Excitations and benchmark ensemble density functional theory for two electrons

Aurora Pribram-Jones, Zeng-hui Yang, John R. Trail, Kieron Burke, Richard J. Needs, Carsten A. Ullrich
2014 Journal of Chemical Physics  
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 (SEHX), is derived. Exact conditions that are proven include the signs of the correlation energy components, the virial theorem for
more » ... exchange and correlation, 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.
doi:10.1063/1.4872255 pmid:24832349 fatcat:eev3rp7bazcwpp4gfj3ffgao34