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