Universal nature of different methods of obtaining the exact Kohn-Sham exchange-correlation potential for a given density

Abstract

An interesting fundamental problem in density-functional theory of electronic structure of matter is to construct the exact Kohn-Sham (KS) potential for a given density. The exact potential can then be used to assess the accuracy of approximate functionals and the corresponding potentials. Besides its practical usefulness, such a construction by itself is a challenging inverse problem. Over the past three decades, many seemingly disjoint methods have been proposed to solve this problem. We show that these emanate from a single algorithm based on the Euler equation for the density. This provides a mathematical foundation for all different density-based methods that are used to construct the KS system from a given density and reveals their universal character.

10 pages, 4 figures

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• Density-potential inversion from Moreau-Yosida regularization
• A first step in the nuclear inverse Kohn-Sham problem: from densities to potentials
• Nuclear energy density functionals from empirical ground-state densities
• Local Exchange-Correlation Potentials by Density Inversion in Solids
• Kohn-Sham inversion with mathematical guarantees
• The complete inverse Kohn-Sham problem: from the density to the energy
• Using random numbers to obtain Kohn-Sham potential for a given density
• Regularised density-potential inversion for periodic systems: application to exact exchange in one dimension
• On the Geometric Potential and the Relationship between the Exact Electron Factorization and Density Functional Theory