Universal nature of different methods of obtaining the exact Kohn-Sham exchange-correlation potential for a given density

TL;DR

This paper demonstrates that various methods for constructing the exact Kohn-Sham potential from a given density are fundamentally connected, revealing their universal mathematical foundation in density-functional theory.

Contribution

It unifies multiple existing methods under a single Euler equation-based algorithm, providing a fundamental mathematical basis for all such approaches.

Findings

All methods originate from a single Euler equation framework.

The approach clarifies the universal nature of different density-based methods.

Facilitates more accurate construction of Kohn-Sham potentials.

Abstract

An interesting fundamental problem in density-functional theory of electronic structure of matter is to construct the exact Kohn-Sham (KS) potential for a given density. The exact potential can then be used to assess the accuracy of approximate functionals and the corresponding potentials. Besides its practical usefulness, such a construction by itself is a challenging inverse problem. Over the past three decades, many seemingly disjoint methods have been proposed to solve this problem. We show that these emanate from a single algorithm based on the Euler equation for the density. This provides a mathematical foundation for all different density-based methods that are used to construct the KS system from a given density and reveals their universal character.