Excitations and benchmark ensemble density functional theory for two electrons.
A new method for extracting ensemble Kohn-Sham potentials from accurate excited state densities is applied to a variety of two-electron systems, exploring the behavior of exact ensemble density functional theory. The issue of separating the Hartree energy and the choice of degenerate eigenstates is explored. A new approximation, spin eigenstate Hartree-exchange, is derived. Exact conditions that are proven include the signs of the correlation energy components and the asymptotic behavior of the potential for small weights of the excited states. Many energy components are given as a function of the weights for two electrons in a one-dimensional flat box, in a box with a large barrier to create charge transfer excitations, in a three-dimensional harmonic well (Hooke's atom), and for the He atom singlet-triplet ensemble, singlet-triplet-singlet ensemble, and triplet bi-ensemble.
Department of Chemistry, University of California-Irvine, Irvine, California 92697, USA.
Aurora
A
Pribram-Jones
Department of Physics and Astronomy, University of Missouri, Columbia, Missouri 65211, USA.
Zeng-Hui
ZH
Yang
Theory of Condensed Matter Group, Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, United Kingdom.
John R
JR
Trail
Department of Chemistry, University of California-Irvine, Irvine, California 92697, USA.
Kieron
K
Burke
Theory of Condensed Matter Group, Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, United Kingdom.
Richard J
RJ
Needs
Department of Physics and Astronomy, University of Missouri, Columbia, Missouri 65211, USA.
Carsten A
CA
Ullrich