A flexible approach to vibrational perturbation theory using sparse matrix methods

Abstract

A sparse linear algebra based implementation of Rayleigh-Schrödinger vibrational perturbation theory is presented. This implementation allows for flexibility in the coordinates used to expand the vibrational Hamiltonian as well as the order to which the perturbation theory is performed. It also provides a powerful tool for investigating the origin of spectral intensity and transition frequencies. Specifically, this flexibility allows for the analysis of which terms in the expansions of the Hamiltonian and dipole surface lead to the largest corrections to the energies and transition intensities, and how these conclusions depend on the coordinates used for these expansions. Comparisons of corrections to transition frequencies are reported for the Morse oscillator when the potential is expanded in Δr and Morse coordinates as well as for water, water dimer, and peroxynitrous acid when the molecular Hamiltonians and dipole surfaces are expanded in Cartesian displacement coordinates and in the displacements of the bond-angle-dihedral internal coordinates. Further comparisons of the corrections to the transitions moments are made for H2O and (H2O)2. It is found that while the transition frequencies and intensities are independent of coordinate choice, a good choice of coordinates leads to a cleaner interpretation of the origins of the anharmonicities in these systems.