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

In this paper, we study numerical discretizations to solve density func-tional models in the “strictly correlated electrons ” (SCE) framework. Un-like previous studies our work is not restricted to radially symmetric densi-ties. 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.