Approximating Two-Electron Atomic Energies Using Scaled Eigenfunctions : Semiempirical Coulomb-Repulsion Integrals

Abstract

If all electron coordinates in an exact atomic eigenfunction are multiplied by a scaling factor, the kinetic, potential and total energies are modified. Exact equations are derived for these changes. The one-electron energy for a two-electron atom is approximated using scaled one-electron eigenfunctions leading to a semiempirical estimate of the (1s1s:1s1s) Coulomb-repulsion integral. Finally, two-electron atomic energies are approximated using scaled eigenfunctions for the corresponding one-electron atom and a two-electron atom of different nuclear charge.