James L. Bills

Atomic orbital energies in calcium to copper

Abstract Three types of orbital energies, classified as ionizable, configurative, and additive, are found for Ca to Cu. The ionizable orbital energies explain the easier ionization of 4s than 3d in M[Ar]4s 2 3d N . The configurative orbital energies select the ground configuration by approximating the Hartree-Fock energy of the transition M[Ar]4s 2 3d N → M[Ar]4s 1 3d N +1 . The additive orbital energies indicate the changes in the valence and core orbitals caused by the above transition. The changes in both the valence energy and the core energy are dominated by the change in valence exchange energy.

Symmetry coordinates and group orbitals from basis functions

The gradients of the basis functions of group theory are vector-valued basis functions. When one of the components of such a gradient is evaluated at atomic positions, and the values are summed over a set of equivalent atoms, the result represents a symmetry coordinate and/or a group orbital.

Probing the Orbital Energy of an Electron in an Atom

This article answers an appeal for simple theoretical interpretations of atomic properties. A theoretical snapshot of an atom, showing the screened nuclear charge and the electron to be ionized at its radius of zero kinetic energy, enables anyone to approximate its ionization energy, I. The trends in the screened charges and in the electronic radii are exhibited for the twenty atoms from H to Ca. Values are also given for the ions He+, Be+, Mg+, Ca+, H–, F–, and Cl–. These charges and radii are used to explain the trends in ionization energies.