SOLVATION STATE-SELECTIVE EXCITATION IN RESONANCE RAMAN-SPECTROSCOPY - II - THEORETICAL CALCULATION

We have reported in the previous paper [J. Chem. Phys. 109, 9075 (1998 )] that the Raman Stokes shifts of the C=O and the C=N stretching mode s in the resonance Raman spectra of a solvatochromic dye, phenol blue (PB), appear to depend on the excitation photon energy in polar or pro tic solvents. The reason was ascribed to the solvation state selective excitation due to the inhomogeneous distribution of the solvation env ironment. In this paper we have made a theoretical model calculation t o demonstrate that the solvation state selective excitation indeed bri ngs about the excitation energy dependence of the resonance Raman Stok es shift in solution. In our model, both the electronic and the vibrat ional transitions are linearly coupled to the same harmonic bath, to e mbody the coupling between the fluctuations of the electronic and the vibrational transition energies. The absorption and the resonance Rama n cross sections are formulated for this model on the basis of the tim e dependent path integral method. In the formulation, the finite relax ation time of the bath mode and the vibrational progressions in the ab sorption spectra are also taken into account. We have calculated the r esonance Raman spectra at various excitation photon energies for the m odel system probable for PB in methanol. The parameters for the calcul ation are estimated from the analysis of the absorption and the resona nce Raman spectra. It is demonstrated that the Raman Stokes shift inde ed depends on the excitation energy for this model. It is noted that t he vibrational dephasing due to the coupling with the solvent bath mod e should be faster than the relaxation time of the bath mode for the e xcitation energy dependence of the Raman Stokes shift to be observed. (C) 1998 American Institute of Physics. [S0021-9606(98)00544-3].