![]() In contrast to the local potential theory, a basic integral equation must be solved to express the above relation in explicit form. (r) the Hartree-Fock spatially dependent density. In particular, using a perturbation expansion of the Dirac density matrix, we obtain the exchange energy as an expansion in the displaced charge Δ H.F.(r)=ρ H.F.(r)-ρ 0, ρ 0 being the average electron density and ρ H.F. The present work considers the full Hartree-Fock theory within the same density functional framework. This local potential, by definition, generated the exact charge density in the (infinite) system considered. In a previous paper, the validity of gradient corrections to the Dirac-Slater exchange energy was discussed within the density functional theory, for a local potential.
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