Towards the Kantorovich dual solution for strictly correlated electrons in atoms and molecules

TL;DR

This paper introduces a new nested optimization approach to directly solve the Kantorovich dual problem, enabling a more general and system-independent treatment of strictly correlated electrons in atoms and molecules.

Contribution

The authors develop a nested optimization method that directly addresses the Kantorovich dual problem, overcoming previous system-specific limitations.

Findings

Enables treatment of strictly correlated electrons in diverse systems.

Provides a direct computational approach to the Kantorovich dual problem.

Facilitates analysis of the exchange-correlation functional in the strong interaction limit.

Abstract

The many-body Coulomb repulsive energy of strictly correlated electrons provides direct information of the exact Hohenberg-Kohn exchange-correlation functional in the strong interaction limit. Until now the treatment of strictly correlated electrons is based on the calculation of co-motion functions with the help of semi-analytic formulations. This procedure is system specific and has been limited to spherically symmetric atoms and strictly 1D systems. We develop a nested optimization method which solves the Kantorovich dual problem directly, and thus facilitates a general treatment of strictly correlated electrons for systems including atoms and small molecules.