Myers, A.B., Mathies, R.A., Tannor, D.J. & Heller, E.J. Excited state geometry changes from preresonance Raman intensities: Isoprene and hexatriene.
J. Chem. Phys. 77, 3857 (1982).
Publisher's VersionAbstractA method is presented for using a single preresonance Raman spectrum and an absorptionspectrum 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 absorptionspectrum of t r a n s‐hexatriene with a Lorentzian linewidth of 175 cm−1. However, the diffuse absorptionspectrum 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.
Bado, P., et al. Picosecond dynamics of I2 photodissociation.
Picosecond Phenomena III: Proceedings of the Third International Conference on Picosecond Phenomena Garmisch-Partenkirchen, Fed. Rep. of Germany June 16--18, 1982 23, 260-263 (1982).
Publisher's VersionAbstractWhile liquid solution reactions are much more important in chemistry, gas phase reactions are much better understood. Given the central importance of solution reactions to inorganic, organic, industrial and biochemistry, it is rather surprising that, as yet, there is not a single such reaction whose molecular dynamics are understood in detail. Theoretical and experimental evidence already makes clear that much of the important molecular dynamic action in solution reactions occurs on the picosecond and subpicosecond time scales. The dihalogen photodissociation and recombination reactions, X 2 + hv→X + X→X 2, involving the simplest possible molecular reactants and products, diatomics, and in rare gas solution involving only two elements, seem excellent candidates for study.
Tannor, D.J. & Heller, E.J. Polyatomic Raman scattering for general harmonic potentials.
J. Chem. Phys. 77, 202 (1982).
Publisher's VersionAbstractLee and Heller’s time‐dependent theory of resonance Raman scattering is reviewed. This theory is formally identical to the traditional Kramer–Heisenberg–Dirac (KHD) theory but, in its wave packet interpretation, the time‐dependent theory has distinct calculational and conceptual advantages over the KHD sum‐over‐states method. For polyatomics with large Franck–Condon displacements and Duschinsky rotations, where typically the KHD sum is over 1010 states with complicated Franck–Condon factors, these advantages are most pronounced. Wave packet propagation on general harmonic potential surfaces (Franck–Condon displacement, frequency shifts, and Duschinsky rotation) is exact. Formulas for the propagated wave packet are given for various levels of harmonic sophistication. The role of symmetry in the wave packet dynamics is discussed and explicit formulas are derived for the overlap of the moving wave packet ‖φ i (t)〉 with the final state of interest ‖φ f 〉. The half Fourier transform of this overlap gives the Raman amplitude α. The transform method of Tonks and Page, relating absorption and Raman excitation profiles, is shown to arise naturally in our approach. We show excitation profiles calculated by the time‐dependent theory for multidimensional harmonic potential surfaces with and without Duschinsky rotation. For the no‐Duschinsky cases, we compare our results with the profiles of Myers and Mathies and of Champion and Albrecht, which were calculated by a sum‐over‐states; we then discuss some discrepancies between the latter’s results and ours.