A new functional form for representing vibrational eigenenergies of diatomic molecules. Application to H2+ ground statea)

Abstract

We propose representing the vibrational eigenenergies Ev in a form Ev=D−(vD−v)m [L/N] where v is the quantum number, D is the energy at the dissociation limit, and vD and m are state dependent parameters. The symbol [L/N] denotes a rational fraction with polynomials in (vD−v) of degree L and N in the numerator and denominator, respectively. This permits interpolation between near equilibrium, where power series expansions in v have validity, and near dissociation, where (vD−v)m forms have theoretical basis. We apply this Ev expression with a variety of [L/N] to the Born–Oppenheimer potential of the H2+ ground state. A [2/2] fit yields more accurate first energy differences ΔE (v+1/2) than a polynomial or any other L+N=4 fit. For a given number of variable parameters, the best fits have terms of degree less than L or N missing in either the numerator or denominator. Our best overall fit has vD=19.76, m=6.08, L=2, N=4, and rms error in calculated ΔE (v+1/2) of only 0.006 cm−1. Difficulties that might be encountered in the use of the above Ev expression are discussed in some detail.