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In the framework of Kohn-Sham density-functional theory, systems withground-state densities that are not pure-state v-representable in thenon-interacting reference system (PSVR) occur frequently. In the presentcontribution, a new algorithm, which allows the solution of such systems, isproposed. It is shown that the use of densities which do not correspond to aground state of their non-interacting reference system is forbidden. As aconsequence, the proposed algorithm considers only non-interacting ensemblev-representable densities. The Fe atom, a well-known non-PSVR system, is usedas an illustration. Finally, the problem is analyzed within finite temperaturedensity-functional theory, where the physical significance of fractionaloccupations is exposed and the question of why degenerate states can beunequally occupied is resolved.

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