Uniform electron gases. II. The generalized local density approximation in one dimension

We introduce a generalization (gLDA) of the traditional Local Density Approximation (LDA) within density functional theory. The gLDA uses both the one-electron Seitz radius r(s) and a two-electron hole curvature parameter eta at each point in space. The gLDA reduces to the LDA when applied to the infinite homogeneous electron gas but, unlike the LDA, it is also exact for finite uniform electron gases on spheres. We present an explicit gLDA functional for the correlation energy of electrons that are confined to a one-dimensional space and compare its accuracy with LDA, second-and third-order Moller-Plesset perturbation energies, and exact calculations for a variety of inhomogeneous systems. (C) 2014 AIP Publishing LLC.