A many-body approach to the vibrational structure in molecular electronic spectra. I. Theory

A general Hamiltonian which describes the coupled motion of electrons and nuclei in a molecule is derived. In the one-particle approximation an exact solution for the vibrational intensity distribution of arbitrary electronic transitions (except those between linear and bent configurations) is given. Only the data of the initial electronic state are required and only linear equations have to be solved in the calculation. A formalism to include many-body effects, in which also only properties of the initial electronic state are needed, is presented. To calculate the gross features of the spectral distribution, especially of importance for the interpretation of low resolution spectra, a moment expansion is derived. The influence of the coupling constants appearing in the Hamiltonian on the vibrational spectrum is briefly discussed.