The complete inverse Kohn-Sham problem: from the density to the energy

TL;DR

This paper presents a comprehensive method to solve the inverse Kohn-Sham problem by determining the effective potential from a given density and then computing the energy through a line integration approach, demonstrated on a nuclear system.

Contribution

It introduces a two-step approach combining potential determination and line integration to solve the inverse Kohn-Sham problem, with a practical benchmark on nuclear systems.

Findings

Successful potential determination from ground state density

Effective energy computation via line integration

Promising results on a simplified nuclear system

Abstract

A complete solution to the inverse problem of Kohn-Sham (KS) density functional theory is proposed. Our method consists of two steps. First, the effective KS potential is determined from the ground state density of a given system. Then, the knowledge of the potentials along a path in the space of densities is exploited in a line integration formula to determine numerically the KS energy of that system. A possible choice for the density path is proposed. A benchmark in the case of a simplified yet realistic nuclear system is shown to be successful, so that the method seems promising for future applications.