Polyatomic Raman scattering for general harmonic potentials

Abstract

Lee 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 ‖φi(t)〉 with the final state of interest ‖φf〉. 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.