ON THE RELATIONSHIP BETWEEN 1ST-ORDER EXCHANGE AND COULOMB INTERACTION ENERGIES FOR CLOSED-SHELL ATOMS AND MOLECULES

First-order Heitler-London interaction energies E(HL)(1), and their first-order Coulomb and exchange components E(C)(1) and E(X)(1), have been computed for the Rg-Rg', H-2-Rg and N2-Rg interactions, where the rare gas Rg or Rg' can be He, Ne, Ar or Kr. High quality self-consistent field wavefunctions are used to represent the isolated species and the results are presented as a function of the interspecies distance and relative orientation (where appropriate). The results are used to investigate the relationship between the first-order exchange and Coulomb energies. and it is found that the often used linear relationship, E(X) = -gamma(1 + aR)E(C)(1), requires modification for interactions involving molecules for physically significant (small) values of R. The modification proposed is E(X)(1) = -gamma(1 + aR)(E(C)(1) - E(S)(1), where E(S)(1) is a correction term for the singularity occurring in E(C)(1), and two versions of E(S)(1) are developed. The importance of the singularity, and the validity of the relationships between E(X)(1) and E(C)(1), are discussed as a function of R, orientation, and intrinsic versus basis set incompleteness errors in the models. The analysis reported here augments earlier studies, related to the original model, based on interactions involving H atoms and the He-He interaction using a product of two screened 1s orbitals to represent He. The general usefulness of the ab initio results for E(HL)(1), E(X)(1) and E(C)(1) is also discussed briefly.