Density-potential inversion from Moreau-Yosida regularization

TL;DR

This paper links density-potential inversion in quantum systems to Moreau-Yosida regularization, providing a mathematical framework that enhances the understanding and systematic improvement of inversion procedures in density-functional theory.

Contribution

It demonstrates how inversion procedures relate to Moreau-Yosida regularization and shows their limit behavior as the regularization parameter approaches zero.

Findings

Inversion procedures can be understood as a limit of Moreau-Yosida regularization.

Provides a systematic way to improve density-potential inversion.

Insights into the role of regularization in density-functional theory.

Abstract

For a quantum-mechanical many-electron system, given a density, the Zhao-Morrison-Parr method allows to compute the effective potential that yields precisely that density. In this work, we demonstrate how this and similar inversion procedures mathematically relate to the Moreau-Yosida regularization of density functionals on Banach spaces. It is shown that these inversion procedures can in fact be understood as a limit process as the regularization parameter approaches zero. This sheds new insight on the role of Moreau-Yosida regularization in density-functional theory and allows to systematically improve density-potential inversion. Our results apply to the Kohn-Sham setting with fractional occupation that determines an effective one-body potential that in turn reproduces an interacting density.