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The total energies and the spin states for atoms and their first ions with Z= 1-86 are calculated within the the local spin-density approximation (LSDA)and the generalized-gradient approximation (GGA) to the exchange-correlation(xc) energy in density-functional theory. Atoms and ions for which theground-state density is not pure-state v-representable, are treated as ensemblev- representable with fractional occupations of the Kohn-Sham system. A newlydeveloped algorithm which searches over ensemble v-representable densities [E.Kraisler et al., Phys. Rev. A 80, 032115 (2009)] is employed in calculations.It is found that for many atoms the ionization energies obtained with the GGAare only modestly improved with respect to experimental data, as compared tothe LSDA. However, even in those groups of atoms where the improvement issystematic, there remains a non-negligible difference with respect to theexperiment. The ab-initio electronic configuration in the Kohn-Sham referencesystem does not always equal the configuration obtained from the spectroscopicterm within the independent-electron approximation. It was shown that use ofthe latter configuration can prevent the energy-minimization process fromconverging to the global minimum, e.g. in lanthanides. The spin valuescalculated ab-initio fit the experiment for most atoms and are almostunaffected by the choice of the xc-functional. Among the systems withincorrectly obtained spin there exist some cases (e.g. V, Pt) for which theresult is found to be stable with respect to small variations in thexc-approximation. These findings suggest a necessity for a significantmodification of the exchange-correlation functional, probably of a non-localnature, to accurately describe such systems. PACS numbers: 31.15.A

Ensemble v-representable ab-initio density functional calculation of energy and spin in atoms: atest of exchange-correlation approximations