There are No Unfilled Shells in Hartree-Fock Theory

TL;DR

This paper proves that in exact Hartree-Fock calculations, atomic shells are always fully filled, extending the result to any system with a repulsive two-body interaction like Coulomb.

Contribution

It establishes a general theorem showing shells are always filled in Hartree-Fock theory, regardless of the atom's position in the periodic table or specific electron configurations.

Findings

Shells are always completely filled in exact Hartree-Fock calculations.

The theorem applies to any system with a repulsive two-body interaction like Coulomb.

This result clarifies the nature of atomic shells in Hartree-Fock theory.

Abstract

Hartree-Fock theory is supposed to yield a picture of atomic shells which may or may not be filled according to the atom's position in the periodic table. We prove that shells are always completely filled in an exact Hartree-Fock calculation. Our theorem generalizes to any system having a two-body interaction that, like the Coulomb potential, is repulsive.