Density-inversion method for the Kohn–Sham potential: Role of the screening density

Abstract

We present a method to invert a given density and find the Kohn-Sham (KS) potential in Density Functional Theory (DFT) which shares that density. Our method employs the concept of screening density, which is naturally constrained by the inversion procedure and thus ensures the density being inverted leads to a smooth KS potential with correct asymptotic behaviour. We demonstrate the applicability of our method by inverting both local (LDA) and non-local (Hartree-Fock and Coupled Cluster) densities; we also show how the method can be used to mitigate the effects of self-interactions in common DFT potentials with appropriate constraints on the screening density.

Approximations based on density-matrix embedding theory for density-functional theories

“…The main problem in both cases is of course how to treat more realistic many-electron problems in three spatial dimensions. But with the advances in the DMET procedure together with novel inversion schemes for the non-interacting mapping [3,22,23,35] it seems worthwhile to further explore a combination of DMET and density-functional-type theories.…”

Approximations based on density-matrix embedding theory for density-functional theories

“…The main problem in both cases is of course how to treat more realistic many-electron problems in three spatial dimensions. But with the advances in the DMET procedure together with novel inversion schemes for the non-interacting mapping [38][39][40][41] it seems worthwhile to Supplemental material for: Approximations based on density-matrix embedding theory for density-functional theories…”

“…where we used the decomposotion of Eq. (41). While this quantity is closely related to the 1RDM, we note that there are two main differences: (i) the T (1) (z 1 , z 2 ) (which for a Hubbard-type of Hamiltonian amounts to next-neighbour hopping term) is included and (ii) z 1 and z 2 do not take all the possible values but only the ones that appear in T (1) (z 1 , z 2 ) (for example in the standard Hubbard it will be only the next neighbors that appear).…”

On the Geometric Potential and the Relationship between the Exact Electron Factorization and Density Functional Theory

“…While the KS system exists and is unique [3], the KS potential v KS cannot be directly obtained from the many-electron wavefunction ψ and/or the one-electron density ρ. Different numerical methods exist to find the exact v KS for a given one-electron density, and some recent discussions and applications of this inverted KS problem can be found in [41,[56][57][58].…”