New Scaled Atoms-in-Molecules Theory for Predicting Diatomic Potential-Energy Curves. II. Studies of the Calibration Technique and Applications to HeH+, HeH, He2+, H2−, and He2

Abstract

Applications of a recently developed scaled atoms‐in‐molecules theory are reported. In general, the basis used in this theory consists of linear combinations of antisymmetrized products of atomic substate eigenfunctions. Each such basis function Ψ n is modified by introducing scaling parameters s n A and s n B into its component atomic eigenfunctions. Exact expressions have been derived for determining, by reference to experimental atomic energies, all intra‐atomic contributions to the energy matrix elements. All remaining contributions, interatomic in nature, are computed using approximate atomic eigenfunctions. In the present study of HeH+, HeH, He2 +, H2 −, and He2, the Ψ n have been constructed exclusively from ground‐state eigenfunctions for H, He+, He− and He, as appropriate. For evaluating interatomic contributions, the optimum 1s 2 orbital approximations for H− and He have been used. For the homopolar molecules, the theory is applied with exact evaluation of all integrals which occur in the interatomic parts; for all molecules considered, calculations also are done using the Mulliken integral approximation. Finally, results of a calibration technique in which the overlap integral S (1s A , 1s B ) , whether appearing directly or through the Mulliken approximation, is replaced by C 1s A C 1s B S(1s A , 1s B ) are also given; here, C 1s H = 0.88 and C 1s He = 0.8936 were previously determined by forcing the computed X 1 Σ g + energies of H2 and He2 + + to be equal to the corresponding exact energies at their potential‐energy minima (a relative minimum for Ee2 ++). With few exceptions, the calibration technique leads to energy predictions which are significantly better than those obtained at this level of approximation with or without the Mulliken integral approximation.