Kohn-Sham assumption

In the Kohn-Sham assumption, for a system of interacting electrons moving in a potential V(R) (i.e. a molecular electron cloud in the field of the nuclei) a local potential, Vks(R), can be introduced, such that a system of non-interacting electrons moving in the Vks (R) field will have the same density as the exact density of the interacting electron system. 

In Kohn-Sham (KS) density functional theory (DFT), the occupied orbital functions of a model state are derived by minimizing the ground-state energy functionals of Hohenberg and Kohn. It has been assumed for some time that effective potentials in the orbital KS equations are always equivalent to local potential functions. When tested by accurate model calculations, this locality assumption is found to fail for more than two electrons. Here this failure is explored in detail. The sources of the locality hypothesis in current DFT thinking are examined, and it is shown how the theory can be extended to an orbital functional theory (OFT) that removes the inconsistencies and paradoxes. 

The details of implementation of scalar relativity in GTOFF were presented in [41] and reviewed in [75], so we summarize the essential assumptions and methodological features here. First, all practical DFT implementations of relativistic corrections of which we are aware assume the validity (either explicitly or implicitly) of an underlying Dirac-Kohn-Sham four-component equation. We do also. The Hamiltonian is therefore a relativistic free particle Hamiltonian augmented by the usual non-relativistic potentials... 

Within the context of Kohn-Sham theory, the assumption underlying the LDA is that each point of the nonuniform electron density is uniform but with a density corresponding to the local value. In the LDA for exchange, the wavefunction is therefore assumed to be a Slater determinant of plane waves at each electron position. The corresponding pair-correlation density g[ r, r p(r) is thus the expectation of Eq. (66) taken with res[ ct to this Slater determinant, with the resulting expression then assumed valid locally. (The superscript (0) indicates the result is derived from uniform electron gas theory.)... 

The Kohn-Sham construction of an auxiliary system rests upon two assumptions ... 

The universality of the aforementioned internal energy function F[n] allows us to define the ground-state wave function go to an N-particle system that delivers the minimum of F r and reproduces Uq. Kohn and Sham (KS) [101] made this more practical by nsing noninteractive electrons that are known as Kohn-Sham electrons. They pnt forward a mathematical assumption [99,101-103] ... 

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