Kohn-Sham inversion with mathematical guarantees

Abstract

We use an exact Moreau-Yosida regularized formulation to obtain the exchange-correlation potential for periodic systems. We reveal a profound connection between rigorous mathematical principles and efficient numerical implementation, which marks the first computation of a Moreau-Yosida-based inversion for physical systems. We develop a mathematically rigorous inversion algorithm which is demonstrated for representative bulk materials, specifically bulk silicon, gallium arsenide, and potassium chloride. Our inversion algorithm allows the construction of rigorous error bounds that we are able to verify numerically. This unlocks a new pathway to analyze Kohn-Sham inversion methods, which we expect in turn to foster mathematical approaches for developing approximate functionals.

6 pages, 4 figures, supporting information see https://github.com/mfherbst/supporting-my-inversion

References in corpus (10)

• Inverse Kohn-Sham Density Functional Theory: Progress and Challenges
• Kohn-Sham calculations with the exact functional
• Understanding density driven errors for reaction barrier heights
• Kohn-Sham theory with paramagnetic currents: compatibility and functional differentiability
• Ab initio electronic density in solids by many-body plane-wave auxiliary-field quantum Monte Carlo calculations
• Accurate Kohn-Sham auxiliary system from the ground state density of solids
• Seven Useful Questions in Density Functional Theory
• Exchange Correlation Potentials from Full Configuration Interaction in a Slater Orbital Basis
• Density-potential inversion from Moreau-Yosida regularization
• Some Problems in Density Functional Theory

Cited by in corpus (3)

• Excited-State-Specific Kohn-Sham Formalism for the Asymmetric Hubbard Dimer
• Regularised density-potential inversion for periodic systems: application to exact exchange in one dimension
• Perspective on Moreau-Yosida Regularization in Density-Functional Theory