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 S 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. Keywords: perturbation theory; computer algebra; molecular spectroscopy; vibration and rotation; diatomic molecules 1 1. INTRODUCTION Perturbation...