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

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 the ground-state density is not pure-state v-representable, are treated as ensemble v- representable with fractional occupations of the Kohn-Sham system. A newly developed 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 GGA are only modestly improved with respect to experimental data, as compared to the LSDA. However, even in those groups of atoms where the improvement is systematic, there remains a non-negligible difference with respect to the experiment. The ab-initio electronic configuration in the Kohn-Sham reference system does not always equal the configuration obtained from the spectroscopic term within the independent-electron approximation. It was shown that use of the latter configuration can prevent the energy-minimization process from converging to the global minimum, e.g. in lanthanides. The spin values calculated ab-initio fit the experiment for most atoms and are almost unaffected by the choice of the xc-functional. Among the systems with incorrectly obtained spin there exist some cases (e.g. V, Pt) for which the result is found to be stable with respect to small variations in the xc-approximation. These findings suggest a necessity for a significant modification of the exchange-correlation functional, probably of a non-local nature, to accurately describe such systems. PACS numbers: 31.15.

Assessment of tuning methods for enfacing approximate energy linearity in range-separated hybrid functionals

A range of tuning methods, for enforcing approximate energy linearity through a system-by-system optimization of a range-separated hybrid functional, are assessed. For a series of atoms, the accuracy of the frontier orbital energies, ionization potentials, electron affinities, and orbital energy gaps is quantified, and particular attention is paid to the extent to which approximate energy linearity is actually achieved. The tuning methods can yield significantly improved orbital energies and orbital energy gaps, compared to those from conventional functionals. For systems with integer M electrons, optimal results are obtained using a tuning norm based on the highest occupied orbital energy of the M and M + 1 electron systems, with deviations of just 0.1–0.2 eV in these quantities, compared to exact values. However, detailed examination for the carbon atom illustrates a subtle cancellation between errors arising from nonlinearity and errors in the computed ionization potentials and electron affinities used in the tuning