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Application of Quantum Mechanical Perturbation Theory to Molecular VibrationalRotational
Analysis
Volume 2, Issue 2
1992
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 RayleighSchrödinger
perturbation theory by means of symbolic formula generation using Mathematica.
Current stateoftheart calculations of this type allow treatment only
up to secondorder 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 highorder perturbation theory
can be accurately and efficiently treated to the appropriate level of approximation
as dictated by the molecular BornOppenheimer potential energy surface.
Requisite integrated forms are generated to arbitrary order using a compact
procedural program. A calculation through 15thorder results in over 3,000
lines of formulas representing a total of 32 terms. FortranForms
of the resulting expressions are incorporated into a large, generalpurpose
program for execution on a mainframe computer. Such a procedure can be
applied to other problems governed by equations of the form treated here.
