Born-Oppenheimer potential energy surfaces for Kohn-Sham models in the local density approximation

TL;DR

This paper demonstrates that the Born-Oppenheimer potential energy surface in Kohn-Sham theory closely resembles that in Thomas-Fermi theory at small nuclear separations and establishes a lower bound on nuclear distances if a minimum exists.

Contribution

It provides a rigorous comparison between Kohn-Sham and Thomas-Fermi potential energy surfaces and proves a lower bound on nuclear distances in Kohn-Sham models.

Findings

Potential energy surfaces are similar up to o(R^{-7}) for small R.

Existence of a minimizing configuration implies a minimum nuclear distance.

The minimal nuclear distance is independent of nuclear charges.

Abstract

We show that the Born-Oppenheimer potential energy surface in Kohn-Sham theory behaves like the corresponding one in Thomas-Fermi theory up to $o(R^{-7})$ for small nuclear separation $R$. We also prove that if a minimizing configuration exists, then the minimal distance of nuclei is larger than some constant which is independent of the nuclear charges.