Correlation Energy in a High-Density Limit from Adiabatic Connection Perturbation Theory
Here the derivation of the Görling-Levy adiabatic perturbation theory is reviewed for the correlation energy, E c [n], in a high-density limit for finite systems, with particular emphasis on the resultant expression in terms of Kohn-Sham orbitals, for the second-order contribution, E c (2)[n]. This contribution occurs through an asymptotic uniform scaling of n(r). The quantity 2E c (2) [n] is especially important because it is the initial slope in the adiabatic connection method (coupling-constant formula) for E c [n], even where n does not belong to a high-density system. The recent bounds and equalities of Ivanov et al, involving E c (2) [n] and its functional derivative, are compared against the numerical results from functional of Perdew-Burke-Ernzerhof and Lee-Yang-Parr.
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