Existence of minimizers in restricted Hartree-Fock theory

Abstract

In this note we establish the existence of ground states for atoms within several restricted Hartree-Fock theories. It is shown, for example, that there exists a ground state for closed shell atoms with N electrons and nuclear charge $Z \geq N-1$. This has to be compared with the general Hartree-Fock theory where the existence of a minimizer is known for $Z >N-1$ only.

Keywords

• Restricted Hartree-Fock functional
• ground states
• variational methods