Rational fraction representation of diatomic vibrational potentials. II. Application to H2 ground state

Abstract

Representation by rational fraction [L/N] is applied to the Born–Oppenheimer potential V for the H2 ground electronic state. Here L and N are the degrees of numerator and denominator polynomials, respectively, in nuclear separation R. To yield the long range form of V, N is restricted to L+6. A [5/11] fitting has an rms error from Kol/os and Wolniewicz’ V of 0.43×10−7 hartrees on 0.7⩽R⩽12 Bohr radii. This [5/11] extrapolates well above R=12. It has a pole at 1.9×10−4 a.u. with residue 0.98, close to the correct values 0 and 1, respectively.