PICOSECOND ANTI-STOKES RAMAN EXCITATION PROFILES AS A METHOD FOR INVESTIGATING VIBRATIONALLY EXCITED TRANSIENTS

A method for estimating vibrational quantum numbers of vibrationally excited transients in solution is proposed. In this method, we calculate anti-Stokes Raman excitation profiles (REPs) which are characteristic of the initial vibrational states involved in the Raman process, and compare them with observed anti-Stokes intensities. We have applied this method to vibrationally hot molecules of canthaxanthin in the So state and those of trans-stilbene in the S1 state. For canthaxanthin, it has been found that the vibrationally excited transients are for the most part on the v level of the C=C stretching mode, and that excess vibrational energy is statistically distributed among all intramolecular vibrational modes. As for S stilbene, vibrational transients are shown to be mostly on the v-level for two vibrational modes examined, while the excess vibrational energy is probably localised on the olefinic C--C stretching mode.


INTRODUCTION
In recent ultrafast studies in solution, knowledge on the intramolecular vibrational redistribution (IVR) processes is increasing. It has *Corresponding author. tPresent address: Department of Chemistry, Faculty of Science, Saitama University, Urawa, Saitama 338, Japan. been suggested that the IVR processes might not be completed within a few picoseconds in some cases. It is important to specify the vibrational quantum states of observed vibrationally excited transients in order to clarify the mechanism of vibrational relaxation. Anti-Stokes Raman scattering arises from only those molecules which are populated in excited vibrational states. It can serve as a direct probe of the vibrational redistribution and/or cooling processes [1][2][3][4]. Frequency shifts of Raman bands can be qualitative measures of excess vibrational energy, but it is usually not easy to specify the quantum numbers since detailed information on anharmonic coupling is needed.
In this paper, we try to obtain information on the energy levels on which vibrationally excited molecules are populated, using picosecond time-resolved anti-Stokes Raman spectroscopy. If [1,4]. The intensity of the anti-Stokes Raman band due to the 'in-phase' C--C stretch rises up to 12 ps, and then decays with a time constant of 15-20 ps. The rise of the intensity of an anti-Stokes Raman band can be attributed to an increase in the population of vibrationally excited transients on the associated energy level generated via internal conversion from the $1 state. We analyzed the C--C stretching anti-Stokes Raman intensity of canthaxanthin in benzene solution at 12 ps by the method proposed above [4]. In order to use the present method, the predictability of anti-Stokes REPs is presumed. We have verified this point for canthaxanthin by observing the cw-excited anti-Stokes and Stokes REPs and simulating them based upon the A term of Albrecht's formula (Franck-Condon mechanism). The observed REPs have been quantitatively reproduced by the simulation. REPs calculated by the same model for several anti-Stokes hot bands of the Franck-Condon active C--C stretching vibration of canthaxanthin are shown in Figure 1. Each REP in for any probe wavelength. On the other hand, if the pump-induced transient is on a highly excited vibrational level, the anti-Stokes Raman intensity arising from the pump-induced transients is expected to increase for a probe wavelength longer than 555 nm. We observed anti-Stokes Raman spectra with 578-nm probe (Fig. 2, lower panel) and compared them with the 555-nm probe spectra. The observed R value seems to be independent of the probe wavelength (R 3.5). This result leads us to a conclusion that the pump-induced anti-Stokes Raman intensity observed in the present study does not arise from highly excited vibrational states but mostly from the lowest excited vibrational state (vc-c 1).
Transient vibrational temperature can be estimated from the Ra value. By comparing the transient temperature from the Ra value and that theoretically calculated by assuming the Boltzmann distribution of excess vibrational energy, we have concluded that the excess energy is statistically distributed among all the intramolecular vibrational modes within 12 ps. The present result suggests that vibrational energy localised first on the C--C stretch is very rapidly redistributed among all vibrational modes.

VIBRATIONAL RELAXATION IN TRANS-STILBENE
As another example, we have studied vibrationally excited transients of trans-stilbene in the S state in a butanol solution. Trans-stilbene is directly excited by ultraviolet light to the vibrationally excited S state if the pump photon has a sufficient excess energy [2,3]. We observed picosecond anti-Stokes Raman spectra of the excited stilbene, with a pump wavelength chosen to give the excess vibrational energy of 5200cm-. With the pump wavelength fixed, the probe-wavelength dependence of picosecond anti-Stokes Raman intensities at 0 ps delay time was recorded and compared with simulated anti-Stokes REPs, to examine the vibrational quantum numbers of the transients. Wavelength/nm FIGURE 3 Probe wavelength dependence of ra, observed (circles) and calculated. The curve denoted as (n, n2) is calculated for the initial vibrational level with the C=C and C--Ph stretching quantum numbers of n and n2, respectively; (0, 1)/(1,0) is calculated on the assumption that the C--C stretching band arises from the (1,0) level and the C--Ph band from (0, 1). the simulated r's (,k0 660nm) for several initial levels included in the anti-Stokes Raman process. The observed r at 0ps delay time is also shown in this figure (filled circles). The observed points are reproduced satisfactorily by the curve calculated on the assumption that the two anti-Stokes Raman bands arise from the lowest excited vibrational levels. This result indicates that the observed vibrationally excited transients are for the most part in the lowest excited vibrational levels, as far as the C---C and C--Ph stretches are concerned.
On the other hand, a further analysis of the relative anti-Stokes intensities suggests that the excess vibrational energy is not statistically distributed among intramolecular vibrational modes. The excess energy seems to be localised on the C--C stretching mode immediately after the photoexcitation.

CONCLUDING REMARKS
In the present study we have shown that anti-Stokes REPs can be used for estimating vibrational quantum numbers of transients. For both of the two systems studied, we have found that the observed transients are in the lowest vibrationally excited states of the Raman-active highfrequency modes. This result is phenomenologically similar to Kasha's rule for electronic excitations, and may possibly be common to a wide range of vibrationally excited transients. It is important to extend the study to a wider range of molecules and to directly observe highly excited transients and their relaxation.