1793
J . Phys. Chem. 1993,97, 1793-1799
Vibrational Raman Optical Activity in Substituted Oxiranes P. L. Polavarapu' Department of Chemistry, Vanderbilt University, Nashville, Tennessee 37235
L. Hecht and L. D. Barron' Chemistry Department. The University, Glasgow GI 2 8QQ. United Kingdom Received: September 1 1 , 1992
Experimental and ab initio theoretical vibrational Raman optical activity (VROA) spectra of methyloxirane and truns-2,3-dimethyloxiranein the 200-1 500 cm-I region are presented. The experimental spectra were measured with high signal-to-noise ratio on a new generation ROA instrument. The theoretical spectra were calculated using different basis sets for normal modes and for cartesian polarizability derivatives, the best predicted spectra being those obtained with normal modes calculated at the MP2 level.
-
Introduction Raman optical activity in vibrational transitions, known as vibrationalRaman optical activity (VROA), has been theoretically formulatedl and experimentally observed2 in the early 19709. However, as the effect is very small (usually one part in loo00 units of ordinary Raman cross sections, which by themselves are weak) and the phenomenon is one of higher order perturbations, the experimental measurements remained difficultand theoretical predictions appcared hopeless. Recent developments have changed this gloomy situation and the course of VROA spectroscopy: it was recognized that VROA can be p r e d i ~ t e d ~from - ~ first principles using ab initio quantum theoretical methods and at about the same time the VROA instrumentation was improved to the point that VROA spectra can be obtained6 with excellent signal-to-noiseratio rather routinely. Also different polarization schemes for ROA measurements have been formulated and impl~mented.~As a result important chemical problems are beginningto be addressed now using VROA spectroscopy. Since optical activity is being probed in the vibrational transitions and each vibrational transition of a chiral molecule in principle can exhibit ROA, the information content in a VROA spectrum contains thecompletestereochemistryof a moleculein the solution phase. Extraction of this information from a given experimental spectrum is not quite straightforward and in this context the reliability of theoretical models employed plays a key role. The ROA spectra of methyloxirane and trans-2,3-dimethyloxirane have been reported and analyzed before,4J using an older generation ROA instrument and modest level theoretical calculations. Now the quality of both experimental and theoretical spectra is improved significantly. The experimentalROA spectra for methyloxirane and trans-2,3-dimethyloxiranehave been measured with a new generation ROA instrument with greatly improved signal quality; and the theoretical predictions obtained with higher theoretical level normal modes. Experimental" ITheoretical Details
The ROA spectra were obtained on a right-angle scattering version of a new multichannel Raman spectrometer developed at Glasgow? A brief dcscription is as follows. The incident laser beam from an Ar+ laser, at 488 nm with -750-mW power at the sample, was modulated between right and left circular polarization states using a KD'P electro-optic modulator at 1 Hz. The depolarized light scattered in the 90° direction with polarization in the scattering plane was collected and dispersed on to a CCD detector by a 0.25 meter spectrograph (JYHR250S). A holographic notch filter (Kaiser Optical Systems) enabled the
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spectra to be measured down to 100 cm-1. The detector was a peltier cooled backthinned CCD camera (Wright Instruments Ltd.) with a quantum efficiency in exof 80%. The light scattered during the left circular polarization excitation was subtracted from that during the right circular polarization excitationand this differencespectrum representsthe depolarized VROA, 1: - I,". For comparison of magnitudes with the theoretical predictions this difference is normalised with the correspondingsum, 1: I,",and the normalised circular intensity difference is represented as Az. Typical exposure time was 0.8 s and total data acquisition time 1 h. The experimental difference and sum spectra are displayed in Figures 1 and 2 for both enantiomers of methyloxirane and of trans-2,3-dimethyloxirane. Excellent mirror image quality is seen for the two enantiomeric spectra and reflects the high quality of ROA spectra one can now obtain on the Glasgow ROA instruments. The ab initio quantum theoretical predictions of Az were obtained from the expressiong
+
where
(3)
by evaluating the polarizability derivatives aaa,/aQ,w1aG'.,s/ dQ, and aA,,,/aQ numerically. Here Q is the vibrational normal coordinate; a,# is the electric dipole-electric dipole polarizability, G'a,3 is the electric dipole-magneticdipole polarizability and A a ~ ?is the electric dipole-electric quadrupole polarizability. These tensor derivatives were obtained in the static limit by evaluating the tensors at the equilibrium geometry and at the geometries displaced by 0.005 A along each cartesian coordinate. The procedure for obtaining the Gla,3tensor in the static limit is due to Amos10 as implemented in the CADPAC programll which simultaneously evaluates the Uag and && tensors. The above mentioned tensor derivatives were obtained with 6-31G and 6-31G* (or 6-31G**) basis sets12-14at the respective fully optimized geometries. Vibrational frequencies
0022-3654/93/2097-l793$04.00/0 Q 1993 American Chemical Society
Polavarapu et al.
1794 The Journal of Physical Chemistry, Vol. 97, No. 9, 1993 I
]4 . 5 ~ 1 0 ~
ROA
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I
I
I
I
I (R)-(+)-Methyloxirane
MP2(6-31G')/6-31(3'
-
(R)-(+)-methyloxirane
:] '
-??N
ROA
4.5~10~
-
- -
0-'
A
v v
~
KN
200
400
600
800
1000 1200 1400
1600
wavenumbers .
I
300
,
.
.
700
.
.
.
15'00
1100
Figure 1. Experimental depolarized Raman sptctrum (top) and ROA spectra for (-) (bottom) and (+) (middle) enantiomers of methyloxirane (neat liquid).
]3 . 1 ~ 1 0 ~
1
ROA
LTN
Y
(2R,3R)-( (2R,3R)-( +)-dimethylorirane +)-dimethylorirane
300
700
1100
Figure3. Comparisonof experimental and theoretical depolarizedRaman and ROA spectra for (R)-(+)-methyloxirane. The theoretical spectra were obtained k t h MP2(6-31G*) normal modes and 6-31G' cartesian polarizability derivatives. The experimental spectra in Figure 1 were d i g i t i d and replotted here. The ab initio frequencies were scaled by 0.95 to provide a bet* match with the experimental band positions. Lorentzian ,bend sham with IO-cm-I half-width (at half-height) were used for the theoretical spectra.
set were combined with the normal modes obtained from different basis sets. In the designation for these calculations, the basis set used for the normal modes is listed first, that for the cartesian polarizability derivatives is listed later and they are separated by a slash. For example in the calculation designated as 6-31G/ 6-31G*, the normal modes obtained from6-31G force constants were combined with the cartesian polarizability derivatives obtained from 6-31G* basis set at the respective optimum geometries, @ping the same orientation of the reference axes. The predicted spectra were simulated with Lorentzian band shapes. The highest level theoretical spectra, in the set of calculations reported here, are compared to the corresponding experimental spectra in Figures 3 and 4 where the theoretical frequencies are multiplied by 0.95 to bring them closer to the experimental frequencies. The normalized VROA magnitudes are given in Tables I and 11. The correspondingvalues reported earlier45 have to be multiplied by 0.529177 due to an error in the unit conversion in the previous calculations. The vibrational assignmentsderived from the MP2(6-3 1G*)calculationsare also listed in Tables I and 11.
1500
Figure 2. Experimental depolarized Raman spectrum (top) and ROA spectra for (-) (bottom) and (+) (middle) enantiomers of trans-2,3dimethyloxirane (neat liquid).
and normal modedescriptionswere obtained with these basis sets and also at the post-SCF level using electron correlation via the MP2 methodI5 and 6-31G* basis set. This later calculation is abbreviated as MP2(6-3 lG*). Toevaluate the basis sot influence on normal modes and on carttsian polarizability derivativetensors separately, two types of mixed calculations are performed. In one type of calculation, the normal modes obtained from a given basis set were combined with cartesian polarizability derivatives obtained with different basis sets. In a second type of calculation, the cartesian polarizability derivativesobtained from a given basis
The experimental data for the (+)-enantiomers and the theoretical data for the (R)-configurations are used in the following discussion. Also the theoretical frequencies cited are those obtained from the MP2(6-31GS) calculation and scaled down by 0.95, unless stated otherwise. Metaylowirrac The vibrational assignments obtained from the MP2(6-31G*) calculation are Quite similar to those obtained from the 6-3 1G*calculation.5 Thedepolarid Ramanspectrum predicted in the MP2(6-31GL)/6-31G+ calculation (Figure 3) compares quite favorably with the corresponding experimental spectrum, with two exceptions. First, the calculated relative intensity in the ls00 an-'region is some what higher than the observed. Second, the substructure in the intensity pattern in
, The Journal of Physical Chemistry, Vol. 97, No. 9, 1993 1795
Optical Activity in Substituted Oxiranes
(2R,3R)-(+)-2.3-dimethyloxirane
n
MP2(6-31 G*)/6-310"
* I I
I
200
I 400
I
600
I 800
I
I
I
1000
1200
1400
wavenumbers
Figure4. Comparisonof experimentaland theoretical depolarized Raman and ROA spectra for (2R,3R)-(+)-fr(1ns-2,3-dimethyloxirane,The theoretical spectra were obtained with MP2(6-31G*) normal modes and 6-31G**Cartesian polarizability derivatives. The experimental spectra in Figure 2 were digitized and replotted here. The ab initio frequencies were scaled by 0.95 to provide a better match with the experimental band positions. Lorentzian band shapes with IO-cm-I half-width (at halfheight) were used for the thmretical spectra.
the 1150 cm-I region does not compare very well in the experimental and theoretical spectra. In the 1400-1500-cm-I region, a positive-negative-positive triplet is seen in the experimentalROA spectrum, a pattern which is correctly reflected in the theoretical spectrum (Figure 3). The weak positive experimental ROA band at 1502 cm-I is predicted to originate from the methylene bend coupled with the ring C-C stretch. The presence of a ring C-C stretch contribution at this rather high frequency is unlikely to be a quantum mechanical artifact, since in molecules such as 1,4-dioxaspiro[2.2]pentanes, which contain two oxirane rings fused through a central carbon, the antisymmetric ring C-C stretch was found16 to be responsible for the observed vibrational band at 1650 cm-*. The negative ROA band at 1460 cm-I is predicted to arise from a methyl asymmetric bend and the positive ROA at 1410cm-*is predicted to arise from a methine bend. The methyl symmetric bending mode is predicted to give weak Raman and ROA signals at 1385 cm-1. The experimental band at 1375cm-I with correspondingly weak Raman and ROA matches this prediction. The predicted positive ROA sign however is at variance with the observed negative sign. The experimental Raman band at 1270cm-I is associated with negative ROA. However the corresponding theoretical mode at 1264cm-I, which is due to a stcond methine bending motion, has positive ROA in clear disagreement with the experimental observation. Themodescontributingin the 1100-1200cm-'regionoriginate from methylene and methyl groups. The experimental ROA spectrum has a well defmed positive-negative-positive triplet which is predicted to arise from four theoretical modes at 1164, 1143,
1119 and 1102 cm-I. At first sight the theoretical predictions appear not to match with the experimental ROA pattern. However if the frequency order of the two modes at 1119 and 1102 cm-I is interchanged, then the simulated spectrum would have a positive-negative-positive pattern as observed; also the substructure of the Raman band profile in this region of the experimental and theoretical spectra would compare well. This provides a good example for the way ROA data can help refine the vibrational band assignments. The twoweakRaman bandsat 1028and952cm-l havenegative ROA, as do the corresponding theoretical modes at 1017 and 956 cm-I. The former mode is due to the methyl group while the second one is associated with the exocyclic C-C stretch coupled with the ring C - 0 stretch. The Raman band at 899 cm-I, with positive ROA, is also predicted correctly and is due to the methylene group. The positive-negative ROA couplet centered at -800 cm-1 is associated with the ring C-0 stretches. The theoretical modes at 838 and 759 cm-l are predicted to exhibit positive and negative ROA, respectively, which compare well with the experimental observation. The two skeletal bending modes at 398 and 354 cm-1 are predicted to have opposite signed ROA, while the corresponding experimental bands at 419 and 382 cm- have the same positive ROA sign. Clearly, the higher frequency mode at 398 cm-I is predicted to have the wrong ROAsign. Finally themethyl torsion mode is predicted to have weak Raman intensity with positive ROA. The experimental Raman spectrum shows weak band at -220 cm-I, which is presumably due to the methyl torsion mode. The corresponding experimental ROA is not seen. In the 1500-100 cm-I region discussed thus far, the ROA sign discrepancy between ab initio predictions and experimental observations occurs for the modes at 1385, 1264 and 398 cm-I. Except for these differences, the overall ROA and Raman predictions agree with the experimental observations. Basis Set Dependence. In the previous discussion the theoretical calculations pertained to the highest level calculation that we could perform. It is important to know how the predictions vary with basis set chosen for force constants and for cartesian polarizability derivatives. This information can be derived for methyloxirane from the comparison in Figures 5 and 6. The depolarized Raman spectra for different choices of basis set combinations are shown in Figure 5 and the corresponding ROA spectra are shown in Figure 6. For example, 6-31G and 6-31G/ 6-31G* calculations used the same 6-31G force constants but used the polarizability derivatives from 6-31G and 6-31G* basis sets, respectively. A comparison of these two calculations would reveal the influence of basis set dependence on the cartesian polarizability derivatives. Similarly, a comparison of 6-3 1G and 6-3 1G*/6-3 1G calculations would reveal the influence of basis set dependence on the normal modes, since these calculations employed the same 6-3 1G cartesian polarizability derivatives, but the force constants were obtained from 6-31G and 6-31G* basis sets, respectively. This analysisindicates that theappearence of the Raman as well as the ROA spectra is not significantly influenced by changing the basis set from 6-31G to 6-31G* for polarizability derivatives; the overall intensities are generally reduced in the latter calculation. When the basis set is varied for force constants, the band positions are influenced significantly and the visual appearance of the relative spectral pattern changes. Therefore, the need for establishing reliable normal modes, and hence force constants, is apparent. Although the negative ROA sign observed for the 1270-cm-1 band has not been reproduced in any of the calculations, the appearance of Raman and ROA spectra in the 800-1350-~m-~ region (unsealed) is definitely improved in relation to the experimental spectra by the MP2(63 1G*) normal modes. Admittedly, the polarizability derivativeshave been evaluated with only two moderate size basis sets (6-31G and 6-31G') and
1796 The Journal of Physical Chemistry, Vol. 97, No. 9, 1993
Polavarapu et al.
TABLE I: Vibrational Frequencies md ROA Parameters for (R)-(+)-Methyloxiraw MP2 (6-31G*) freq 1588 1561 1546 1498 1458 1330 1225 1203 1178 1160 1070 1006 935 882 799 419 373 218
Scaled" 1509 1483 1469 1423 1385 1264 1164 1143 1119 1102 1017 956 888 838 759 398 354 207
6-31Gb 3.7 -2.1 0.2 2.0 1.2 0.7 10.1 -5.3 1.o -2.4
A~ x 104 6-31G*
-4.0 -2.1 2.9 1.9 -0.6 -1.7 3.5 5.4
4.2 -2.7 0.6 2.9 0.6 0.7 6.8 -6.6 2.5 -2.8 -4.1 -2.3 3.7 1.9 -0.3 -3.1 4.7 7.6
experimentd freq 1502 1460
104 2.5 -2.2
assignmente CH2 scissor C W H 2 str CHI asym bend CH3 asym bend H-C* bend + CH3 sym bend + C*-CH3 str CHI sym bend + H-C* bend H-C*- bend + C W H 2 str CHI rock + H-C* bend CHI rock CH3 rock + H-C* bend C*-CHa str CH2 wag CH2 rock CH3 rock CH3 rock + CH2 twist H-C* bend C - 0 str C*-CH3 str CH3 rock CHI twist C*-0 str C W H 2 str C*-0 str C - 0 str O-C*-CH3 bend C-C*-CH3 bend C-C*-CH3 bend O-C*-CH3 bend CHI torsion
AzX
1410 1375 1270 1174 1139 1107
6.8 -3.1 -0.6 6.4 -3.5 3.0
1028 952 899 833 750 419 382
-7.7 -0.9 6.0 3.4 -1.9 3.5 3.1
+
+ +
+
+ + +
+ +
+ +
a Frequencies obtained by scaling the MP2 (6-31G*) frequencies by 0.95. Az values obtained with MP2 (6-31G*) normal modes and 6-31G Cartesian polarizability derivatives. Same as in (b), but with 6-31G' Cartesian polarizability derivatives. Experimental Az values are the averages of measurements on (+) and (-) enantiomers. e Obtained from MP2 (6-31G') normal modes; C* represents the ring carbon atom attached to the CHI group.
TABLE Ik Vibrational Frequencies and ROA Parameters for (zR,3R)-2,3-(+)-~thyIoxiraw MP2 (6-31G*) SYm A
B A
B A
B A
B A A
B A
B B A
B A A
B B A
B A
B A
freq (cm-1) 1577 1560 1555 1545 1536 1471 1467 1410 1325 1228 1207 1186 1172 1078 1072 lo00 936 853 776 473 469 289 254 218 196
scaled" 1498 1482 1477 1468 1459 1397 1394 1340 1259 1167 1147 1127 1113 1024 1018 950 889 810 737 449 446 275 24 1 207 186
6-31Gb 9.9 -9.9 4.7 0.6 2.2 10.0 -2.9 4.6 -1.1 21.7 -4.2 -2.6 -23.8 -0.0 4.1 4.4 0.9 0.5 0.0 14.0 -0.3 -2.8 4.6 -14.3 17.8
A~ x 104 6-31G**
13.1 -11.5 4.4 1.1 2.5 12.3 -2.8 4.1 -1.1 14.1 -3.7 -3.8 -37.4 1.9 2.3 6.2 0.7 0.7 0.2 15.3 -0.5 -3.0 5.5 3.4 20.8
experimentd freq A~ x 104 1494 2.5 1461 -3.6 1446 1428
1.9 1.5
1385 1338 1258
-4.0
1158
3.6
1116
2.2
1019 96 1 888 814 723 48 1 458 292 269
-5.1 2.2 1.7 -0.5 1.9
204
25.6
-2.5 -4.4
0.8 5.4
assignmente C*-C* str + H-C* bend CH3 asym bend CH3 asym bend CH3 asym bend CH3 asym bend CH3 sym bend CHI sym bend H-C* bend H-C* bend C*-C* str H-C* bend CH3 rock H-C* bend CHI rock + C*-C str C*-C str + CH3 rock C*-C str C*-0 str CH3 rock CH3 rock + H-C* bend CHJ rock H-C* bend C*-0 str CH3 rock C*-C str C*-C* str CH3 rock C*-0 str 0-C*-C bend C*-C*-C bend C*-C*-C bend 0-C*-C bend CH3 torsion CH3 torsion
+ +
+ + + +
+
+
Frequencics obtained by scaling the MP2 (6-31G*) frequencies by 0.95. Azvalues obtained with MP2 (6-31G*) normal modesand 6-3 1G Cartesian polarizabilityderivatives. Sameasin (b), butwith 6-31G** Cartesianpolarizabilityderivatives. Experimental Azvaluesaretheaverageaof measurements on (+) and (-)enantiomers. Obtained from MP2 (6-31G*) normal modes; C* represents the ring carbon.
higher level basis sets need to be investigated. This could not be accomplished due to the finite nuclear displacement procedure that had to be employed for the polarizability derivatives. When analytic methods become available for the derivatives of GIa6, a more complete evaluation of basis set dependence for cartesian polarizability derivatives can be attempted. b.lrp.2,3-Dimetbyloxir8neoxirme. The vibrational assignments obtained from the MP2(6-31G*) calculation aresomewhat different from the ones reported earliersJ7 using the 6-31G basis set. The depolarized Raman spectrum obtained in the MP2(6-3 1G*)/ 6-31G** calculation compares reasonably well with the corresponding experimental Raman spectrum with one major exception: the relative intensity predicted for the bands grouped at
-1500 cm-1 is nearly two-fold larger than observed. The comparison of corresponding ROA spectra reveals some discrepancies as discussed below. On the high frequency side, a positive-negative-pitive triplet seen in the experimental ROA spectrum is reproduced in the predicted ROA spectrum (Figure 4). The positive ROA at 1494 cm-' is predicted to arise from the ring C-C stretch coupled with a methine bend. The remaining negative-positiveportion of the triplet is predicted to originate from four methyl bending modes. The two methyl bending modes at 1397 and 1394 cm-I have oppositely signed overlapping ROA with a net positive features in the simulated spectrum. The correspondingexperimental ROA band is negative. Similarly the weak negativeexperimentalROA
Optical Activity in Substituted Oxiranes I
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The Journal of Physical Chemistry, Vol. 97, No. 9, 1993 1797
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Depolarized Raman
Aethyloxirane
I
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MP2(6-31 G')/6-31 G'
d
L
*
h
4
MP2(6-31G')16-31 G'
I
MP2(6-31G')/8-310
MP2(6-31G')16-31 G
6-31G"16-31G' A
A*
6-31G"16-31 G
* 8-31 G'16-310
3-310'
Y
Y C
8-31G18-31G' A
hL.
6-31G
c 200
I
(R)-Methyloxlrane u 400
600
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800
1000
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Is00
Depolarized ROA]
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200
400
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800
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1200
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1600
wavenumbers Figure 5. Basis set dependence for depolarized Raman spectra of methyloxirane. The ab initio frequencies were not scaled. See text for the description of the notation used. Lorentzian bandshapcs with 5-cm-I half-width (at half-height) were used for the theoretical spectra.
wavenumbers Figure 6. Basis set dependence for depolarized ROA spectra of (R)methyloxirane. The ab initio frequencies were not scaled. See text for thedescriptionof thenotation used. Lorentzian band shapes with 5-cm-' half-width (at half-height) were used for the theoretical spectra.
at 1338 cm-l is incorrectly predicted by the theoretical mode at 1340 cm-I that is due to a methine bend. The next Raman band at 1258 cm-I has strong negative ROA. The corresponding mode at 1259 cm-I, which is also a methine bend, has the correct ROA sign but its relative intensity does not match with experiment. The two modes at 1167 and 1147 cm-I give rise to the band at 1158 cm-I. These two modes are due to methine bending motions and have oppositelysigned ROA with a net positive ROA. This is also the sign seen for the experimental band at 1 158 cm-1. The neighboring band at 1 116 cm-I also has positive ROA, but this is not reproduced in the theoretical spectrum. This band is associated with two theoretical modes at 1 127 and 1 1 13 cm-I, the former due to methyl groups and the latter due to exocyclic C-C stretch, and both modes are predicted to have negative ROA in contradictionto the experimentalobservation. The same problem is present for the negative ROA band at 1019 cm-l which is associated with two modes at 1024 and 1018 cm-I with positive ROA. The next three Raman bands at 961,888 and 814 cm-I have positive ROA as do the corresponding theoretical modes at 950,889 and 810 cm-l which are associated with methyl bend, ring C - 0 stretch and ring C-C stretch respectively. Another mode originating from the ring has weak positive ROA at 737 cm-I, but the corresponding experimental ROA band at 723 cm-1 is negative. Thus there are sign discrepancies between the experimental and theoretical predictions for five of the modes discussed in this paragraph, namely those at 1127, 1 1 13, 1024, 1018 and 737 cm-I. Thediscrepancyassociatedwiththesemodes might partly be ascribed to the inaccuracies in the normal mode descriptions. The two skeletal bending modes at 449 and 446 cm-I give rise to positive ROA, despite the opposite signs associated with individual modes. The correspondingobserved Raman (or ROA) band is not resolved into two individual components, and gives
the appearance of a single band. The observed ROA is positive here, as predicted. The next four modes are due to skeletal bends and methyl torsions with frequencies 275,241,207 and 186 cm-1. Three experimental bands, corresponding to these four modes, are seen at 292,269 and 204 cm-I. While the experimental ROA here is positive, three theoretical modes are predicted to have positive ROA and the one at 275 cm-l is predicted to have negative ROA. If the frequencies of these calculated modes were closer as in the experimental spectra, then this negative ROA would not be present in the simulated spectrum. The experimental band at 204 cm-I with positive ROA is associated with the symmetric methyl torsion and the utility of methyl torsion ROA for configurational determination has been discussed elsewhere.I8 Bash Set Dependence. As in methyloxirane, changing the basis set for calculating the cartesian polarizability derivatives does not seem to alter the appearance of the simulated Raman and ROA spectra (Figures 7 and 8); the overall Raman intensities are generally reduced when polarization functions are added to the 6-31G basis set. The variation of basis set for normal modes does significantly affect the predicted spectra. The basis sets for Cartesian polarizability derivatives were limited to 6-3 1G and 6-3 1 G** for practical reasons, but when analytic methods for the derivatives of GIap become available larger basis sets should be investigated. The discrepancies noted between theoretical ROA predictions and experimental observations for the experimental region of 1000-1200 cm-1 persist in all the calculations (Figure 8). This seems to indicate that either the normal modes obtained even in the fairly large MP2(6-31GS) calculation are not completely satisfactory or the Cartesian polarizability derivatives have to be evaluated with larger basis sets than those employed here. This is somewhat surprising since the predictions obtained for methyloxirane, at approximately the same level of theory, appear to be satisfactory in general. Also, the vibrational circular
1798 The Journal of Physical Chemistry, Vol. 97, No. 9, 1993 frans-2.3.dimethyloxirane
Polavarapu et al.
Depolarized Raman MP2(6-31 G')/6-31 G"
A
MP2(6-310')/6-31G"
A
- 6-31Q"/6-310
I
6-310"
,
6-31016-310"
,
6-31016-310"
I
a
.II
6-310
(2R,3R)-trans-2.3-dlmethyloxlrane
200
wavenumbers Figure 7. Basis set dependence for depolarized Raman spectra of frons2,3-dimethyloxirane. The ab initio frequencies were not scaled. Sec text for the description of the notation used. Lorentzian band shapes with IO-cm-' half-width (at half-height) were used for the theoretical spectra.
dichroism spectra for trans-2,3-dimethyloxiranecould be. reproduced17satisfactorily with a simple 6-3 1G basis set, but the same basis set is not completely satisfactory for predicting the ROA spectra here. The predicted Raman spectra for dimethyloxirane show clear improvement,in relation to the experimentalspectrum, on going from the simple 6-3 1G basis set calculation to the fairly large MP2(6-31G*)/6-31G** calculation. This improvement is presumably due to the improved quality of the normal modes at the MP2(6-31G*) level, although the differences in the experimental and predicted ROA make the accuracy of the normal mode descriptionsand (or) of cartesian polarizability derivatives suspect. It is possible that the theoretical Raman and ROA predictions for dimethyloxirane can be brought to closer in agreement with the corresponding experimental observations (a) by scaling the ab initio force constants using the procedure suggested by Pulay and coworkers19 and Blom and Altonazo;or (b) by using larger basis sets. However the resulting improvements must be.evaluated21.2z simultaneouslyfor absorption and circular dichroism intensities as well. Moreover it would be appropriate to include the spectroscopic data for isotopomers in evaluating these effects. The ROA studies for deuterium substituted methyloxirane and dimethyloxirane are currently in progress. We hope to evaluate these effects in a future study by including the data on isotopically substituted oxiranes.
conclusions Depolarized ROA spectra with excellent signal-to-noise ratio for methyloxirane and trans-2,3-dimethyloxiranepermit a definitive test for the ab initio model of ROA intensities. The predicted ROA spectrum for methyloxirane is in satisfactory agreement with experiment. A similar, satisfactory agreement is not obtained for dimethyloxirane,wen though the calculations employed the same level of theory for both molecules. Further theoretical studies on dimethyloxiraneusing larger size basis sets are warranted. Limited basis set dependence studies indicate
400
600
800
I
Rod
1000 1200 1400 1600 1800
wavenumbere Figure& Basis set dependence for depolarized ROA spectra of (2R,3R)rranss-2,3-dimethyloxiranc. The ab initio frequencies were not scaled. Sec text for the description of the notation used. Lorentzian band shapes with IO-cm-I half-width (at half-height) were used for the theoretical spectra.
that the normal mode compositions are more sensitive than the cartesian polarizability derivatives to the choice of basis set. Further studies emphasizing a larger variety of higher quality basis sets are required to confirm this observation.
A c L n o r r ~ t Grants . from National Science Foundation (CHE 8808 18), the Science and Engineering Research Council, the Wolfson Foundation and the Deutsche Forschungsgemeinschaft (Habilitandenstipendium I1 C1-He 1588/3-1) are gratefully acknowledged.
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