Exact Kohn-Sham potential of strongly correlated finite systems

TL;DR

This paper derives an exact analytical form of the Kohn-Sham potential for strongly correlated finite systems at dissociation, demonstrating its universality and validating it with numerical calculations on a model system.

Contribution

It provides the first explicit analytic expression for the Kohn-Sham potential in strongly correlated dissociation limits, highlighting its universal form.

Findings

Numerical results approach the derived dissociation limit.

The functional form of the potential is universal across systems.

The analytic expression accurately describes strongly correlated dissociation.

Abstract

The dissociation of molecules, even the most simple hydrogen molecule, cannot be described accurately within density functional theory because none of the currently available functionals accounts for strong on-site correlation. This problem has led to a discussion of properties that the local Kohn-Sham potential has to satisfy in order to correctly describe strongly correlated systems. We derive an analytic expression for this potential at the dissociation limit and show that the numerical calculations for a one-dimensional two electron model system indeed approach and reach this limit. It is shown that the functional form of the potential is universal, i.e. independent of the details of the system.