On the relationship between the Kohn-Sham potential, the Pauli potential, and the Exact Electron Factorization

The EEF is an exact one-electron theory of a many-electron problem where many-electron effects are described by a potential v in a one-electron Schrödinger equation. This equation is identical to the central equation of Orbital-Free DFT. However, the constructions of v are very different: OF-DFT typically relies on Kohn-Sham DFT and separates v into KS-potential and Pauli potential. In the EEF, v is a sum of physically transparent terms. A particular advantage of the EEF formalism is that it provides explicit equations for the components of v in terms of the many-electron wavefunction, which are neither available for KS-DFT nor for OF-DFT.

The two constructions of v are discussed and illustrated with model systems. Comparison of the EEF to OF-DFT provides also insights into the origin of features of the KS- and Pauli-potential. In this way, the EEF illuminates the link between the fictitious non-interacting KS system and the interacting problem, and it provides fresh ideas for how to solve the many-electron problem efficiently.

References:

E. Kraisler, A. Schild, Phys. Rev. Research 2, 013159 (2020).
J. Kocák , E. Kraisler, A. Schild, to be submitted.