Physics & Astronomy ETDs

Publication Date



A method is presented for approximating a diatomic molecular vibrational potential by fitting to modified forms of the potential. Power's numerical Born-Oppenheimer potential for the H2+ electronic ground state is the potential used in this thesis. The modification procedure is to multiply the potential by various powers of the internuclear separation. This removes the troublesome Coulomb pole at zero internuclear separation. Graphs of the modified forms are presented. Polynomials were fitted directly to the potential, to the modified forms, and to the pure electronic energy. Comparisons are made among the various representations of the potential obtained from the fits. Generally, polynomial fits directly to the potential give the worst results. Fits to the pure electronic energy give results comparable to the best obtained from fits to the other modified forms. There is no pattern as to which fits (including those to the pure electronic energy) yield the best representation of the potential. Rational fractions whose long-range behavior is proportional to the known long-range behavior of the potential and of some of the modified forms are fit to the potential and some of the modified forms, respectively. With the exact long-range behavior forced, a number of fits yield representations which approximate the potential well over a large range of internuclear separation. The best overall representation is a fit directly to the potential with a 5th degree polynomial in the numerator and a 9th degree polynomial in the denominator. Representations of the potential obtained from fits to the pure electronic energy are good only in the region of small internuclear separation. The H2+ ground state potential was used as a test case. It is hoped that the procedure described in this thesis can be applied to other diatomic molecules.

Degree Name


Level of Degree


Department Name

Physics & Astronomy

First Committee Member (Chair)

Charles Leroy Beckel

Second Committee Member

James Daniel Finley III

Third Committee Member

Howard Carnes Bryant



Document Type