Coupling of vibration,rotation, and electron spin in multiplet states

The effective Hamiltonian of Van Vleck (1) for energy calculations of rotating molecules in multiplet states, is extended to include the effect of vibrational angular momentum, within a given nondegenerate electronic state. H_C and H_S operators are defined, to account for vibration-rotation (Coriolis) and spin-vibration interactions, respectively. Such interactions are discussed for degenerate E vibrational states of symmetric tops, as well as for the occurrence of vibrational angular momentum involving different vibrational states, with accidentally low energy separation. Following the classification of Hund's case (b) for the spin-rotation wave function (coupled representation), we find that H_C operators do not mix different F components, whereas H_S operators give also matrix elements between F components differing by one unit in the quantum number N, for given J.