6632
J . Phys. Chem. 1989, 93, 6632-6631
Calculations of the Infrared and Vibrational Circular Dichroism Spectra of Ethanol and Its Deuterated Isotopomers Hoang Dothe, Marian A. Lowe, Department of Chemistry, Boston University, Boston, Massachusetts 0221 5
and Joseph S. Alper* Department of Chemistry, University of Massachusetts-Boston, (Received: January 30, 1989; In Final Form: March 30, 1989)
Boston, Massachusetts 021 25
The scaled quantum mechanical force field method together with the Stephens formalism for the evaluation of rotational strengths has been used to calculate infrared and vibrational circular dichroism (VCD) spectra of ethanol and its deuterated isotopomers. For the IR spectra, agreement between the calculated and experimental spectra is extremely good; the root-mean-squaredeviation between the calculated and experimental frequencies for all 12 isotopomers is 15 cm-'. The calculated VCD spectra are also in good agreement with the experimental ones when the evaluation of the rotational strengths is carried out using the distributed origin gauge. Both the IR and VCD results confirm the earlier conjecture that the gauche conformer predominates over the trans, even though the trans has a slightly lower SCF energy.
Introduction Calculations of the vibrational circular dichroism (VCD) spectra of molecules which are in good agreement with the experimental spectra require accurate force fields and accurate dipole and rotational strengths. The scaled quantum mechanical force field method (SQM), which combines data obtained from the experimental spectra with ab initio calculations, has been shown to produce accurate force The Stephens formalism5 for calculating rotational strengths has been used successfully in conjunction with the SQM in obtaining calculated VCD spectra in good agreement with experimental spectra.6-'0 In this paper we study the force field and VCD of ethanol and its deuterated isotopomers. The extensive study of the IR spectra of 12 of the deuterated isotopomers of ethanol by Perchard and Josien" (to be referred to here as PJ) provides a wealth of experimental data for the construction of the SQM force field. The experimental VCD spectra of two of the four chiral isotopomers of ethanol, (R)-CH3CHDOH and (R)-CH3CHDOD, were reported by Pultz.I2 Consequently, we can compare our calculated VCD spectra for these two isotopomers with the experimental ones in order to determine the best choice of gauge and to evaluate the calculational method. We have also calculated the VCD spectra of the other two chiral isotopomers of ethanol, (R)CD,CHDOH and (R)-CD3CHDOD. Method and Calculations The calculation of the force field of a molecule using the SQM method has been described in detail elsewhere', so that only an abbreviated outline with emphasis on the particulars of the calculation of ethanol will be given here. When the method is applied (1) Fonarasi. G.:Pulav. P. Annu. Rev. Phvs. Chem. 1984. 35. 191. (2j Lo&, M: A,; Alp.;, J. S.; Kawiecki, R.{Stephens, P. J. J. Phys. Chem. 1986. 90. 41. ( 3 ) Aiper, J. S.; Dothe, H.; Lowe, M. A. Chem. Phys. 1988, 125, 77. (4) Alper, J . S . ; Lowe, M. A. Chem. Phys. 1988, 121, 189. (5) Stephens, P. J. J . Phys. Chem. 1985,89, 748. (6) Stephens, P. J.; Lowe, M. A. Annu. Rev. Phys. Chem. 1985,36, 213. (7) Lowe, M. A.; Alper, J. S . J . Phys. Chem. 1988, 92, 4035. (8) Kawiecki, R. W.; Devlin, F.;Stephens, P. J.; Amos, R. D.; Handy, N. C. Chem. Phys. Lett., submitted for publication. (9) Jalkanen, K. J.; Stephens, P. J.; Amos, R. D.;Handy, N. C. J . Am. Chem. SOC.1988, 110, 2012. (10) Lowe, M. A.; Stephens, P. J.; Segal, G.A. Chem. Phys. Lett. 1986, 123, 108. ( 1 1 ) Perchard, J.-P.;Josien, M.-L.J . Chim. Phys. Phys.-Chim. B i d . 1968, 65, 1834. (12) Pultz, V. M. Vibrational Circular Dichroism Studies of Some Small Chiral Molecules. Dissertation, University of Microfilms, Int., Ann Arbor, ~
1983. (13) May, P. In Modern Theoretical Chemistry; Schaefer 111, H. F., Ed.; Plenum: New York, 1977; pp 153-185.
0022-3654/89/2093-6632$01.50/0
TABLE I: Optimized 6-31G** Geometry and Energy for the Trans and Gauche Conformers of Ethanol" bond length, bond angle, or torsion internal coordinate trans gauche 02-H1 C3-02 C3-02-H1 c4-c3 C4-C3-02 C4-C3-02-H1 H5-C3 H5-C3-02 H5-C3-C4 H6-C3 H6-C3-02 H6-C3-C4 H7-C4 H7-C4-C3 H7-C4-C3-02 H8-C4 H8-C4-C3 H8-C4-H7 H9-C4 H9-C4-C3 H9-C4-H7
0.94241 1.40389 109.850 1.51500 108.065 180.000 1.08951 110.678 110.054 1.08951 110.678 110.054 1.08571 110.626 180.000 1.08444 110.298 108.663 1.08444 110.298 108.663
0.943051 1.402644 109.583 1.520860 112.511 64.399 1 .OS9473 110.703 110.189 1.083239 105.930 110.095 1.086133 110.807 177.456 1.084601 110.383 108.612 1.0875 15 110.050 107.779
energy
-154.09016093
-1 54.09000100
" Distances in angstroms, angles in degrees, and energy in hartrees. TABLE 11: SQM Scale Factors gauche trans stretch stretch stretch stretch methylene methyl C-0-H bend C-C-0 bend H-C-0 bend 0-H C-0 C-C C-H
0.774 0.778 0.745 0.757 0.815 0.838
0.840 0.840 0.819 0.786 0.787 C-C-H bend 0.800 H-C-H bend (methyl) 0.797 H-0-C-H, H-C-C-H torsions 0.890
B
A
0.844, 0.806' 0.844 0.832 0.856 0.794 0.802 0.796 0.850
0.778 0.752 0.839 0.846, 0.798O 0.846 0.828 0.859 0.788 0.806 0.794 0.897
'For the gauche forms, the methylene C-H stretch on the opposite side of the hydroxyl hydrogen is given an independent scale factor.
to ethanol, a complication arises. The two most stable conformers of ethanol, the trans and gauche, are nearly degenerate. As a result, it is not evident whether in either the gas or liquid phase both species are present in significant amounts or one species
0 1989 American Chemical Society
Spectra of Ethanol and Its Deuterated Isotopomers
W
/
J
0
Figure 1. Geometry of ethanol: (top) trans conformer; (bottom) gauche conformer.
predominates. Therefore, in this work all calculations were performed for each of the conformers. The ab initio optimized geometry, force constant matrix, vibrational frequencies, normal modes, potential energy distributions, and intensities for each conformer were calculated by using GAUSSIAN 82 within the S C F approximation using the 6-31G** basis set.I4 The 6-31G** optimized geometry and energy for each conformer are given in Table I, and the geometry is illustrated in Figure 1. Note that the two conformers differ in energy by only 1.6 X lo4 hartree or 0.1 kcal/mol. The transformation of the force constant matrix expressed in Cartesian coordinates for each conformer to one expressed in terms of internal coordinates was performed using the previously described modification of the vibrational program of McIntosh and Peter~0n.l~Each force constant matrix was then scaled, and the scaling factors were optimized by means of a nonlinear leastsquares fit of the scaled calculated frequencies to the observed ones. The set of internal coordinates used in this work together with the optimized values of the 10 scale factors used for the trans conformer and the 11 used for the gauche conformer are shown in Table 11. All 12 of the isotopomers reported by PJ were used in the construction of the scaled force constant matrices for each of the two conformers of each of the isotopomers. Unfortunately, PJ were unable to give complete assignments of their spectra. In some cases, they could not make definitive determinations of which of the observed frequencies are the fundamentals, and so reported all possible candidates. Moreover, they could not be certain as to which observed frequencies corresponded to which conformer. Nevertheless, on the basis of the existence of certain splittings which they attributed to couplings among the modes in the lower symmetry gauche conformer, they surmised that the gauche conformer was the dominant one. The additional scale factor for the gauche conformer was introduced as a result of the analysis of the SQM fit to the experimental spectra. We first scaled the force constant matrix for the trans conformer using 10 scale factors, each set to an initial value of 0.8. We then scaled the force constants for the gauche (,l4),Binkley, J. S.; Frisch, M. J.; DeFrees, D. J.; Raghavachari, K.; Whiteside, R. A.; Schlegel, H. B.; Fluder, E. M.; Pople, J. A. GAUSSIAN 82, Revision H Version, Carnegie-Mellon University, 1986. (15) McIntosh, D. F.; Peterson, M. R. Q C P E Indiana University; Bloomington, IN. (16) Galwas, P. A. Ph.D. Thesis, University of Cambridge, Cambridge, UK, 1983. Buckingham, A. D.; Fowler, P. W.; Galwas, P. A. Chem. Phys. 1987, 112, 1 .
The Journal of Physical Chemistry, Vol. 93, No. 18, 1989 6633 conformer using the same 10 scale factors, again initializing each of them to 0.8. For the gauche conformers containing a C H D group, the order of several of the bands was reversed from that of the corresponding trans conformer and from the PJ analysis. Moreover, examination of the scaled force constant matrices for the two conformers showed that whereas the values of the diagonal elements describing the CH, methyl group stretching motions were nearly the same for the trans and gauche conformers, there were significant differences in the values of the diagonal elements describing the CHD methylene group stretching motions between the trans and the gauche. These differences reflect the different environments of the two stretching bands. For these reasons we used an additional scale factor for the gauche conformer, allowing the two stretches of the methylene group to be independent of each other. A further complication arises from the fact that there are two distinguishable gauche conformers for (R)-ethanols containing a CHD group: the H of the CHD group can lie on either the same or the opposite side of the molecule as the H or D of the hydroxyl group. We will refer to these forms as A and B, respectively. In scaling these two gauche forms, we found that the final scale factors were essentially the same. However, as we shall discuss below, the use of two gauche forms can account for at least one of the experimentally determined fundamentals that cannot be fit by using the trans and one of the gauche conformers alone. Our assignment of the fundamentals for each species shown in Table I11 was made in two steps: First, only those experimental frequencies whose assignment as fundamentals seemed to be most certain, based on their intensities and on the changes resulting from deuteration, were used in the fit. These assigned fundamentals were used to fit scale factors for the trans and gauche conformers. The reasonableness of the assignments was confirmed by the agreement of the calculated potential energy distribution of the SQM modes with the assignments proposed by PJ for these frequencies and by a comparison of calculated and experimental intensities. Throughout the study the calculated intensities were used in a qualitative manner only. In particular, the intensity results were used only to ensure, for example, that a weak calculated line was not fitted to a strong experimental one. We did not use intensity results more quantitatively because our previous work has shown that quantitatively accurate intensities are difficult to obtain even if basis sets significantly larger than the 6-3 1G** are Second, the calculated fundamental frequencies not assigned in the first step were compared with the table of experimental frequencies. Comparisons of the calculated and experimental frequencies together with comparisons of the calculated and experimental intensities and of the calculated potential energy distributions with the PJ assignments were used to decide which of the experimental frequencies should then be included in the fitting procedure. This process was continued until the best fit was obtained. Out of a possible total of 21 X 12 or 252 fundamental frequencies, 201 were used in the final fit of the trans conformer and 201 were also used for the gauche. The final calculated frequencies are shown in Table 111. The dipole and rotational strengths, D and R, respectively, are functions of the atomic polar tensors and atomic axial tensors. Although the calculated atomic polar tensors are always independent of the position of the origin used in their calculation, the atomic axial tensors are not necessarily so. If exact wave functions or even exact Hartree-Fock wave functions are used in the calculation of the tensors, then the rotational strengths are independent of the choice of origin even though the axial tensors themselves are origin dependent. However, if basis sets of poorer quality than the exact Hartree-Fock set are used, the choice of origin does affect the value of the rotational strength. In this work, two choices of gauge have been used. In the common origin gauge, all the axial tensors are calculated by using a single origin fixed at the center of mass of the molecule. In the distributed origin gauge, the atomic axial tensor for a given nucleus is calculated by using the equilibrium position of this nucleus as the origin.
6634 The Journal of Physical Chemistry, Vol. 93, No. 18, 1989
Dothe et al.
TABLE 111: Vibrational Frequencies (em-') of Ethanol and Its Deuterated IsotopmersoVb calcd calcd obsd trans gauche obsd trans gauche obsd trans
calcd gauche
obsd
calcd trans gauche
CH3CH20H 3676 2975 2975 2928 2928 2894
3687 2997 2988 2924 2910 2886
3687 2999 2976 2926 2917 289 1
1480 1445 1445 1380 1370
1486 1457 1440 1430 1372
1482 1451 1443 1401 1372
3676 2973 2973 2931
3687 2996 2987 2923 2164 2100
3687 2998 2975 2918 2176 2105
1460 1443 1374 1293 1157
1454 1439 1389 1301 1177
1450 1441 1386 1292 1 I85
3676 2928 2884 2229 2229 2123
3687 2912 2887 2221 2214 2102
3687 2926 2892 2223 2204 2100
1480 1385 1325 1225 1130
1484 1425 1237 1224 1127 1087
1480 1391 1344 1203 1138
3676 2233 2233 2184
3687 2222 2214 2163 2107 2094
3687 2224 2205 2174 2109 2096
1291 1172 1128 1064 1050
1314 1156 1116 1061 1046
1291 1198 1127 1065 1043
3676 2972 2972 2931 2899 2145
3687 2997 2987 2923 2898 2131
3687 2997 2975 2919 2902 2143
1460 1444 1374 1374 1333
1456 1440 1403 1358 1339
1452 1442 1390 1367 1332
3676 2898 2229 2229 2154 2120
3687 2900 2221 2214 2131 2101
3687 2905 2223 2205 2143 2099
1377 1326 1259 1135 1059
1380 1339 1220 1133 1062
1372 1331 1256 1146 1063
2975 2975 2927 2927 2893 2713
2997 2987 2924 2910 2886 2685
2999 2976 2926 2917 2891 2685
1482 1454 1445 1393 1386
1486 1456 1440 1413 1369
1482 1451 1442 1397 1367
2973 2973 2930 2713
2996 2987 2923 2685 2164 2099
2998 2975 2918 2685 2176 2105
1458 1442 1375 1192 1157 1120
1454 1439 1386 1205 1160 1111
1450 1440 1385 1187 1154 1117
2930 2882 2713 2228 2228 2124
2912 2887 2685 2221 2214 2102
2927 2892 2684 2223 2204 2100
1481 1386 1280 1133
1484 1403 1237 1138 1087
1480 1381 1279 1140 1125
2713 2229 2229 2173 2114 2098
2685 2222 2214 2163 2107 2094
2685 2223 2205 2174 2109 2096
1215 1121 1066 1048
1231 1130 1070 1046 1038 1017
1206 1132 1076 1049 1041 1034
1262 1243 1150 1064 1010
1345 1249 I105 1058 1033
880 800 427
867 787 398 293 255
863 774 418 303 262
1111 1095 99 1 930 897
1130 I098 1011 943 871
849 67 1 42 1
828 660 393 29 1 252
825 65 1 412 300 259
1059
1051
742 668
1035 1022 923
1036 1029 892
IO57 I040 1037 1017 916
740 65 1 356 287 197
737 643 373 298 200
1038 969 930 896 863
1039 963 946 884 860
736 589
723 574 352 28 7 191
720 566 368 296 195
1243 1131 1078 1004 917
1265 1132 1103, 1056 1027 908
866 717 427
855 703 395 29 2 253
847 692 414 301 260
1046 1036 993 916 878
1043 1037 982 91 1 886
743 609
732 604 354 287 194
729 596 370 296 197
1262 1150 1136 1039 894
1289 1195 1098 1048 876
885 802 423
824 787 388 263 210
853 763 412 269 218
1046
1035 994 938
819 670 420
814 660 383 258 210
797 644 406 263 217
1241 1080 1050 1030
CH3CD20H 1126 1093 1005 958 890
CD3CHzOH
CDjCD2OH 960 897 878
CHSCHDOH 1252 1126 1098, 1039 1022 920
CD3CHDOH 1043 98 1 91 1
CH3CH20D 1290 1185 1 IO6 1055 885
CH,CD,OD 958 848
958 897 832
827
CD,CH,OD 1076 1045 1036 967 808
1053 1039 1036 944 837
748 668
738 650 348 214 195
730 642 368 229 192
96 1
969
736 588
904
896 884 794
956 945 883
721 573 344 212 190
714 564 364 223 189
1062 1040 958 850
CD3CDZOD
1013
804
783
The Journal of Physical Chemistry, Vol. 93, No. 18, 1989 6635
Spectra of Ethanol and Its Deuterated Isotopomers TABLE I11 (Continued) calcd obsd trans gauche
obsd
trans
calcd gauche
2974 2974 2930 2898 2713 2143
2997 2987 2924 2899 2685 2131
2998 2975 2919 2902 2684 2144
1460 1443 1376 1344 1329
1456 1440 1393 1345 1337
1452 1441 1389 1345 1331
2897 2713 2229 2229 2149 2124
2900 2685 2222 2214 2131 2101
2905 2684 2223 2205 2142 2100
1348 1326 1143 1070 1043
1351 1338 1148 1079 1046
1346 1330 1151 1097 1046
obsd CH3CHDOD 1117 1062, 1049 976, 953 872
trans
calcd gauche
obsd
trans
calcd gauche
1148 1125 1046 943 861
1140 1126 1080, 1039 917, 960 868
836 712 424
819 702 386 260 210
824 684 408 266 217
1040 1025 969 896 800
1040 1031 966 904 806
748 619
731 603 346 213 192
722 594 366 226 190
CDpCHDOD 962 918 825
a Observed frequencies are PJ values measured in 0.1 M solution of CC1, or CS1. Calculated gauche frequencies are the averages of the values from the two gauche forms. When two frequencies are given, they correspond to gauche forms A and B, respectively.
The theory of VCD implemented for the calculations reported in this work was developed by Galwas, Fowler, and Buckingham.16 Equations for D and R and for the atomic tensors for the two choices of gauge were derived by Stephens.17 The atomic polar and axial tensors were calculated as previously described! The numerical evaluation of these tensors requires evaluation of the ground-state electronic wave functions evaluated at the equilibrium geometry and at geometries in which each atom is displaced from its equilibrium position along the three Cartesian coordinate axes. In addition, for the evaluation of the axial tensors, the ground-state wave function in the presence of an external magnetic field is required. In the present calculation, displacements of *0.005 8, were taken along each of the Cartesian coordinate axes. In calculating the atomic axial tensors, we used a magnetic field strength of 1 X lo7 G. The calculation of these wave functions and tensors was performed using the GAUSSIAN 80 program,’* modified to incorporate the effect of an external magnetic field. The 6-31G* basis set was used throughout. The calculated Cartesian atomic tensors were transformed to internal coordinate tensors by means of the atomic displacement matrix derived from the SQM force field.
Results and Discussion ZR Spectra. As previously mentioned, the electronic energies of the trans and gauche conformers calculated by using S C F wave functions are nearly degenerate; their difference is approximately 17% of kT at room temperature. Consequently, the actual relative stability of the two conformers could be reversed because of inadequacies in the S C F calculation, interactions neglected by the Born-Oppenheimer approximation, or, in the liquid phase, the neglect of intermolecular interactions. In their studies of ethanol and its deuterated isotopomers, Perchard and Josien concluded that the gauche conformer is dominant. They argued that the experimental data, especially that for CH3CH20Hand CD3CH20H, provide evidence for a coupling between the COH bending and the CH2twisting motions. This coupling is symmetry forbidden in the trans conformer because in the point group of that conformer of ethanol, C,, the two motions belong to the A’ and A” representations, respectively, and so cannot mix. Our calculations support the PJ conclusion. The root-meansquare deviation of the calculated from the experimental frequencies in the final fit of all 12 isotopomers was 19 and 15 cm-’ for the trans and for the two gauche conformers, respectively. As mentioned earlier, although two distinguishable forms of the gauche conformer for those isotopomers containing a CHD group exist, the calculated optimized force fields for the two forms differ little from each other.
Of greater importance than the lower rms deviation for the fit using the gauche force field is the fact that no individual deviation from an experimental frequency exceeds 30 cm-I, whereas for the trans force field, there are deviations for modes in several of the isotopomers exceeding 50 cm-’. The largest deviations occur in C H 3 C H 2 0 H and CD3CH20H, the two isotopomers which PJ single out to support their argument for the dominance of the gauche conformer. The deviations between the observed frequencies at 1080 cm-l in C H 3 C H 2 0 H and at 1325 cm-l in CD3CH20Hand the corresponding calculated frequenices obtained by using the trans force fields are 70 and 88 cm-I, respectively. The corresponding frequencies calculated by using the gauche force fields produce deviations of only 25 and 19 cm-l, respectively. For the gauche conformers, the vibrational mode corresponding to the experimental 1080-cm-l band is a CH3 parallel-rock + CH2 rock, while the calculated frequency corresponding to the 1325-cm-l band arises from a C O H bend CH2 twist. Both these mixtures of motions are symmetry forbidden in the trans conformer. The fact that a better fit to the observed spectra is obtained assuming that the gauche species predominates does not preclude the possibility that both species are present in significant amounts. However, the absence of fundamentals in the experimental spectra at frequencies that would be expected if the trans conformer were present in observable amounts, for example at 1150 and 1430 cm-I in the CH3CH20H spectra, leads us to believe that the gauche conformer does indeed predominate. Our conclusion that the gauche conformer predominates is supported by the interpretation of matrix isolation spectra of C H 3 C H 2 0 Hand CH3CH20D. In their matrix isolation study, Barnes and Hallam19 assumed on the basis of earlier work that the trans predominates. They argued that the ratio of the trans to gauche is 2: 1 on the basis of the relative intensities of the two components of the doublet appearing in the OH or O D region. They attributed these two components to the presence of the trans and gauche conformers, respectively. More recent work indicates that the ratio should in fact be reversed. Murto et a1.20quote the conclusions of Schiel and Richterz1in making the following argument: The S C F calculations show that the trans and gauche conformers are nearly degenerate. Their energies differ by only 0.3 kcal/mol using the 4-31G basis set. (We found an energy difference of 0.1 kcal/mol using the 6-31G**.) Since there is a statistical factor of 2 in favor of the gauche conformer (there are two gauche forms), it is more reasonable to believe that the Barnes and Hallam 2:l ratio is that of gauche to trans. The differences in the calculated frequencies between the two forms of the gauche conformers containing the C H D group are
(17) Stephens, P. J. J . Phys. Chem. 1987, 91, 1712. (1 8) Binkley, J. S.; Whiteside, R. A.; Krishnan, R.; Seegar, R.; DeFrees, D. J.; Schlegel, B.; Topiol, S.;Kahn, L. R.; Pople, J. A. QCPE; Indiana University: Bloomington, IN.
(19) Barnes, A. J.; Hallam, H. E. Trans. Faraday SOC.1970, 66, 1932. (20) Murto, J.; Rasanen, M.; Aspiala, A,; Lotta, T. J . Mol. Spectrosc. 1984, 108, 99. (21) Richter, W.; Schiel, D. Ber. Bunsen-Ges. Phys. Chem. 1981, 85, 548. Schiel, D.; Richter, W. J . Chem. Phys. 1983, 78, 6559.
+
6636 The Journal of Physical Chemistry, Vol. 93, No. 18, 1989
Dothe et al.
TABLE I V Rotational Strengths of Optically Active Isotowmers of Ethanol
frequencies, cm-' calcd obsd
gauche
R, lo4 esu2.cm2
trans
gauche A
gauche B
2972 2972 293 1 2899 2145 1374 1374 1333
2997 2975 2919 2902 2143 1390 1367 1332
2997 2987 2923 2898 2131 1403 1358 1339
(R)-CH3CHDOH -6.5 +4.3 +1.5 -2.4 -9.0 -0.72 +13.9 -1.8 +1.3 -3.6 -1.1 +6.2 -2.7 +8.2 -11.0 -1.3
2974 2974 2930 2898 2713 2143 1376 1344 1329
2998 2975 2919 2902 2684 2144 1389 1345 1331
2997 2987 2924 2899 2685 2131 1393 1345 1337
(R)-CH,CHDOD -6.3 +4.3 +1.5 -2.7 -9.1 -0.6 +13.4 -2.6 -0.08 +0.7 +1.1 -2.7 -1.5 -0.34 +6.3 +6.4 -9.5 -1.7
2898 2229 2229 2154 2120 1377 1326
2905 2223 2205 2143 2099 1372 1331
2900 2221 2214 2131 2101 1380 1339
(R)-CD3CHDOH +O. 13 -1.5 -3.7 +5.5 +4.2 -2.6 +0.24 -2.6 +0.96 -1.8 +2.4 +14.2 -13.7 -1.9
2897 2713 2229 2229 2149 2124 1348 1326
2905 2684 2223 2205 2142 2100 1346 1330
2900 2685 2222 2214 2131 2101 1351 1338
(R)-CD,CHDOD -2.4 -0.32 +0.56 -0.01 +5.5 -3.6 -2.7 +4.4 -2.8 -0.08 -1.7 +1.0 +8.3 +7.9 -2.3 -12.4
av -1.1 -0.5 -4.9 +6.1 -1.2 +2.6 +2.8 -6.1 -1.0 -0.6 -4.3 +5.9 +0.35 -0.8 -0.92 +6.3 -5.6 -0.7 +0.9 +0.8 -1.2 -0.45
obsd
+ 10.0'
-0.84b +lo.? 1.026
+
-2.97' -17.8'
trans -5.3 +4.5 +2.8 -2.6 +0.58 -0.92 -1.6 +11.2 -5.3 +4.6 +2.8 -2.3 -0.01 -0.2 +0.3 1 +11.5 f0.62
-7.8
-0.94 +3.5 -2.3 -1.6 +1.4 -3.1 +9.1
-1.4 +0.28 +0.9 +0.9 -1.4 -0.35 +8.1 -7.4
-0.58 -0.01 +3.4 -2.3 -2.3 +1.4 +11.1 +1.7
+8.1
From ref 1 1. From ref 12. slight. For nearly all the modes in the two forms, the difference between observed and calculated frequency is on the order of or less than the overall rms deviation of the fit, namely, 15 cm-I. However, in CH3CHDOH and in CH3CHDOD, there exist several differences significant enough to indicate that both forms of the gauche conformers are represented in the IR spectrum. In CH,CHDOH, for example, the calculated frequencies for the same mode in the gauche forms were 1103 and 1056 cm-I. In their Table I1 for this isotopomer, PJ show unassigned bands at 1098 and 1039 cm-' which could very well arise from the presence of both of the two gauche conformers. VCD Spectra. Rotational strengths were calculated for the trans and the two gauche conformers of the four optically active isotopomers of ethanol: (R)-CH3CHDOH, (R)-CH,CHDOD, (R)-CD3CHDOH, and (R)-CD3CHDOD. As described above, the polar and axial tensors were computed by using the Stephens formalism both in the distributed origin gauge with the origins taken at each of the nuclei and in the common origin gauge with the origin taken at the center of mass of the molecule. The appropriate SQM force fields were then used to produce the final rotational strengths. Because the absorption frequencies for the two gauche forms are practically identical for nearly all the absorption bands and because both forms are likely to be present in roughly equal amounts, we report only the average R value for the two forms. Rotational strengths for the trans and averaged gauche conformers in the distributed origin gauge of the four isotopomers are shown in Table IV. Experimental VCD data exist in the 2100-3000-~m-~region for (R)-CH3CHDOH and in the 2100-3000- and 1300-1400-~m-~ regions for CH3CHDOD.I2 The R values for these fundamentals,
derived from liquid-phase spectra, are also shown in Table IV. In comparing the results obtained using the two different origin gauges, we found that the distributed origin gauge gave significantly better results. The major differences between the gauges were in the signs of the rotational strengths of the largest bands in the stretching region and in the relative magnitudes of the rotational strengths in the mid-IR region. In all cases the distributed origin gauge results gave much better agreement with experiment. Consequently, our discussion will focus exclusively on this choice of gauge. We should note that although these results on the ethanols are in agreement with Stephens' recommendation that the distributed origin gauge be used for all VCD calculations?2 our previous study of methylthiiraneZ3showed that for this molecule the common origin gauge with the origin taken at the center of mass gave significantly better results. In comparing the experimental and calculated spectra, we first note that the most prominent features of the experimental spectra lend further support to the argument that the gauche conformers are predominant over the trans. The two strongest experimental bands are the strong positive band at approximately 2900 cm-I associated with the C*-H stretch and the strong negative band at approximately 1330 cm-l associated with a C H D bend. As Table IV shows, the R values calculated for the trans conformer are in serious disagreement with the experimental results, whereas the values calculated for the gauche conformers reproduce the two bands. Because of these results, our discussion of the com(22) Jalkanen, K.J.; Stephens, P.J.; Amos, R. D.; Handy, N. C. J . Phys. Chem. 1988, 92, 1781. ( 2 3 ) Dothe, H.; Lowe, M. A.; Alper, J. S . J. Phys. Chem. 1988,92,6246.
Spectra of Ethanol and Its Deuterated Isotopomers parison between the experimental and calculated spectra will focus on the calculated gauche conformers. We must, however, keep in mind the possibility that the trans conformer does contribute to the spectra, although to a much lesser extent. We now discuss the 2100-3000-~m-~region in greater detail. Although we were able to reproduce the large positive band at 2900 cm-I associated with the C*-H stretch found in the experimental VCD spectra of both CH3CHDOH and CH3CHDOD, we were unable to reproduce the small positive peak observed at approximately 2930 cm-' associated with a CH3symmetric stretch. Instead, we found a negative rotational strength at 2919 cm-I, the calculated frequency assigned to this peak. This calculated band differs by only 17 cm-I from the calculated band at 2902 cm-I associated with the C*-H stretch. It is difficult to obtain accurate force constant matrix elements that involve nearly degenerate modes so that the poor calculated VCD result for the 2930-cm-I band may well be the result of inaccuracies in the force field due to the mixing of nearly degenerate bands. Thus, such inaccuracies in the force field should be reflected in the potential energy distributions which describe the contributions of the various types of motions to each mode. An analysis of the potential energy distribution of the two modes lends support for this hypothesis. The PED for the 2902-cm-I mode in the A form of the gauche conformer shows a small admixture of CH3 symmetric stretch in the predominantly C*-H mode; the corresponding mode of the B form of the gauche shows negligible mixing. The rotational strength of this mode in the B form, calculated to be due to the C*-H mode alone, is small and negative. The large and positive rotational strength shown by the A form at 2902 cm-', which overpowers the small negative contribution from the B form, is, therefore, most likely due to the mixing. As additional evidence, we note that the trans conformer, like the B form of the gauche, shows no mixing in its C*-H stretching mode at 2899 cm-I and also exhibits a small and negative rotational strength. Experimental VCD spectra of the isotopomers containing the CD3 group would, we believe, provide more evidence of the importance of the mixing. Our calculations indicate that the rotational strength of the C*-H stretch band at 2900 cm-I should be much smaller for these isotopomers than for the two measured ones because there is no mixing with a CH3 stretch. The problematic calculated band at 2919 cm-l, although predominantly C H 3 symmetric stretch, shows a small contribution from the C*-H stretch. An accurate description of this mixing, which would require a better force field, is probably crucial in obtaining the small positive rotational strength at 2930 cm-l. It should also be noted that the problem in assigning the C H 3 symmetric stretch could be due to Fermi resonance between this stretch and one of the lower frequency bending modes. The calculated rotational strengths for the two small negative peaks around 2975 cm-I associated with the other two C H 3 stretches, a small positive band at 2684 cm-I (in ( R ) CH3CHDOD) associated with the OD stretch, and a small negative band at 2144 cm-l attributed to the C*-D stretch all agree with the experimental data. We must mention, however, that all of these bands feature R values that are very similar in magnitude and have opposite signs in the A and B gauche forms (see Table IV). Small changes in the force fields could change these values slightly, but enough so that their average could change sign. Such switches would not be surprising since the two forms are nearly mirror images and many of the vibrational motions are almost identical. There is some experimental evidence for a dependence
The Journal of Physical Chemistry, Vol. 93, No. 18, 1989 6637 on the environment which may be changing the force field. Pultz'* reports that the VCD spectra in the gas phase show positive bands for the CH3 stretches at 2975 cm-I. The environmental changes may in this case, however, be stabilizing the trans conformer. We also report in Table IV rotational strengths for ( R ) CD3CHDOH and (R)-CD,CHDOD. There are no experimental spectra for these isotopomers at this time. Unlike the two isotopomers discussed in the previous paragraphs, the rotational strength for the C*-H stretch at 2900 cm-I of these two isotopomers is small and negative. As was mentioned previously, because the methyl group is deuterated, the symmetric methyl stretches no longer mix with the C*-H stretch. As a result, the motion is essentially the same in each of the two gauche forms of each isotopomer (pure C*-H stretch) so that the R values are nearly equal and of opposite sign. Thus, the averaged rotational strength has a small magnitude and its sign could depend on the details of the force field. The calculated rotational strengths for the OD stretch at 2684 cm-I and the C*-D stretch near 2142 cm-I were small and positive and small and negative, respectively. These results are consistent with those found for the other two isotopomers. The rotational strengths for the CD3 stretches were also small: two positive peaks around 2229 cm-' and a negative one around 2120 cm-l. These bands are also likely to be very sensitive to the details of the force fields for the reasons outlined above. Turning now to the 1300-1400-~m-~ region, we find that experimental data exist for (R)-CH3CHDOD only so we restrict our discussion to this isotopomer. The two bands in this region are both negative: a large band near 1329 cm-I and a small one at 1376 cm-I. The calculated VCD spectrum reproduces the small negative band, placing it at 1389 cm-I, but the larger band is more problematic. The calculated spectrum in the 1325-cm-I region consists of a large negative peak at 1331 cm-I and a large positive one at 1345 cm-'. Both these modes are characterized by predominantly CHD bending motions. The calculated VCD spectrum for CD3CHDOD shows these same two peaks. We believe that the large negative experimental band in this region is most likely a superposition of two unresolved negative peaks. The near superposition of the two peaks, arising from mixtures of the same motions, suggests that the force field is most likely inaccurate in this region. We can summarize our findings as follows. Both the IR and VCD calculations provide further evidence that PJ's suggestion that the gauche conformer of ethanol predominates over the trans is correct. This predominance of the gauche conformer explains why the experimental VCD spectra show so little detail. The two forms of the gauche conformer are nearly mirror images of each other. As a result, many of the bands have rotational strengths that are nearly equal and of opposite sign for the two forms and so tend to cancel. For the ethanols, unlike the case of methylthiirane, the VCD calculation carried out using the distributed origin gauge gives better results than the calculation carried out using the origin set at the center of mass of the molecule. The present VCD calculation using the Stephens formalism in the distributed origin gauge produces spectra that are in quite good agreement with the experimental ones. Acknowledgment. We thank Dr. Vaughan M. Pultz for directing our attention to the Perchard-Josien paper and for providing us with some of his unpublished results. M.A.L. gratefully acknowledges a grant from the National Science Foundation (CHE-8519526) for financial support of this work. Registry No. CH3CH20H,64-17-5; D2, 7782-39-0.
