Discussion of the He-He interaction energy in the average energy approximation

Using the Unsöld average energy method a double perturbation theory expression for the interaction energy through second order is obtained which includes intra-atomic correction terms arising from the use of trial wavefunctions to represent the non-interacting molecules. These formal expressions are applied to the ground state He-He interaction and results for the interaction energy are obtained that compare favourably with recent semiempirical and ab initio calculations. The Unsöld calculations are used to investigate approximations that have been introduced into the average energy calculation by other workers, and as a model for discussing the relative importance of second-order charge overlap and exchange effects and the convergence of the multipole treatment of the interaction energy for this typical non-bonded interaction. The results illustrate the importance of knowing as many terms as possible in the R ^-1 expansion of the energy. Finally a portion of this work required the recalculation of the He-He repulsive energy obtained by using the Eckart wavefunction to represent the helium atom. The resultant energy is approximately 25 per cent lower than that previously obtained using this wavefunction for most values of R.