Symbolic implementation of arbitrary-order perturbation theory using computer algebra: Application to vibrational–rotational analysis of diatomic molecules

Abstract

Theoretical details necessary to calculate arbitrary-order correction terms to vibrational–rotational energies and wave functions in Rayleigh–Schrödinger perturbation theory are presented. Since manual derivation of high-order perturbation formulae is not feasible due to the lengthy algebra involved, the commercial computer algebra software Mathematica® is employed to perform the symbolic manipulations necessary to derive the requisite correction formulae in terms of universal constants, molecular constants, and quantum numbers. Correction terms through sixth order for 1∑ diatomic molecules are derived and then evaluated for H 2, HD, N 2, CO, and HF. It is thus possible, with the aid of computer-generated algebra, to apply arbitrarily high-order perturbation theory successfully to the problem of intramolecular nuclear motion.