Density-potential inversion from Moreau-Yosida regularization

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. We demonstrate how this and similar inversion processes can be understood in terms of the Moreau-Yosida regularization of density functionals. 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