Density-functional theory (DFT) is a standard method to explore the electronic structure of matter. Atoms are among the simplest physical systems DFT can be applied to. In the present contribution, a systematic calculation of atoms and first ions throughout the periodic table is reported. The results obtained with the local spin-density (LSDA) and the generalized gradient (GGA) approximations are compared to the experimental data. For many atoms the ground state density is not pure-state v-representable (PSVR) and the use of fractional occupations in the Kohn-Sham system is required. As a result, a new algorithm to treat non-PSVR densities within the known mathematical restrictions on the density domain is proposed. The Fe atom is used as an illustration. Finally, the problem of v-representability 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 [1].

[1] E. Kraisler, G. Makov, N. Argaman and I. Kelson, "Fractional occupation in Kohn-Sham density-functional theory and the treatment of non-pure-state v-representable densities", Phys. Rev. A 80, 032115 (2009).