The calculation of potential-energy curves from band-spectroscopic data

Analytical expressions equivalent to the Rydberg-Klein graphical construction have been derived for the calculation of potential-energy curves of diatomic molecules from band-spectroscopic data. These expressions have been shown to lead to satisfactory values for De and re and, in contrast to the Rydberg method, enables the potential-energy (p.e.) curve to be evaluated with accuracy in the region of the minimum. The Morse function has been shown to satisfy the analytic expressions where a quadratic in (v+½) has been used to express the band data. A method for dealing with electronic states in which a discontinuity in the law of force occurs has been outlined. By using a series of quadratics to satisfy the band data, the calculation of p.e. curves by the use of expressions given in this paper is reduced to a rapid and accurate procedure. The methods outlined have been illustrated by the computation by several procedures of the p.e. curve for the 3Π0+u state of the bromine molecule.