Isolation of Raman optical activity invariants

Volume 189, number I

CHEMICAL PHYSICS LETTERS

24 January 1992

Isolation of Raman optical activity invariants Diping

Che and Laurence

A. Nafie

Department of Chemistry, Syracuse University, Syracuse, NY 13244-4100,

USA

Received 29 October 199 I

We report the first isolation of individual Raman optical activity (ROA) invariants. In the far-from-resonance approximation, where ROA intensity is comprised of three invariants, a specific procedure for isolating all three invariants is proposed. For depolarized right-angle incident or scattered circular polarization (ICP or SCP) and backscattering in-phase dual circular polarization (DCP,) ROA only two invariants contribute, the anisotropic magnetic-dipole and the electric-quadrupole optical-activity tensor invariants. These two invariants are isolated experimentally for ( + )-trans-pinane and ( - )-a-pinene.

1. Introduction During the past several years ROA has undergone rapid instrumental and theoretical development. The original incident circular polarization (ICP) ROA theory [ 1,2] has been extended to include scattered (SCP ) [ 2-41, dual in-phase (DCP, ) and dual outof-phase (DCPii) ROA [ 5,6] as other forms of circular polarization (CP) ROA measurements. Recently, a complete formalism has been developed for Raman and ROA intensities for all forms of CP ROA as functions of tensor invariants and scattering angle [ 71. Experimentally, new forms of CP ROA measurements, including those at forward and backward scattering angles, have been implemented [4,8-l 61. These improvements in instrumentation and experimental strategy are allowing routine ROA measurements of aqueous solutions of biological molecules [ 8,15-231. ROA is now a very promising new technique for investigations of molecular conformation in wide varieties of chiral molecules. Carrying out various ROA measurements not only provides the experimental basis for identifying favorable experimental configurations for practical purposes, it also has theoretical significance. For example, the comparison of right-angle ICP and SCP ROA spectra [ 12,241, measured under nearly identical optical configurations at the laser-excitation wavelength of 488 nm, has shown that the equivalence of ICP and SCP ROA, and hence Stokes and

anti-Stokes equivalence [ 31, is preserved for transpinane, a fused chiral ring molecule with no functional groups, and is nearly preserved for a-pinene, which has one double bond. The virtual equivalence of the backward DCP, and unpolarized ICP ROA spectra of trans-pinane [ 141 provides additional evidence for the basic far-from-resonance nature of Raman scattering by this compound. Further, forward and backward scattering unpolarized ICP ROA measurements of P-pinene [ 111 show that a large contribution from the isotropic magnetic-dipole optical-activity tensor invariant exists for at least two vibrational modes in this sample. Other theoretically interesting aspects of ROA measurements of different configurations include the isolation of tensor invariants [ 71. In the far-fromresonance approximation, the complete CP ROA invariant set has only three distinct invariants. It is possible, in principle, to perform three ROA experiments whose ROA intensity expressions are linearly independent and isolate the three ROA invariants, although the relative instrumental performances for the three experimental setups is also required. In a single measurement it is now possible to isolate the isotropic and anisotropic magnetic-dipole opticalactivity invariants from the electric-quadrupole optical-activity invariant by a new magic angle technique [ lo]. Setting the analyzing polarizer at the magic angle for right-angle scattering excludes the contribution from the electric-quadrupole optical-

0009-2614/92/$ 05.00 0 1992 Elsevier Science Publishers B.V. All rights reserved.

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activity invariant and permits the measurement of only the contribution from the isotropic and anisotropic magnetic-dipole optical activity invariants. However, the extraction of a single ROA invariant spectrum by this method alone is not possible. The first isolation of individual ROA invariant spectra is reported here. The method employed is a simplification of a general scheme presented below for unambiguously isolating all three ROA invariants from scattering data in the far-from-resonance approximation. The method is based on the measurement and exact scaling of two theoretically equivalent pairs of Raman intensities and one such pair of ROA intensities which then lock the corresponding three pairs of experimental setups into exact intensity relationships even though the setups differ in optical configuration. For the two examples illustrated in this paper, the anisotropic magnetic-dipole and electric-quadrupole optical-activity invariant spectra of ( + )-transpinane and ( - )-a-pinene are isolated. From the analysis of other relevant experimental ROA results [ 12,14,24] for these molecules, it is concluded that the non-resonance approximation is excellent for trans-pinane and very nearly satisfied for a-pinene when the excitation wavelength is 488 nm. Within this approximation, the depolarized right-angle SCP (or ICP) and backward scattering DCP, ROA involve only the anisotropic magnetic-dipole and electric-quadrupole optical-activity invariants in two different combinations, whereas the ordinary Raman intensity involves the same single anisotropic polarizability invariant in the two experimental configurations. By appropriate scaling of experimental Raman intensities, the two ROA spectra can be brought into exact instrumental equivalence and the ROA invariants isolated by appropriate addition and subtraction of the two scaled ROA spectra.

2. Theory The general level of the complete CP ROA theory [ 7 ] involves ten optical-activity tensor invariants and three Raman tensor invariants. In the far-from-resonance limit all the antisymmetric anisotropic tensor invariants vanish and the distinction between the Roman and script tensor invariants vanishes to 36

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within a minus sign such that there is no difference between ICP and SCP measurements for right-angle scattering [ 3,4,7,12,15,16,24]. The invariant set then reduces to only three ROA and two Raman tensor invariants. The Raman and ROA intensity expressions, circular intensity sum (CIS) and difference (CID), respectively, for right-angle depolarized ICP (or SCP) and backward scattering DCP, in this approximation are: depolarized

right-angle

ICP:

CID: Z,R(90”)-Zk(90”) =8(&/c)

]3Z3(G’)2-KA)21

>

(1)

CIS:Z,R(90°)+Z:(90”) = 12K,P( a)2 ) backscattering CID:Z;(

DCP,:

lSO”)-Zk(

=32(&/c)

(2)

180”)

]3P(G’)2+NA)21

>

(3)

C1S:Z~(180”)+1~(180”) =24Kb/3((-\!)*.

(4)

The superscripts and the subscripts on the intensity symbols represent the polarization state of the incident and scattered light, respectively, and the scattering angle is given in parentheses. The theoretical quantities /I( a)2, /3( G’ )2, and /3(A)’ are anisotropic invariants of the polarizability, the magnetic dipoleelectric dipole optical-activity tensor and the electric quadrupole-electric dipole optical-activity tensor, respectively [ 8 1. The constants Kd and Kb contain the information necessary to specify the experimentally observed intensities from the pure moleculebased scattering invariants, /?, and c is the speed of light in vacua. The prime distinguishes the constant for backscattering from that of right-angle scattering, and the subscript “d” refers to the basic depolarized nature of the CIS spectra described by eqs. (2) and (4), which are the same to within a constant factor for both experimental setups. The corresponding expressions for polarized rightangle scattering ICP (or SCP) and unpolarized backscattering ICP Raman and ROA intensities are given by:

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right-angle

PHYSICS

ICP:

CID: 1:(90”)-&(90”) =~(K,/c)[~~~xG’+~/?(G’)~+B(A)~],

(5)

cIs:r::(90°)+z~(900) =2K,[45a2+7/?(a)‘], unpolarized CID: I:(

backscattering

180”)-I:(

=32(~~ic)

(6) ICP:

180”)

[3P(G')*+8(A)*l 9

as: If)< 18o”)+zb( =4&[45o2+78(&)2]

(7)

180°) )

(8)

where K, and Kb are the polarized analogues of the depolarized intensity constants presented above, and cwG’ is the isotropic magnetic dipole-electric dipole optical-activity invariant [ 81. We note that the CIS intensities for the two setups are the same to within a scale factor and correspond to polarized Raman scattering. We also note that ROA intensities in eqs. (3) and (7) are exactly proportional, as has been demonstrated experimentally in two setups where the constants K:, and Kb where virtually the same [ 141. The essence of the isolation procedure for all three ROA invariants is to measure all eight intensities specified in eqs. ( 1 )-( 8) and then: ( 1) use the exact proportionality of eqs. (2 ) and (4) to express Kb in terms of Kd, thereby eliminating K&; (2 ) use the exact proportionality of eqs. (6 ) and (8 ) to express KI, in terms of Z$, thereby eliminating Kb; and (3) use the exact proportionality of eqs. (3) and (7) to eliminate either K, or Kd leaving only one constant K for all eight experimental intensities. All four experimental setups are quantitatively calibrated with respect to one another and the measured ROA can be algebraically combined to isolate the three ROA invariants and the two Raman invariants to within the multiplicative value of a single experimental constant K. It is straightforward to see that although eight different ROA and Raman intensities are measured, there are three pairs of intensities with theoretically redundant combinations of invariants, two Raman and one ROA. This leaves two linearly independent Raman measurements to isolate two Raman invar-

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iants and three linearly independent ROA measurements to isolate three ROA invariants. The three redundancies allow the reduction of four experimental scattering constants to a single constant K which relates the theoretical invariants to the measured intensities. The full analysis can also be viewed as performing eight measurements to find live invariants and three ratios of constants relating the four different experimental setups. A simpler subset of this analysis is to use only the four depolarized expressions in eqs. ( 1 )-( 4) to solve for two ROA invariants, one Raman invariant and one ratio of two constants relating the two experimental setups. It is this latter analysis that we demonstrate below for ( + )-trans-pinane and ( - )-apinene.

3. Experimental The instrumentation and relevant results of backscattering DCP, ROA measurements have been reported previously [ 141, and the only modification of this setup is the placement of the analyzing polarizer just before the camera lens rather than just after it. The setup for depolarized ICP and SCP rightangle scattering corresponds to a minor modification of our previous SCP instrument [ 131 and the modification has been described more fully in a recent paper [ 241. As before, the transmitting axis of the linear polarizer in the scattered beam and the polarization plane of the exciting laser beam are set parallel to the scattering plane. In the present setup a second quarter-wave plate is added to the previous SCP setup and placed in the incident beam before the focusing lens. As in the backward scattering experiment [ 141, the collecting lens is an 85 mm f/1.2 Canon camera lens. To measure depolarized SCP ROA intensity, the fast or slow axis of the quarterwave plate in the incident radiation is first aligned parallel to the polarization plane of the laser beam, whereas the slow or fast axis of the quarter-wave plate in the scattered radiation is aligned 45’ to the transmitting axis of the linear analyzing polarizer. Simply rotating both quarter-wave plates by 45’ switches the setup from the depolarized SCP( 90” ) to the depolarized ICP (90” ) configuration. ROA intensity in all experiments is obtained by subtracting data sets 37

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of Raman intensity collected from settings of the appropriate quarter-wave plate that differ from one another by 90”. The samples of ( + )-trans-pinene and ( - )-u-pinene were obtained from commercial sources and purified by distillation.

4. Results The CID spectra of depolarized DCP, ( 180” ) and ICP/SCP(90”) measurements, along with the depolarized CIS spectrum, for ( + )-trans-pinane are given in fig. 1. The depolarized ICP/SCP (90” ) CID spectrum was obtained by adding equivalent data sets of ICP and SCP spectra acquired under exactly the same conditions. Since under these conditions there are virtually no differences between these two measurements for trans-pinane, we have measured and summed these two kinds of ROA spectra to verify the quality of our alignment and to improve the S/ N ratio of the ROA spectrum. The relative values of the constants Kd and Kb are found by scaling the ICP/SCP(90’ ) CIS spectra to be equal to the DCP, ( 180” ) CIS spectra, thus eliminating the need to use different constants Kd for these two CIS spectra (represented simply by Kin fig. 1). The ICP/SCP CID spectrum was then scaled by the same factor used to produce the CIS equality to eliminate the different constants Kd in the ROA expressions in eqs. ( 1) and (3). Thus, DCP, and ICP/SCP CID spectra in figs. Id and lc, respectively, are both associated with the one depolarized CIS spectrum presented in fig. 1e. The equivalence of the CIS spectra measured in these two experimental configurations was veritied and found to be the same within the visual limits of the presented CIS spectrum. The resulting pair of ROA spectra can then be added and subtracted in the appropriate way to isolate the spectra for the invariants /.I(G’ )’ and /I( A)2. The isolation of the two ROA invariant spectra is illustrated in the upper two spectra, figs. la and lb. The appropriate factors associated with the isolation of the P(G’ )’ and j?(A)’ invariant spectra are included in these spectra such that their sum equals the DCP, CID spectrum and one-half of their difference is the ICP/SCP CID spectrum. These combinations can be carried out, to a certain extent, by visual in38

-0. 3 5 ” 9 b

-5. c

Icp/scP(Wl:

-+

[3PKi’)2.P(A)2]

51

(+I- tram -ptnnne .5 3 0 9 4

4 2 0 705

500

1100

1300

1500

WAVENUYEERS (an-') Fig. 1. Raman and ROA spectra of ( + )-trans-pinane showing the anisotropic (a) electric-quadrupole and (b) magnetic-dipole optical-activity invariants as separated from the (c) ICP/SCP (90”) and (d) DCP,( 180”) ROA spectra which are both proportionately associated with (e) the same depolarized Raman spectrum comprised of only the anisotropic polarizability invariant. The intensity scale is in ADC units registered by the CCD detection system.

spection since the intensity scales on all four CID spectra in fig. 1 are the same. Since the contribution of the jI( A) 2 invariant is small on the ROA intensity scale, we present in fig. 2 the two isolated invariants without the pre-factors used in fig. 1 but with the same intensity scale. For reference we include the CIS spectrum which itself is a single invariant. Thus all three depolarized scattering invariant spectra are presented in fig. 2. We note that the two ROA invariant spectra bear a close relationship to one an-

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IcPISCP(9M:+

4

e\ IfA

(-)-a-pinene

4

2

20 700

900

1100

1300

1, 0

Fig. 2. ROA and Raman invariant spectra for ( + )-trans-pinane where the two ROA invariants have the same proportionality factors.

other and thep(A)* spectrum contains features that are either smaller than or approximately equal to the corresponding features in the p( G’ )* spectrum. In figs. 3 and 4 are presented the corresponding CIS and CID spectra for ( - )-a-pinene. The general pattern of the results is close to that for trans-pinane, except that the p(A)* spectrum for a-pinene bears much less resemblance to the P(G’ )* spectrum, although the ROA intensities associated with the couplet near 1450 cm-’ is the same for both ROA invariant spectra.

5. Discussion From the earliest stages in the development

of ROA

1992

1313G32'P(A~21

Raman:

24Kp(a)2

h

I

’

OA, 700

900

1100

1300

1500

WAVENUMBERS (cni')

Fig. 3. Raman and ROA spectra of ( - )-a-pinene showing the anisotropic (a) electric-quadrupole and (b) magnetic-dipole optical-activity invariants as separated from the (c) ICP/SCP( 90” ) and (d) DCP,( 180”) ROA spectra which are both proportionately associated with (e) the same depolarized Raman spectrum comprised of only the anisotropic polarizability invariant.

there has been considerable interest in the relative importance of the magnetic-dipole and electricquadrupole mechanisms for generating CID intensity. One of the principal motivations for the early attempts of Hug [ 25 ] to obtain backscattering ROA was to address the question of the relative importance of these two mechanisms. By comparing a backscattering ROA spectrum to the corresponding right-angle polarized ROA and depolarized ROA spectra, one has three theoretically independent ROA spectra from which information on the relative importance of these mechanisms can be assessed, as39

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.a .4 0 -.4

7

.a

2 .4

-. a

v)

z

4

i -2

2

0 700

900

1100

1300

l!

WAVENUMBERS (cd) Fig. 4. ROA and Raman invariant spectrafor ( - )-a-pinene where the two ROA invariants have the same proportionality factors.

suming the availability of information on the relative instrumental efficiencies of the three setups used to obtain the ROA spectra. Further progress along this line was reported in a series of papers on the ROA of P-pinene in which polarized right-angle scattering [26] and then magic polarization angle [ lo] right-angle scattering were used to draw the tentative conclusion that a pair of CID bands (716 and 765 cm-’ ) that are strong in the polarized and magic angle spectra but nearly vanish in depolarized scattering had their origin in electric-quadrupole scattering. The particular interest in the magic angle measurements from the standpoint of isolation of invariants is that only contributions of a magnetic dipole nature are measured, 40

24 January I992

namely fi( G’ )* and aG’. However, further isolation of the three ROA invariants requires an additional CID measurement away from the traditional rightangle scattering geometry [ 2,25,27]. Subsequently, measurement of the forward scattering ROA of p-pinene [ 111 revealed that these unusual contributions had their origin in the isotropic magnetic dipole invariant, (YG’. Even though CID was available for three different right-angle CID measurements and one at forward scattering, the data were not combined to obtain isolated CID spectra for all three ROA invariants because of the problem of relating the ROA intensities from different ROA setups, particularly between forward and right-angle scattering experiments. The problem of relating scattering intensities between polarized and depolarized right-angle Raman and ROA intensities has been addressed previously where a half-wave plate, placed just before the entrance to the spectrograph, was rotated by 45” to maintain horizontally polarized scattered light incident upon the spectrograph when the analyzed light was switched between horizontal and vertically polarized [ 281. Provided the optical efficiency of the spectrograph remained the same under this operation, a necessary assumption, the intensities of the two sets of CID intensities, depolarized and polarized, could be directly related without any numerical scaling. With the exception of the ROA efficiency analysis discussed below, the method of isolating invariants presented in this paper requires no assumption regarding the equivalence of performance of any two experimental setups. As explained above, all CID spectra are related on the basis of equating equivalent CIS spectra through scaling or equating two equivalent CID spectra through scaling if necessary. The entire procedure rests on the far-from-resonance approximation which reduces 10 CID invariants and 3 CIS invariants to 3 CID and 2 CIS invariants, respectively. This approximation holds very well for trans-pinane and is just beginning to break down for a-pinene, although probably not enough to affect the analysis to the level of the noise of our spectra. The efficiency analysis referred to above concerns minor differences in the cone of solid angle collection for the right-angle and backward scattering experimental setups. There are small differences in the

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width of solid angle collection in the two setups and the presence of a small prism in backscattering that blocks the light scattered at and close to 180”. We have carried out a numerical integration of the theoretical Raman and ROA intensities over the range of the experimental scattering angles in the two setups. The results show that as long as the Raman intensities for the two measurements are the same, there is no need for a correction factor to scale the CID intensities relative to the scaling of the CIS intensities. Since we acquired virtually identical Raman spectra, the deviation of the pair of ROA spectra from that of identical solid-angle collections is negligible to within the signal-to-noise limits of our ROA spectra. One of the most important models for understanding ROA intensity is the bond polarizability model [ 2 1, which itself is a generalization of the two-group model of ROA [29]. An important limit of this model is the one in which the molecular polarizability is comprised of axially symmetric bond contributions [ 301. Under these conditions the isotropic magnetic-dipole optical-activity invariant vanishes and the two anisotropic invariants, the magnetic-dipole and electric-quadrupole optical activity invariants, become equal to one another, namely aG’=O, /?(G’)2=j3(A)2.

(9) (10)

In this limit, the ratio of polarized to depolarized right-angle ICP or SCP CID intensities should be 2 for all CID intensities and the corresponding ratio of backscattering DCP, or unpolarized ICP to right-angle depolarized ICP or SCP CIDs should be 8. These ratios are easily verified by inspection of eqs. ( 1 ), (3) (5) and (7). For the ROA spectra in figs. 1 and 3, after scaling the depolarized CIS spectra to be equal, the expected CID ratio of DCP, to depolarized ICP/SCP in the bond polarizability model with axially symmetric bonds is 4. The observed ratio for most of the principal ROA features in both figures is between 2 and 3, close to but noticeably below the expected number of 4. By inspection of figs. 2 and 3 we determine the degree of validity of eq. ( 10 ). The equality is met in part for trans-pinane where the two spectra generally

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have the same form although the larger features of the electric-quadrupole invariant are noticeably smaller than those of the magnetic-dipole invariant. However, some of the smaller features marked with a star in each spectrum have the same form and size, thereby satisfying eq. (10). In the case of a-pinene, the correspondence between the two spectra is much lower for most of the large features. The large couplet (or triplet) near 1450 cm-’ is the same for both invariants, as is the case for a smaller couplet near 1050 cm-‘. Beyond these two regions there is little resemblance between the two spectra. We note that the 1450 cm-’ region, corresponding to the methyl bending vibrations, is also a region of agreement in the invariant spectra of trans-pinane. The tendency for the CID invariant spectra for trans-pinane to bear a closer resemblance to one another than those for a-pinene may be a reflection of one of two factors or both. First, as has been demonstrated through a comparison of right-angle ICP and SCP ROA for both trans-pinane and a-pinene, trans-pinane satisfies the far-from-resonance criterion to a higher degree than a-pinene, most likely due to the absence of a double bond or functional group in trans-pinane. Second, the bonds comprising transpinane may be more axially symmetric than those of a-pinene, again due in part to the absence of a double bond in the former but not the latter. Finally, we note that the related molecule, p-pinene, has some relatively strong features in its forward scattering ICP ROA spectrum, which is in violation of the conditions in eqs. (9) and ( 10) which require forward scattering ICP ROA to vanish [ 111. It is thus not surprising that a-pinene also shows a substantial departure from this limiting form of the far-from-resonance ROA theory.

6. Conclusions We have presented a complete methodology for the systematic isolation of the three ROA invariants and two Raman invariants in the far-from-resonance limit of the general theory of CP ROA. We have illustrated part of this methodology by experimentally isolating the anisotropic ROA and Raman invariants of transpinane and a-pinene. Comparison of these experimental results with the predictions of the bond po41

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larizability model in the limit of axially symmetric bonds reveals better agreement for trans-pinane than for a-pinene, as expected. The comparison of transpinane reveals some discrepancies in intensity for the strong ROA bands, although some bands in some regions show close agreement, as is also true for apinene. The isolation of ROA invariants is significant for understanding the origin of ROA intensities and for the comparison of experimental ROA intensities to the results of the theoretical calculations of the same intensities [ 3 1,321. Our general finding in the two molecules studied is that, at its strongest, the electric-quadrupole ROA invariant is equal in intensity to its magnetic-dipole counterpart, as predicted in eq. ( 10). In all other cases it appears to be smaller. Given that for the experimental configurations considered in this paper the electric-quadrupole invariant contributes at a level at least three times smaller than the magnetic dipole anisotropic invariant, the influence of the electric-quadrupole scattering mechanism for the molecules considered in this paper is relatively minor and nearly unimportant.

Acknowledgement The authors express their appreciation tional Institutes of Health for support GM-23567.

to the Nafrom grant

References [ I ] L.D. Barron and A.D. Buckingham, [2] [3] [4] [5]

[ 61 [ 71

42

Mol. Phys. 20 ( 197 I ) 1111. L.D. Barron, Molecular light scattering and optical activity (Cambridge Univ. Press, Cambridge, 1982 ). L.D. Barron and J.R. Escribano, Chem. Phys. 98 (1985) 437. K.M. Spencer, T.B. Freedman and L.A. Nafie, Chem. Phys. Letters 149 (1988) 367. L.A. Nafie and T.B. Freedman, Chem. Phys. Letters 154 ( 1989) 260. L. Hecht and L.D. Barron, Appl. Spectry. 44 ( 1990) 483. L. Hecht and L.A. NaIie, Mol. Phys. 72 ( 1991) 441.

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[S] L. Hecht, L.D. Barron and W. Hug, Chem. Phys. Letters 158 (1989) 341. [ 9 ] L.D. Barron, L. Hecht, W. Hug and M.J. Macintosh, J. Am. Chem. Sot. I1 1 (1989) 8731. [lo] L. Hecht and L.D. Barron, Spectrochim. Acta 45A (1989) 671. [ II] L.D. Barron, L. Hecht, A.R. Gargaro and W. Hug, J. Raman Spectry. 21 (1990) 375. [ 12 ] D. Che, L. Hecht and L.A. Nafie, in: Proceedings of the 12th International Conference of Raman Spectroscopy, eds. J.R. Durig and J.F. Sullivan (Wiley, New York, 1990) p. 846. [ 131 L. Hecht, D. Che and L.A. Nalie, Appl. Spectry. 45 (1991) 18. [ 141 D. Che, L. Hecht and L.A. Nalie, Chem. Phys. Letters 180 (1991) 182. [ 15 j L.A. Nafie, D. Che, G.-S. Yu and T.B. Freedman, in: SPIE Proc. Biomol. Spectry. II 1432 (1991) 37. [ 161 L.A. NaIie, in: Lecturesand Posters ofthe 4th International Conference on Circular Dichroism, Bochum, Germany, eds. H. Klein and G. Snatzke (Ruhrgebiet, Essen, 199 I ) p. 10 1. ‘1 L.D. Barron, A.R. Gargaro and L. Hecht in: Proceedings of the 12th International Conference of Raman Spectroscopy, eds. J.R. Durig and J.F. Sullivan (Wiley, New York, 1990) p. 834. ;] L.D. Barron, A.R. Gargaro and Z.Q. Wen, J. Chem. Sot. Chem. Comm. (1990) 1034. [ 19 ] L.D. Barron, A.R. Gargaro, Z.Q. Wen, D.D. MacNicol and C. Butters, Tetrahedron: Asymmetry 1 ( 1990) 5 13. [ 201 L.D. Barron, A.R. Gargaro and Z.Q. Wen, Carbohydr. Res. 210 (1991) 39. [ 211 L.D. Barron, A.R. Gargaro, L. Hecht and P.L. Polavarapu, Spectrochim. Acta A, in press. [22] L.D. Barron, A.R. Gargaro, L. Hecht and P.L. Polavarapu, Spectrochim. Acta A, submitted for publication. [ 231 L.D. Barron, Z.Q. Wen and L. Hecht, J. Am. Chem. Sot., submitted for publication. [24] L. Hecht, D. Che and L.A. Nafie, J. Phys. Chem., to be submitted for publication. [ 25 ] W. Hug, in: Raman spectroscopy, eds. J. Lascombe and P.V. Huong ( Wiley-Heyden, Chichester, 1982) p. 3. [26] L.D. Barron and J.R. Escribano, Chem. Phys. Letters 126 (1986) 461. [27] D.L. Andrews, J. Chem. Phys. 72 (1980) 4141. [28] L.D. Barron, J.F. Torrance and D.J. Cutler, J. Raman Spectry. 18 (1987) 281. [29] L.D. Barron and A.D. Buckingham, J. Am. Chem. Sot. 96 (1974) 4769. [ 30 ] L.D. Barron, J.R. Escribano and J.F. Torrance, Mol. Phys. 57 (1986) 653. [ 3 11 T.M. Black, P.K. Bose, P.L. Polavarapu, L.D. Barron and L. Hecht, J. Am. Chem. Sot. 112 ( 1990) 1479. [32] P.K. Bose, P.L. Polavarapu, L.D. Barron and L. Hecht, J. Phys. Chem. 94 ( 1990) 1734.