On the relationship between first-order exchange and Coulomb interaction energies for closed shell atoms and molecules

Abstract

First-order Heitler-London interaction energies E ⁽¹⁾ _HL, and their first-order Coulomb and exchange components E ⁽¹⁾ _C and E ⁽¹⁾ _X, have been computed for the Rg-Rg′, H₂-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 = -γ(1 + aR)E ⁽¹⁾ _C, requires modification for interactions involving molecules for physically significant (small) values of R. The modification proposed is E ⁽¹⁾ _X = -γ(1 + aR)(E ⁽¹⁾ _C - E ⁽¹⁾ _S), where E ⁽¹⁾ _S is a correction term for the singularity occurring in E ⁽¹⁾ _C, and two versions of E ⁽¹⁾ _S are developed. The importance of the singularity, and the validity of the relationships between E ⁽¹⁾ _X and E ⁽¹⁾ _C, 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 ⁽¹⁾ _HL, E ⁽¹⁾ _X and E ⁽¹⁾ _C is also discussed briefly.

Additional information

Notes on contributors

William J. Meath

Associated with the Centre for Interdisciplinary Studies in Chemical Physics, University of Western Ontario, and with CEMAID.