Perturbation theory with an approximate perturbation: The effect of charge overlap on interatomic interactions

✍ Scribed by Walter J. Deal; Ralph H. Young

• Book ID: 104578841
• Publisher: John Wiley and Sons
• Year: 1976
• Tongue: English
• Weight: 472 KB
• Volume: 10
• Category: Article
• ISSN: 0020-7608
• DOI: 10.1002/qua.560100305

✦ Synopsis

Abstract

The evaluation of interatomic interactions at large separations (R) typically involves neglecting electron exchange, treating the Coulomb interaction between atoms as a perturbation, neglecting third‐ and higher‐order energy contributions, and approximating the Coulomb interaction by a short expansion in spherical harmonics and, usually, powers of R^−1^. This last approximation, using an approximate perturbing Hamiltonian to evaluate a second‐order perturbed energy, is examined here; error bounds and a simple correction are introduced. Three illustrative applications to the HH^+^ interaction are given: the error incurred by truncating the spherical‐harmonic expansion is bounded, the R^−1^ expansion is corrected for the overlap of the “atomic” charge distributions, and the R^−1^ expansion is analyzed to see why it works as well as it does.