Uniform Electron Gases. II. The Generalized Local Density Approximation in One Dimension

Abstract

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 $\rs$ 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, is 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 Møller-Plesset perturbation energies and exact calculations for a variety of inhomogeneous systems.

26 pages, 2 figures, accepted for publication in Journal of Chemical Physics

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• Chemistry in One Dimension
• Exchange functionals based on finite uniform electron gases
• Generalized local-density approximation and one-dimensional finite uniform electron gases
• A Wigner molecule at extremely low densities: a numerically exact study
• Nodal surfaces and interdimensional degeneracies
• Uniform electron gases: III. Low-density gases on three-dimensional spheres
• Basis-set correction based on density-functional theory: Rigorous framework for a one-dimensional model
• Basis functions for electronic structure calculations on spheres
• Symmetry-broken local-density approximation for one-dimensional systems
• Excited-State Wigner Crystals in One Dimension
• Exact wave functions and entropies of the one dimensional Regularized Calogero model
• Transient Uniform Electron Gases