Kohn-Sham inversion with mathematical guarantees

TL;DR

This paper introduces a mathematically rigorous Kohn-Sham inversion method using Moreau-Yosida regularization, providing error bounds and demonstrating its application to bulk materials, bridging rigorous mathematics and computational physics.

Contribution

It presents the first implementation of a Moreau-Yosida-based inversion for physical systems with verified error bounds, connecting mathematical theory with practical computation.

Findings

Successful inversion for bulk silicon, gallium arsenide, and potassium chloride

Verified numerical error bounds for the inversion method

Established a new pathway for analyzing and developing approximate functionals

Abstract

We use an exact Moreau-Yosida regularized formulation to obtain the exchange-correlation potential for periodic systems. We reveal a profound connection between rigorous mathematical principles and efficient numerical implementation, which marks the first computation of a Moreau-Yosida-based inversion for physical systems. We develop a mathematically rigorous inversion algorithm which is demonstrated for representative bulk materials, specifically bulk silicon, gallium arsenide, and potassium chloride. Our inversion algorithm allows the construction of rigorous error bounds that we are able to verify numerically. This unlocks a new pathway to analyze Kohn-Sham inversion methods, which we expect in turn to foster mathematical approaches for developing approximate functionals.