title: Numerical Methods for a Kohn-Sham Density Functional Model Based on Optimal Transport.
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.
authors.affiliation: Zentrum Mathematik, Technische Universität München , Boltzmannstraβe 3, 85747 Garching bei München, Germany.
authors.forename: Huajie
authors.initials: H
authors.lastname: Chen
authors.affiliation: Zentrum Mathematik, Technische Universität München , Boltzmannstraβe 3, 85747 Garching bei München, Germany.
authors.forename: Gero
authors.initials: G
authors.lastname: Friesecke
authors.affiliation: Zentrum Mathematik, Technische Universität München , Boltzmannstraβe 3, 85747 Garching bei München, Germany.
authors.forename: Christian B
authors.initials: CB
authors.lastname: Mendl