Effective Hamiltonians for Coriolis-coupled nearly degenerate modes: Illustrative examples

Abstract

Using an angular momentum dependent Bogoliubov–Tyablikov (BT) transformation technique effective rotational Hamiltonians are derived for four molecules all of which have a pair of nearly degenerate strongly coupled vibrational modes. The BT transformation is applied to a two-vibrational-mode Hamiltonian obtained by using perturbation theory to eliminate the coupling between all but the nearly degenerate modes. Energy levels computed from the BT effective rotational Hamiltonians and accurate variational calculations agree very well. BT effective Hamiltonians are derived and tested for ozone, formaldehyde, its singly deuterated analog, and chlorodifluoromethane.