United-Atom Configuration-Interaction Treatment of the He–He Repulsion

Abstract

The repulsive interaction between two normal He atoms is treated by the one-center method, using Slater-type orbitals, for the united-atom configurations 1s22s2 and 1s22pσ2 which are appropriate at smaller and larger internuclear distances, R, respectively. A previous calculation by Huzinaga treated by 1s22pσ2 but not the 1s22s2 configuration. We find the 1s22s2 energy to be below the 1s22pσ2 energy when R < 0.56 a.u. Mixing these two configurations leads to little improvement in the energy; the further admixture of 1s23dσ2 gave a negligible improvement. However, when the basic configuration at small R, 1s22s2, was mixed with the singly excited configuration 1s3dσ2s2, a significant improvement was found (6.2 eV at R=0.5 a.u.). When the singly excited configuration is admixed, the one-electron interaction with the two nuclei contributes to the nondiagonal matrix element and this leads to a greater configuration interaction than for the doubly excited configurations. Although the two-center method gives better results at R=1 a.u., the one-center method with only two configurations appears to be definitely superior for R≲0.6 a.u. when compared with extrapolated energies obtained from the best two-center calculations. With other configurations included, the one-center method should compete with two-center calculations at R=0.75 a.u. Our results tend to confirm the disagreement found between the latest scattering experiments and the most accurate two-center calculations.