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Symbolic Implementation of Arbitrary-Order Perturbation Theory Using Computer Algebra: Application to Vibrational-Rotational Analysis of Diatomic Molecules

J. Herbert
W. Ermler
Journal / Anthology

Computers in Chemistry
Year: 1998
Volume: 22
Issue: 2-3
Page range: 169-184

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 ^1E diatomic molecules are derived and then evaluated for H2, HD, N2, CO,and HF. It is thus possible, with the aid of computer-generated algebra, to apply arbitrary high-order perturbation theory successfully to the problem of intramolecular nuclear motion.

*Science > Astronomy