Resonance Raman spectra of photodissociating CH3I and CD3I in solution

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RESONANCE RAMAN SPECTRA OF PHOTODISSOCIATING

23 March 1990

CHJ AND CDJ IN SOLUTION

Frances MARKEL and Anne B. MYERS ’ Department ofChemistry University ofRochester, Rochester, NY I4627, USA Received 27 December 1989

Raman spectra of CHJ and CDJ in hexane, including absolute cross sections for CHJ, have been obtained using 266 nm excitation, on resonance with the directly dissociative 3Q0state. Both isotopic species exhibit long vibrational progressions in the C-I stretch and its combination bands with the methyl umbrella mode. The relative intensities of the C-I overtones in CHJ are similar in vapor and solution phases, indicating that the early photodissociation dynamics are not greatly altered by solvation. The higher overtone transitions are significantly broadened and shifted to lower frequencies in solution. The absorption spectra and resonance Raman intensities of CHaI have been simulated by parameterizing an uncoupled two-oscillator model in which the C-I stretch is taken as a Morse oscillator in the ground state with an exponential repulsive potential in the excited state.

1. Introduction The gas phase photodissociation of alkyl halides in general, and methyl iodide in particular, has been studied extensively as a prototypical example of a pseudodiatomic photodissociation occurring on a purely repulsive potential surface. Numerous experiments have been carried out to measure the product state distributions (I/I* branching ratios, vibrational excitation of the CH3 fragment and translational energy distribution of the fragments) as a function of excitation energy [ l-31. Photofragment anisotropies [ 4,5] as well as direct time-resolved measurements [6] confirm that the dissociation is rapid compared with rotational motion. In the mid1980s Imre, Kinsey and co-workers observed the gas phase resonance Raman spectra of CHJ and later, CDJ [ 7,8], and pointed out that the extensive overtone and combination band progressions could be related to the dissociation dynamics through Heller’s time-dependent theory of resonance Raman intensities [ 91. There has since been much work on parameterizing various models for the ground and excited state potential energy surfaces with the goal of reproducing the CHJ and CDJ Raman frequencies and intensities as well as the product state distri’ To whom correspondence should be addressed.

butions [ 10,111. While none of the models lit the data completely, and neither resonance Raman spectra nor product state distributions have been reported over a wide range of excitation frequencies, it appears that at least the principal features of the gas phase photodissociation dynamics are well understood. In contrast, there has been little work on the photodissociation dynamics of alkyl iodides in solution, although related systems such as I2 have been studied in detail, mainly through direct pump-probe time-resolved methods [ 121. Methyl iodide is in many ways a simpler system than I2 in that dissociation occurs directly from the state that carries most of the oscillator strength, although curve crossing to other dissociative states also occurs [ 5,131. In one of the few experiments addressing photodissociation dynamics in a condensed phase, Brus and Bondybey [ 141 excited methyl iodide in cold rare gas matrices and observed a broad, weak, vibronically structured emission band in the near-infrared, which they attributed to vibrationally relaxed emission from molecules trapped in a potential minimum on the excited electronic surface. They estimated the quantum yield for photodissociation under their experimental conditions to be less than lOoh. Evidently the dy namics of methyl iodide photodissociation are severely modified by solvation in a frozen rare gas ma-

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trix. We wish to address the question of how and whether the photodissociation is modified by solvation in an ordinary molecular liquid. Many of the methods traditionally employed to study reaction dynamics in the gas phase simply are not applicable to solution phase processes because collisions with solvent cause the photofragments to rapidly lose memory of their initial linear and angular momentum and vibrational energy distribution. In solution, it is desirable to probe the photodissociation process while it is occurring, either directly in the time domain via subpicosecond pumpprobe methods or indirectly through frequency-domain techniques such as resonance Raman. Here we employ resonance Raman spectroscopy to compare the dynamics of photodissociation in vapor and solution phase. As a bonus, the frequencies and bandwidths of the high overtone transitions also provide a window onto the vibrational dynamics of the ground electronic state at high vibrational energies.

2. Experimental CH31 (Baker) was distilled before use, while CD,1 (Aldrich) was used without further purification. The solvent was spectroscopic grade hexane from Fisher Scientific. The 266 nm excitation was generated from the fourth harmonic of a Nd:YAG laser operating at 20 Hz. Samples of approximately 75 mL of 0.1-0.5 M CHJI or CD,1 in hexane, cooled in an ice bath, were flowed through a dye jet to intersect the laser beam (~50 pJ/pulse), which was lightly focused with a 0.5 m focal length lens. The Raman scattered light was collected in a ~45” backscattering geometry using achromatic reflective optics into a single monochromator, and detected with an intensified diode array. Corrections were made for the wavelength dependence of thi: detection efficiency and for reabsorption of the scattered light by the sample. Frequencies were calibrated using known Raman frequencies of cyclohexane and acetonitrile, H2 Raman-shifted laser lines, and Hg emission lines. The integrated areas of the CHsI and CD,1 spectra following solvent subtraction were determined by nonlinear least-squares fitting to Lorentzian lineshapes. A detailed description of the excitation and detection apparatus and methods was given in ref. [ 15 1. 176

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Most of our spectra were obtained using a slit width of 75 pm giving an instrumental resolution of x 12 cm-’ (full width at half maximum ), but the low-frequency region (150-l 300 cm-‘) was also examined using a higher dispersion grating to obtain a resolution of z 6 cm-‘, while at the largest Raman shifts (above 5500 cm-’ for CH31 and above 3500 cm-’ for CD,I) slit widths of 200-600 pm were used, resulting in a resolution of 24-52 cm- I, The reported bandwidths have been corrected for the contribution of the instrument function, taken to be Lorentzian at a 75 pm slit width (where the resolution is limited by crosstalk between channels of the microchannel plate intensifier) and rectangular at 200-600 ym (where the resolution is limited by the physical slit width). For the absolute Raman cross section measurement, the concentration of CH31 in hexane was determined spectrophotometrically immediately before and after the Raman measurement. The maximum molar extinction coefficient in hexane solution was found to be 375 M-’ cm-’ at 257.5 nm, in good agreement with the values reported by Kimura and Nagakura [ 161, compared with 345 M-’ cm-’ at 258 nm in the vapor [ 171. Absorption spectra showed a decrease of approximately 15% in the CH31 concentration during the experiment due to evaporation and photodecomposition. The average concentration was used in the absolute cross section calculation. The absolute Raman cross sections of CH31 were obtained by comparison with the CH stretches of hexane as an internal standard, which were referenced to the CH stretches of acetonitrile and cyclohexane [ 18] in separate experiments on the pure solvents. The absolute cross section at 266 nm for the CH stretching band of hexane (integrated over the region from 2100 to 3700 cm-‘) was found to be 21.8~ IO-” A’ molecule-‘. Because methyl iodide is a relatively weak resonance Raman scatter, high concentrations were required to prevent the hexane scattering from swamping the methyl iodide Raman lines. In the vapor phase, aggregation has been shown to shift both the bandshape and the position of the maximum of the Q-band transition [ 191. We examined the absorption spectrum in hexadecane over a range of concentrations using short path length cells (0.1 to 1 mm) and found negligible changes over the concen-

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tration range 0.0075 to 0.43 M. (Hexadecane was used instead of hexane because our 0.1 mm path length two-piece cell could not hold hexane without leakage_) The Raman spectra also appeared to be unchanged over the concentration range 0.05 to 0.45 M. These observations give us some confidence that solute-solute interactions are not significant in spite of the high solute concentrations employed.

3. Computational An uncoupled two-oscillator model was employed to obtain a simple theoretical model of the resonance Raman spectra in solution. The C-I stretching mode was treated as a one-dimensional Morse potential in the ground electronic state,

v,,,(r)=D{l--xp[-8(r-r,)l}*,

(1)

where r, is the equilibrium bond length (taken here as the distance between the I atom and the center of mass of the CH3 group) and D is the dissociation energy. The parameters 1 and D were estimated from a Birge-Sponer plot and then slightly adjusted to obtain a qualitative best fit to the experimental ground state frequencies. The purely repulsive ‘Qu excited state potential surface was taken to be an exponential of the form V,,c-I(4)=DQ+Cexp(-Bq),

(2)

where q is the displacement from the ground state equilibrium position in the ground state dimensionless coordinate, related to the bond length by g= (~~,/h)i’*(u-~~), where p is the reduced mass of the vibration and o,=/3(2Dhc/p)‘/* is the ground state harmonic frequency. D, is the asymptotic energy of the 3Q0 excited state, assumed to be 7597 cm-i greater than D, where 7597 cm-’ is the I*/1 energy splitting in the gas phase [ 201. The parameters C and B were adjusted to approximately reproduce the peak wavelength and half-width of the 3Q0 component of the absorption spectrum as deduced by Gedanken and Rowe from magnetic circular dichroism measurements [ 171. Our calculated absorption spectrum is thus slightly narrower than the experimental one and shifted slightly to the red. The methyl umbrella mode was treated as an uncoupled harmonic oscillator having equal ground and

23 March 1990

excited state frequencies and a small change in equilibrium geometry, which was adjusted to best reproduce the combination band intensities observed in the resonance Raman spectrum. The symmetric CH stretching mode (u, ), which appears as a fundamental in the gas phase and in our CD31 spectrum (it is hidden by a solvent peak in CH31), was not included in our modeling, nor did we make any effort to reproduce the intensity of the u2 fundamental. We assume, following ref. [ lo], that these fundamentals gain much of their intensity through preresonance enhancement from higher electronic states, The absorption spectrum (uA( EL) ) and resonance Raman cross sections ( u~,~_~(&) ) were calculated using the time-domain method of Heller [9,21]: 4neZM2EL I*=

3fi2c.

xexp[i(EL+eO)l/ZI] %cR,04f(EL) = --

OD Re

s 0

dWlW))

exp(-rtlh)

,

(3)

dt (flO( t)> 2

xexp[i(EL+eO)f/Jt]

exp( -Tt/fi)

>

,

(4)

where t,, and EL and Es are the energies of the initial state and of the laser and scattered photons, respectively, and n is the solvent refractive index. Because the relevant ground state vibrational frequencies are fairly high ( > 500 cm- I ), hot band contributions were ignored. The ground state Morse wavefunctions were calculated as described by Sension and Strauss [ 22 1. Propagation of the n =O Morse wavefunction on the anharmonic excited state potential was accomplished numerically using the split operator technique of Feit and Fleck [23] as described in ref. [ 241. The overlap of the final state ( f] with IO(t) > was then computed by numerical integration. The overlaps (010(t)> and (flO(t)) for the umbrella mode were taken from ref. [ 2 11. The electronic transition length M was set to 0.145 A to give the correct absorption strength. The electronic dephasing width r was set to zero in our calculations, as the rapid wavepacket motion on the dissociative surface causes all of the overlaps to decay within tens of femtoseconds, and the experimental absolute Ra177

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man cross sections indicate that r must be small (see section 4). The Fourier transforms in eqs. (3 ) and (4) were then evaluated by numerical integration using 100 time steps with a step size of 0.5 fs.

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31

4. Results Figs. 1 and 2 show the resonance Raman spectra of CH,I and CD,1 in hexane with 266 nm excitation following intensity correction and solvent subtraction. Tables 1 and 2 give the frequencies, bandwidths and integrated intensities of the observed Raman lines for the two isotopic species, together with those reported in the vapor [ 8,111. Table 1 also shows the ground state frequencies and intensities calculated from our simple uncoupled two-oscillator model for CH31, and fig. 3 compares the calculated and experimental solution phase absorption spectra. Table 3 gives the parameters of the model. Both Raman spectra exhibit long progressions in the C-I stretch ( v3) together with combination bands between the stretch and the methyl umbrella mode (Ye). The combination bands have much more intensity in the deuterated species, in qualitative agreement with the vapor phase results. The relative

I

31

il

3,

I

I 750

2250 Raman

3750 Shift

5250

6750

I

(cmA1)

Fig. 1. Resonance Raman spectrum of CHsI in hexane, intensity corrected and solvent subtracted. The region of the spectrum between 2800 and 3000 cm-l is not shown due to noise resulting from subtraction of the strong CH stretching bands of hexane. The observed bands are labeled according to the number of quanta in the methyl umbrella mode (uz) and the C-I stretch (I+).

118

600

1800 ~aman

3000 Shift

4200

5400

(m-1)

Fig. 2. Resonance Raman spectrum of CD,1 in hexane, intensity corrected and solvent subtracted. The noise in the 2800-3000 cm-’ region results from subtraction of the solvent CH stretching bands. The CD,1 bands are labeled as in fig. 1; v, is the symmetric CD stretching mode.

intensities of the various members of the C-I stretching progression in CHJ do not differ greatly between vapor and solution phases, although the O-+3 through 0+6 transitions appear to have more intensity in solution. The absorption bandshapes in vapor and solution are very similar. Assuming that the dominant contribution to the absorption bandwidth in both phases is the Franck-Condon activity in the C-I stretch, this would indicate that the excited state potential surface in both gas and solution phase has very nearly the same shape in the region near the ground state geometry. The similar relative intensities of the first nine C-I overtones imply that the potential for C-I stretching in the excited state is not dramatically altered by solvation up to distortions from the ground state geometry of ~0.4 A, the approximate outer classical turning point corresponding to n=9. The combination band intensities in CHJ appear to differ considerably more from the vapor phase values, possibly indicating a solvation effect on the opening of the CH3 dihedral angle accompanying dissociation; however, the signal-tonoise ratio of the present data does not allow us to draw any firm conclusions from the combination band intensities. In the deuterated species considerably larger intensity differences are observed between vapor and solution. In particular, the intensity

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Table I Resonance Raman lines of CHJ Transition

freq. (cm-‘)

3, 3, 2,

Solution phase (this work)

Vapor [ 8,111

528 1050 1254

33 213, 34

1567 (1780) 2082

2,32 35 2133 36 2,3. 37 2,33 38 2,36 39 2137 3 2:;s 3 II 3 IZ 313 3 14 315

(2297) 2587 2797 3092 3307 3588 3799 4073 (4304) 4562 4781 5044 5277 5516 5982 6446 6896 7347

Calculated

rel. int. ‘)

freq. (cm-‘) b,

rel. int. c,

width (cm-‘) a)

freq. (cm-‘)

1.00 0.90 0.10 0.56 <0.02 0.50

531 1053 1242 1565 1759 2076

9 14 16 22 <6 36

528 1050 I242 1565 1770 2074

<0.02 0.39 0.02 0.42 0.08 0.40 0.08 0.36 <0.07 0.26

2288 2579 _ 3070

1.00 0.98 0.14 0.83 0.03 0.64 (13.2x10-“)” 0.06 0.60 _ 0.84 f,

27 49

2292 2576 2807 3072 3316 3562 3818 4046 4314 4523 4804 4994 5288 5458 5916 6368 6813 7253

3558 3787 4045 4276 4518 4766 4995 5234 5450 5906 6366 6813 7244

0.41 0.03 0.41 0.12 0.28 0.02 0.45 0.06 0.40 0.43 0.34

76” 68 31 74 70 88 24 114 (48) 104 98 110

rel. int.

1.oo 0.75 0.02 0.60 0.03 0.51 (7.9X lo-“) 0.03 0.44 0.03 0.39 0.04 0.35 0.04 0.32 0.04 0.29 0.03 0.27 0.03 0.25 0.23 0.22 0.20 0.19

*)

‘) Converted from the relative transition probabilities given in ref. [S] by multiplication by w,, [ 31. ‘I Estimated uncertainties are about 2 cm-’ for 31 to 3,, 4 cm-’ for 2,32 to 39, and 6 cm-’ for the remaining transitions. ‘) Relative intensity baaed on integrated areas. Estimated uncertainties are about 10%for the fundamentals and the first five C-I stretching overtones, 20%for 3, to 3,,, and z 50%for all combination bands. ‘) Full width at half maximum of best-fit Lorentzian, corrected for instrumental width. Estimated error limits are about 20%. ‘) Experimental and calculated absolute Raman cross sections for 3, in A’ molecule-‘. f, Approximately 40% uncertainty due to solvent subtraction.

alternation within the first few members of the C-I stretching progression observed in the vapor phase [ 8 ] does not appear in solution. It is unclear whether this should be interpreted as a ground state or an excited state effect, as there is believed to be a relatively strong ground state 2: 1 Fermi resonance between the stretch and the umbrella mode in CDJ that has a substantial effect on the intensities [lo]. Significant solvent effects are observed on the Raman band frequencies and linewidths, which are properties of the ground electronic surface. Table 1 indicates that the lower members of the C-I stretching progression in CHJ are a few wavenumbers higher in hexane solution than in the gas phase, while

the highest observed overtones are shifted to lower frequencies by 80-100 cm-’ upon solvation. This would imply greater vibrational anharmonicity for the C-I stretch in solution as compared to the vapor phase. However, the gas phase fundamental vibrational frequency of 528 cm- ’ reported in ref. [ 81 is 5 cm- ’ below the gas phase value given by Duncan et al. [25]. Assuming the correct gas phase frequency is actually 533 cm-‘, our result for the gas to solution frequency shift, upas- v,,,, is 2 cm-’ in hexane, in reasonable agreement with the value of 3 cm-’ measured using nonresonant Raman by Constant and Fauquembergue [26]. In the published gas phase data the bandwidths of all observed CHJ vibra179

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Table 2 Resonance Raman lines of CDJ Transition

3r 21 32 213, 33 2132 3, 1, 2,3, 3, 2,3, 3, 2,3, 37 2i36 38 2137 39 2i3r 3 10 2139 3 2:;,, 3IL?

Gas phase [ 8 ]

Solution phase (this work)

freq. (cm-‘) pi

rel. int. 10

502 954 1000 1442 1492 1931 2000 2153 2418 2465 2893 2951 3368 3428 3843 3907 4324 4392

0.33 I.13 0.30 0.76 0.39 I .06 0.17 0.37 0.39 0.36 0.39 0.20 0.31 0.24 0.20 0.22 0.17

1.00

freq. (cm-‘) b,

ml. int. ‘)

width (cm-‘) dr

1434 1492 1925 1974 2147 2403 2459

0.22 0.85 0.17 0.40 0.23 0.30 0.09 0.25 0.22

11 6 14 14 14 23 20 <6 40 29

3351 3415

0.27 0.14

61 44

(3844)

(0.49)

(134)

(4306)

(0.60)

(150)

(4767)

(0.64)

(162)

(5226)

(0.52)

(188)

(5674)

(0.34)

(154)

501 950

1000

1.00

a) Converted from the relative transition probabilities given in ref. [ 81 by multiplication by o,,, [ 31. w Estimated uncertainties are about 3 cm-i. Numbers in parentheses are apparent peak frequencies of unresolved C-I stretching overtones with combination bands. c, Relative intensities based on integrated areas. Estimated uncertainties are about 20%. ‘i Full width at half maximum of best-fit Lorentzian, corrected for instrumental width. Estimated error limits are about 20%, and up to 40% for the widths in parentheses.

Table 3 CHJ model potential parameters

Fig. 3. Absorption cross section of CHJ in hexane, experimental (solid curve) and calculated from the parameters of table 3 (dashed). 180

Ground state

Excited state

CHJ stretch (eq. ( 1) ) R= 22490 cm-’ /?=1.59A-’ r,=2.14 8,

CH91stretch (eq. (2) ) Do=30087 cm-’ C= 8748 cm-’ E10.285

methyl umbrella mode w= 1242 cm-’

methyl umbrella mode cu= 1242 cm-’ 141=0.3”

*) Separation between ground and excited state potential minima in dimensionless coordinates.

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tional Raman peaks were limited by the instrumental resolution of = 30 cm-’ [ 81. In solution, the bandwidths are strongly dependent on vibrational quantum number and range from 9 cm-’ for the fundamental to > 100 cm-’ for the highest observed overtones. The vibrational line broadening in CD,1 in solution is even more pronounced, making it impossible to separate the overtone and combination bands at high quantum numbers.

5. Discussion Comparison of the CHJ relative Raman intensities in vapor and solution phases suggests that solvation does not greatly affect the dynamics of photodissociation at least up to an increase in C-l bond length of ~0.4 A. This lack of an observable effect on the photodissociation may not be surprising given that our experiment is sensitive to the dynamics only at very short times; the time-dependent overlap for the O-9 Raman transition is significantly different from zero only for times less than ~20 fs. Our experiment also probes the upper state potential surface only over regions where there is still a fairly strong driving force for dissociation; based on our simple model parameters of table 3, the slope of the excited state surface along the C-I stretching coordinate at a displacement of 0.4 8, is 6900 cm-l/A, which may well be very large compared with any restoring force exerted by the solvent. Clearly it would be helpful to obtain accurate intensities in both vapor and solution phases up to higher levels of vibraTable tional excitation, and this is being pursued. 1 shows that the simple excited state model potential we have employed (eq. (2) ) does a reasonable job of reproducing the relative intensities of the various members of the C-I stretching progression. One notable point of disagreement is that the O-2 to O+ 1 ratio is observed in both vapor and solution phase to be considerably higher than calculated. Changes in the excited state potential have little effect on this ratio as long as the potential is constrained to reproduce the correct absorption bandwidth, which is determined essentially by the slope of the upper surfa?e at the ground state geometry. In fact, calculations in which the excited state was modeled as a harmonic potential having a low frequency and very

LETTERS

23 March 1990

large equilibrium displacement (a reasonable approximation to a globally unbound surface for propagation times short compared with the harmonic frequency) gave results very similar to those obtained from the exponential potential. The more complex two-dimensional coupled anharmonic potential employed by Sundberg et al. [ lo] fits the O-+2: O+ 1 C-I ratio even less well than does our simple model. Curve crossing to other potential surfaces and/or coordinate dependence of the transition moment may be required to account for the observed intensities; the calculations of Shapiro, which include both of these effects, actually predict more intensity in the O-t2 transition than in the fundamental [ 271. The calculated absolute Raman cross section for the 3, transition is about 40% lower than observed, in spite of the fact that our calculation includes no electronic dephasing; if r were nonzero, the predicted Raman intensities would be even lower. In all likelihood this discrepancy arises from the same factor( s) that cause the calculated relative intensities to be somewhat in error. It would be very helpful to have absolute cross sections in the gas phase as well, but these have not yet been measured. While there is some uncertainty about the gas phase vibrational frequencies as discussed in section 4, it appears that for CHJ Ihe C-I stretching frequencies are all lower in solution than in the vapor, with the magnitude of the shift increasing with increasing vibrational quantum number. This is in qualitative agreement with the results of Kiefer and Bernstein on IZ in various solvents [ 281, and indicates that the attractive long-range dispersion forces dominate the repulsive nearest-neighbor collisional interactions for this system [ 29-3 11. The increased bandwidths for highly excited vibrational levels in solution could be due either to an “inhomogeneous” distribution of different local environments for different scatterers or to rapid phase or energy relaxation of individual molecules excited to high quantum levels. Future work will seek to employ existing theories of vibrational frequency shifts and line broadening in solution 130,311 to quantitatively evaluate these contributions. Prior work of our group has focused on the analysis of resonance Raman intensities as a probe of excited state dynamics. However, even for small molecules the interpretation of the measured intensities I81

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relies upon having an accurate description of the ground state vibrations. Furthermore, eq. (4) for the resonance Raman cross section applies only to the integrated area of a particular isolated transition. A complete description of the resonance Raman spectrum, including peak positions and vibrational linewidths as well as intensities, contains a three-time integral involving dynamics on both the ground and excited state potential surfaces. Future work on CHJ and, particularly, CD,1 will involve employing more realistic models for both the ground and excited state potential surfaces, as well as extending our own experimental work to other solvents and the gas phase and to other excitation frequencies.

Acknowledgement The authors acknowledge Dr. Roseanne Sension for providing us with her program for calculating Morse oscillator wavefunctions and Dr. David Phillips for many helpful discussions. This work was supported by grants from the NSF (CHE-8709485 and CHE-89 5722 1). ABM is the recipient of a Dreyfus Distinguished New Faculty Award, a Packard Fellowship in Science and Engineering, a Sloan Research Fellowship, and an NSF Presidential Young Investigator Award.

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[6] L.R. Khundkar and A.H. Zewail, Chem. Phys. Letters 142 (1987) 426. [ 7 ] D. Imre, J.L. Kinney, A. Sinha and J. Krenos, J. Phys. Chem. 88 (1984) 3956. [S] M.O. Hale, G.E. Galica, S.G. Glogover and J.L. Kinsey, J. Phys. Chem. 90 (1986) 4997. (91 E.J. Heller, R.L. Sundberg and D. Tannor, J. Phys. Chem. 86 (1982) 1822. [lo] R.L. Sundberg, D. Imre, M.O. Hale, J.L. Kinsey and R.D. CoaIson, J. Phys. Chem. 90 (1986) 5001. [ 111 B.R. Johnson, J.L. Kinsey and M. Shapiro, J. Chem. Phys. 88 (1988) 3147. [12] DE. SmithandC.B. Harris, J.Chem.Phys. 87 (1987) 2709, and references therein. [ 131 L.J. Butler, private communication. [ 141 L.E. BNS and V.E. Bondybey, J. Chem. Phys. 65 ( 1976) 71. [ 151 A.B. Myers, B.LiandX.Ci, J. Chem.Phys. 89 (1988) 1876. [ 161 K. Kimura and S. Nagakura, Spectrochim. Acta. 17 ( 1961) 166. [ 171 A. Gedanken and M.D. Rowe, Chem. Phys. Letters 34 (1975) 39. [ 181 B. Li and A.B. Myers, J. Phys. Chem., in press. [ 191 D.J. Donaldson, V. Vaida and R. Naaman, J. Chem. Phys. 87 (1987) 2522. [ 201 P. Brewer, P. Das, G. Ondrey and R. Bersohn, J. Chem. Phys. 79 (1983) 720. [21] A.B. Myers, R.A. Mathies, D.J. Tannor and E.J. Heller, J. Chem. Phys. 77 (1982) 3857. [22] R.J. Sension and H.L. Strauss, J. Chem. Phys. 85 (1986) 3791. [23] M.D. Feit, J.A. Fleck Jr. and A. Steiger, J. Comput. Phys. 47 (1982) 412. [24] X. ci, M.A. Pereira and A.B. Myers, J. Chem. Phys., submitted for publication. [25] J.L. Duncan, A. Allan and D.C. McKean, Mol. Phys. 18 (1970) 289. [26] M. Constant and R. Fauquembergue, J. Chem. Phys. 72 (1980) 2459. [27] M. Shapiro, J. Phys. Chem. 90 (1986) 3644. [28] W. Kiefer and H.J. Bernstein, J. Raman Spectry. 1 (1973) 417. [29] D. Ben-Amotz, M.R. Zakin, H.E. King Jr. and D.R. Herschbach, J. Phys. Chem. 92 (1988) 1392. [ 301 KS. Schweizer and D. Chandler, J. Chem. Phys. 76 ( 1982) 2296. [ 311 M.R. Zakin and D.R. Herschbach, J. Chem. Phys. 89 ( 1988) 2380.