arXiv subjects

Eli Kraisler

Publications and source records attributed to Eli Kraisler.

21 records · Page 2Linked to original sources

arXiv2013

Piecewise Linearity of Approximate Density Functionals Revisited: Implications for Frontier Orbital Energies

In the exact Kohn-Sham density-functional theory (DFT), the total energy versus the number of electrons is a series of linear segments between integer points. However, commonly used approximate density functionals produce total energies that do not exhibit this piecewise-linear behavior. As a result, the ionization potential theorem, equating the highest occupied eigenvalue with the ionization potential, is grossly disobeyed. Here, we show that, contrary to conventional wisdom, most of the required piecewise-linearity of an arbitrary approximate density functional can be restored by careful consideration of the ensemble generalization of DFT. Furthermore, the resulting formulation introduces the desired derivative discontinuity to any approximate exchange-correlation functional, even one that is explicitly density-dependent. This opens the door to calculations of the ionization potential and electron affinity even without explicit electron removal or addition. All these advances are achieved while neither introducing empiricism nor changing the underlying functional form. The power of the approach is demonstrated on benchmark systems using the local density approximation as an illustrative example.

cond-mat.mtrl-sci↗

arXiv2010

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

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.

physics.chem-ph↗

arXiv2010

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.A

physics.chem-ph↗