Numerical methods for a Kohn-Sham density functional model based on optimal transport

TL;DR

This paper develops numerical methods for solving Kohn-Sham density functional models based on optimal transport, specifically addressing the strongly correlated electrons regime without symmetry restrictions, and applies it to the dissociating H2 molecule.

Contribution

It introduces a new numerical discretization for the Kohn-Sham-SCE equations applicable to non-symmetric densities and proves its correctness for the dissociating H2 molecule.

Findings

Numerical discretization successfully applied to H2 molecule.

Validated the SCE density functional model in dissociating limit.

Extended methods beyond radially symmetric densities.

Abstract

In this paper, we study numerical discretizations to solve density functional models in the "strictly correlated electrons" (SCE) framework. Unlike previous studies our work is not restricted to radially symmetric densities. In the SCE framework, the exchange-correlation functional encodes the effects of the strong correlation regime by minimizing the pairwise Coulomb repulsion, resulting in an optimal transport problem. We give a mathematical derivation of the self-consistent Kohn-Sham-SCE equations, construct an efficient numerical discretization for this type of problem for N = 2 electrons, and apply it to the H2 molecule in its dissociating limit. Moreover, we prove that the SCE density functional model is correct for the H2 molecule in its dissociating limit.