Approximating Twohyphen;Electron Atomic Energies Using Scaled Eigenfunctions : Semiempirical Coulombhyphen;Repulsion Integrals

摘要

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 onehyphen;electron energy for a twohyphen;electron atom is approximated using scaled onehyphen;electron eigenfunctions leading to a semiempirical estimate of the (1s1s:1s1s) Coulombhyphen;repulsion integral. Finally, twohyphen;electron atomic energies are approximated using scaled eigenfunctions for the corresponding onehyphen;electron atom and a twohyphen;electron atom of different nuclear charge.