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 (12)

• Numerical Methods for the Inverse Problem of Density Functional Theory
• Inverse Kohn-Sham Density Functional Theory: Progress and Challenges
• Differentiable but exact formulation of density-functional theory
• Universal nature of different methods of obtaining the exact Kohn-Sham exchange-correlation potential for a given density
• Guaranteed Convergence of a Regularized Kohn-Sham Iteration in Finite Dimensions
• KS-pies: Kohn-Sham Inversion Toolkit
• Kohn-Sham theory with paramagnetic currents: compatibility and functional differentiability
• Generalized Kohn-Sham iteration on Banach spaces
• Building Kohn-Sham potentials for ground and excited states
• Disorder and interactions in systems out of equilibrium: The exact independent-particle picture from density functional theory
• Some properties of the potential-to-ground state map in quantum mechanics
• Domains of time-dependent density-potential mappings

Cited by in corpus (10)

• The structure of the density-potential mapping. Part II: Including magnetic fields
• Exchange energies with forces in density-functional theory
• Kohn-Sham inversion with mathematical guarantees
• Excited-State-Specific Kohn-Sham Formalism for the Asymmetric Hubbard Dimer
• Solution of the v-representability problem on a one-dimensional torus
• Exchange-only virial relation from the adiabatic connection
• Exchange-Correlation Potentials and Energy Densities through Orbital Averaging and Aufbau Integration
• Regularised density-potential inversion for periodic systems: application to exact exchange in one dimension
• Perspective on Moreau-Yosida Regularization in Density-Functional Theory
• Constrained Search in Imaginary Time