SYMBOLIC IMPLEMENTATION OF ARBITRARY-ORDER PERTURBATION-THEORY USING COMPUTER ALGEBRA - APPLICATION TO VIBRATIONAL-ROTATIONAL ANALYSIS OF DIATOMIC-MOLECULES

Theoretical details necessary to calculate arbitrary;order correction terms to vibrational-rotational energies and wave functions in Rayleig h-Schrodinger perturbation theory are presented. Since manual derivati on of high-order perturbation formulae is not feasible due to the leng thy algebra involved, the commercial computer algebra software Mathema tica(R) is employed to perform the symbolic manipulations necessary to derive the requisite correction formulae in terms of universal consta nts, molecular constants, and quantum numbers. Correction terms throug h sixth order for (1) Sigma diatomic molecules are derived and then ev aluated for H-2, HD, N-2, CO, and HF. It is thus possible, with the ai d of computer-generated algebra, to apply arbitrarily high-order pertu rbation theory successfully to the problem of intramolecular nuclear m otion. (C) 1998 Published by Elsevier Science Ltd. All rights reserved .