Cancellation of Kinetic and Potential Energy in Atoms, Molecules, and Solids

TLDR

In valence electron energy levels, large negative core potential energy is largely canceled by large positive kinetic energy, as shown by Phillips and Kleinman via a repulsive pseudopotential. The paper further develops the explicit pseudopotential representation to more clearly demonstrate the extent of this cancellation. The formalism validates common valence‑electron models and enables comparison of similar atoms across periodic rows, elucidating systematic trends in alkali and noble metal energy levels.

Abstract

In the energy levels of valence electrons in atoms, molecules, solids, and liquids, there is a contribution from the large negative potential energy inside the core of the atom and the large positive kinetic energy which the electron has there. Phillips and Kleinman have shown how the kinetic energy can be represented by a repulsive pseudopotential which cancels most of the potential energy inside the core. The explicit representation of the pseudopotential is now developed further to demonstrate more clearly the extent of the cancellation. The formalism justifies the simple models which are in common use for treating valence electrons. It is also used to relate similar atoms from different rows of the periodic table, and in particular to discuss the systematic trends in the energy levels of the alkali and noble metal atoms.