Positive orbital energies and the instabilities of orbital-optimized wave functions

Abstract

A simple relation between positive orbital energies and the instability of many‐particle wave functions is established for many‐particle systems. Positive orbital energies in Hartree–Fock wave functions imply many‐particle wave function instability. Positive orbital energies in multiconfiguration self‐consistent‐field wave functions do not necessarily imply total wave function instability. The determining factor is the occupation number of the orbital having the positive energy. Based on this, an approximate stability condition is stated for general multideterminantal wave functions.