Related papers: Testing and Using the Lewin-Lieb Bound in Density …
Lieb's convex formulation of density-functional theory is presented in a pedagogical manner, emphasizing its connection to Hohenberg-Kohn theory and to Levy's constrained-search theory. The Hohenberg-Kohn and Lieb variation principles are…
A widely used approximation to the exchange-correlation functional in density functional theory is the local density approximation (LDA), typically derived from the properties of the homogeneous electron gas (HEG). We previously introduced…
We construct a Laplacian-level meta-generalized gradient approximation (meta-GGA) for the non-interacting (Kohn-Sham orbital) positive kinetic energy density $\tau$ of an electronic ground state of density $n$. This meta-GGA is designed to…
Physically valid and numerically efficient approximations for the exchange and correlation energy are critical for reduced density-matrix functional theory to become a widely used method in electronic structure calculations. Here we examine…
We prove a Lieb-Oxford-type inequality on the indirect part of the Coulomb energy of a general many-particle quantum state, with a lower constant than the original statement but involving an additional gradient correction. The result is…
An alternative type of approximation for the exchange and correlation functional in density functional theory is proposed. This approximation depends on a variable $u$ that is able to detect inhomogeneities in the electron density $\rho$…
Bounds on the exchange-correlation energy of many-electron systems are derived and tested. By using universal scaling properties of the electron-electron interaction, we obtain the exponent of the bounds in three, two, one, and quasi-one…
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 study the properties of the lower bound on the exchange-correlation energy in two dimensions. First we review the derivation of the bound and show how it can be written in a simple density-functional form. This form allows an explicit…
Eleven density functionals are compared with regard to their performance for the lattice constants of solids. We consider standard functionals, such as the local-density approximation and the Perdew-Burke-Ernzerhof (PBE)…
We extend the previously proposed one-parameter double-hybrid density-functional theory [K. Sharkas, J. Toulouse, and A. Savin, J. Chem. Phys. 134, 064113 (2011)] to meta-generalized-gradient-approximation (meta-GGA) exchange-correlation…
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 prove a new lower bound on the indirect Coulomb energy in quantum mechanics in terms of the single particle density of the system. The new universal lower bound is an alternative to the classical Lieb--Oxford bound (with a smaller…
We investigate fundamental properties of meta-generalized-gradient approximations (meta-GGAs) to the exchange-correlation energy functional, which have an implicit density dependence via the Kohn-Sham kinetic-energy density. To this…
We present a new nonempirical density functional generalized gradient approximation (GGA) that gives significant improvements for lattice constants, crystal structures, and metal surface energies over the most popular Perdew-Burke-Ernzerhof…
We revisit the two derivations of the PBE correlation functional: The real-space cut-off of the exchange-correlation hole and the imposition of exact conditions. These differ in the Lieb-Simon limit, exemplified by the scaling of neutral…
By combining the upper and lower bounds to the free energy as given by the Gibbs inequality for two systems with the same intermolecular interactions but with external fields differing from each other only in a finite region of space Gamma,…
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…
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…
The uniform electron gas and the hydrogen atom play fundamental roles in condensed matter physics and quantum chemistry. The former has an infinite number of electrons uniformly distributed over the neutralizing positively-charged…