Variation-perturbation treatment of the molecular interaction energy in H2+

Abstract

A new variation-perturbation method is developed to treat the interatomic interactions in one-electron diatomic molecules at all distances. For a diatomic molecule with nuclear charges Za and Zb a variable charge-shifting perturbation is defined as (Zb − ζ)/ra − Zb/rb, where ra and rb are the distances from the electron to the two nuclei. The adjustable parameter ζ, when determined variationally, leads to a small perturbation at all distances. Limiting cases are ζ = 0 and ζ = Zb at zero and infinite separations, respectively. The method is tested by calculations of the ground-state energy of the hydrogen molecular ion, for which the first-order wavefunction is obtained in closed form. Following the procedure of Chang [J. Chem. Phys. 59, 1790 (1973)], both one- and two-center calculations are performed. The results compare favorably with the exact values and converge correctly to the appropriate united- and separated-atom limits. The largest deviation occurs near the equilibrium distance, where the relative error of energy, in the case of two-center treatment, is 0.6%. Several other variational calculations are reported using various united- and separated-atom functions as the basis set. Extension of the perturbation method to HeH+ is briefly discussed.