1206.6158 (Tim Gould et al.)

The ambiguous nature of exchange, correlation and Hartree physics in
ensemble density functional theory, and what to do about it    [PDF]

Tim Gould, John F. Dobson

By considering the physics of non-interacting ensembles we better generalise the notion of `exact exchange' (EXX) to systems with fractional occupations in the frontier orbitals (called LEXX), in part by exploiting ambiguities in the definitions of `correlation', `exchange' and `Hartree' physics in ensemble systems. The LEXX is employed in an optimised effective potential (OEP) approach (OLEXX) to approximate groundstate energies, where it is bounded by the `ensemble EXX' (EEXX) energy and standard fractional OEXX energy via $E^{\EEXX}\leq E^{\OLEXX} \leq E^{\OEXX}$. Analysis of the OLEXX explains the success of standard OEP methods for diatoms at large spacing, and why they can fail when both spins are allowed to be non-integer. The OLEXX is demonstrated on H, Li and Na with fractional electron number with improvements over OEXX for all cases.

View original: http://arxiv.org/abs/1206.6158