Variational rovibrational calculations for tetra atomic linear molecules using Watson’s isomorphic Hamiltonian, I: The C8v4 approach

Abstract

The implementation of an algorithm for the variational determination of rovibrational state energies and wave functions for linear tetra atomic molecules is presented. The approach, termed C8v4, is based on Watson’s isomorphic Hamiltonian formulated in normal coordinates. Products of harmonic oscillator and rigid-rotor functions are used to expand the rovibrational wave function. Intricacies related to the coupling of the bending–rotation basis and the vibrational angular momentum in linear molecules require a careful study of symmetry properties to set up a symmetry adapted basis set. Kinetic energy matrix elements can be evaluated in a fast mixed numerical/analytical fashion. The main computational bottlenecks are the integration of the potential energy matrix and the diagonalization of the Hamiltonian. These can be overcome by exploiting the block structure of the Hamiltonian which is discussed in some detail. Test calculations on acetylene (HCCH) and boranimine (HBNH) are presented and the C8v4 results reproduce previous variational calculations based on a Hamiltonian formulated in internal coordinates.