Monotonicity of Born-Oppenheimer electronic energies for excited molecular states

Abstract

The authors consider adiabatic molecular systems consisting of one electron and N>or=2 nuclei with arbitrary positive charges. If all the nuclei are arranged on a line, the angular momentum around the internuclear axis is conserved; using the corresponding separability in cylindrical coordinates it is shown that the lowest electronic energies in each symmetry sector of fixed angular momentum increase if the internuclear distances become larger. This extends previous monotonicity results for the ground state by Lieb and Simon (1978). For the physically most important case N=2 (or N=3) they give a separate proof that emphasizes the basic role of reflection positivity in this context.