Unified construction of Fermi, Pauli and exchange-correlation potentials

 Viktor N.StaroverovEgorOspadov

 

 

Abstract

The exchange-correlation potential of the Kohn–Sham density-functional scheme is the difference between the Fermi potential—an effective potential appearing in the one-electron Schrödinger equation for the square root of the electron density—and the Pauli potential, i.e., v_XC(r) = v_F(r) − v_P(r). We show that, for a given external potential and electron number, knowledge of v_F(r) alone is sufficient to generate the corresponding v_P(r) and v_XC(r). The Fermi potential itself can be computed from the system's interacting two-electron reduced density matrix or modeled directly. The unified treatment of these three potentials provides a practical method for accessing accurate functional derivatives of the exchange-correlation, Pauli kinetic, and Levy–Perdew–Sahni energy functionals without having to tackle functional differentiation and numerical challenges of other construction techniques.

 

https://sci-hub.se/https://doi.org/10.1016/bs.aiq.2019.04.002