Exposing minimal composition of Kohn-Sham theory and its extendability

TL;DR

This paper reformulates Kohn-Sham theory using the 1-body density matrix to identify its minimal components and explores its extendability to other physical quantities and systems.

Contribution

It exposes the minimal composition of Kohn-Sham theory through reformulation with the 1-body density matrix and discusses criteria for its extendability.

Findings

Distinguished $v$- and $N$-representabilities from those in the Hohenberg-Kohn theorem.

Reformulation clarifies the minimal ingredients needed for KS theory.

Addresses criteria for extending KS theory to other quantities and systems.

Abstract

Reducing the many-fermion problem to a set of single-particle (s.p.) equations, the Kohn-Sham (KS) theory has provided a practical tool to implement \textit{ab initio} calculations of ground-state energies and densities in many-electron systems. There have been attempts to extend the KS theory so that it could describe other physical quantities, or it could be applied to other many-fermion systems. By generalizing and reformulating the KS theory in terms of the 1-body density matrix, we expose the minimal composition of the theory that enables the reduction of the many-fermion problem to the s.p. equations. Based on the reformulation, several basic issues are reconsidered. The $v$- and $N$-representabilities for the KS theory are distinguished from those for the Hohenberg-Kohn theorem. Criteria for the extendability of the KS theory are addressed.