Group-theoretical study on the Raman tensor patterns in vibrational resonance Raman scattering: Application to the hexabromoiridate (IV) ion

Abstract

A group-theoretical method is described which enables one to calculate the Raman tensor patterns for vibrational Raman scattering under the ’infinitely sharp’ resonance condition. A special attention is paid to the application to the molecules having degeneracy in their ground electronic states. The process of vibrational resonance Raman scattering is recognized as a succession of two vibronic transitions and its initial, intermediate, and final states are considered in vibronic space. The first-order perturbation theory is used to find the effective intermediate states for vibrational Raman scattering, a vibronic interaction Hamiltonian linear in the normal coordinates in the ground electronic state being assumed. The electric dipole transition moments are calculated group-theoretically for the transitions from the initial to intermediate and from the intermediate to final states. They are combined according to Kramers–Heisenberg dispersion formula. The method is applied to the IrBr62− ion, which has a doubly degenerate ground electronic state. The Raman tensor patterns for the three 1←0 vibrational transitions of ν1, ν2, and ν5 modes are derived and are shown to have the antisymmetric part, being consistent with the observation of the anomalous polarization in the vibrational resonance Raman scattering of this ion. The way of calculating the depolarization degrees and reversal coefficients are illustrated.