.46
4.57
2.50 2.24 2.74
a Electronic energies are relative to that for the trans-NMA-pp conformer, which is -247.006 161 808 hartrees at 631G*, -247.750 305 47 at MP2/6-31G*. and -247.092 716 633 8 at TZP level. 6-31G*. MP2/6-31G*. TZP. e Relative electronic energies in kcallmol.
lab~ratory.~'For the sake of comparison with ROA predictions the vibrational circular dichroism (VCD) intensities listed in CADPAC36output using the distributed origin gauge39are also summarized for the chiral conformers. The VCD intensity for jth mode is represented by the rotatory strength, Rj, given as Im(OIpIl).(llmlO) where p and m are respectively the electric dipole moment and magnetic dipole moment operators; (01 and 11) are respectively the wave functions of the ground and first excited vibronic wave functions belonging to the same ground electronic state. The dimensionless measure of VCD is given by the dissymmetry factor g = 4R/D where D is the dipole strength given as (Olpll)*. All theoretical spectra were simulated with Lorentzian band shapes with 5 cm-' bandwidth.
Results and Discussion Achiral and Chiral Conformers. The structures were optimized first in the HF approximation with the 6-3 lG* basis set by imposing C, symmetry for both trans and cis conformers of NMA. This symmetry restriction requires that the C-CN-C and 0-C-N-H dihedral angles are fixed at 180" for trans-NMA and at 0" for cis-NMA. The hydrogen atoms of the two methyl groups, however, can be positioned in four different orientations within this C, constrained symmetric structure. These four Orientations (see Table 1 and Figure 1) differ in their relative positions with respect to the N-H and C-0 positions; one of the hydrogen atoms (atom 1 in Figure 1) of the methyl group attached to N atom can be either cis or trans to the N-H bond, and that (atom 10) of the methyl group attached to C atom can be either trans or cis to the C=O bond. We will use the designations cc, ct, tt, and tc where the first letter refers to the orientation of H-N-C-H and the second letter refers to the corresponding orientation of H-C-C=O. For example, trans-NMA-ct will represent trans-NMA with cis H-N-C-H and trans H-C-C=O orientations. The energies of these four different conformers are within -0.2 kcal/mol for trans-NMA and within -2 kcal/mol for cis-NMA. The stabilities of these conformers can be judged by investigating whether or not these structures represent minima on the potential energy surface. A structure which has a minimum on the potential energy surface with respect to all normal modes will yield all real vibrational frequencies, while the one which has a maximum on the potential energy surface with respect any one of the normal modes will have an imaginary vibrational frequency.
The vibrational frequencies for four conformers each of trunsand cis-NMA with C, symmetry are given in Tables 2 and 3. The mode descriptions for the predicted vibrational frequencies are also given in these tables under the assignment column, in terms of the intemal symmetry coordinates which are defined in Table 4. All these conformers are found to have at least one imaginary vibrational frequency with a magnitude -50- 120 cm-'. Two of these conformers, trans-NMA-cc and transNMA-tc, have two imaginary vibrational frequencies each, originating from the two methyl group torsional motions. The remaining six conformers have one imaginary vibrational frequency each, originating from one of the two methyl group torsions. The presence of imaginary vibrational frequencies clearly indicates that the symmetry-imposed methyl group orientations leading to C, symmetry for NMA represent unstable orientations, at the 6-31G* level, and therefore there must be other methyl group orientations where NMA should have all real vibrational frequencies. Since the rotation of methyl hydrogen atoms by 60" will take one C, conformer to another C, conformer, a rotation of hydrogen atoms by less than 60" will remove C, symmetry and may provide stable orientations. Thus, full optimization was undertaken without symmetry constraints with starting geometries where methyl group hydrogen atoms were positioned significantly away from the C, symmetry positions. This lead to the identification of one chiral conformer each for trans- and cis-NMA (see Table 1). In the structures of these chiral conformers the H-N-C-H and H-C-C=O segments have p chiralities and therefore will be designated as trans-NMA-pp and cis-NMA-pp. Here p chirality denotes a positive dihedral angle (the angle of rotation needed, viewing along the central bond, to make the group closest to the observer eclipsed with the one farther away from the observer). The influence of basis set and of electron correlation on the relative energies of NMA conformers was investigated by undertaking full structural optimizations with the TZP basis set and with the MP2 method using the 6-31G* basis set. The structures obtained at the HF/6-3 lG* level were used as starting point. Since cis-NMA-tt is found to have a fairly large relative energy at the 6-31G* level, this conformer was not pursued further. The energies and structural parameters resulting from these calculations are also included in Table 1. The relative energy ordering for cis-NMA conformers is essentially the same in all
9922 J. Phys. Chem., Vol. 98, No. 39, 1994
rranr-NMA-cc
A
trans-NMA-cr
trans-NMA.tc rrans-NMA-It
cis.NMA-ct
cis-NMA-lt
Polavarapu et al. optimizations for the conformers of trans-NMA at even higher levels of theory. Their results also indicate that the lowest energy trans-NMA conformer deviates from plane of symmetry. The structural parameters of chiral NMA conformers vary little in the three calculations and are quite interesting (see Table 1). First, the 0-C-N-H dihedral angle deviates from planarity dihedral angle also deviates from by -5". The C-C-N-C planarity, the deviation being -4" in trans-NMA-pp and -810" in cis-NMA-pp. Second, in trans-NMA-pp, the H-NC-H dihedral angle is approximately -20" and the H-CC-0 dihedral angle is -40". Then the two methyl groups of trans-NMA-pp, when viewed along the line connecting the two methyl carbon atoms, will appear nearly eclipsed. The situation for cis-NMA-pp is somewhat different; the H-N-C-H dihedral angle is approximately same as that in trans-NMA, but H-C-C-0 dihedral angle is only -2". Unfortunately, we could not find any experimental structures for isolated NMA to verify these predictions; the electron diffraction study7mentioned in the introduction assumed a plane of symmetry for NMA. The HF/6-3 lG* electronic energy difference for the stable (chiral) conformers, Eel(cis) - Eel(trans), is 2.5 kcaVmol (see Table 1). The difference in vibrational energy (after scaling the 63 lG* vibrational frequencies by 0.886), ,??(cis) - ,??(trans), is -0.03 kcaVmo1. The rotational and translational energies are the same for both isomers. The net sum of energy difference, 2.5 - 0.03 = 2.47 kcaVmo1, is comparable to the experimental enthalpy difference of 2.3 kcaVmol estimated23 from the vibrational spectra of matrix-isolated molecules. The vibrational entropy difference, SV(cis) - SV(trans), is -0.003 kcaV(mo1 deg). The rotational entropy is nearly the same, and translational entropy is identical for the two isomers. Thus, at 298 K the nuclear motions contribute -0.9 kcaVmol higher energy for the cis isomer leading to a total Gibbs energy difference, AG = G(cis) - G(trans), of 2.5 0.9 = 3.4 kcaV mol at 298 K. As the cis-trans electronic energy difference predicted among the HF/6-3 1G*, HF/TZP, and MP2/6-3 lG* calculations varied from 2.2 to 2.7 kcaVmo1, the abovementioned AG varies from 3.1 to 3.6 kcaVmol among these three calculations (using 6-3 1G* vibrational energies). The corresponding value in different solvents is found41 to be -2.5 kcaVmol . Vibrational Spectra. The structures of NMA can be influenced by intermolecular hydrogen bonding. The nonplanarity of the heavy atom skeleton predicted a b initio for free molecules may or may not be applicable in the solution phase. It is also possible that the imaginary vibrational frequencies obtained for achiral conformers may not be present when the potential incorporating the hydrogen-bonding effects with the solvent molecules are included. Then it would be prudent to inquire if there would be any significant differences between the vibrational spectra of chiral and achiral conformers and if the experimental spectra will correlate strongly with one or more of these conformers. For this reason we have listed the 6-31G* vibrational intensities for all of the conformers in Tables 2, 3, 5, and 6, and the simulated spectra are shown in Figures 2-5. In the simulated spectra the theoretical frequencies were multiplied by 0.886 to bring them closer to the experimental frequencies. It may be noted that such uniform scaling does not alter the a b initio predicted normal modes and intensities. These uniformly scaled frequencies will be used in the discussion unless specifically mentioned otherwise. A comparison of the vibrational absorption spectra (Figure 2) for trans-NMA indicates that the overall spectral pattern is essentially the same for all five conformers of trans-NMA. It
+
Figure 1. Achiral (A) and chiral (B) conformers and atom numbering of N-methylacetamide (NMA). The atom numbering shown for trans"MA-ct (A) applies to other achiral conformers with the following convention: hydrogen atom 1 of the N-methyl group is either cis or trans to the N-H group; similarly, hydrogen atom 10 of the acetyl CH3 group is either cis or trans to the C=O group. For chiral conformers trans-NMA-pp (B) and cis-NMA-pp (B) the dihedral angles listed are those obtained in the MP2/6-31G* calculation. See Table 1 for details.
three calculations: pp conformer is lowest in energy, cc has slightly more energy than pp conformer, and tc and ct conformers have higher energies. For trans-NMA conformers, the relative ordering changes in the three calculations although the energy differences are small. Importantly, the trans-NMA-pp conformer is predicted to be either the lowest or one of the two lowest energy conformers; in all these cases the energy difference between the two lowest energy conformers is very small, being 20-50 caVmol. In order to ensure that the transNMA-pp conformer is at a minimum of the energy surface, vibrational frequency calculations were also undertaken for this conformer with the TZP basis set. All vibrational frequencies were again found to be real. On the basis of our preliminary results, Krimm and c o - w ~ r k e r shave ~ ~ pursued geometry
Vibrational Properties of the Peptide Group
J. Phys. Chem., Vol. 98, No. 39, 1994 9923
3E i
a i
e
w
, c )
B P
3
4 x
5 i
3E
9924 J. Phys. Chem., Vol. 98, No. 39, I994
Polavarapu et al.
TABLE 3: Vibrational Properties" of Achiral Conformers of cis-N-MethylacetamideObtained with 6-316* Basis Set cis-NMA-cc cis-NMA-tc cis-NMA-ct v , cm-' scaled S e A mode v,cm-' scaled S e A mode v,cm-' scaled S e A mode 3875 3433 65.5 0.26 42.5 S3 3855 3416 69.1 0.26 35.8 Sj 3870 3429 66.1 0.26 42.4 S3 3340 2959 68.3 0.60 11.0 S7 3340 2959 61.2 0.73 8.7 S7, SI 3328 2949 44.9 0.74 26.7 S7 3308 2931 76.1 0.63 32.0 SI 3336 2956 48.9 0.47 25.6 SI,S7 3307 2930 79.1 0.62 33.3 Si 3278 2904 67.3 0.75 30.9 Si, S9 3280 2906 50.9 0.75 18.6 S9, Ss 3302 2926 69.0 0.75 8.8 Si, S9 3263 2891 35.5 0.75 36.4 Sio, Si1 3260 2888 92.7 0.75 49.5 SII,Si0 3268 2896 59.4 0.75 48.9 Sii, Si0 3221 2854 147.7 0.02 21.3 Ss,Ss, S7 3220 2853 126.5 0.03 12.4 Si, S9,S7 3237 2868 122.7 0.02 5.6 Ss,Sg,S7 3210 2844 52.5 0.01 34.3 Sio,Sii,Si 3212 2846 110.7 0.07 59.9 Sii,Slo,Si 3213 2847 98.1 0.02 44.8 Sii, Slo,Si 1971 1746 9.0 0.44 508.2 Ss 1965 1741 9.2 0.43 508.8 S5 1961 1738 11.5 0.51 511.0 5'5 1672 1481 17.7 0.74 41.2 Si3 1688 1496 16.9 0.72 58.5 Si3,S18 1672 1481 15.4 0.75 44.6 Si3 1645 1458 8.3 0.75 13.2 Si4 1646 1458 13.7 0.75 0.2 S14. S23 1647 1459 8.7 0.75 58.5 S22, S4 1635 1449 2.6 0.47 23.1 Si2 1644 1457 1646 1458 17.9 0.75 2.7 Si4 6.3 0.67 40.1 S13, Sls 1628 1442 2.7 0.51 47.4 Si8 1636 1450 2.2 0.34 8.7 Si2 1631 1445 9.0 0.57 1.6 Si2,Sis 1626 1441 27.9 0.75 2.5 S23 1628 1442 18.7 0.75 11.3 S23. Si4 1624 1439 15.8 0.75 5.0 S23 1612 1428 15.5 0.74 13.3 S22 1612 1428 17.8 0.74 8.2 S22,Si2 3.6 0.75 15.8 S18,S22 1620 1435 1563 1385 0.6 0.74 64.9 S21 1562 1384 0.6 0.75 75.1 S21 1556 1379 3.4 0.75 65.7 S2i 1470 1302 1.4 0.74 193.1 S4, SZI 1476 1308 1.0 0.75 191.3 Sq,S21 1479 1310 1.8 0.75 213.0 S,, S21 1319 1169 1288 1141 2.7 0.57 4.2 Sis,Sz 2.8 0.71 22.9 Sis,S2 1321 1170 2.6 0.57 4.3 S15, S2 1261 1117 3.6 0.75 0.3 si6 1258 1115 2.8 0.75 1.8 si6 1261 1117 3.4 0.75 0.3 si6 1194 1058 1.8 0.71 31.9 S2, S24 1199 1062 1189 1054 1.7 0.70 35.6 S2, S24 4.3 0.68 18.9 S21, S24 1167 1034 1165 1032 1.0 0.75 10.2 s25,S27 1.3 0.75 9.3 S25, S27 1172 1038 0.6 0.75 13.1 S25, S27 1094 969 1087 963 3.4 0.47 26.7 s24, sis 986 4.0 0.48 23.6 s 2 4 , s6, s i 5 1113 2.7 0.55 45.3 &,si5 868 769 10.8 0.11 2.3 S6, 5'4 860 762 10.9 0.10 3.5 &,S4 856 758 10.1 0.11 2.3 &,S4 671 595 0.6 0.75 67.9 S27 693 614 0.0 0.75 114.1 S26, S27 696 617 0.5 0.75 81.8 S27 612 542 614 544 2.4 0.69 21.3 S20 3.4 0.66 15.7 S20rS19 615 545 3.5 0.63 17.4 s20,s19s ,i7 529 469 570 505 0.4 0.57 11.9 Szo, Si9 464 524 4.0 0.75 40.3 S27, S26 2.6 0.75 66.6 ,926, Szi 509 451 2.5 0.75 74.0 5'26 531 471 520 461 0.3 0.68 11.3 Si9, S20 0.6 0.51 12.6 S2o,si9 298 264 324 287 0.3 0.03 2.4 s17, Si9 0.4 0.40 2.0 Si7, Si9 314 278 0.2 0.07 2.6 Sl9, S7 184 163 177 0.1 0.75 0.1 S29 1.0 S ~ S , S ~ O 200 0.5 0.75 177 157 0.7 0.75 0.2 S30, Szs 115 101 115 102 0.3 0.75 2.6 s26, szs 91 81 0.5 0.75 1.9 Szs,s26 0.2 0.75 2.8 s28, s z 6 im im im im im im
+
Scaled vibrational frequencies were obtained by multiplying the 6-31G* frequencies with 0.886. The Raman activity (S),defined as 4 5 d 7p2,is given in A4/amu, and the depolarization ratio (e)is 3p2/(45iX2 4p2). Infrared absorption intensities (A) are in "01. The modes which have major potential energy contribution for a given fibrational frequency are given in terms of intemal symmetry coordinates, which are defined in Table 4.
+
TABLE 4: coord
s13 SI4
sl5 a
Internal Coordinate Definitions" for N-Methylacetamide definition description coord CN-H stretch N-C(H3) stretch N-H stretch N-C(0) stretch C=O stretch C-C stretch Cc-H stretch Cc-H stretch Cc-H stretch CN-H stretch CN-H stretch sym C N Hbend ~
definition
asym CNHjbend asym CNH3bend CNH~ rock Aro,brepresents change in bond length between atoms a and b; A&,b.Crepresents change in angle of a-b-c;
description CNH~ rock CNC bend in-plane N-H bend CCN bend in-plane C=O bend sym CcH3 bend asym CcH3 bend asym CcH3 bend CcH3 rock CcH, rock out-of-plane N-H bend out-of-plane C=O bend C-C-N-C torsion CcH3 torsion CNHJtorsion the atom numbers are shown in
Figure 1; CcH3 represents acetyl CH3 group; C N Hrepresents ~ CH3 attached to N. is common practice to label the vibrations originating predominantly from the amide group in the decreasing order of vibrational frequency as amide A, I, 11,111,etc. Amide A refers to the N-H stretch (represented here by internal coordinate S3; see Table 4),I refers to the C=O stretch (represented by Ss), I1 refers to in-plane N-H bending (represented by S18) with significant mixing from (0)C-N stretch (represented by &), and I11 refers to the (0)C-N stretching with significant mixing from N-H bending. The mode descriptions for amide IV-VI are not uniquely defined in the literature. Amide I, 11, and I11 absorption bands, predicted to be at -1700, 1500, and 1250
cm-', respectively, have large intensities for all trans-NMA conformers (see Table 2 and Figure 2 ) , and no significant differences are noticed in their relative intensities from one conformer to another. Similarly, the out-of-plane N-H bending mode (represented here by S26) predicted to occur in the 320420 cm-' range has significant intensity in all trans-NMA conformers. This pattern is also the one found in the experimental absorption spectrum of matrix-isolated molecules.23 Thus, by looking at the overall pattern of strong absorption bands, it is not possible to select one conformer over the other. The positions of these bands, however, are slightly different
J. Phys. Chem., Vol. 98, No. 39, 1994 9925
Vibrational Properties of the Peptide Group 1
1
I
I
I
I
I
I
d trans-NMA-ct (non-uniformly scaled)
-
trans.NMA-pp
experiment (Ataka et al)
+
-
trans-NMA-pp
trans-NMA-tt
trans-NMA-tc
I
h
' 1
trans-NMA.tt
trans-NMA-ct
,.I trans-NMA-cc L
n
400
600
800
1000 1200 wavenumber
1400
1600
400
1800
Figure 2. A b initio infrared absorption spectra for achiral and chiral conformers of rruns-NMA obtained with the 6-31G* basis set in the 400- 1800 cm-' region. Each spectrum is labeled with the appropriate conformer. The experimental spectrum of NMA isolated in N2 matrix as reported by Ataka et al.23is replotted here for direct comparison with the theoretical spectra. The intensity of the experimental band at 1707 cm-' is not shown fully; and the sharp experimental band at -1600 cm-I is due to water. for these conformers. The frequencies are within 9 cm-' for amide I, 21 cm-' for amide 11, and 10 cm-' for amide III. Thus, one would expect these bands to be split if more than one conformer is present in the vapor phase. Although some splittings are present for amide I and 11bands and for the N-H out-of-plane bending band at -420 cm-' in the experimental absorption spectra23of matrix-isolated molecules, similar splittings are not observed for amide 111. This casts doubt on the assignment of splittings to different conformers of trans-NMA, and the observed splittings for some of the bands in the experimental spectra may be originating from the matrix effects. One major discrepancy between the experimental and ab initio predicted absorption spectra (Figure 2 ) is that the former shows an absorption band at 1367 cm-', attributable to the symmetric bending mode (represented by S21) of the acetyl CH3 group, with approximately the same intensity as that observed for the amide 111 band. The corresponding theoretical mode is at -1375 cm-', but in all of the trans-NMA conformers the intensity of this mode is -6 times lower than that of the predicted intensity for amide I11 mode. It is possible that the level of theory employed here is not sufficient to reproduce the relative intensities under discussion. The conclusion emerging from the discussion in this paragraph is that the experimental absorption spectrum of matrix-isolated NMA can be explained to the same degree of confidence using the predicted spectrum for any one of the five conformers of trans-NMA. In the experimental absorption spectrum of matrix-isolated molecules the amide I band is most intense; amide I1 and I11 bands have significantly lower intensities. Although no quantitative numbers were available for these intensities, the relative intensities for amide I, 11, and I11 bands can be approximated
800
600
1000 1200 wavenumber
1400
1600
1800
Figure 3. A b initio polarized Raman spectra for achiral and chiral conformers of trans-NMA obtained with the 6-31G* basis set in the -400-1800 cm-' region.
I
cis-NMA-pp
4 CIS-NMA-ct
1
cis-NMA-cc
I
400
r
I
600
800
1000 1200 wavenumber
1400
1600
1600
Figure 4. A b initio infrared absorption spectra for achiral and chiral conformers of cis-NMA obtained with the 6-31G* basis set in the 4001800 cm-I region. The spectrum for cis-NMA-tt was not calculated as this conformer is found to be of much higher energy over other conformers. from the spectra of Ataka et al.23 as 3:lS:l. The ab initio predicted spectra for the trans-NMA conformers have qualitatively similar trends for these three amide bands. The relative intensity of the symmetric bending mode of the acetyl CH3
Polavarapu et al.
9926 J. Phys. Chem., Vol. 98, No. 39, 1994
1
400
600
800
1 0 0 0 1200 wavenumber
1400
1600
18'00
Figure 5. Ab initio polarized Raman spectra for achiral and chiral conformers of cis-NMA obtained with the 6-31G* basis set in the 4001800 cm-l region. The spectrum for cis-NMA-tt was not calculated as this conformer is found to be of much higher energy over other conformers.
group (vide supra), however, is not correctly reproduced in the predicted spectra. To investigate this discrepancy further, the theoretical force constants were adjusted using a literature procedure. It is well-known that the a b initio predicted vibrational frequencies are usually larger than the experimental frequencies by about 10-15%. A scaling procedure was suggested42 to correct for these deficiencies in the predicted frequencies where different types of force constants are scaled by differing constants. This procedure can work well when experimental vibrational frequencies of a large set of isotopically related molecules were included in deriving these scale factors. When such data are not available, scaling constants are usually chosen to fit the frequency data of a single molecule. A set of scaling factors for NMA were suggested in the literature15 for the force constants obtained with the 4-31G* basis set. Since the normal modes obtained with the 4-31G* basis set were mentioned15 to be nearly identical to those obtained with the 6-3 1G* basis set, we have used these literature scale factors to scale the 6-31G* force constants and obtained the frequencies and normal mode compositions. These normal mode compositions were in turn combined with the Cartesian dipole moment derivatives to obtain the absorption intensities. The spectrum for trans-NMA-ct (the lowest energy achiral conformer of transNMA) resulting from this process is labeled "nonuniformly scaled" and compared with the original ab initio prediction and with the experimental absorption spectrum in Figure 2. The effect of scaling on the intensities of other conformers i s similar to that for trans-NMA-ct. A comparison of the spectra in Figure 2 indicates that the scaling factors used here are not quite successful in improving the predicted spectra. A comparison of theoretical polarized Raman spectra for the five conformers of trans-NMA is provided in Figure 3. The most striking difference between the Raman spectra of chiral and achiral conformers is evident for the C=O bending modes.
The achiral conformers have a very weak Raman intensity for the out-of-plane C=O bending mode (represented by S27) but have a moderately strong intensity for the in-plane C=O bending mode (represented by S20). These modes are within 13 cm-' separation and give rise to an unresolved band at -600 cm-'. In trans-NMA-pp conformer (Table 5) the lack of symmetry causes these two modes (616 and 587 cm-') to mix, leading to a larger separation of 29 cm-' with nearly equal intensity for both modes. If these predictions are accurate, the trans-NMApp conformer should be detectable in the Raman spectrum of matrix-isolated molecules. Unfortunately, these spectra are not available in the literature. The absorption spectra of matrixisolated molecule^^^-*^ are not helpful here because the absorptions of C=O bending modes are weak (see Tables 2-5). The Raman spectrum for a neat liquid sample can be expected to be different from that for isolated molecules due to intermolecular hydrogen bonding in the liquid phase. This hydrogen bonding may in fact force the molecules to adopt the C, symmetry, as in the crystalline phase.6 This possibility can be tested by comparing the experimental (nonresonance) Raman spectra24 with those predicted for achiral conformers. The experimental Raman spectrum has a strong band at 627 cm-', assigned to in-plane C=O bending, and a weak lower frequency shoulder presumably from out-of-plane bending. The lower energy achiral conformers, trans-NMA-ct and trans-NMA-tt, exhibit identical features (Table 2, Figure 3) with strong Raman intensity for the in-plane C=O bending mode at 608 cm-I and weak intensity for the out-of-plane C=O bending mode at 597 cm-'. The chiral conformer of trans-NMA exhibits (Table 5, Figure 3) nearly equal intensities for these two modes, contrary to that seen in the Raman spectrum of liquid NMA. The situation for the experimental data on cis-NMA is different. Since cis-NMA has very little population at room temperature, the experiment has to be conducted at higher temperatures, and only the strong bands are detectable. A few experimental bands reported for cis-NMA isolated in lowtemperature matrices are collected in Table 6, and the vibrational spectra for three achiral conformers cis-NMA-cc, cis-NMA-tc, and cis-NMA-ct and of the chiral conformer cis-NMA-pp are shown in Figures 4 and 5. The vibrational spectra for the fourth achiral conformer, cis-NMA-tt, have not been obtained due to the relatively higher energy of this conformer (see Table 1). The absorption spectra of cis-NMA conformers are all similar, with amide I(-1700 cm-') an amide I11 (-1300 cm-') modes being the most intense (Tables 3 and 6 and Figure 4). Note that, unlike in trans-NMA, the amide I11 mode for cis-NMA is mostly C-N stretch coupled to the symmetric bending mode of the acetyl CH3 group. The experimental band corresponding to the latter mode was found at 1325 cm-' in the absorption spectrum of matrix-isolated molecules,23 while the former was probably hidden beneath the C==O stretching band of the transNMA. In the Raman spectra of cis-NMA conformers (Figure 5) the most notable difference is at -475 cm-'. The achiral conformers have three modes in this region, two of which have strong Raman intensity and one weak, thereby showing only two separated strong Raman bands in the simulated spectrum. These originate from CCN bend, in-plane C=O bend, and outof-plane N-H bending motions. In chiral cis-NMA-pp conformer the latter mode mixes with the first two and leads to the appearance of three separate bands. Vibrational Mode Descriptions. Resonance Raman spect r o s ~ o p y of ~ ~liquid - ~ ~ NMA has been used to suggest the mode descriptions of the bands originating from the peptide group. It is suggested that the Raman bands which exhibit resonance enhancement in the ultraviolet region indicate the involvement
J. Phys. Chem., Vol. 98, No. 39, I994 9927
Vibrational Properties of the Peptide Group
TABLE 5: Vibrational Propertie@of Chiral fruns-N-Methylacetamide Obtained with 6-316* Basis Set frequencies (cm-I) Raman ROA infrared exptb 6-31G* scaled S e AZ A X A* A180 AO A R 3498 3008 2973 2958 2915 1707 1511 1472 1446 1432 1419 1370 1266 1168 1089 1037 980 857 658 619 439 429 279
3907 3324 3319 3289 3286 3224 3222 1961 1714 1658 1634 1632 1615 1607 1555 1407 1309 1263 1195 1171 1089 950 695 663 459 396 288 167 62 39
3462 2945 2940 2914 2911 2856 2855 1737 1519 1469 1447 1446 1431 1424 1378 1247 1160 1119 1059 1038 965 842 616 587 406 35 1 255 148 55 34
48.9 56.4 69.2 70.9 60.0 121.8 96.0 5.2 7.3 9.6 10.3 21.9 13.4 7.4 3.4 2.9 5.4 3.7 1.5 0.7 2.4 8.0 3.7 4.3 0.7 1.2 0.3 0.1 0.4 0.3
0.25 0.73 0.66 0.64 0.75 0.04 0.02 0.50 0.64 0.74 0.75 0.75 0.75 0.74 0.75 0.75 0.26 0.74 0.59 0.73 0.44 0.19 0.38 0.37 0.30 0.72 0.45 0.75 0.65 0.75
-0.4 0.6 0.3 -0.9 -0.0 -5.3 0.2 -1.8 1.4 -2.1 -12 7.0 0.0 -4.4 1.o -1.2 -1.2 -0.0 -1.8 -4.1 1.5 0.9 2.7 -2.4 -0.2 -0.2 -2.7 9.3 -8.4 5.5
0.0 0.9 0.4 -0.6 -0.3 -1.0 0.2 -3.0 1.7 -3.1 -16 9.4 1.1 -6.1 0.9 -1.3 -0.1 0.8 -2.3 -6.2 0.9 1.3 0.6 -0.8 -1.8 -0.6 -1.0 12 -8.3 5.8
-0.1 0.8 0.4 -0.7 -0.2 -1.2 0.2 -2.7 1.6 -2.8 -15 8.7 0.8 -5.6 0.9 -1.3 -0.3 0.6 -2.2 -5.6 1.o 1.2 1.1 -1.2 -1.5 -0.5 -1.4 11 -8.3 5.7
-0.2 1.3 1.3 -2.3 -0.8 -0.5 0.2 -5.1 2.7 -6.0 -31 18 2.7 -12 1.5 -2.4 0.1 1.1 -4.0 -13 2.4 0.9 0.4 -0.6 -1.1 2.1 -4.5 22 -13 10
0.2 0.6 -0.4 1.o 0.1 -1.6 0.2 -0.9 0.8 -0.2 -1.6 1.o -0.5 -0.6 0.3 -0.3 -0.3 0.5 -0.6 0.8 -0.6 1.6 0.9 -1.0 -2.6 -3.3 2.6 1.9 -3.3 1.4
38.0 22.2 12.1 43.8 23.8 50.3 11.0 339 290 7.7 15.6 5.6 14.7 6.3 22.8 129 1.5 4.6 6.8 13.4 13.7 4.9 7.0 7.6 12.6 109 9.0 20.0 3.1 4.2
-1.0 -2.6 1.8 -4.7 -8.9 18.8 0.3 9.0 2.9 3.9 -30.0 8.3 4.7 19.3 5.0 -3.0 0.9 -1.1 -2.6 -4.6 6.7 1.4 35.2 -17.1 -21.9 12.4 11.1 -2.3 2.0 3.5
R
assignment
-0.1 -0.4 0.5 -0.4 -1.2 1.2 0.1 0.1 0.0 0.8 -3.1 2.4 0.5 5.0 0.3 -0.0 0.8 -0.3 -0.5 -0.4 0.5 0.3 3.5 -1.5 -0.8 0.1 0.4 -0.0 0.0 0.0
+
Scaled vibrational frequencies were obtained by multiplying the 6-31G* frequencies with 0.886. The Raman activity (S),defined as 45a2 7p2, is given in A4/amu, and the depolarization ratio (e)is 3p2/(45C2 4p2). Infrared absorption intensities (A) are in ludmol. The modes which
+
have major potential energy contribution for a given vibrational frequency are given in terms of internal symmetry coordinates, which are defined esu2 cm2. Experimental frequencies for matrix-isolated trans-NMA from ref 23. in Table 4. Rotatory strength ( R ) is in units of I n is mainly C-N stretching. (For example, see mode of a normal mode that distorts the geometry toward that of the resonant electronic excited state. The involvement of C-N descriptions of the 1443 and 1302 cm-' modes of cis-NMA-pp stretch, N-H bend, and torsion around C-N bond was in Table 6.) The resonance enhancement of the experimental suggested on this b a ~ i s . ~ ~ -In ~ Otrans-NMA the resonance 1495 cm-' band for cis-NMA was attributedz9 to the C-N enhancement was found for the amide I1 band and for another stretch, partly because this band is unaffected by the deuteration band at 1385 cm-' which has been convincingly s h o ~ nby~ ~ , ~of~the hydrogen of N-H. However, the C-N stretching mode Wang et al. to arise from acetyl CH3 group and assigned to its is predicted in the present calculations to be at -1300 cm-' symmetric bending mode S21. This latter band was designated for all cis-NMA conformers. The predicted ab initio Raman amide S. The resonance enhancement of amide S was thought spectra (Figure 5) for cis-NMA indicate that in the amide I1 to arise from the coupling of this mode with the in-plane N-H region several modes (most importantly the hydrogen bending bending mode, Sls. The amide S mode in the present calculamodes of the CH3 group attached to the N atom) possessing tions for trans-NMA-pp is at 1378 cm-'. (As the overall significant Raman intensity overlap. The internal coordinate conclusion to be made in this paragraph is valid for all displacements for the calculated 1481 cm-l mode indicate that conformers of trans-NMA, we need not worry about the the in-plane N-H bending coordinate Sls is significantly preference of achiral vs chiral conformer of trans-NMA and displaced and coupled with a bending mode Si3 of the CH3 group use trans-NMA-pp as an example.) The potential energy attached to the nitrogen; the relative displacements for this mode distribution for this mode indicates only 1% mixing of the inare 813/aQ = 1.4 and aS1s/aQ = -0.6 in cis-NMA-pp and 1.4 plane N-H bending coordinate S18 with the symmetric bending and -0.5 in cis-NMA-cc. If a bending mode of CH3 (attached coordinate S21 of the acetyl CH3 group; the relative displaceto N) is assigned to the experimental 1495 cm-' band in cisments of these two internal coordinates in this mode are &/ NMA, then the experimental observation of this band being aQ = 1.7 and aSls/aQ = 0.2. A similar or even larger amount unaffected by the deuteration of N-H can be explained. of the in-plane N-H bending is present for other modes, for However, this explanation does not answer all of the pending example, the bending modes of CH3 attached to nitrogen. Thus, questions because there are other modes which have as much the reasons for selective resonance enhancement of acetyl CH3 in-plane N-H bending contribution but are not resonance symmetric bending mode appear uncertain. enhanced. For example, the calculated 1385 cm-' amide S Similar questions also arise for cis-NMA. On the basis of mode in cis-NMA-pp (or in cis-NMA-cc) is also found in the the cis-NMA frequencies c a l ~ u l a t e dwith ~ ~ a~trans-NMA ~~ force present calculations to have significant in-plane N-H bending field, it was suggested that the amide 11 mode is mainly C-N with relative displacements of Xzl/aQ = 1.7 and aSls/i3Q = stretching in character and amide I n is mainly N-H bending 0.4. If the presence of coupling with the in-plane N-H bending in character. But the present ab initio calculations indicate coordinate is a criterion for resonance enhancement of amide S contributions of reverse order for all of the cis-NMA conformers; Le., amide I1 is mainly due to in-plane N-H bending and amide band, then cis-NMA has more of that coupling than trans-NMA,
9928 J. Phys. Chem., Vol. 98, No. 39, 1994
Polavarapu et al.
TABLE 6: Vibrational Properties" of Chiral cis-N-MethylacetamideObtained with 6-31G* Basis Set frequencies (cm-I) Raman ROA infrared exptb 6-31G* scaled S e A? A, A* Also Ao A R 3458
1454 1485 1432 1387 1325 1075
607 510
3869 3339 3308 3278 3270 3220 3205 1972 1672 1646 1635 1629 1626 1611 1563 1470 1316 1258 1194 1167 1094 867 671 616 546
501 300 175 129 70
3428 2958 293 1 2904 2897 2853 2840 1747 1481 1458 1449 1443 1441 1427 1385 1302 1166 1115 1058 1034 969 768 600 546 484 449 266 155 114 62
66.5 68.5 72.4 68.9 43.1 117.6 82.2 9.1 16.6 12.4 4.6 5.7 18.1 16.7 0.6 1.3 2.5 3.8 2.2 1.1 3.2 10.8 0.4 3.4 1.6 1.6 0.2 0.5 0.4 0.1
0.26 0.61 0.67 0.74 0.40 0.02 0.06 0.44 0.75 0.73 0.64 0.62 0.74 0.74 0.75 0.74 0.61 0.69 0.69 0.75 0.41 0.11 0.61 0.65 0.70 0.75 0.07 0.72 0.71 0.39
-0.4 -0.0 -0.0 1.8 -4.9 -4.0 -3.7 0.4 1.6 0.3 -13 9.8 1.o -3.2 -1.9 -0.1 -2.7 1.1 0.5 -0.2 -0.6 0.4 2.2 0.5 -5.4 2.6 - 10 7.5 -0.3 -47
-0.1 0.1 0.0 2.4 -4.4 -0.7 -1.1 0.4 2.1 0.3 -13 11 0.8 -3.9 -1.8 -0.0 -2.2 2.1 0.6 0.3 -1.1 0.2 -3.1 0.8 -4.9 1.5 -0.5 7.0 -1.1 -33
-0.0 0.1 0.0 2.6 -4.3 -0.6 -0.9 0.4 2.3 0.3 -13 12 0.7 -4.2 -1.7 0.0 -2.0 2.5 0.6 0.5 -1.3 0.2 -5.1 1.o -4.7 1.1 0.2 6.8 -1.5 -29
-0.2 0.3 0.3 5.2 -11 -0.6 -0.3 0.2 4.4 0.7 -24 23 0.9 -7.9 -2.7 0.3 -3.2 3.6 0.4 0.9 -2.3 0.1 0.9 2.3 -6.4 0.4 -3.3 11 -2.5 -46
0.1 -0.0 -0.3 0.1 2.1 -0.7 -1.5 0.6 0.2 -0.1 -2.1 0.7 0.4 -0.5 -0.7 -0.2 -0.8 1.3 0.8 0.1 -0.3 0.2 -11 -0.4 -3.0 1.7 3.7 2.6 -0.4 - 13
40.1 11.0 32.8 32.2 30.2 12.8 48.2 502 42.9 10.4 26.3 23.1 16.8 15.1 66.0 192 5.1 4.5 29.4 10.6 27.1 2.1 80.5 13.6 44.2 39.3 2.0 1.2
1.8 2.4
-3.1 -0.2 0.0 -7.7 7.3 - 12.1 15.4 -15.7 15.5 9.2 -19.0 -17.4 26.2 -0.2 5.4 -4.1 -2.3 1.6 -0.8 -11.4 5.0 -0.6 46.2 21.2 -78.0 81.2 1.7 2.5 -0.7 -4.2
g
assignment
-0.3 -0.1 0.0 -0.8 0.8 -3.2 1.o -0.1 0.6 1.5 -1.2 -1.2 2.5 -0.0 0.1 -0.0 -0.6 0.5 -0.0 -1.9 0.2 -0.3 0.4 1.o -1.0 1.1 0.3 0.4 -0.1 -0.1
+
Scaled vibra9onal frequencies were obtained by multiplying the 6-31G* frequencies with 0.886. The Raman activity (S), defined as 4 5 2 7p2, is given in A4/amu,and the depolarization ratio (e) is 3p2/(45Ci2 4p2). Infrared absorption intensities ( A ) are in km/mol. The modes which
+
have major-potential energy contribution for a given vibrational frequency are given in terms of internal symmetry coordinates, which are defined in Table 4. Rotatory strength ( R ) is in units of esu2 cm2. Experimental frequencies for matrix-isolated cis-NMA from ref 23. and yet resonance enhancement was found for the amide S band of trans-NMA, not of cis-NMA. In summary, the mode descriptions perceived in the interpretations of resonance enhancement of certain Raman bands of NMA do not appear consistent with those obtained a b initio. It is possible that these discrepancies may be related to the influence of hydrogen bonding in the solutions. Vibrational Optical Activity. In the vibrational absorption spectrum we noted earlier that the amide I, 11, and I11 bands have strong absorption while most of the remaining modes have very weak absorption. In the Raman spectrum larger intensities are found for the bending modes of CH3 groups, N-C(0) stretch coupled with C-C stretch, and C=O bending modes. The optical activity associated with the vibrational motions of chiral NMA conformers (see Figures 6 and 7) provides additional information that is complementary to the previous data. For trans-NMA-pp large VOA signals are found to be associated with the coupled asymmetric bending modes of the two methyl groups and for the coupled bending modes of the C=O group. Note that the absorption intensities associated with these modes are very weak, and therefore the absorption spectrum does not reveal much information from these modes. One of the asymmetric bending modes of the CH3 group attached to the N atom and similar bending mode associated with the CH3 group attached to C atom are coupled to give bisignate VOA at -1450 cm-'. Noting that these two methyl groups are approximately eclipsed, when viewed along the axis connecting the two carbon atoms of the methyl groups, the optical activity of these modes in trans-NMA-pp can be seen to be induced by the nonplanar heavy atom skeleton. Since the signs of VOA associated with these modes are controlled by the chirality of the heavy atom skeleton, the methyl groups are expected to serve as excellent
probes of the chirality of peptide skeleton. The in-plane and out-of-plane bending modes of the C=O group are coupled in trans-NMA-pp due to the absence of symmetry for this molecule, and these two modes give rise to a bisignate VOA couplet. The signs associated with the components of this couplet reflect the chirality associated with trans-NMA-pp and hence serve as sensitive structural probes. Although the ROA and VCD associated with the vibrational modes of trans-NMApp provide similar information, from a practical viewpoint ROA measurement is much more convenient than the VCD. This is because VCD measurements are not yet feasible below -700 cm-', which rules out the use of large VCD associated with the C=O bending modes for stereochemical information. Also, normalized VCD intensities associated with the amide I, 11, and I11 modes are rather small compared to the corresponding ROA intensities (see g and A values in Table 5). On the other hand, VCD is useful for the C-H and N-H stretching regions where ROA has not yet been measured successfully. Large VCD signals are found (see Table 5) to be associated with the stretching modes of the CH3 hydrogens. It is useful to know which type of ROA measurement is more likely to give a better signal-to-noise for peptide groups. From the spectra presented in Figures 6 and 7 it is apparent that forward ROA measurement is least preferred due to weak signals. While there is no strong preference among the remaining experimental ROA geometries, 90" depolarized ROA appears to be better for measuring ROA associated with the C=O bending modes. This is because the ROA magnitudes associated with these modes are larger in the 90" geometry than in the other ROA geometries (see Figure 6 and A values in Table 5 ) .
J. Phys. Chem., Vol. 98, No. 39, 1994 9929
Vibrational Properties of the Peptide Group
I
forward ROA L
v -
c
magic angle ROA
A
. "
V
A
c
forward ROA
magic angle ROA
. - .
v
-
90 dep ROA
A +
Y
90 pol ROA
A
-
Y
90 pol ROA
A
180 ROA
A , *
L
90 dep ROA
--
.
A - .
V
Y' 180 ROA
-
Raman
Raman
d
V
k
A
h -
MA absorption
absorption
VCD
V
N
A
V
I
chiral trans-N-melhylacetamlde I
I
I
I
200
400
600
800
I 1000
I
I
1200
1400
1
chiral cis-N-methylacetamlde I
I
1
200
400
EO0
wavenumber
I
I
EO0 1000 WAMNUMBER
I
I
1200
1400
1
traces) and vibrational circular dichroism (VCD) spectrum (bottom trace) for trans-NMA-pp obtained with the 6-31G* basis set in the 100-1600 cm-' region. The absorption and Raman spectra are same as those in Figures 1 and 2 but are shown here to correlate them with the optical activity. Two traces of Raman spectra correspond to polarized and depolarized spectra overlayed on the same scale.
Figure 7. Ab initio Raman optical activity (ROA) spectra (top five traces) and vibrational circular dichroism (VCD) spectrum (bottom trace) for cis-NMA-pp obtained with the 6-31G* basis set in the 1001600 cm-' region. The absorption and Raman spectra are same as those in Figures 1 and 2 but are shown here to correlate them with the optical activity. Two traces of Raman spectra correspond to polarized and depolarized spectra overlayed on the same scale.
Significantly different optical activity effects are predicted for cis-NMA-pp. Here the out-of-plane C=O and N-H bending modes are coupled with the in-plane C=O bending and CCN bending to give four modes of closely placed frequencies. The VOA pattern associated with these modes is significantly different from that in trans-NMA-pp, thereby differentiating between the trans and cis chiral NMA conformers. The overall optical activity magnitudes for cis-NMA-pp are smaller than those for trans-NMA-pp. This can be understood from the structural information because in cis-NMA-pp a H-C-N-0 dihedral angle is only slightly different from being planar, and therefore most of the optical activity in cis-NMA-pp comes from the chirality of methyl group attached to N atom.
with a peptide bond, can distinguish surprisingly well between chiral and achiral conformers. We have computed the a b initio characteristic VOA spectra for NMA that should be observable only in chiral structures. In addition, the predicted VOA spectra indicate that the C=O bending modes and CH3 bending modes should serve as excellent probes of peptide stereochemistry. Finally, in light of the present predictions of low-energy stable chiral conformers of N-methylacetamide and the recent electron diffraction experiments indicating a nonplanar skeleton in N,Ndimethylf~rmamide~~ and theoretical calculations* predicting a nonplanar skeleton for N,N-dimethylacetamide, it may be useful to further investigate the experimental data relating to equilibrium molecular structures.
Conclusions
Acknowledgment. This work was supported by the grants from the Pittsburgh Supercomputer Center and Vanderbilt University .
Figure 6. Ab initio Raman optical activity (ROA) spectra (top five
All the a b initio computations reported herein predict that the chiral and achiral forms of NMA are very similar in energy for both cis and trans conformers. These results indicate not only that the torsional potential for the methyl groups is very low but also that significant deformation of the peptide backbone may simultaneously occur. A detailed analysis of the normal modes has been compared with the conclusions of resonance Raman spectra. For some bands there is good agreement, while for others there are discrepancies that are likely to be related to the effects of solvent. The predicted HF/6-3 lG* vibrational absorption spectra of NMA are consistent with those observed for molecules isolated in low-temperature matrices but are fairly similar for chiral and achiral structures. However, the predicted HF/6-3 lG* vibrational Raman spectra indicate that the experimental Raman spectra for matrix-isolated NMA, and by inference other species
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