Rational fraction representation of diatomic vibrational potentials. III. Application to H2+ 2pπu electronic state

Abstract

Rational fractions [L/N] are used to represent the Born–Oppenheimer potential V for the H2+ 2pπu electronic state. Numerator and denominator polynomials in R are of degree L and N, respectively, with N contrained to be L+3. This state has a maximum at R∼26 a.u. (Bohr radii) and a minimum at 7.9 a.u. Hence, it places rather severe demands on a V(R) functional representation. In spite of this, we find that a [6/9] fitting achieves an rms error at 74 R values in 5⩽R⩽90 a.u. of only 6.44×0−9 hartrees. The [6/9] is reliable for interpolation. It extrapolates at low R to a pole at −1.5×10−6 a.u. with residue 0.92 in place of correct values 0 and 1, respectively. The reliability of the extrapolation near R=0, even though no fitting points below 5 a.u. were used, is probably due to the dominance at intermediate R of the nuclear repulsion over the purely electronic energy.