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J . Phys. Chem. 1994,98, 1068-1072
Raman Excitation Spectra of Exciton-Phonon Modes of Aggregated 2,2‘-Cyanine Using an Internal Raman Standard D. L. Akins,’ Y. H. Zhuang, H.-R. Zhu, and J. Q. Liu Center for Analysis of Structures and Interfaces, Department of Chemistry, The City College of The City University of New York,New York,New York 10031 Received: August 30, 1993; In Final Form: November 18, 1993”
Intramolecular vibrational bands in the R a m a n spectrum of aggregated, adsorbed 2,2’-cyanine are shown to be appropriate internal Raman standards to normalize excitation spectra of two low-frequency intermolecular (exciton-phonon) modes to surface coverage and excitation frequency changes. I t is postulated that the relative widths of the low-frequency intermolecular Raman bands a r e determined by their energies and that k-state dephasing, which depopulates the substates from which allowed transitions occur, is faster the higher the energy. Frequency maxima a t 575.5and 577.5 n m for Raman excitation spectra of the two exciton-phonon modes are interpreted as indicating the peak absorption wavelengths for the two J-aggregates of 2,2’-cyanine. The widths of the excitation profiles are rationalized in terms of the relative energies of the two J-bands. I t is suggested that the cis aggregate is of higher energy and has fewer excitonic sublevels (k-states) with allowed transitions to the ground state. Measurements associated with the present experiment have been facilitated through the use of a charge-coupled device camera, and nearly insurmountable difficulty would accompany the use of a single-channel detector.
Introduction In recent publications, we have reported on Raman scattering Our by cyanine dyes adsorbed onto metallic silver interest in the cyanines is ultimately aimed at determination of the influence of molecular structure on mechanisms and elementary reaction rates for electron injection into semiconductors when cyanines function to sensitive semiconductors to light that is not intrinsically absorbede8 Such sensitization is referred to as spectral sensitization and is of broad interest because the interstitial electrons that are created can lead to important processes and reactions in solar cells, photographic film, and photocatalytic and electrophotographic system^;^ in addition, the spectral sensitizer can be chosen to optimize the interaction with the spectral emittance of the light source. Our more immediate interest in the cyanines has focused on aggregated molecules and how do intermolecular forces, that are implicit in the aggregate state, influence aggregate structure and participation in electron-transfer dynamical processes. This latter interest derives from the fact that adsorbed, aggregated structures formed by sensitizer dyes (and the resultant aggregateabsorptions) are often made use in the applications mentioned above. Furthermore, our general interest in aggregated molecules stems from the ubiquity of aggregated structures in biological systems where they function to convert optical radiation into chemical energy and promote charge-transfer processeslo and the prospect that aggregated molecules may find utility as structures with enhanced nonlinear optical susceptibi1ities.l ]-I4 We have used spontaneous Raman scattering with the aim of structural characterization and quantitation of scattering species concentration (through vibrational band intensities). It has proved necessary to advance a quantum theory derived analytical intensity expression to explain the occurrence of various vibrational Raman bands as well as an enhancement of intensities for aggregated molecules (viz., “aggregation enhancement”). The resultant Raman intensity expression reveals an increased-size effect and near-resonance terms.lJ The former effect is associated with additivity of single molecule polarizabilities, while the latter is attributable to small energy separations between the molecular aggregate ~ t a t e and ~ - ~other electronic states.’X6
* Abstract
published in Advance A C S Abstracts, January 1, 1994.
In general, we have found that the aggregate’s polarizability = A + B, where i and j represent can be expressed as polarization directions, g indicates the ground electronic state, and u’ and v” refer to upper and lower vibrational states in the scattering problem. The A term has been shown to be principally responsible for the dramatic relative intensity enhancement, upon resonance excitation, of a few low-frequency bands. These enhanced bands (Le., A term bands) have half-widths nearly twice that of bands that are present when either off-resonant or resonant excitation is used, Le., B term bands. These A term bands, in addition to the additivity and frequency resonance effects, are interpreted as owing their existence to nonvanishing overlap integral products involving intramolecular and intermolecular wave functions.*I6 The B term has been shown to lead to Raman intramolecular vibrational bands. This latter deduction arose through the application of several approximations, including Herzberg-Teller intensity borrowing from allowed transitions and the use of vibrational closure relationships in the off-resonance situati~n.~.~J~ An important approximation that enabled association of the A term with specific vibrational motions was the assumption of the “strong-coupling” case for exciton formation, as discussed by Kasha,Is which corresponds to little impediment to the excitation roaming through the aggregate structure. The net result of this assumption is that the associated A term cannot contribute to the appearance of Raman bands resulting from the overlap of intramolecular ground and intramolecular vibro-excitonic modes: the electronic excitation would be spread over many molecules, resulting in each molecule having essentially the same electronic structure as a ground-state molecule and, as a result of the Franck-Condon principle, zero vibrational overlap integral between excited- and ground-state levels.16 However, there is no Franck-Condon proscription for nonzero overlap integral products between vibrationally excited lattice modes of the aggregate (Le., intermolecular vibrations) and ground-state intramolecular modes. Thus, the Raman modes excited through this term are expected to be lattice modes, most likely ones with substantial motion in the aggregate formation direction. Consequently, as we have suggested? the excited-state lattice modes, which can be represented by a superposition of appropriate single molecule intramolecular modes, will possess nonzero vibrational overlap
CY^"^''
0022-3654194120981068$04.50/0 0 1994 American Chemical Society
Exciton-Phonon Modes of Aggregated 2,2’-Cyanine integral products with ground-state intramolecular modes as required for nonvanishing of the A term. An equivalent explanation for the appearance of the bands ascribed to the A term is that they arise as a result of excitonphonon coupling. This conclusion is arrived at because the coupling between lattice vibrations and intramolecular vibrations, implicit with the nonvanishing overlap integral concept, derives from electronic charge movement associated with latticevibrations and charge separation due tovibrations of the individual molecules comprising the aggregate. On the other hand, exciton-phonon coupling can be viewed as arising from an electron density moment along the aggregation formation direction coupling with oscillations of the lattice. This latter representation is clearly simplistic, as the more correct view is that phonons are the allowed lattice oscillations for the electronic distribution defined by the presence of the so-called exciton. In any case, charges interact, which leads to coupling, in the Born-Oppenheimer approximation, between electronic and vibrational degrees of freedom. The above assessment allows us to interpret certain aspects of the Raman spectrum of aggregated 2,2‘-cyanine dye in accord with several of the recently reported theoretical simulations of exciton spectra and Such simulations have been based on an exciton-phonon coupling model that focuses on dephasing-induced emission dynamics and spectral profile changes (shifts and widths of bands) of J-aggregates of 2,2’-cyanine, more widely referred to as pseudoisocyanine (PIC). For further background note that recently, by showing that the two broad, low-frequency bands of 2,2’-cyanine (at 232 and 278 cm-) in room temperature Raman excitation spectra exhibit resonance maxima at two different frequencies, we have provided experimental support for the proposition that the low-frequency resonance bands result from different aggregate configurations, with their associated different excitonic state^.^ In addition, we have proposed two geometrical molecular structures (cisand trans arrangements of the ethyl molecules in the 2,2’-cyanine monomer) that give rise to the two electronic state model.4 Our Raman excitation spectra studies were interpreted as indicating that the trans configuration leads to the low-energy form of the so-called J-aggregate while the cis configuration leads to the high-energy form of the J-aggregatee4 In the present paper, we use dephasing rate arguments common to the exciton-phonon picture to address the impact of exciton substate (i.e., k-state) dynamics on the widths of the two lowfrequency Raman bands. We also reinvestigate the excitation wavelength dependence of the low-frequency Raman bands of 2,2’-cyanine and correlate excitation profile widths with the widths of J-band absorptions found in low-temperature ethylene glycol/ water glass systems. In these latter studies, we utilize an internal Raman standard line against which relative intensity changes can be measured, unlike our earlier study which required the incident laser intensity to be held as near constant as possible with changing excitation frequency (which introduced a significant noise factor). It is to be noted that we recently published a Raman excitation spectral study for a lone low-frequency band (at 212 cm-I) that arises upon resonance excitation of an inferred aggregate absorption for l,l’-diethyl-4,4’-quinocyanine(referred to hereinafter as 4,4’-~yanine),~ that utilized the internal Raman standard-mode approach; the present investigation for 2,2’-cyanine has as one of its purposes the evaluation of the general utility of using an internal Raman band for normalization of frequency and surface coverage changes. Additionally, in this study (1) we utilize a charge-coupled device (CCD) multiplex-type detector and spectrometer, instead of a scanning instrument with photomultiplier detection, which introduced a sizable fluctuation in band intensity measurements, and (2) we have increased the resolution of our excitation wavelength change from 1 to 0.1 nm, because of the increased data acquisition rate accompanying use
The Journal of Physical Chemistry, Vol. 98, No. 4, 1994 1069
of the CCD camera, thus dramatically improving the signal-tonoise of our measurements. Experimental System and Procedures Tunable, continuous wave (CW) laser radiation was supplied by a Coherent dye laser, Model CR-599, with R6G as the dye. The pump laser was a 20-W, CW, Coherent Innova 200 argon ion laser. The spectral range of the excitation used was from 570 and 610 nm, with incremental steps of ca. 0.1 nm near the center of the aggregate absorption band and larger steps (0.2-0.4 nm) in the wings. The precision of the wavelength setting was ascertained to be ca. f0.02 nm using a calibrated, scanning monochromator with a photomultiplier detector, which has been described in detail e l s e ~ h e r e . ~ - ~ ~ ~ ~ ~ Raman excitation spectra were acquired using a 0.6-m-focal length, triple spectrometer (SPEX Triplemate, Model 1877) in combination with a SPEX Spectrum-One CCD detector cooled to 140 K using liquid nitrogen. All spectra were acquired with a spectral slit width that was about 3 cm-*. It is to be noted that the CCD system makes the present study possible: the simultaneous exposure of all pixels eliminates the influence of laser fluctuation on relative intensity of Raman bands; the low noise and high red sensitivity gives large signal-to-noise ratios; and the rapid data collection inherent with its use allows for stable experimental conditions, including maintenance of sample integrity. Raman scattering was excited in an electrochemical cell consisting of a silver working electrode, a Pt counter electrode, and a saturated calomel referenceelectrode (SCE). The working electrode was polished using very fine alumina, rinsed with distilled water, and sonicated for several minutes, resulting in a visually smooth electrode. Principally polished working electrodes, not oxidation-reduction pretreated as customary for surface-enhanced Raman scattering (SERS) studies, were used in the present investigation. Electrodes of this nature are not commonly known to support strong SERS signals, as are the signals found for the present system. The cell was designed with a ca. 70’ Pyrex window in near contact with the working electrode to minimize aperture effects associated with absorption of scattered radiation and to direct specularly reflected laser excitation away from the collection optic^.^ In general, incident radiation impinged from below and scattered radiation were collected by an optical system with axis perpendicular to the propagation direction and polarization of the incident laser excitation. Solutions and chemicals were prepared and purchased as indicated earlier.26 The silver electrode was immersed in a solution consisting of 5 X 10“ M 2,2‘-cyanine iodide and 0.1 M KCl, with a pH adjusted with N a O H to 12. Nitrogen deoxygenation was conducted, the analyte was allowed several hours to equilibrate on the electrode, and the potential of the silver electrode was held at -0.1 V vs SCE during the acquisition of spectra. Results and Discussion The room temperature absorption spectrum of aggregated 2,2’cyanine typically exhibits bands attributable to monomeric species as well as a somewhat sharper red band attributed to the J-aggregate.7 The J-aggregate absorption, in such a system, occurs at ca. 576 nm and appears to be but one line. It is known, however, that at low temperature, e.g., 1.5 Kin an ethyleneglycol/ water glass, the J-band splits into two absorptions, with maxima a t ca. 569 and 576 nm and line widths of 24 and 34 cm-l, respectively.20 The room temperature Raman spectrum of 2,2’-cyanine iodide adsorbed onto a smooth silver electrode and excited with 578-nm radiation is shown in Figure 1. As mentioned earlier, the two low-frequency bands at 232 and 278 cm-i have been attributed to two aggregate arrangements, despite the fact that at room temperature no discernible doublet exists in the absorption
Akins et al.
1070 The Journal of Physical Chemistry, Vol. 98, No. 4, 1994
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AT (cm-') Figure 1.
Raman spectrum of 2,2'-cyanine iodide adsorbed onto a smooth, polished silver electrode in an electrochemical cell containing the dye at a concentration of 5 X 10-6 M in deionized, triply-distilled water, with 0.1 M KC1 used as the supporting electrolyte; the pH of the solution was made 12 by addition of NaOH; the surface potential was held at -0.1 V vs SCF; the excitation wavelength was 578 nm supplied by a Coherent 599 dye laser, pumped by Coherent Innova 200 argon ion laser; a SPEX 1404 double monochromator was used, with entrance and exit slits of 300 pm and intermediate slits of 400 pm, resulting in a resolution of ca. 3 cm-I; and the detector was an RCA 31034 photomultiplier tube. A background emission has been eliminated using line segments matched to the emission profile, leading to peak intensities of the 232- and 278cm-I bands of 1.3283 X lo5 and 1.1968 X lo5 counts, respectively.
spectrum. Measured half-widths for the 232- and 278-cm-l bands from the Raman spectrum shown in Figure 1 are 2 1 and 17 cm-l, respectively, when these bands are fit to a Gaussian form (see experimental condition in figure legend). Other bands in the Raman spectrum typically have narrower widths. As examples, the 425-, 847-, and 1128-cm-l bands are found to have halfwidths of 12,13, and 12 cm-', respectively. The latter two bands (847 and 1128 cm-I) are used as internal Raman standards in this study (vide infra). The widths of the two low-frequency Raman bands have implications regarding k-state dephasing rates, if as we have speculated the bands result from exciton-phonon coupling. Specifically, the narrower width for the 278-cm-1band is consistent with the association of this vibration with the higher-energy cis aggregate.416 The k-state dephasing argument is that the higher the energy of a state, the more rapid is the transition between k-states due to perturbation by phonons. However, the Raman transition is allowed from a low exciton k-state (k = 1 for a linear aggregate) to the ground state, as is the case for both absorption and dephasing redistributes the and fluorescence population of the upper energy states, thus decreasing intensity in the wings of the Raman bands. The main effort in the present work is a refinement of the Raman excitation spectrum of the low-frequency exciton-phonon Raman bands. We measured the intensities of the bands relative to those of internal Raman standards. Since the exciton-phonon bands arise due to a nonvanishing Albrecht A term and other bands (of the aggregate species), present even under nonresonance conditions, are attributed to the B term, we chose to ratio the intensities of the exciton-phonon bands to that of an intramolecular band for each laser excitation frequency; we also account for the v3 dependence for photon counting.27 By taking such ratios, bands assigned to the B term can be used to normalize the intensity of the band due to the A term in terms of both excitation frequency and surface coverage, thus serving as internal Raman standards. However, as shown in eq 3 of ref 3, the intensity of B term bands is expected to be influenced by applied surface potential through an energy factor E,O -E? in the denominator
Figure 2. Raman spectra of 2,2'-cyanine on a silver electrode under the same conditions as those mentioned in Figure 1 except that the incident laser power at the sample was approximately 10 mW. The four spectra were selected from a series of near-resonantly-excited Raman spectra. Theexcitation wavelengths were (A) 574, (B) 578, (C) 585, and (D) 590 nm. Background emissin has been eliminated using line segments as in Figure 1; the heights ofthe 1128-cm-l band have been made approximately constant for visual purposes though they correspond for parts A-D to countsof 993, 1015,1018, and 1001, respectively,foranintegrationtime of 5 s. The spectrograph-detector system used was a SPEX 1877 Triplemate and Spectrum-One CCD camera, as described in the text. The width of the entrance slit was ca. 10 pm, resulting in the spectral resolution being determined by the pixel width of the CCD detector. Since at least 3 pixels are required to define a peak, we deduce that the resolution for our studies is ca. 3 cm-I.
of the B term, where r represents an excited vibronic state of the scatterer and s represents excitonic states that can experience a "Stark effect" tuning due to the coupling between the permanent dipole moment of the aggregate and the applied surface potential. For a fixed surface potential, ratios of intensities of the band attributed to the A term and bands attributed to the B term, as a function of excitation frequencies, are expected to cancel all factors which affect signal strength in the Albrecht A term, except the absorption resonance profile and vibrational overlap terms. In earlier studies, we determined through the dependence of Raman band intensities on solution pH change, excitation frequency, electrode potential, etc., which intramolecular bands in the Raman spectrum of 2,2'-cyanine were due to aggregated or polycrystalline a d ~ o r b a t e . ~The . ~ 847- and 1128-cm-1 bands which have been shown to belong to the 2,2'-cyanine dye molecule incorporated into an aggregate structure are the bands we chose as our references.6 Hence, experimental ratios (e.g., Z232/11128 and Z278/Z1128)at the various excitation frequencies werecorrected for the relative spectral sensitivity of the spectrometer/CCD system at the position of the two respective bands (e.g., the 232and 1128-cm-1 bands). The resultant corrected relative intensity plots correspond to the excitation profile referenced to the particular intramolecular vibration band. Raman spectra were taken using excitation frequencies ranging from 570 to 610 nm (see experimental section for more details). In Figure 2 we show Raman spectra, uncorrected for the spectral
Exciton-Phonon Modes of Aggregated 2,2'-Cyanine
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The Journal of Physical Chemistry, Vol. 98, No. 4, 1994 1071
.
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to theoretical calculations of aggregate absorption spectra. Such calculations indicate that the J-bands are due to transitions involving zero-phonon states of the lower bandedge of the excitonic state.28 The apparent insignificance of phonon modes leads us to postulate a differing k-state electronic energy spread for the two types of aggregates in adsorbed 2,2'-cyanine. Specifically, we postulate that both the absorption spectrum and the Raman excitation spectra track the density-of-states (k-state density) of the aggregate's excited excitonic state, and there are fewer k-states with allowed transition moments close to the band origin of the higher-energy aggregate transition than to that of the lowerenergy aggregate transition. In support of this latter postulate, we note that the energy of the excitonic sublevel has been represented by the expression €k = -2Mcos[?rk/(N l)], with k = 1,2, ...,N, and as mentioned earlier, M is the dipoledipole interaction energy,' which has been determined to be about 600 cm-1.29 In this expression both N (the number of molecules in the linear aggregate) and M determine the number and energy spacing of k-states. (Note that k = 1 corresponds to the lowest state.) Allowing for differences between the effective number of molecules in the cis (high energy) and trans (low energy) aggregate species, as well as for the interaction energies between next-nearest-neighbor molecules in the two types of species, one might expect the trans species would involve more molecules and possess a greater coupling energy than the cis species. An argument in favor of a larger value of M for the longer wavelength absorbing aggregate is that the larger M is, the greater the red shift of the J-aggregate absorption from the monomer absorption, so that the Raman excitation profilewith maximum at 577.5 nm should be associated with greater M. As regards the relative value for N for the two forms of the aggregate, we have shown using FT-Raman relative band intensities as a function of electrode potential that the trans structural conformer in the J-aggregate, as represented by a conformer-specific band such as the 1348-cm-' band, appears to be thermodynamically favored as the potential is made negative.6 For a surface potential of -0.1 V vs SCE, as is used for the present study, our FT-Raman measurements suggest that the surface concentrations of the cis and trans components are nearly the same.6 Hence, the expected relative magnitudes of the dipole-dipole energies and the similar magnitudes of the N for the trans vs cis component point to a lower k-state density for the latter and, as a result, a narrower absorption band and a narrower excitation profile.
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Figure 3. Ratios of the Raman intensitiesof the two low-frequencybands at 232 and 278 cm-I to that of the 1128-cm-I band as a function of excitation wavelength. (A) 1232/II128, (B) 1278/11128. Each data point is determined from a Raman spectrum such as shown in Figure 2. The calculated fits to the data utilize Gaussian curves. The peak wavelength
positions found for the two excitation profiles are 577.5 and 575.5 nm, with half-widths of 14.5 k 0.8 nm (434 f 25 cm-*) and 10.6 0.7 nm (321 k 20 cm-I), respectively. Theuncertainties in themeasured widths are defined through an empirical approach involving broadening or narrowing the Gaussian fit to bracket the measured data points. The two dashed lines in part A indicate the error estimate technique.
*
sensitivity of our spectrometer/CCD system, starting a t ca. 200 out to 1200cm-1 from the laser line for four excitation wavelengths (574, 578, 585, and 590 nm) within the range used. The spectral sensitivity and v3-corrected excitation profiles of the 232- and 278-cm-I low-frequency bands referenced to the 1 128-cm-' intramolecular band for 2,2'-cyanine are shown in parts A and B of Figure 3, respectively. Figure 3 shows about 120 excitation relative intensity measurements with an applied surface potential of -0.1 V vs SCE. It is found that the 232- and 278-cm-' bands have maxima at 577.5 and 575.5 nm, respectively; the same result is found using the 847-cm-1 band as the internal standard. These values are essentially the same as those determined earlier (577 and 575 nm, respectively) using the constant incident power excitation method.5 It follows that an internal Raman standard band can be exploited in determining the frequency at which the Raman excitation profile maximizes. Such frequency maxima corresponds to the frequencies at which aggregated molecules absorb; thus, the use of a Raman internal standard defines a general method for peak absorption determination. The half-widths of the excitation profiles in Figure 3 are 434 f 25 and 321 f 20 cm-I for the 232- and 278-cm-' bands, respectively. The width of the excitation profile of the 232-cm-1 band (whose excitation spectrum maximizes at 577.5 nm) is greater than that of the 278-cm-1 band (whose excitation spectrum maximizesat 575.5 nm). This finding isconsistent with thegreater width of the 576-nm aggregate absorption band for the lowtemperature ethylene glycol/water system (34 cm-I) compared to that of the accompanying 569-nm aggregate band (24 cm-1).20 The explanation that we advance for these observations is tied
Conclusion Intramolecular vibrational bands in the Raman spectrum of aggregated, adsorbed 2,2'-cyanine can be used as internal Raman standards to normalize excitation spectra of two low-frequency exciton-phonon modes (associated with the excitonic state) to surface coverage and excitation frequency changes. The relative widths of two low-frequency exciton-phonon modes are rationalized using dephasing rate arguments. It is suggested that the widths of the low-frequency Raman bands are determined by their energies and that k-state dephasing, which depopulates the substates from which allowed transition can occur, is faster the higher the energy. The frequency maxima for Raman excitation spectra of the two low-frequency modes are interpreted as indicating the peak absorption wavelengths for the two J-aggregates of 2,2'-cyanine. The widths of the excitation profiles are rationalized in terms of the relative energies of the two J-bands. It is suggested that the cis aggregate, being of higher energy, has fewer excitonic sublevels (k-states) with allowed transitions to the ground state. Measurements associated with the present experiment have been greatly facilitated through the use of a CCD camera, and
1072 The Journal of Physical Chemistry, Vol. 98, No. 4, 1994
nearly insurmountable difficulty would accompany the use of a single-channel detector.
Acknowledgment. Support for this research by the National Science Foundation (NSF) under Grant RII-8504995is gratefully acknowledged. References and Notes (1) Akins, D. L. J . Phys. Chem. 1986, 90, 1530. (2) Akins, D. L.; Lombardi, J. R. Chem. Phys. Lett. 1987, 136, 495. (3) Akins, D. L.; Akpabli, C. K.; Li, X. J . Phys. Chem. 1989,93, 1977. (4) Akins, D. L.; Macklin, J. W. J. Phys. Chem. 1989, 93, 5999. (5) Akins, D. L.; Macklin, J. W.; Parker, L. A.;Zhu, H.-R. Chem. Phys. Lett. 1990, 169, 564. (6) Akins, D. L.;Macklin, J. W.; Zhu, H.-R. J . Phys. Chem. 1991.95, 793. (7) Akins, D. L.; Zhu, H.-R. Langmuir 1992,8, 546. (8) Gilman, P. B. Photogr. Sci. Eng. 1974, 18, 418. (9) James, T.H., Ed. The Theory of the Photographic Process, 4th ed.; Macmillan: New York, 1977. (10) Feher, G.;Okamura, M. Y. In The PhotosyntheticBacteria; Clayton, K., Sistrom, W. F., Eds.; Plenum: New York, 1978. (11) Hanamura, E. Phys. Rev. B 1988, 37, 1273.
Akins et al. (12) Spano, F. C.; Mukamel, S.Phys. Rev. A 1989, 40, 5783. (13) Ishihara, H.; Cho, K. Phys. Rev. A 1990, 42, 1724. (14) Wang, Y. Chem. Phys. Lett. 1986, 126, 209. (15) Kasha, M. Radiat. Res. 1963, 20, 55. (16) Fischer, G. Vibronic Coupling the Interaction between the Electronic and Nuclear Motions: Academic: New York. 1984. (17) Albrecht, A. C.J . Chem. Phys. 1961, 34, 1476. (18) Knapp, E. W. Chem. Phys. 1984,85, 73. (19) De Boer, S.;Vink, K. J.; Wiersma, D. A. Chem. Phys. Lett. 1987, 137, 99. (20) De Boer, S.; Wiersma, D. A. Chem. Phys. Lett. 1990, 165, 45. (21) Fidder, H.; Knoester, J.; Wiersma, D. A. Chem. Phys. Lett. 1990, 171, 529. (22) Fidder, H.; Terpstra, J.; Wiersma, D. A. J . Chem. Phys. 1991, 94, 6895. (23) Spano, F. C.; Kuklinski, J. R.; Mukamel, S. J. Chem. Phys. 1991, 94, 7534. (24) Muenter, A. A,; Brumbaugh, D. V.; Apolito, J.; Horn, L. A,; Spano, F. C.; Mukamel, S . J. Phys. Chem. 1992, 96, 2783. (25) Li, X.;Gu,B.; Akins, D. L. Chem. Phys. Lett. 1984, 105, 263. (26) Gu,B.; Akins, D. L. Chem. Phys. Lett. 1985, 113, 558. (27) Hamaguchi, H. In Advances in Infrared and Raman Spectroscopy; Clark, R. J. H., Hester, R. E., Eds.; Wiley: New York, 1985;Vol. 12. (28) Scherer, P. 0.J.; Fischer, S. F. Chem. Phys. 1984, 86, 269. (29) Kopanisky, B.;Hallermeier, J. K.; Kaiser, W. Chem. Phys. Lett. 1981, 83, 498; 1982, 87, 7.
