Excited state geometry changes from preresonance Raman intensities: Isoprene and hexatriene

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Abstract
A method is presented for using a single preresonance Raman spectrum and an absorption spectrum to obtain changes in equilibrium geometry upon electronic excitation. The relative displacements along each of the vibrational normal coordinates are obtained from the Raman intensities, while the overall scaling of the displacements is determined by the absorption band shape. The absorption spectra, as well as Raman excitation profiles, are calculated using either a sum over vibronic states or a formally equivalent time‐dependent method [S.‐Y. Lee and E. J. Heller, J. Chem. Phys. 71, 4777 (1979)]. The time‐dependent method is computationally much faster than the vibronic sum for large multidimensional systems. Our analysis, which assumes isolated molecules and separable, harmonic surfaces, yields a good fit to the vapor phase absorption spectrum of trans‐hexatriene with a Lorentzian linewidth of 175 cm−1. However, the diffuse absorption spectrum of isoprene cannot be adequately reproduced using Lorentzian line shapes, even when all 33 normal modes are included. Finite temperature and excited state frequency changes are also found to have little effect on the calculated band shapes. These results suggest that inhomogeneous broadening may be a major factor, but calculations using Gaussian broadening fail to accurately reproduce the experimental spectrum.