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

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.

References in corpus (4)

• Density Functional Theory -- an introduction
• Degeneracy in Density Functional Theory: Topology in v- and n-Space
• Thermodynamics as an alternative foundation for zero-temperature density functional theory and spin density functional theory
• Occupation numbers in density-functional calculations

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• First-principles derivation and properties of density-functional average-atom models
• Ionization Potentials and Fundamental Gaps in Atomic Systems from the Ensemble-DFT Approach
• Simulating one hundred entangled atoms using projected-interacting full configuration interaction wavefunctions corrected by projected density functionals
• Spherical vs. Non-Spherical and Symmetry-Preserving vs. Symmetry-Breaking Densities of Open-Shell Atoms in Density Functional Theory