J. Phys. Chem. 1995,99, 835-843
835
Experimental Measurement and ab Initio Calculation of Raman Optical Activity of L-Alanine and Its Deuterated Isotopomers Gu-Sheng Yu, Teresa B. Freedman,* and Laurence A. Nafie* Chemistry Department, Syracuse University, Syracuse, New York 13244
Zhengyu Deng and Prasad L. Polavarapu Department of Chemistry, Vanderbilt University, Nashville, Tennessee 37235 Received: July 27, 1994; In Final Form: October 20, 1994@
Backward scattering in-phase dual circular polarization (DCPI) Raman optical activity (ROA) spectra of L-alanine, ~-alanine-2-& ~ - a l a n i n e - 3 , 3 , 3 4in H2O and DzO solution in the 800- 1700 cm-l frequency region are presented. Ab initio calculations of normal modes and Raman and ROA intensities have been carried out with a 6-31G* basis set and inclusion of a solvent reaction field for stabilization of the zwitterionic forms. Excellent agreement is found between experiment and calculation for both Raman and ROA spectra. However, some discrepancies are noticed between the experimental and theoretical ROA intensities for alanine-2-4.
Introduction Over the past two decades, Raman optical activity (ROA) has emerged as a spectroscopic technique with potential for unique stereochemical ROA is defined as the circular intensity difference (CID) between left and right circularly polarized incident and/or Raman scattered radiation. The corresponding parent Raman intensity is referred to as the circular intensity sum (CIS). In recent years, the availability of modem technology, principally high sensitivity charge coupled device (CCD) detection systems, has further advanced ROA as a promising approach to the study of biologically significant molecules in solution.2-16 Due in part to the complex nature of both experiment and theory, a variety of ROA measurements are p o ~ s i b l e , ’ ~and - ~ ~some have been implemented.29-34 By using different scattering geometries and modulation methods, experimental observations have been made of incident (ICP)29and scattered circular polarization (SCP),30 and magic angleu ROA for right-angle scattering. Similarly, ICP?’ SCP?2 and in-phase ( D C P I ) ~and ~ out-of-phase (DCPn)” dual circular polarization ROA have been carried out for backward scattering, and one instance of ICP35ROA for forward scattering has been reported. Experimental and theoretical studies have shown clear ROA intensity advantages for backward scattering, and now both unpolarized ICP and depolarized DCP1 ROA measurements have become standard methods for routine ROA studies on biological molecules. Although the general expressions for ROA intensities show differences for these two measurements, they become equal in the far-fromresonance case.1~6,*3,16,20,u~31,33 Since the backward scattering DCPI ROA has less Raman scattered intensity due to its depolarized nature, the noise introduced from photon counts in the detector is less than that of the unpolarized ICP form for the same collection optics, and hence the signal-to-noise ratio for DCPr ROA is enhanced. In addition, since polarized bands have greatly reduced intensity in backscattering DCP1 ROA, artifacts in general are more easily ~ o n t r o l l e d .Thus, ~ ~ for a variety of reasons we have elected to carry out our ROA measurements for biological molecules using the backscattering DCP1 experimental configuration.
* To whom correspondence should be addressed. @Abstractpublished in Advance ACS Absrrucrs, December 1, 1994.
The interpretation of experimental ROA spectral from a fundamental viewpoint has been difficult due to the complexity in the phenomenological quantities involved. Recent recognit i ~ that n ~ROA ~ intensity can be predicted from first principles and the subsequent implementation of an ab initio algorithm for ROA predictions have resulted in more confident interpretations of the experimental spectra. Tests on several molecule^^^-^^ lead to the conclusion that the theoretical method employed provides reliable predictions. The vibrational assignments for alanine and its deuterated isotopomers in solution have been previously proposed based on the infrared and Raman solution- and solid-phase spectra, in conjunction with a Urey-Bradley normal coordinate analysis.44 More recently, Barron and co-workers have carried out ab initio calculations of the Raman and ROA intensities of isolated zwitterionic L-alanine with 6-3 1G and 6-31G* basis sets.7 Good agreement was found between the experimental and theoretical parameters at the 6-31G* level in the lower frequency region. However, the calculated ROA signs of several bands did not correspond to experiment, and the calculated frequency separations for the antisymmetric and symmetric amino deformations and antisymmetric and symmetric carboxylate stretches were much larger than the experimental values. These discrepancies most likely arise from omitting the interaction between the zwitterion and the aqueous solvent. To simulate such solvent effects, the Onsager reaction field model has been developed, in which a molecule is placed in a spherical cavity surrounded by a continuous medium of dielectric constant .5?5-48 This field has been incorporated into self-consistent ab initio geometry optimization and frequency calculations, as a self-consistent reaction field (SCRF) option in the calc~lation.4~ Although ab initio calculations of ROA intensities have shown good agreement with experiment for a number of molecule^,^^^^-^^ a systematic exploration of the sources of strong ROA intensity, in terms of contributions from specific types of nuclear motions and the importance of coupling among such motions, has not previously been addressed. In contrast, for the companion chiroptical spectroscopy, vibrational circular dichroism (VCD), descriptive mechanisms for intensity generation, such as the coupled oscillator mechanism, have proven valuable for spectral interpretati~n.~~ The availability of a
0022-3654/95/2099-0835$09.00/00 1995 American Chemical Society
836 J. Phys. Chem., Vol. 99, No. 2, 1995
Yu et al.
number of deuterated isotopomers of alanine makes this molecule ideal for investigating contributions to ROA intensity from specific group vibrations. We report here a comparison of experimental ROA measurements on L-alanine isotopomers with refined ab initio ROA intensity calculations that incorporate an improved SCRF geometry and force field for the alanine zwitterion.
Experimental Section Aqueous solutions of L-alanine (Sigma Co.) and two isotopomers, ~-alanine-2-d1and ~-alanine-3,3,343(MSD Isotopes, Inc.) were prepared by dissolving sample crystals into deionized distilled water or DzO (the deuteration ratio is up to 95% for the samples in D20 solutions). Backscattering DCPI Raman and ROA spectra were recorded on the instrument constructed at Syracuse University, which has been described in detail e l ~ e w h e r e . The ~ ~ ~sample ~ ~ ~ ~solutions ' were filtered into a quartz cell through a 0.2 p m pore-size disposable filter, and sample impurity fluorescence was quenched in a 1 W 514 nm laser beam until the Raman scattering background stabilized. All the spectra were obtained for a single enantiomer with 15 cm-' spectral resolution. Ab initio calculations of geometries and vibrational frequencies were performed with the 6-31G* basis set by using the Gaussian 92 program package$9 running on an HP 700 workstation in the New York State Center for Advanced Technology in Computer Applications and Software Engineering (CASE) at Syracuse University. To stabilize the zwitterionic form of alanine as occurs in aqueous solution, the Onsager reaction field (SCRF) was included in the calculation to simulate solvent effects. A dielectric constant of 80 was used for the aqueous solvent calculations. The spherical volume of the reaction field was reduced by 0.5 8, in radius from the default recommended value of 3.7 A, which gave better agreement with experimental frequencies in the amino deformation region. Geometry optimization and frequency calculation required about 30 and 4 CPU h, respectively. The expressions for backward scattering DCPI Raman (CIS) and ROA (CID) intensities can be written in terms of tensor invariants in the far-from-resonance appro~imation:',~~ CIS: CID:
g(180") + g(180")
e(
180") = 24@(a)'
CALCULATED RAMAN
~
0 60
- 800
1io0
1600
WAVENUMBERS (cm-l) Figure 1. Observed backscattered DCPI Raman and ROA spectra of 1.60 M L-alanine in H20 and their ab initio simulated spectra. The total exposure time for observed spectra is 123.2 h.
I
4
n
I
(1)
+
- e(180") = 32(K/~)[3/3(G')~
B(A>21 (2) where the superscripts and subscripts on the intensity I indicate the polarization state of the incident and scattered radiation, respectively, K is a constant, c is the speed of light, is the anisotropic polarizability invariant, /3(G ')2 is the magnetic dipole anisotropic optical activity invariant, and /3(A)z is the electric quadrupole optical activity invariant. The tensor invariants were evaluated from the first derivatives of the polarizability and optical activity tensors as described previ0us1y.~~The polarizability and optical activity tensors were calculated with the 6-31G* basis set but without the solvent reaction field. These calculations were carried out at Vanderbilt University using a Cray Y-MP at the Pittsburgh Supercomputer Center, with the employment of the geometry and force constants provided by the group at Syracuse University. The descriptive assignments of each normal mode were obtained by visualizing the calculated nuclear displacements and animating the normal modes with HyperChem Version 3.0 from Autodesk Inc., running on a 486 IBM compatible computer.
800
1200
1600
WAVENUMBERS (cm-l) Figure 2. Observed backscattered DCPI Raman and ROA spectra of 1.50 M L-alanine in DzO and their ab initio simulated spectra. The total exposure time for observed spectra is 70.4 h.
Results Experimental backscattering DCPl Raman and ROA spectra of L-alanine, ~-alanine-2-&,and ~-alanine-3,3,3-d3in HzO and D20 solution are compared with calculated spectra in Figures 1-6. Since the calculated ab initio frequencies are typically higher than the observed frequencies, a linear frequency scaling factor of 0.9 has been applied to the calculated spectra in the figures. In the simulated spectra, calculated intensities were converted to Lorentzian bands with a half-width of 7 cm-l for all modes. The intensities of calculated Raman and ROA spectra have been scaled by adjusting the simulated ROA spectra to be comparable in magnitude to the observed and employing that same scale factor for the corresponding calculated Raman spectrum. The experimental and calculated frequencies, intensities, and mode assignments in the 1700-700 cm-' region are compiled in Tables 1-6. The rocking motion of the amino
J. Phys. Chem., Vol. 99,No. 2, I995 837
Raman Optical Activity of L-Alanine
CALCULATEDRAMAN 0 15
1200 1600 WAVENUMBERS (cm-l) Figure 3. Observed backscattered DCP1 Raman and ROA spectra of 1.25 M ~-alanine-2-d,in HzO and their ab initio simulated spectra. The total exposure time for observed spectra is 98.0 h.
8iO
800
1200
44 CALCULATED ROA
aoo
1
3
1 zoo
1600
1200
1 600
WAVENUMBERS (cm-l) Figure 5. Observed backscattered DCPI Raman and ROA spectra of 1.50M ~-alanine-3,3,3-d3in HzO and their ab initio simulated spectra. The total exposure time for observed spectra is 105.6 h.
1600
WAVENUMBERS (cm-l) Figure 4. Observed backscattered DCPI Raman and ROA spectra of 1.25 M ~-alanine-2-d,in DzO and their ab initio simulated spectra. The total exposure time for observed spectra is 98.0 h.
WAVENUMBERS (cm-l) Figure 6. Observed backscattered DCPI Raman and ROA spectra of 1.50 M ~-alanine-3,3,3-d3in DzO and their ab initio simulated spectra. The total exposure time for observed spectra is 70.4 h.
and methyl groups are assigned as primarily parallel (11) or to the xz plane defined in I. The numbers perpendicular (I) identifying each Raman and ROA band in the figures correspond to the numbers in the f i s t column of the appropriate table.
The tabulated ROA parameters, Aobs and Ash, are obtained by taking the ratio of CID/CIS from the peak maxima for the experimental and simulated spectra, respectively. For DCPl calculations, the ratio, &d, is obtained from the equations2
Y
Ad=
4 I
- - - - -W H3C//;I/GL i' '-' INH3+
i z
co2I
X
96/9(G')2
+ 32p(A)2
244(
(3)
Comparison of Aobs to Ash is more relevant for most of spectral features in evaluating the agreement between experiment and calculation, because of cancellation or overlap in the observed ROA spectra at 15 cm-' resolution.
Discussion The calculation of vibrational frequencies and Raman and ROA intensities by using ab initio wave functions with the
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838 J. Phys. Chem., Vol. 99, No. 2, 1995
TABLE 1: Experimental and Calculated ROA Parameters for L-Alanine in € I 2 0 ab initio calculation on gas-phase zwitterion (6-31G*Y ab initio calculationon solution-phasezwitterion (6-31G*) exp exP ICP ICP DCPl freq DCPl freq freq 4exp ACd assignment assignmentC no. (cm-l) A,hb freq (cm-l)C Asimd va coz-, 6 a NH3+ 1996 va coz-3.4 1613 1876 (1688) 1882 6 a NH3+ 1836 (1652) 3.6 6" NH3+ 1790 daNH3+ NH3' 3.5 1802 (1621) 1459 1641 3.0 4.1 PCH3 2.8 6'NH3+, anCH3, vaCOz1652 (1487) 1503 1639 -0.7 -2.7 d"CH3 1.o daCH3,6 C*-H 1457 1.5 1642 (1478) 1501 -12.5 6 C*-H,tCOzdaCH3, 6' NH3+, 6 C*-H 1635 (1472) -1.7 -1.3 1410 1523 -2.4 2.5 6' NH3+, 6 C'-H, V' COz1541 (1387) V' COz-, d5CH3,6 C'-H, -7.0 1412 -6.1 va CC'C, 5' NH3+ 1375 1568 -0.6 -3.5 d'CH3 1578 (1420) 6' CH3,6 C'-H, V' Cot-, 8 1374 -3.2 -6.9 6 s NH3+, v' CC'C 1351 1447 2.6 -21.7 6Cg-H,6NH3+ 9 1352 6.4 6 C'-H, 5' NH3+, 3.1 1501 (1351) 5' CH3,V' COT1301 1395 4.0 11.2 6' NH3+, 6 CO, 6 C'-H 10.0 6 C'-H, e' NH3+, 1452 (1307) 10 1302 4.5 5' CH3, V' COze' NH3+, 5' CH3,6 C*-H, 1220 1314 -3.4 -18.0 cNH3+, CCH3, v C'C(H3) 1317 (1185) -5.5 11 1217 -2.8 6 (Hs)CC*N,v C'C(0z) 1145 1205 14.8 2.7 6 C*-H, 5 CH3,5 NH3' 12 1139 6.4 1222 (1100) 4.0 6 C'-H, NH3+, CH3, y COz-, 6 CC'C, v C'N 1110 1164 4.1 14.3 5 NH3+,5 CH3, v (H3)CC'N 1113 1.6 1186 (1067) 3.1 6 C'-H, 5' NH3+, CH3, V' (H3)CC'N 5' NH3+, 5' CH3,d C'-H 1001 1080 -7.0 -9.8 NH3+, 5 CH3, v C'C(H3) -3.0 1060 (954) 14 1003 -5.0 995 1060 -0.4 5 NH3+, 1; CH3 1048 (943) 0.2 15 NH3+, C CH3, 6 C*-H,v C'CH3 922 942 17.7 6.5 v C'C(O), daCOz-, v C'N, 970 (873) 16 922 8.3 7.1 va (02)CC'N, 6 COz-, CH3, NH3' 850 881 -2.4 -2.6 vC*N,~'COZ-5.2 y COz-, 6 COz-, 5' HC'C(Oz), 893 (804) 17 848 -5.9 5' CH3,5' I'JH3' 775 838 -11.7 -0.7 y COZ-,~'COz-2.4 844 (760) y COz-, 6 COz-, va (H3)CC'N, 18 781 -3.5 5' HC'C(Oz), CH3,6 C'-H Data are obtained from ref. 5 . Observed DCPI (CID/CIS) x 104. Frequencies in parentheses are scaled by 0.9. DCPI (CIDKIS) x 10" from simulated calculated spectra with 7.5 cm-' half-high bandwidth. e v, stretch; 6, deformation; 5, rock; y , wag; t torsion; a, antisymmetric;s, symmetric; I,perpendicular to the xz plane; 11, parallel to the xz plane.
contrast ~~ to the methyl antisymmetric deformations, in which the chiral environment acts as a small perturbation of C3" symmetry degenerate modes, the methine deformations are 50 cm-' apart, with distinctly different force constants for deformation toward the amino group or toward
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842 J. Phys. Chem., Vol. 99, No. 2, 1995
the carboxylate group and cannot be viewed as arising from the breakdown of local symmetry. (d) Efsects of Methine Motion on ROA Intensity. For the methine deuterated species, although a complex pattern of Raman bands appears in the 900-1500 cm-l region, the ROA intensity is much lower than for the parent isotopomer. The average of the absolute value of Aobs is -4.0 x in the parent alanine spectrum but drops to less than 1.0 x with methine deuteration. The C*-D deformation is expected near 800 cm-l, where the large ROA intensities are observed in the alanine-2-dl spectra, such as the peak at 832 cm-l for the species in H20 and the peaks at 825 and 770 cm-' for the species in DzO. Therefore, the influence of methine motion on the ROA intensities is dramatic. These observations also suggest that the C*H bending motion mixes with rocking and skeletal motions in the entire 900- 1500 cm-' region, in agreement with the assignments from the a b initio calculation. However, the calculation does not correctly predict the overall ROA intensities in this region for alanine-Zdl, which are about 3-5 times larger in magnitude than the experiment. The error in the ROA calculation tends to be larger for modes with a predominant contribution from hydrogen deformations. In addition, the calculated spectrum of alanine-2-dl in H20 in the region below 1300 cm-l has two large positive ROA bands that are not present in the observed spectrum. (e) Dominant Low-Frequency Features. Three prominent ROA peaks, 14, 16, and 17, are observed in the frequency region below 1100 cm-l in the parent alanine spectrum with negative, positive, and negative ROA intensities at 1003, 922, and 848 cm-', respectively. Examination of the overall nuclear motion involved in these modes reveals that the negative ROA intensities correlate with contributions from the rocking motions of CH3, and N H 3 + groups generally perpendicular to the xz plane defined in I, and the positive ROA band correlates with contributions from the rocking motions generally parallel to the plane. This correlation with ROA sign is independent of the relative phasing of the rocking motions involved in each mode. Similar correlations of positive ROA with parallel and negative ROA with perpendicular rocking motion are found for peaks 16-18 (849,815, and 776 cm-l) for alanine-N-d3; peak 17 (832 cm-') for alanine-Zdl; peaks 16-18 (845,825, and 770 cm-l) for alanine-2-dl-N-d3; peaks 15, 17, and 18 (931, 804, and 773 cm-l) for alanine-3,3,3-d3; and peaks 14-16 (857, 821, and 796 cm-l) for alanine-3,3,3-d3-N-d3. It will be interesting to search for similar correlations in other molecules as an understanding of mechanisms for ROA intensities is further developed.
Conclusions The a b initio self-consistent reaction field calculations of vibrational frequencies and Raman and ROA intensities with the 6-31GY basis set for alanine and its isotopomers yield good agreement between experiment and theory for most of the vibrational bands. By the direct visualization and animation of nuclear motions, a better insight into the structure of the vibrational modes is unveiled. The studies of the deuterated isotopomers, combined with the ab initio calculations, have highlighted the importance of contributions from local group motions such as the methine and methyl deformations, carboxylate symmetric stretch, and rocking modes in generating large ROA signals. These studies reveal that the phase of coupling among group vibrations does not appear to influence the sign of the ROA signal, in contrast to VCD, for which the phasing of coupled oscillators plays a major role in determining the VCD sign. The dramatic decrease of
h o b s when the methine is deuterated underscores the importance of methine motion in generating ROA intensity, which parallels the contribution of methine motion to large VCD signals. The discrepancies between experimental and theoretical ROA intensity for alanine-2-dl suggest the need for higher level calculations to achieve a comparable level of agreement for this species. By supplying another dimension to vibrational spectroscopy, ROA measurement in chiral molecules, enhanced by ab initio calculation of ROA intensity, makes possible a deeper understanding of vibrational optical activity and provides an effective basis for refining vibrational force fields and evaluating methods for simulating solvent effects.
Acknowledgment. We are grateful for the support from the National Institutes of Health, Grant GM-23567 (L.A.N., T.B.F.), and to the Pittsburgh Supercomputer Center for a computer grant (P.L.P.). References and Notes (1) Nafie, L. A.; Che, D. In Modem Nonlinear Optics, Part 3, Advances in Chemical Physics Series, Evans, M.; Kielich, S., Eds.; John Wiley & Sons: New York, 1994, Vol 85, p 105. (2) Barron, L. D.; Hecht, L. Biomolecular Spectroscopy, Pari B, Advances in Spectroscopy; Clark, R. J. H., Hester, R. E., Eds.; John Wiley & Sons: New York, 1993, Vol. 21, p 235. (3) Ford, S. J.; Wen, Z. Q.; Hecht, L.; Barron, L. D. Biopolymers 1994, 34, 303. (4) Barron, L. D.; Gargaro, A. R.; Wen, Z. Q.; MacNicol, D. D.; Butters, C. Tetrahedron: Asymmetry 1990, 1, 513. (5) Wen, Z. Q.; Hecht, L.; Barron, L. D. J. Am. Chem. SOC. 1994, 116, 443. (6) Nafie, L. A.; Che, D.; Yu, G.-S.; Freedman, T. B. Biomol. Spectrosc. I1 SPlE 1991, 1432, 37. (7) Barron, L. D.; Gargaro, A. R.; Hecht, L.; Polavarapu, P. L. Spectrochim. Acta A 1991, 47A, 1001. (8) Bell, A. F.; Barron, L. D.; Hecht, L. Carbohydr. Res. 1994, 116, 5155. (9) Wen, Z. Q.; Hecht, L.; Barron, L. D. Protein Sei. 1994, 3, 435. (10) Bell, A. F.; Hecht, L.; Barron, L. D. J. Am. Chem. SOC. 1994,116, 5155. (11) Barron, L. D.; Gargaro, A. R.; Hecht, L.; Polavarapu, P. L. Spectrochim. Acta 1992, 48A, 261. (12) Hecht, L.; Barron, L. D.; Gargaro, A. R.; Wen Z. Q.; Hug, W. J. Raman Spectrosc. 1992, 23, 401. (13) Nafie, L. A.; Freedman, T. B. In Methods in Enzymology Riordan, J. F., Vallee, B. L., Eds.; Academic Press: San Diego, 1993, p 226. (14) Barron, L. D.; Cooper, A.; Ford, S. J.; Hecht, L. Wen, Z. Q. Faraday Discuss. 1992, 93, 259. (15) Wen, Z. Q.; Barron, L. D.; Hecht, L. J. Am. Chem. Soc. 1993, 115, 285. (16) Nafie, L. A. Proceedings 4th International Conference on Circular Dichroism, Bochum, 1991. (17) Barron, L. D.; Buckingham, A. D. Mol. Phys. 1971, 20, 1111. (18) Barron, L. D. Mol. Phys. 1976, 31, 1929. (19) Hug, W.; Surbeck, H. Chem. Phys. Lett. 1979, 60, 186. (20) Andrews, D. L. J. Chem. Phys. 1980, 72, 4141. (21) Barron, L. D. Molecular Light Scattering and Optical Acfivify, Cambridge University Press: Cambridge, 1982. (22) Barron, L. D.;'Escribano, J. R. Chem. Phys. 1985, 98, 437. (23) Nafie, L. A.; Freedman, T. B. Chem. Phys. Lett. 1989, 154, 260. (24) Hecht, L.; Barron, L. D. Spectrochim. Acta 1989, 45A, 671. (25) Hecht, L.; Ndie, L. A. Mol. Phys. 1991, 72, 441. (26) Hecht, L.; Nafie, L. A. Chem. Phys. Lett. 1990, 174, 575. (27) Harris, R. A.; McClain, W. M. Chem. Phys. Lett. 1992, 195, 633. (28) Hecht, L.; Nafie, L. A. Chem. Phys. Lett. 1992, 195, 631. (29) Barron, L. D.; Bogaard, M. P.; Buckingham, A. D. Nature 1973, 241, 113. (30) Spencer, K. M.; Freedman, T. B.; Nafie, L. A. Chem. Phys. Lett. 1988, 149, 367. (31) Hecht, L.; Barron, L. D.; Hug, W. Chem. Phys. Lett. 1989, 158, 341. (32) Che, D. Ph.D. Dissertation, Syracuse University, 1992. (33) Che, D.; Hecht, L.; Nafie, L. A. Chem. Phys. Lett. 1991,180, 182. (34) Yu, G.-S.; Nafie, L. A. Chem. Phys. Lett. 1994, 222, 403. (35) Barron, L. D.; Hecht, L.; Gargaro, A. R.; Hug, W. J. Raman Spectrosc. 1990, 21, 375. (36) Che, D.; Nafie, L. A. Appl. Spectrosc. 1993, 47, 544.
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Raman Optical Activity of L-Alanine (37) Polavarapu, P. L. J. Phys. Chem.1990,94,8106; Chem Phys. Le#. 1990,174, 511. (38) Bose, P. K.; B m n , L. D.; Polavarapu, P. L. Chem. Phys. Lett. 1989,155,423. (39) Bose, P. K.; Polavarapu, P. L.; B m n , L. D.; Hecht, L. J. Phys. Chem. 1990,94,1734. (40) B m n , L. D.; Gargaro, A. R.; Hecht, L.; Polavarapu, P. L.; Sugeta, H. Spectrochim. Acta 1992,48A, 1051. (41) Polavara~u.P. L.: Pickad. S.T.: Smith. H. E.: Black T. M.: B m n , L. D.;’Hecht, L.’Talanta’1993,73, 545. (42) PolavaraDu, P. L.; Hecht, L.; B m n . L. D. J. Phys. Chem. 1993, 97,’1793.Polav&apu, P. L.; Bose, P.K.; Hecht, L.; Barron, L. D. J. Phys. Chem. 1993,97,11211. 143) PolavaraDu. P. L.: Black. T. M.: Barron. L. D.: Hecht. L. J. Am. Chem.’Soc. 199$ iis, 7136. (44)Diem. M.: PolavaraDu. P.L.; O W , M.; Nafie, L. A. J. Am. Chem SO;. 1982,104,3329. (45) Wong, M. W.; Frisch, M. J.; Wiberg, K. B. J. Am. Chem. Soc. 1991,113,4776. (46) Wong, M. W.; Wiberg, K. B.; Frisch, M. J. J. Am. Chem. Soc. 1992,114, 523. (47) Wong, M. W.; Wiberg, K. B.; Frisch, M. J. J. Am. Chem. Soc. 1992,114, 1645. ’
(48) Frisch, M.; Foresman, J.; Frisch, A. Gaussian 92 User’s Guide, 1992. (49) Gaussian 92, Revision C, Frisch, M. J.; Trucks, G. W.; HeadGordon, M.; Gill, P. M. W.; Wong, M. W.; Foresman, J. B.; Johnson, B. G.; Schlegel, H. B.; Robb, M. A.; Replogle, E. S.;Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley, J. S.;Gonzalez, C.; Martin, R. L.; Fox, D. J.; Defrees, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. A. Gaussian, Inc., Pittsburgh PA, 1992. (50) Freedman, T. B.; Nafie, L. A. In Modem Nonlinear Optics, Part 3, Advances in Chemical Physics Series, Evans, M., Kielich, S.,a s . ; John Wdey & Sons; New York, 1994, Vol. 85, p 207, and references therein. (51) Hecht, L.; Che, D.; Nafie, L. A. Appl. Spectrosc. 1991, 45, 18. (52) The notation 2p(a)2is equivalent to pz,2p(G ’) to y2, and 2B(A)z to d2 in refs 7 and 37-43. (53) Nafie, L. A.; Polavarapu, P. L.; Diem, M. J. Chem. Phys. 1980, 73, 3530. (54) Diem, M. J. Am. Chem. Soc. 1988,110, 6967. (55) Freedman, T. B.; Chemovitz, A. C.; Zuk,W. M.; Paterlini, M. G.; Nafie, L. A. J. Am. Chem. Soc. 1988,110, 6970. Jp94 1943J
