J . Phys. Chem. 1990, 94, 1734-1740
1734
ARTICLES Ab Initio and Experimental Raman Optical Activity in (+)-( R)-Methyloxirane P. K. Bose, P. L. Polavarapu,* Department of Chemistry, Vanderbilt University, Nashville, Tennessee 37235
L. D. Barron, and L. Hecht Chemistry Department, The University, Glasgow GI 2 8QQ. UK (Received: February 21, 1989; In Final Form: August 2, 1989)
Ab initio Raman and Raman optical activity (ROA) intensities were evaluated for methyloxirane with 6-31G, 6-31G*, and 6-31G**basis sets. The experimental depolarized, polarized, and “magic angle” Raman and ROA spectra were also measured. There is a good qualitative agreement between the theoretical predictions and the experimental observations.
Introduction
The recent availability of sophisticated quantum mechanical programs,lt2 employing the applications of coupled perturbed Hartree-Fock method^,^-^ permits detailed investigations on the higher order vibrational properties of moderate size molecules. Vibrational Raman optical activity (ROA) is one recently developed6s7branch of vibrational spectroscopy that has not been systematically investigated from an ab initio quantum mechanical perspective. ROA, which is a measure of differential Raman scattering by chiral molecules when the incident radiation is modulated between right and left circular polarization states, is expected to be useful for deducing the three-dimensional stereochemical structure of molecules in the solution phase. Recently we have reported* the a b initio predictions of ROA for (+)(R)-methylthiirane and compared them with the corresponding experimental spectra. A remarkably good qualitative agreement was noted between the theoretical predictions and experimental observations. In this paper we extend these ROA investigations to methyloxirane. In the past few years considerable attention has been paid to methyloxirane because of its suitable size for detailed theoretical analyses. The earlier calculations on methyloxirane pertain to vibrational circular dichroism (which is the infrared analogue of ROA), to infrared absorption intensities, and to vibrational analyses which included an ab initio calculationg at the theoretical minimum energy structure using a 6-31G basis set and scaled ab (1) Frisch, M. J.; Binkley, J. S.;Schlegel, H. B.; Raghavachari, K.; Melius, C. F.; Martin, R. L.; Stewart, J. J. P.; Bobrowicz, F. W.; Rohlfing, C. M.; Kahn, L. R.; Defrees, D. J.; Seeger, R.; Whiteside, R. A,; Fox, D. J.; Fleuder, E. M.; Pople, J . A . GAUSSIAN 86; Carnegie-Mellon Quantum Chemistry Publishing Unit: Pittsburgh, PA, 1986. (2) Amos, R. D.; Rice, J. E. CADPAC: The Cambridge Analytic Derivatives Package, issue 4.0, Cambridge University, 1987. (3) Frisch, M. J.; Yamaguchi, Y.; Gaw, J. F.: Schaefer, 111, H. F.;Binkley, J. S . J . Chem. Phys. 1986, 84, 5 3 1 . (4) Amos, R. D. Chem. Phys. Lett. 1986, 124, 376. ( 5 ) Amos, R. D. Chem. Phys. Lett. 1982, 87, 23. (6) Barron, L. D.; Buckingham, A. D. Annu. Reo. Phys. Chem. 1975,36, 381. (7) Barron, L. D. Molecular Light Scattering and Optical Actiuity; Cambridge University Press: London, 1982. ( 8 ) Bose. P. K.; Barron, L. D.; Polavarapu, P. L. Chem. Phys. Lett. 1989, 155, 423. (9) Polavarapu, P. L.; Hess, Jr.. B. A.; Schaad, L. J. J . Chem. Phys. 1985, 82. 1705.
0022-3654/90/2094- 1734$02.50/0
initio calculationslOJ’at corrected theoretical geometries employing 4-31G and 6-31G** basis sets. Ab initio Raman intensities for methyloxirane have not yet been investigated. The focus of the present calculations is on the vibrational Raman and ROA intensities and their comparison with the experimental observations. A recent development which greatly facilitates the comparison of ROA theory with experiment is the discovery of an experimental strategyI2 to measure ROA spectra that arise from the normalcoordinate derivatives of the electric dipole-magnetic dipole polarizability alone. This is achieved by setting the transmission axis of the Polaroid analyzer in the 90’ scattered beam at the “magic angle” of f35.26’ to the vertical. In the conventional depolarized and polarized ROA spectra, contributions from the normal-coordinate derivatives of both the electric dipolemagnetic dipole and electric dipole-electric quadrupole polarizabilities are present. These two contributions can reinforce or oppose each other depending on the nature of a given normal node.'^,'^ Since the magic-angle ROA spectra contain only the former contribution they permit a direct comparison with the ab initio predictions of electric dipole-magnetic dipole polarizability contributions. Experimental and Computational Details
The ROA spectra were measured on a multichannel Raman ~pectr0meter.l~The liquid sample was held in a micro quartz fluorescence cell and ROA spectra were obtained using a focused 600-mW argon ion laser beam at 488 nm with an effective spectral slit width (fwhh) of 6 cm-I. The earlier single-channel depolarized ROA spectrum16 was remeasured together with polarized and magic-angle ROA spectra. However, only the magic-angle ROA spectra are presented here (Figure 1) as these have the best signal quality. Geometry optimization, vibrational frequency, and intensity calculations were carried out with 6-31G, 6-31G*, and 6-31G** basis sets using the GAUSSIAN86 program.’ For the purpose of (10) Lowe, M. A.; Alper, J . S.; Kawiecki, R.; Stephens, P. J. J . Phys. Chem. 1986. 90. 41. (11) Lowe, M. A.; Alper, J. S. J . Phys. Chem. 1988, 92, 4035. (12) Hecht, L.; Barron, L. D. Spectrochim. Acta A 1989, 4SA, 671. (13) Barron, L. D.; Polavarapu, P. L. Mol. Phys. 1988, 65, 659. (14) Barron, L. D.; Hecht, L.; Polavarapu, P. L. Chem. Phys Lett. 1989, 154 .~
251
( l j j Barron, L. D.; Cutler, D. J.; Torrance, J. F. J . Raman Spectrosc. 1987, 18, 281. (16) Barron, L. D.; Vrbancich, J. Mol. Phys. 1983, 48, 833.
0 1990 American Chemical Society
The Journal of Physical Chemistry, Vol. 94, No. 5, 1990 1735
Raman Optical Activity in (+)-(R)-Methyloxirane TABLE
I: Cartesian Coordinates (A) for the Optimum Geometry of the ( R ) Configuration of Metbyloxirane
atom no.
IO
6-31G
6-31G*
atom
X
Y
Z
H
0.0 0.0 1.2676 1.8276 1.8354 -0.3309 -0.5445 -0.1750 -0.2546 -1.6265
0.0 0.0 0.0 0.9092 -0.9030 -0.9337 1.2339 2.1243 1.2708 1.2464
0.0 1.463 1 0.7304 0.643 I 0.6347 1.8753 2.1 182 1.6259 3.1627 2.0657
X 0.0000 0.0000 1.2438 1.8108 1.8160 -0.3 220 -0.5 3 9 3 -0.1847 -0.2276 -1.6241
ab initio calculations, Placzek's approximation was invoked to write the depolarized, polarized, and magic-angle ROA intensities for scattering in the 90° direction, expressed as the normalized circular intensity difference (CID), in the form
_3 _aa,, _ - _a_~ _' , ,_ - -1 aa,, w aQi
aQi
w dQj
a~',, dQi
6-31G**
Y
Z 0.0000 1.4044 0.6527 0.5574 0.5501 1.8320 2.0767 1.5753 3.1 162 2.0485
0.0000 0.0000 0.0000 0.9113 -0.9068 -0.9370 1.2338 2.1270 1.2701 1.2367
X
Y
Z
0.0000 0.0000 1.2438 1.8111 1.8163 -0.3216 -0.5391 -0.1850 -0.2268 -1.6239
0.0000 0.0000 0.0000 0.91 15 -0.9070 -0.9371 1.2337 2.1266 1.2700 1.2362
0.0000 1.4044 0.6528 0.5586 0.5510 1.8330 2.0764 1.5742 3.1158 2.0488
TABLE 11: Internal Coordinates Used for Force Constant Calculations
coord definition"
coord
definition"
coord definition'
RI R2 R3
r1,2
R11
r1,3
R18
r2.3
R19
R4
r3,4
R20
RS
r3.5
R2 1
R6
r2,6
R22
R7 R8
r2,7
R23
ri,a
R24
'r1,2, for example, is the distance between atoms I and 2; L Y ~ , is~ ,the ~ angle made by the atoms 1,3, and 4; ~ g , 7 , 2 , 6is the torsional angle between the planes of atoms 8, 7, and 2 and of 7, 2, 6. The numbering of atoms and their coordinates is given in Table I.
A*
=i 27r -
x
(3)
where CY,, is the electric dipole-electric dipole polarizability, Gha is the electric dipole-magnetic dipole polarizability, A,,y is the electric dipole-electric quadrupole polarizability, Qi is the ith vibrational normal coordinate, and X is the exciting wavelength with angular frequency w . The gradients required in eq 1-3 were w-'C',,, and obtained numerically by evaluating the tensors CY,,, A,#, at the optimized geometry and by displacing each atomic coordinate by 0.005 A. The procedure for evaluating these tensors is due to Amos,5 as implemented in the CADPAC program2 The calculations were done with the origin at the 0 atom. To evaluate the influence of gauge origin on (dG/,,/aQi), some calculations were also done with the gauge origin at the center of charge of the molecule. The CIDs were evaluated for the exciting wavelength of 488 nm used in the experiment. The theoretical Raman and ROA spectra (Figures 2-4) were simulated with a 5-cm-l bandwidth.
Results and Discussion A. Vibrational Analysis. The geometries optimized with the 6-31G, 6-31G*, and 6-31G** basis sets are presented in Table I. In order to facilitate the discussion of band assignments obtained with these different basis sets, the particular internal coordinate force constants which provide a major potential energy contribution to a given normal mode are determined. The internal coordinate definitions employed for this purpose and the abovementioned internal coordinate force constants are summarized in Tables I1 and 111, respectively. The vibrational intensities are given in Table IV. The vibrational assignments and Raman intensities obtained with the 6-31G** basis set are identical with those obtained with the 6-31G* basis set. For this reason, the discussion associated with the 6-31G* results will also apply to the 6-31G** results, even though the latter results may not be
specifically referred to in the discussion. The vibrational frequencies and assignments obtained with the 6-31G basis set are , ~ only difference being equivalent to the earlier 6-3 1G r e s ~ l t sthe that the present calculations were done using the analytical gradient method,] while the previous frequency calculationg was done numerically. The discussion in this paper is limited to the experimental bands in the 1600-100-cm-' region, since the ROA spectra in the C-H stretching region are not yet sufficiently reliable. In the 1500-1300-~m-~region of the experimental Raman spectrum, there are five bands at 1498, 1460, 1450, 1403, and 1365 cm-l, which were correlatedg with the 6-31G theoretical bands of 1676, 1652, 1641, 1592, and 1567 cm-I, respectively. The first three theoretical bands are respectively due to a CH2 bending and two methyl antisymmetric bending motions and the frequency order of these three modes is also supported by the 6-3 1G* calculations. There are some differences, however, in the sources for potential energy contributions. For instance, the CH2 bending mode of 1697 cm-' in the 6-31G* calculation reveals a significant potential energy contribution from the ring C-C stretching force constant while the corresponding mode of 1676 cm-' in the 6-31G calculation does not. The experimental Raman bands at 1403 and 1365 cm-l were correlated9 with the 6-31G modes of 1592 and 1567 cm-l which originate from the methyl symmetric bending and a C*-H bending motion, respectively. This frequency order is reversed in the 6-3 1G* predictions, where the corresponding 1597- and 1549-cm-' modes are due to C*-H bending and methyl symmetric bending motions, respectively. From a comparison of the relative Raman intensities of these two modes with those observed in the experiment, it would appear that the 6-31G* results, and therefore the 6-3 1G* vibrational assignments, might be preferable. Corresponding to the intense Raman band at 1262 cm-l in the experimental spectrum, the ab initio calculations also predict an intense Raman band with a frequency of 1389 cm-l in the 6-31G calculation and 1415 cm-' in the 6-31G* calculation. All calculations suggest that this band originates from the ring C-C stretch coupled with an H-C*-0 bending motion. On the low-frequency side of the above-mentioned intense band, the experimental Raman spectrum consists of four bands at 1164, 1140, 1135, and 1101 cm-' grouped together and an isolated band at 1020 cm-I. The relative intensity pattern for the first
-
-
-
-
1736 The Journal of Physical Chemistry, Vol. 94, No. 5, 1990
Bose et al.
I
WAVENUMBERS
266 50.10i
396
588
776
966
1156
I
: 1346
1536
1726
Figure 2. Ab initio Raman (top) and R O A (bottom) spectra corresponding to the experimental spectra in Figure 1, obtained with the 6-31G basis set. See text for the discussion on the 1218- and 1139-cm-I bands.
I
c II-
c cm-'
200
300
LOO
500
600
700
800
900
1000
110t
I
I
I
I
I
1
I
I
I
I
I
,
WAVENUMBERS 266
396
5B6
776
966
1156
1346
1536
1728
Figure 3. Ab initio Raman (top) and ROA (bottom) spectra corresponding to the experimental spectra in Figure 1, obtained with the 6-31G* basis set. See text for the discussion on the 1246- and 1147-cm-' bands.
0
WAVENUMBERS
cm-' 730
800
903
1000
'100
1200
1300
1600
1500
Figure 1 . Experimental magic-angle Raman and ROA spectra in the (A) 100-1 100-cm-l and (B) 600-1600-cm-' regions. Raman (top) and ROA (bottom) spectra were obtained with the transmission axis of the analyzer set at -35' to the vertical.
four bands is not well reproduced by the 6-3 1G calculation where the corresponding bands are at 1318, 1296, 1276, and 1218 cm-'. The relative Raman intensities of the corresponding 6-3 1G* bands at 1322, 1300, 1277, and 1246 cm-I are also not in good agreement with the experimental relative intensities. From an analysis of the ROA spectra and infrared absorption intensities, it appears that the calculated bands corresponding to the last two of the five experimental bands discussed here might have an interchanged frequency ordering (vide infra). From the theoretical mode de-
266
398
586
776
968
1156
1346
1536
1728
Figure 4. Ab initio Raman (top) and ROA (bottom) spectra with normal coordinates obtained from the 6-3 1G basis set and Cartesian polarizability derivatives obtained from the 6-31G* basis set. See text for the discussion on the 12 18- and 1139-em-' bands.
scriptions, the five bands discussed in this paragraph originate from hydrogen bending motions; but there are significant differences between the 6-31G and 6-31G* predictions on the compositions of internal coordinate displacements for a given experimental band. The strongly polarized Raman band at 946 cm-I in the experimental spectrum does not derive a unique assignment from the calculations. On the basis that the corresponding strongly polarized intense Raman band at 870 cm-' of methylthiirane was predicted* to have a major contribution from the exocyclic C-C
Raman Optical Activity in (+)-(R)-Methyloxirane TABLE 111: Force Constants Providing Major Potential Energy Contributions' to the ab Initio Normal Modes in Methvloxirane freq, cm-I major PE contributor
The Journal of Physical Chemistry, Vol. 94, No. 5, 1990 1737 TABLE IV: Ab Initio Vibrational Frequencies and Intensities for Methvloxirane'
~~
intensities Raman
6-3 1G Basis Set 1676 1652 1641 1592 1567 1389 1318 1296 1276 1218 1 I39 1049 995 872 806 440 399 210
F14, FIS,
F14,1S, Fll,
F12
F 2 4 ~ F22,24 F22r F22,23, F23 F19, F203 F21r F7 F16r F13 Fl3, F3
F24, F22,24r F23.24 F23, F14, F l l , F13
F23, F23.24r F24 F121 FII, F 2 0 F22, F I I , F19, F24r FIS, F14, FI, F3 Fl, F 2 F17 F17r,F18,
torsion
F12r F22,23, F20 F2r F7 F2, F7r F14.1S
F22
6-3 1G* Basis Set 1697 1641 1628 1597 1549 1415 1322 1300 1277 1246 1 I47 1080 995 952 860 442 397 221
F14, F3r F I S , F l l ? F12, F24. F22.24. F23,24 F223 F22.23, F23 F16, F7r F13 F213 F20, F16, F19
F13, F3 F24, F23,24* F23, F22,24,
Fll, FIS F19, F23, F7 F12, Fll F22, F203 F22.23
F,
6-31 1686 1625 161 1 1585 1534 1410 1315 1295 1270 1240 1 I40 1078 989 950 857 442 397 220
Fl8
torsion
'There is some arbitrariness in limiting the number of force constants that appear in this table. The criterion used here is that those force constants which provide potential energy contributions that are approximately within 50% of the most dominant contribution are considered, but the total number is limited to six. The force constants are listed in the decreasing order of their contributions. F, represents the force constant associated with ith internal coordinate;FiJ represents the interaction force constant associated with internal coordinates i and j . stretch, one might expect a similar origin for the 946-cm-' band of methyloxirane. The corresponding 6-31G* band at 1080 cm-I does have a contribution from the exocyclic C-C stretch, but it is the 6-31G* band at 860 cm-' that has a primary potential energy contribution from the exocyclic C-C stretching force constant. But this is contradicted by the 6-3 1G prediction that the corresponding lower frequency band at 806 cm-l is due to a C-0
freq, cm-I 1676 1652 1641 1592 1567 1389 1318 1296 1276 1218 1139 1049 995 872 806 440 399 210
+
45a2 3p(a)2 6-3 IG Basis Set 2.52 1.66 10.5 7.86 9.18 6.89 3.35 2.03 2.97 1.09 16.2 5.15 2.76 0.8 1 1.54 0.97 4.87 3.24 6.06 4.01 0.46 0.15 7.85 1.45 8.66 3.37 7.49 5.54 10.7 7.1 1 1.13 0.33 0.32 0.24 0.07 0.05
IR 1.66 8.56 5.86 12.0 5.79 3.56 1.60 4.93 2.84 10.6 4.68 8.04 1.86 58.9 4.25 4.41 10.0 0.83
1697 1641 1628 1597 1549 1415 1322 1300 1277 1246 I I47 1080 995 952 860 442 397 221
6-31G* Basis Set 1.83 0.82 8.32 6.17 7.74 5.80 5.15 2.90 2.43 1.16 15.3 4.70 3.25 1.41 1.55 1.16 2.93 2.00 3.06 2.25 1.01 0.53 5.38 1.61 3.27 2.45 6.21 4.39 8.66 4.41 0.68 0.15 0.4 1 0.26 0.08 0.06
7.99 4.35 2.79 17.1 5.73 6.37 7.76 0.95 5.28 9.35 8.46 21.5 2.92 48.6 6.59 6.18 4.22 0.69
1686 1625 1611 1585 1534 1410 1315 1295 1270 1240 1 I40 1078 989 950 857 442 397 220
6-31G** Basis Set 1.79 0.68 7.66 5.64 7.27 5.44 5.57 3.17 2.32 1.10 15.2 4.69 3.22 1.40 1.50 1.12 2.85 1.88 2.80 2.07 1.06 0.57 5.20 1.63 3.10 2.31 6.13 4.31 8.69 4.32 0.64 0.14 0.43 0.26 0.08 0.06
8.84 4.55 3.25 16.7 4.73 6.69 7.62 0.87 5.30 9.45 9.45 21.0 2.95 47.4 6.41 6.30 4.21 0.68
'Raman intensities are given in units of A4/amu; IR intensities are given in km/mol. stretching motion. In the 6-31G* predictions the exocyclic C-C and a C - O stretching motion are so strongly mixed that the bands at 1080 and 860 cm-' cannot be separately assigned as one exocyclic C-C stretch and one C-0 stretch. This is not so in the 6-31G calculations. The experimental Raman band at 892 cm-I corresponds to the 6-31G* band at 995 cm-l, which is due to a CH, bending motion. This assignment is also supported by the corresponding 6-3 1G band at the same frequency. The two experimental Raman bands at 824 and 742 cm-l were assigned9 to the C-0 stretches, based
Bose et al.
1738 The Journal of Physical Chemistry, Vol. 94, No. 5, 1990 TABLE V: Exwrimental and Theoretical ROA Parameters for (+)-(R)-Methyioxirane" ab initio 6-3 IG basis set
6-31G* basis set
A, x 104
*
z
X
freq, cm-l
*
A ~ 104 X
cm-I
z
X
freq, cm-I
1676 1652 1641 1592 I567 I389 1318 1296 1276 I 139' 1218' 1049 995 872 806 440 399 210
2.8 (2.7) -3.1 (-3.1) 0.4 (0.6) 0.7 (3.0) 5.4 (4.3) 1.2 (0.7) 3.8 (3.0) -0.6 (-1.9) -7.9 (-7.2) 27.4 (25.3) -3.1 (-2.8) -4.1 (-4.1) 5.1 (4.8) 3.2 (3.0) -1.6 (-1.4) 1.0 (0.9) 9.2 (11.0) 3.3 (2.1)
2.0 (2.0) -2.3 (-2.3) 0.3 (0.5) 0.5 (3.0) 4.6 (3.4) 1.5 (0.8) 11.4 (9.5) -1.0 (-2.1) -7.0 (-6.3) 39.0 (36.9) -3.0 (-2.7) -7.7 (-7.5) 4.5 (4.0) 2.8 (2.6) -1 .O (-0.9) 0.5 (0.5) 8.1 (9.8) 3.9 (2.1)
3.1 (3.0) -3.5 (-3.5) 0.5 (0.7) 0.8 (3.0) 5.7 (4.6) 1.1 (0.7) 2.1 (1.6) -0.4 (-1 3 ) -8.2 (-7.6) 24.5 (22.4) -3.1 (-2.8) -3.5 (-3.5) 5.3 (5.1) 3.4 (3.2) -1.8 (-1.7) 1.2 (1.0) 9.7 (11.5) 3.1 (2.2)
1697 1641 1628 1597 1549 1415 1322 1300 1277 1 147' 1246' 1080 995 952 860 442 397 221
9.9 -8.7 1.8 7.4 2.5 0.9 9.4 3.8 -20.9 3.7 -3.3 -3.5 8.3 3 .O -0.2 -5.6 9.1 2.9
9.6 -7.1 1.7 7.0 1.6 1.o 10.3 2.5 -16.9 6.0 -3.5 -4.6 5.4 2.6 0.6 -10.8 8.6 4.3
10.0 -9.4 1.9 7.5 2.8 0.9 9.2 4.3 -22.4 3.0 -3.3 -3.3 9.5 3.2 -0.5 -4.7 9.3 2.2
1498 1460 1450 1403 1365 1262 1164 1140 1135 1101 IO20 946 892 824 742 419 360 200
freq,
experimental A, x 104
*
z
X
2.4 -3.4 2.4 1.7 b
1.0 -2.7 0.8 3.1 b
2.8 -2.0 2.8 4.3 c c c -1.3 -2.0 3.4 -5.5
c
c
-2.9 -3.6 3.4 -6.2 c 4.0 3.2 -1.4 3.5 1.6 +b
C
4.0 -3.3 -3.8 1.2 -5.1 8.3 4.6 1.5 -3.1 5.0d 2.5d +b
C
1.5 2.6 -2.0
f f
f
"A, with (Y = z , x, and * correspond to the CIDs given by eq 1-3. These values given in parentheses were obtained with the origin at the center of the charge of the molecule, while the others correspond to the origin at the 0 atom. *Weak feature. 'Possible polarization artifact contribution. dReference 16. 'Frequency ordering for these theoretical bands is changed as discussed in the text. !Not measured.
on the 6-31G calculations, and we adhere to those assignments. The next two Raman bands at 419 and 360 cm-l in the experimental spectrum were assignedg to the C-C*-CH3 and 0C*-CH3 bending motions, respectively. The 6-31 G* predictions suggest that the higher frequency band has a major contribution from the 0-C*-CH3 bending motion, and the lower one has a major contribution from the C-C*-CH3 bending motion. Despite the difference in the source for a major contribution to these bands, both calculations agree with the experimental observation that the higher frequency band is more polarized than the lower frequency band. In summarizing the comparison of vibrational band assignments derived from different basis sets, the following observations are useful. The relative Raman intensities predicted in the 6-31G* calculation, in particular for the bands corresponding to the experimental ones at 1403,1365, 1164, 1140,1135, 1101,and 892 cm-I, are perhaps an improvement over those predicted in the 6-31Gcalculation. For the experimental bands at 946,742,419, and 360 cm-I the predictions of assignments by the 6-31Gand 6-31G*calculations differ. The reason for these differences can be traced to the C - O bond lengths predicted (Table I) in the two calculations. In the 6-31G*calculation, the C - 0 bond lengths are predicted to be -0.06 8, shorter than those predicted in the 6-31Gcalculations. Since the C-0 bond lengths obtained in the 6-31G calculation are closer to the experimental values,17 it is reasonable to believe that the assignments associated with C-0 motions are more likely to be accurate in the 6-31Gcalculation. Similar effects were found for trans-2,3-dimethylo~irane.~~ B. Raman Optical Activity. With this background information on the vibrational assignments, we turn our attention to the ROA spectra. We have computed ROA intensities with 6-31G and 6-31G*basis sets but not with the 6-31G**basis set (vide infra). This is because the mode assignments and Raman intensities obtained with the 6-31G**basis set are found to be identical with those obtained with the 6-31G*basis set (see Tables 111 and IV). Therefore, it is unlikely that there will be any significant differences in the ROA predictions with these two basis sets. The 6-31GROA calculations were done with the gauge origin at the oxygen atom and also at the center of charge of the molecule. Both calculations predict identical ROA sign patterns (17) Swalen, J. D.; Hershbach, D. R. J . Chem. Phys. 1957, 27, 100. Creswell, R. A.; Schwendeman, R. H. J . Mol. Specirosc. 1977, 64, 295. (18) Black, T. M.; Bose, P. K.; Polavarapu, P. L.; Barron, L. D.; Hecht, L. J . Am. Chem. Soc., in press.
(Table V) and suggest that the ROA predictions are not significantly affected by the choice of gauge origin. The same conclusion was1* reached for trans-2,3-dimethyloxirane. In the 1500-1300-cm-' region of the experimental ROA spectra (Figure 1) a negative-positive-positive feature, seen from the high-frequency side, is associated with the bands at 1460,1450, and 1403 cm-I. The same pattern is also seen in the earlier single-channel depolarized ROA spectrum.I6 The polarized ROA spectrum (not shown) is also similar except for an additional positive ROA band at 1498 cm-I. The corresponding four bands in the computed ROA spectra (Figures 2 and 3) show similar behavior in both calculations with the exception that the ROA intensity associated with the first higher frequency band is prominent in the theoretical spectra but not in the experimental depolarized and magic-angle spectra. The band at 1365 cm-' in the experimental depolarized ROA spectrum has a weak negative intensity (positive for the ( S ) enantiomer).I6 The corresponding feature is not clear in the magic-angle ROA spectrum (Figure I), while in the polarized ROA spectrum it is uncertain due to the possibility of an S-shaped artifact. The corresponding band in the 6-31G*calculation at 1549 cm-I yields a weak positive ROA (see Figure 3) while that in 6-31Gcalculation at 1567 cm-l yields (see Figure 2) a significantly larger positive ROA. For the Raman band at 1262 cm-I the experimental ROA spectra do not provide unambiguous signs due to the possibility of polarization artifacts. Both 6-31Gand 6-31G*calculations predict a positive ROA for this band. The Raman bands at 1164,1140,and 1135 cm-l are associated with positive negative and negative ROA features, respectively, in the depolarizedI6 spectra. This sign pattern is correctly reproduced by the calculations using the 6-31G basis set. The magic-angle ROA spectrum shows the same behavior except that the 1164-cm-I band is dominated by an S-artifact. The bands at 1101 and 1020 cm-' have positive and negative signs, respectively, in both the magic-angle (Figure 1) and the depolarizedI6 ROA spectra. The polarized experimental ROA features of these bands (not shown) have the same signs but significantly larger magnitudes. Both the 6-31Gand 6-31G*calculations predict the opposite signs for these two bands. The reason for the discrepancy in the experimental and theoretical ROA signs for these two bands is probably due to the interchanged frequency ordering predicted in the ab initio calculations. This hypothesis is supported by the comparison of infrared absorption intensities (Table IV). In the experimental infrared spectrum9 the absorption intensities of bands
The Journal of Physical Chemistry, Vol. 94, No. 5, 1990 1739
Raman Optical Activity in (+)-(R)-Methyloxirane
TABLE VI: Evaluation of tbe Basis Set Influence" on Cartesian Polarizability Derivatives and Normal Modes
6-3 1G* /6-3 1G Raman
6-3 1G/6-3 1G* Raman
6-31G**/6-31G Raman
6-3 lG**/6-31G* Raman
~~
1676 1652 1641 1592 1567 1389 1318 1296 1276 1139' 1218b 1049 995 872 806 440 399 210
2.10 8.90 7.81 2.63 2.77 14.31 2.24 1.50 3.47 0.54 4.85 5.74 6.34 6.34 6.89 0.94 0.23 0.09
1.50 6.66 5.86 1.66 1.16 4.48 0.77 0.96 2.52 0.20 3.25 0.96 2.69 4.64 4.43 0.24 0.16 0.05
2.7 2.1 -3.9 -3.0 1.0 0.9 2.8 2.5 4.0 3.3 1.5 1.6 3.3 7.5 -0.6 -0.9 -10.6 -9.3 12.4 20.2 -2.6 -2.6 -3.3 -7.4 6.0 6.0 3.0 2.7 -1.1 -0.6 -0.2-1.5 11.9 10.6 4.7 8.9
1697 1641 1628 1597 1549 1415 1322 1300 1277 1147' 1246' 1080 995 952 860 442 397 221
2.69 9.62 9.15 6.19 2.79 17.69 5.27 2.04 3.45 1.04 3.84 8.73 3.87 7.72 10.72 0.81 0.51 0.12
0.94 7.14 6.86 3.29 1.34 5.49 1.82 1.46 2.49 0.49 2.75 2.76 2.88 5.79 5.89 0.18 0.35 0.07
7.6 8.1 -7.1 -5.6 0.9 1.0 5.4 5.0 3.6 2.7 0.5 0.8 8.9 12.0 0.3 -0.6 -18.1 -14.0 5.6 8.0 -3.0 -3.0 -2.5 -3.8 6.9 4.1 3.0 2.3 -1.0 -0.2 -3.8 -7.6 7.4 6.8 0.0 -0.6
1686 1625 1611 1585 1534 1410 1315 1295 1270 1140' 1240' 1078 989 950 857 442 397 220
2.81 9.26 9.07 6.89 2.81 17.47 5.29 2.06 3.46 1.12 3.73 8.63 3.80 7.67 10.76 0.80 0.52 0.12
0.85 6.82 6.79 3.78 1.38 5.49 1.85 1.45 2.48 0.53 2.68 2.82 2.84 5.75 5.87 0.17 0.35 0.07
7.5 8.5 -8.5 -6.7 1.5 1.3 5.3 5.8 3.2 2.3 0.8 0.5 9.0 12.1 0.3 -0.6 -18.7 -14.6 4.0 6.5 -2.6 -2.7 -2.3 -3.5 6.7 4.0 3.1 2.4 -1.0 -0.2 -4.3 -8.4 7.4 6.8 -0.0 -0.7
1.87 8.06 7.68 5.74 2.44 15.14 3.27 1.55 2.95 1.08 2.97 5.30 3.23 6.16 8.72 0.67 0.42 0.08
0.73 5.94 5.75 3.30 1.17 4.69 1.44 1.15 1.98 0.57 2.19 1.64 2.41 4.36 4.40 0.14 0.26 0.06
9.9 10.2 -10.2 -8.4 2.4 2.2 7.8 7.2 2.1 1.2 0.9 1.0 9.6 10.5 3.8 2.4 -21.4 -17.5 2.6 5.0 -2.9 -3.1 -3.3 -4.3 8.1 5.3 3.1 2.6 -0.2 0.6 -6.0-11.7 9.0 8.6 2.7 4.2
" Raman intensities are in units of A4/amu; A,, with a = * and z corresponding respectively to the magic-angle and depolarized CIDS given by eq 1 and 3. Due to space considerations A, values are not listed. Frequency ordering for these bands is changed as discussed in the text.
'
at 1104 and 1023 cm-l (corresponding to the Raman bands under discussion at 1101 and 1020 cm-I) are in the approximate ratio of 1:2. The corresponding 6-31G bands at 1218 and 1139 cm-I give the infrared absorption ratio as 2:l. In the 6-31G* and 6-31G** calculations the corresponding bands (at 1246 and 1147 cm-' and at 1240 and 1 140 cm-l, respectively) have nearly equal infrared intensities. Thus if we physically interchange these two theoretical bands, the theoretical ROA and infrared absorption predictions would give much better agreement with the corresponding experimental observations. The experimental ROA associated with the 946-cm-I band is not clearly established in any of the measurements due to the polarization artifacts. The experimental ROA features for the next three bands at 892, 824, and 742 cm-' in the magic-angle and depolarized spectra are positive, positive, and negative, respectively. The corresponding theoretical ROA bands in the 6-31G calculation at 995, 872, and 806 cm-l have an identical sign pattern. The 6-31G* theoretical bands at 995,952 and 860 cm-' also have the same sign pattern, but the ROA magnitude predicted for the 860-cm-l band is significantly less (see Figure 3) than that observed for the corresponding experimental band. Also the sign reversal on going from depolarized to polarized ROA predicted for the 6-31G* theoretical band at 860 cm-l does not match with the experimental observation where the 742-cm-' band has the same sign in the depolarized and polarized ROA spectra. The experimental Raman bands at 419 and 360 cm-' have the same ROA signs, being positive for the ( R ) enantiomer [negative16 for the (S)enantiomer]. The 6-31G calculations also yield positive ROA signs for the corresponding bands at 440 and 399 cm-I. The 6-3 l G * calculation, however, yields a bisignate feature for the corresponding bands at 442 and 397 cm-l. We mentioned earlier that, although both calculations predict relative depolarization ratios correctly, the assignments obtained in the 6-3 lG* calculation differ from those obtained in the 6-31G calculation. Since the 6-31G ROA predictions are in agreement with the experimental observations, it appears that the 6-3 1G band assignments are to be relied upon for the two bands under consideration. For the methyl torsion vibration both the calculations predict a positive ROA. The corresponding experimental ROA is not clearly established in the depolarized spectrum and is probably positive in the magic-angle spectrum (Figure 1). Overall, the 6-3 1 G theoretical predictions are in remarkably good qualitative agreement with the experimental ROA spectra. It should be mentioned that we have not given emphasis to the comparison of the magnitudes of ROA intensities because it is not pragmatic to expect quantitative agreement between experimental and theoretical ROA intensities at the S C F level of the theory employed. There are also uncertainties in the experimental
magnitudes due to the potential polarization artifacts in the state-of-the-art instrumentation. If we can identify the vibrational modes that would show configurationally consistent ROA features in related molecules then the application of ROA to problems in molecular stereochemistry can be established. The ROA features associated with the ring C-C and exocyclic C-C stretching modes are unlikely to be suitable for this purpose, because these modes are strongly polarized and the associated ROA features in methyloxirane are not well-defined. The hydrogen bending motions appearing in the 1200-900-~m-~region are very sensitive to molecular environment and have different compositions in methyloxirane and methylthiirane. They cannot be individually identified in a unique manner in different molecules. The ROA features associated with the C-0 stretches in methyloxirane and with the C-S stretches in methylthiirane* are, however, configurationally consistentI3 and could therefore be useful for stereochemical studies. C. Basis Set Effects on Raman Intensities. The reliability of theoretical Raman or ROA intensities depends on two independent quantities: the normal-mode compositions and the Cartesian polarizability derivatives. The accuracy of normal-mode compositions, which depends on the accuracy of force constants, does not ensure the accuracy of the Cartesian polarizability derivatives and vice versa. When the agreement between the theoretical and experimental Raman intensities is not satisfactory it is not clear if the disagreement should be attributed to the uncertainty in the normal-mode compositions or to that in the Cartesian polarizability derivatives, or to both. Two plausible approaches can be envisioned to resolve this problem. The normal-mode compositions, which translates into evaluating the force constants, can be determined by using a higher level of theory: alternatively, the Cartesian polarizability derivatives can be evaluated by using a higher level of theory, while evaluating the normal-mode compositions at a lower level. It is not clearly established as to which one of these two approaches is to be preferred when both normal-mode compositions and Cartesian polarizability derivatives cannot be evaluated at a higher theoretical level. In order to obtain a better understanding of this aspect, we have performed mixed calculations; i.e., normal coordinates obtained with one basis set are combined with Cartesian polarizability derivatives obtained with another basis set. For example the calculation labeled 6-31G/6-31G* (Table VI) uses normal coordinates obtained with the 6-31G basis set at the 6-31G optimum geometry and Cartesian polarizability derivatives obtained with the 6-31G* basis set at the 6-31G* optimum geometry (both in the same orientation of Cartesian axes). If these results are not significantly different from those obtained entirely with the 6-3 1G basis set it would mean that the Cartesian polarizability derivatives
J . Phys. Chem. 1990, 94. 1740-1745
1740
obtained with the 6-31G and 6-31G* basis sets are not significantly different. On the other hand if the 6-31G/6-31G* results are not significantly different from those obtained entirely with the 6-31G* basis set then it would mean that the normal mode displacements predicted by the 6-31G and 6-31G* basis sets are not significantly different. Four different calculations of this type are presented in Table VI, where the normal coordinates obtained with the 6-31G, 6-31G*, and 6-31G** basis sets are combined with the Cartesian polarizability derivatives obtained with the 6-3 1G* and (or) 6-31G basis sets. The relative intensities in the 6-31G/6-31G* Raman and ROA spectra (shown in Figure 4) are essentially identical with those in Figure 2 which were obtained entirely with the 6-31G basis set. From overlaying Figure 4 on Figures 2 and 3, one finds that for some bands intensity variations to a certain degree arise from basis set influence on Cartesian polarizability derivatives as well as on normal-mode compositions. However, the relative intensity patterns in Figure 4 resemble more closely those in Figure 2 than those in Figure 3. The overall picture emerging from these calculations and those is that the relative Raman and on trans-2,3-dimethyIoxirane1* ROA intensities are influenced much more by the variations in normal-mode compositions when polarization functions are added to the 6-31G basis set than by the associated relative variations in the Cartesian polarizability derivatives. In other words, the
changes in structural parameters resulting from the addition of polarization functions lead to significant change in force constants (and therefore normal-mode compositions) and only to less important changes in Cartesian polarizability derivatives. A similar observation was noted for the hydrogen stretching vibrations of several ring molecules including methyloxirane. Exceptions from the above general conclusion are the 6-31G** bands at 1295,857, and 220 cm-I (and corresponding 6-31G* bands at 1300,860, and 221 cm-I) where the associated ROA signs are influenced by the variations in Cartesian polarizability derivatives. This observation is useful from a practical viewpoint since one can use higher levels of theory, such as the Merller-Plesset perturbation scheme, to determinelJJg the normal-mode compositions, whereas formulations for evaluating the Cartesian polarizability derivatives analytically at the Merller-Plesset level are not yet a~ailable.’~~~’~
Acknowledgment. Grants from SERC, NIH (GM29375), NSF (CHE8808018), Vanderbilt University, and the Deutsche Forschungsgemeinschaft (11102-He 1588/1-1) are gratefully acknowledged. (19) Pople, J. A.; Krishnan, R.; Schlegel, H. B.; Binkley, J. S. Znf. J . Quantum Chem. 1979, 13, 225.
Mechanisms of Deactivation of the Low-Lying Electronic States of 2,2’-Bipyridlne E. Castellucci, L. Angeloni, Dipartimento di Chimica, Uniuersitci di Firenze, Italy
G . Marconi,* E. Venuti, Istituto F.R.A.E. del C.N.R..Bologna, Italy
and 1. Baraldi Dipartimento di Chimica. Uniuersitci di Modena, Italy (Received: March 6, 1989; In Final Form: June 30, 1989)
The photophysical properties of 2,2’-bipyridine have been investigated in different solvents by means of lifetime measurements on the picosecond scale, quantum yield temperature dependence, and CS-INDO CI calculations. Both experimental and theoretical results indicate that in inert solvents the very low fluorescence quantum yield of this molecule is due to a very effective intersystem crossing to a local triplet state. The picture emerging from these data helps to gain insight into the elusive photophysical behavior of this compound.
Introduction Like other azaaromatics, 2,2’-bipyridine (hereafter bpy) shows a tiny fluorescence emission in inert solvents which can be hardly detected. In fact, it has been claimed that the molecule does not fluoresce in inert solvents, whereas its protonated adducts luminesce, the amount and type of emission depending on the pH of the solutions.’ HarrimanZfirst reported on the fluorescence of bpy in cyclohexane and stressed its very low quantum yield and subnanosecond lifetime. Phosphorescence occurs at low temperature with a rather large quantum yield. Other difficulties encountered while characterizing the photophysics of the isolated molecule arise from its ability in complexing ions like ZnZ+,giving species with a very high quantum yield of fl~orescence.~ Moreover, emission and absorption studies as a function of the
concentration in different solvents4 have shown that formation of aggregates can very likely take place. In the same range of concentration experiments of twephoton excitation have also been rep~rted.~ In this paper we report the results of a reinvestigation of the photophysics of bpy based on fluorescence lifetime measurements with picosecond resolution in different solvents, on the temperature dependence of the fluorescence quantum yield, and on semiempirical calculations on the relevant potential curves of the excited states of the free molecule. A critical analysis of previously reported preliminary lifetime measurements in cyclohexane6 is also made. (4) Agresti, A,; Bacci, M.; Castellucci, E.; Salvi P. R. Chem. Phys. Lett. 1982, 89, 324.
(1) Henry, M.
S.;Hoffman, M. Z. J . Phys. Chem. 1979, 83, 618 (2) Harriman, A. J . Photochem. 1978,8, 205. ( 3 ) Kotlicka, J.; Grabowski, Z. R. J . Photochem. 1979, 1 1 , 413.
0022-3654/90/2094- 1740$02.50/0
( 5 ) Castellucci, E.; Salvi, P. R.; Foggi, P. Chem. Phys. 1982, 66, 281. (6) Angeloni, L.; Castellucci, E.; Salvi, P. R. J . Mol. Slruct. 1986, 141, 433.
0 1990 American Chemical Society
