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The exchange-correlation hole and potential of the homogeneous electron gas have been investigated within the random-phase approximation, employing the plasmon-pole approximation for the linear density response function. The angular…
We introduce a new paradigm for finite and infinite strict-one-dimensional uniform electron gases. In this model, $n$ electrons are confined to a ring and interact via a bare Coulomb operator. In the high-density limit (small-$r_s$, where…
From a simplified version of the mathematical structure of the strong coupling limit of the exact exchange-correlation functional, we construct an approximation for the electronic repulsion energy at physical coupling strength, which is…
The homogeneous electron gas is one of the most studied model systems in condensed matter physics. It is also at the basis of the large majority of approximations to the functionals of density functional theory. As such, its…
We devise a nonlocal correlation energy functional that describes the entire range of dispersion interactions in a seamless fashion using only the electron density as input. The new functional is considerably simpler than its predecessors…
We use the exact strong-interaction limit of the Hohenberg-Kohn energy density functional to approximate the exchange-correlation energy of the restricted Kohn-Sham scheme. Our approximation corresponds to a highly non-local density…
We present a detailed study of the exchange-correlation hole and exchange-correlation energy per particle in the Si crystal as calculated by the Variational Monte Carlo method and predicted by various density functional models. Nonlocal…
Most density functionals have been developed by imposing the known exact constraints on the exchange-correlation energy, or by a fit to a set of properties of selected systems, or by both. However, accurate modeling of the conventional…
We use variational quantum Monte Carlo to calculate the density-functional exchange-correlation hole n_{xc}, the exchange-correlation energy density e_{xc}, and the total exchange-correlation energy E_{xc}, of several electron gas systems…
The construction of density-functional approximations is explored by modeling the adiabatic connection em locally, using energy densities defined in terms of the electrostatic potential of the exchange-correlation hole. These local models…
In principle, many-electron correlation energy can be precisely computed from a reduced Wigner distribution function ($\mathcal{W}$) thanks to a universal functional transformation ($\mathcal{F}$), whose formal existence is akin to that of…
We put forward new approach for the development of a non-local density functional by a direct modeling of the shape of exchange-correlation (xc) hole in inhomogeneous systems. The functional is aimed at giving an accurate xc-energy and an…
We train a neural network as the universal exchange-correlation functional of density-functional theory that simultaneously reproduces both the exact exchange-correlation energy and potential. This functional is extremely non-local, but…
Electronic correlation is a fundamental topic in many-electron systems. To characterize this correlation, one may introduce the concept of exchange-correlation hole. In this paper, we first briefly revisit its definition and relation to…
The correlation holes for densities of equal and opposite spin around a test electron are determined from the Schr\"{o}dinger equation with proper boundary conditions. The traditional "exchange" term follows from the boundary condition…
We consider density functionals for exchange and correlation energies in two-dimensional systems. The functionals are constructed by making use of exact constraints for the angular averages of the corresponding exchange and correlation…
Radial, angular and total correlation energies are calculated for four two-electron systems with atomic numbers Z=0-3 confined within an impenetrable sphere of radius R. We report accurate results for the non-relativistic, restricted…
We present a practical and accurate density functional for the exchange-correlation energy of electrons in two dimensions. The exchange part is based on a recent two-dimensional generalized-gradient approximation derived by considering the…
The capability of density-functional theory to deal with the ground-state of strongly correlated low-dimensional systems, such as semiconductor quantum dots, depends on the accuracy of functionals developed for the exchange and correlation…
We consider electronic exchange and correlation effects in density-functional calculations of two-dimensional systems. Starting from wave function calculations of total energies and electron densities of inhomogeneous model systems, we…