KLEIN–DUNHAM POTENTIAL ENERGY FUNCTIONS IN SIMPLIFIED ANALYTICAL FORM

Abstract

A simple formula, based originally on the work of Klein and Rees, is developed for calculating potential energy curves, except near the dissociation limit, for electronic states of diatomic molecules. Classical turning points r_1,2 are given as functions of vibrational quantum number (V ≡ ν + 1/2), with coefficients depending on observed spectroscopic constants, in the form[Formula: see text]where[Formula: see text]For most states convergence is rapid, but as a rule more so for heavy molecules than for light molecules. Assuming it to be close to the 'true' potential, such a representation affords a convenient means of assessing the accuracy of the Morse or other empirical potential function. Morse curves have also been fitted by least squares to Klein–Rees turning points.Term-by-term comparison between the inverted Dunham series and an equivalent form of the above has led to the surprising discovery that if Dunham's small correction terms are neglected, Klein and Dunham potentials are mathematically identical. This is contrary to the generally held belief that the two should be used in mutually exclusive regions. In the present form these series exhibit better behavior over a wider range than a series giving potential energy as a function of internuclear separation.