Continued-fraction expansion of the Born-Oppenheimer potential-energy function for diatomic molecules

Abstract

Expansion of the internuclear Born-Oppenheimer potential for diatomic systems, in the form of a continued fraction, has been investigated. This function satisfies all criteria applicable to a real potential curve of molecules in a stable electronic state; it asymptotically approaches a finite value in the dissociation limit, exhibits a minimum energy at the equilibrium internuclear separation, and approaches a positive value greater than a dissociation energy as the separation decreases. The proposed expansion is applied in quantitative analysis of the infrared, microwave, and Raman spectra of BrCl, NaCl, and ${\mathrm{N}}_{2}.$ The observed transitions are reproduced within experimental errors by making use of fewer fitted parameters than in the approach that employs a power expansion of the potential-energy function.