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Investigation on exchange and correlation holes in a strongly confined electron gas

The nonlocal weighted density approximation (WDA) is compared with the local density approximation (LDA) and generalized gradient approximation (GGA) for a broad range of inhomogeneous electron gas densities that are confined in three dimensions (uniform confinement) and along just one dimension (non-uniform confinement), using a model external potential. All three functionals display similar properties in the uniformly confined case; however LDA and GGA energies diverge with respect to the WDA in the non-uniform strongly confined case. This is caused by the strong anisotropy in the XC hole, demonstrated by the WDA.