Configuration interaction studies of the HeH+ molecular ion. I Singlet sigma states

Abstract

The method of superposition of configurations is applied to the singlet sigma states of HeH⁺ which correlate to the separated atom states of principal quantum number less than or equal to 3. The calculations are carried out for internuclear separations in the ranges 0(.1)34.5, 35.0(.5)50.0 bohr. Energy eigenvalues and the expectation values of the electron coordinate along the internuclear line are discussed in this paper. Dipole transition matrix elements and radial coupling matrix elements are presented in a companion paper. The quality of the calculations is exhibited by comparisons of the length and velocity forms of the dipole matrix elements, by the Hellmann‐Feynman theorem, and by the approach to atomic properties at large internuclear separations. Supplementary calculations of higher quality wavefunctions for the lowest states are also reported. These are used to help estimate the extent to which the results of the main calculations have converged toward the exact values. Comparisons with other work are given. It is shown that for internuclear separations greater than about 3 bohr a one‐electron electron model potential approach is quite successful for the excited states. At smaller internuclear separations, and as the united atom limit is approached, current model potential methods cannot be trusted. In this region the model potential, being based on the separated atoms, cannot describe the actual changing charge distributions of the core electron. This work demonstrates the feasibility, for simple systems, of the ab initio structure calculations required for the quantitative description of low‐energy atom‐atom collisions.