Related papers: Leading correction to the local density approximat…
The non-relativistic large-$Z$ expansion of the exchange energy of neutral atoms provides an important input to modern non-empirical density functional approximations. Recent works report results of fitting the terms beyond the dominant…
Exact density functionals for the exchange and correlation energies are approximated in practical calculations for the ground-state electronic structure of a many-electron system. An important exact constraint for the construction of…
We study numerically the strong-interaction limit of the exchange-correlation functional for neutral atoms and for Bohr atoms as the number of electrons increases. Using a compact representation, we analyse the second-order gradient…
Careful extrapolation of atomic correlation energies suggests that $E_c$ tends to $-AZ\log{Z} + BZ$ as $Z$ tends to infinity, where $Z$ is the atomic number, $A$ is known, and $B$ is about 38 milliHartrees. The coefficients roughly agree…
The Hohenberg-Kohn density functional was long ago shown to reduce to the Thomas-Fermi approximation in the non-relativistic semiclassical (or large-$Z$) limit for all matter, i.e, the kinetic energy becomes local. Exchange also becomes…
Under a certain scaling, the electron densities of finite systems become both large and slowly-varying, so that the gradient expansions of the density functionals for the Kohn-Sham kinetic and exchange energies become asymptotically exact…
We derive a generalized gradient approximation to the exchange energy to be used in density functional theory calculations of two-dimensional systems. This class of approximations has a long and successful history, but it has not yet been…
We test the Coulomb exchange and correlation energy density functionals of electron systems for atomic nuclei in the local density approximation (LDA) and the generalized gradient approximation (GGA). For the exchange Coulomb energies, it…
Local density approximation for the exchange energy is made for treatment of excited-states in density-functional theory. It is shown that taking care of the state-dependence of the LDA exchange energy functional leads to accurate…
In the present work, we revisit the problem of the inhomogeneous electron gas under the influence of a weak external potential, which allows us to calculate the gradient corrections to the density functional within linear response, an…
The electron density, its gradient, and the Kohn-Sham orbital kinetic energy density are the local ingredients of a meta-generalized gradient approximation (meta-GGA). We construct a meta-GGA density functional for the exchange-correlation…
We derive an exact representation of the exchange-correlation energy within density functional theory (DFT) which spawns a class of approximations leading to correct long-range asymptotic behavior. In what amounts to be the simplest…
We develop relativistic short-range exchange energy functionals for four-component relativistic range-separated density-functional theory using a Dirac-Coulomb Hamiltonian in the no-pair approximation. We show how to improve the short-range…
Lewin and Lieb have recently proven several new bounds on the exchange-correlation energy that complement the Lieb-Oxford bound. We test these bounds for atoms, for slowly-varying gases, and for Hooke's atom, finding them usually less…
The role of the exchange-correlation potential and the exchange-correlation kernel in the calculation of excitation energues from time-dependent density functional theory is studied. Excitation energies of the He and Be atoms are…
In order to assess the accuracy of commonly used approximate exchange-correlation density functionals, we present a comparison of accurate exchange and correlation potentials, exchange energy densities and energy components with the…
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…
We propose a simple gradient-dependent bound for the exchange-correlation energy (sLL), based on the recent non-local bound derived by Lewin and Lieb. We show that sLL is equivalent to the original Lieb-Oxford bound in rapidly-varying…
We propose approximations which go beyond the local density approximation for the short-range exchange and correlation density functionals appearing in a multi-determinantal extension of the Kohn-Sham scheme. A first approximation consists…
We study the asymptotic expansion of the neutral-atom energy as the atomic number Z goes to infinity, presenting a new method to extract the coefficients from oscillating numerical data. We find that recovery of the correct expansion is an…