Couplings between normal modes studied by the correlation function. Duschinsky effect and fermi resonance

Abstract

The dynamical information contained in a correlation function obtained by the Fourier transform of an electronic spectrum can be used to study strong intermode couplings, such as the Duschinsky effect (DE) and the Fermi resonance (FR). Both of them complicate the calculation of the correlation function by destroying its factorizability. In some particular cases, the DE can greatly simplify the form of the correlation function by concealing one of its inherent frequencies. The DE never leads to a beat or to a systematic decrease of the correlation function. A simple classical approximation for the correlation function which takes into account the Lissajous motion of the center of the wave packet, but does not allow for its deformation or spreading is found to be useful in a harmonic model. The FR leads to a beat in the correlation function which results from a periodic energy transfer from the active to the inactive mode. A practical method is given to extract the perturbed and unperturbed energies as well as the coupling matrix element of a FR from a low-resolution spectrum by Fourier transformation of just that part of the spectrum which corresponds to the quasidegenerate interacting states. The case of the B 2Σ u + state of CS 2 + is treated as an example.