Density-potential inversion from Moreau-Yosida regularization

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.

References in corpus (2)

• Kohn-Sham theory with paramagnetic currents: compatibility and functional differentiability
• Domains of time-dependent density-potential mappings

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• Constrained Search in Imaginary Time