Theoretical investigation of the Renner-Teller effect in Δ electronic states of tetra-atomic molecules. 1. Variational calculation of vibronic structure in the 1¹Δ<inf>g</inf> state of B<inf>2</inf>H<inf>2</inf>

Abstract

A variational approach for the ab initio handling of the Renner-Teller effect in Δ electronic states of tetra-atomic molecules is presented. The model Hamiltonian involves four nuclear degrees of freedom which correlate for a linear nuclear arrangement with two doubly degenerate bending modes. The bond lengths are assumed to be kept fixed at their equilibrium values and the effect of end-over-end rotations is neglected. The kinetic energy operator and the general form of the potential surfaces employed allow in principle for a treatment of large amplitude bending vibrations. However, because of restrictions implied, such as neglect of coupling between bending and stretching vibrations and interactions with other electronic states, the approach is aimed primarily at molecules bending with relatively small amplitudes around their linear equilibrium geometries. Two algorithms are developed, one for symmetric acetylene-like (A-B-B-A) molecules, the other for asymmetric (A-B-C-D) species. The approach is applied to calculate the vibronic spectrum of the lowest lying excited state, 1Δg, of B2H2, employing ab initio computed potential energy surfaces. © 1999 Taylor & Francis Group, LLC.