Fractional occupation in Kohn-Sham density-functional theory and the treatment of non-pure-state v-representable densities

TL;DR

This paper introduces a new algorithm for solving Kohn-Sham density-functional theory systems with non-pure-state v-representable densities, emphasizing the role of fractional occupations and ensemble v-representability.

Contribution

A novel algorithm is proposed that exclusively considers non-interacting ensemble v-representable densities, addressing challenges with non-PSVR systems in DFT.

Findings

The algorithm successfully handles non-PSVR systems like the Fe atom.

Fractional occupations are physically meaningful within finite temperature DFT.

Degenerate states can have unequal occupations due to ensemble considerations.

Abstract

In the framework of Kohn-Sham density-functional theory, systems with ground-state densities that are not pure-state v-representable in the non-interacting reference system (PSVR) occur frequently. In the present contribution, a new algorithm, which allows the solution of such systems, is proposed. It is shown that the use of densities which do not correspond to a ground state of their non-interacting reference system is forbidden. As a consequence, the proposed algorithm considers only non-interacting ensemble v-representable densities. The Fe atom, a well-known non-PSVR system, is used as an illustration. Finally, the problem is analyzed within finite temperature density-functional theory, where the physical significance of fractional occupations is exposed and the question of why degenerate states can be unequally occupied is resolved.