Density-potential inversion from Moreau-Yosida regularization

• URL: http://arxiv.org/abs/2212.12727v3
• Date: Sat, 1 Apr 2023 12:48:03 GMT
• Title: Density-potential inversion from Moreau-Yosida regularization
• Authors: Markus Penz, Mih\'aly A. Csirik, Andre Laestadius
• Abstract summary: Zhao-Morrison-Parr method is used to compute the effective potential that yields precisely that density. We show how this and similar inversion procedures relate to the Moreau-Yosida regularization of density functionals on Banach spaces.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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