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Application of Quantum Mechanical Perturbation Theory to Molecular Vibrational-Rotational Analysis

Volume 2, Issue 2
Magdalena M. Dudas and Hsiuchin C. Hsieh, Stevens Institute of Technology
Walter C. Ermler, Molecular Science Research Center and The Ohio State University

The quantum mechanical Schrödinger equation for the vibrational motion of a diatomic molecule is solved to arbitrary order of Rayleigh-Schrödinger perturbation theory by means of symbolic formula generation using Mathematica. Current state-of-the-art calculations of this type allow treatment only up to second-order for polyatomic molecules (i.e. those composed of three or more atoms). It is demonstrated that, by using Mathematica, the lengthy algebraic equations resulting from high-order perturbation theory can be accurately and efficiently treated to the appropriate level of approximation as dictated by the molecular Born-Oppenheimer potential energy surface. Requisite integrated forms are generated to arbitrary order using a compact procedural program. A calculation through 15th-order results in over 3,000 lines of formulas representing a total of 32 terms. FortranForms of the resulting expressions are incorporated into a large, general-purpose program for execution on a mainframe computer. Such a procedure can be applied to other problems governed by equations of the form treated here.

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