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Solving the fundamental and optical gap problems, which yield information about charged and neutral excitations in electronic systems, is one of the biggest challenge in density-functional theory (DFT). Despite their intrinsic difference,…

Chemical Physics · Physics 2018-08-29 Bruno Senjean , Emmanuel Fromager

In density functional theory the exchange-correlation (XC) energy functional can be defined exactly through the coupling-constant ($\lambda$) averaged XC hole $\bar{n}_\text{xc}(\mathbf{r},\mathbf{r}')$, representing the probability…

Chemical Physics · Physics 2023-03-31 Lin Hou , Tom J. P. Irons , Yanyong Wang , James W. Furness , Andrew M. Teale , Jianwei Sun

The discontinuous character of the exact exchange-correlation $(xc)$ energy functional of Density Functional Theory is shown to arise naturally in the subband spectra of semiconductor quantum wells. Using an \emph{ab-initio} $xc$…

Mesoscale and Nanoscale Physics · Physics 2009-11-13 S. Rigamonti , C. R. Proetto

In spin-density-functional theory for noncollinear magnetic materials, the Kohn-Sham system features exchange-correlation (xc) scalar potentials and magnetic fields. The significance of the xc magnetic fields is not very well explored; in…

Materials Science · Physics 2019-09-25 Edward A. Pluhar , Carsten A. Ullrich

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…

Strongly Correlated Electrons · Physics 2009-05-21 E. Rasanen , S. Pittalis , K. Capelle , C. R. Proetto

We present the current-density functional theory for the superconductor immersed in the magnetic field. The order parameter of the superconducting state, transverse component of the paramagnetic current-density, and electron density are…

Superconductivity · Physics 2016-10-04 Katsuhiko Higuchi , Masahiko Higuchi

We present here novel insight into exchange-correlation functionals in density functional theory, based on the viewpoint of optimal transport. We show that in the case of two electrons and in the semiclassical limit, the exact…

Analysis of PDEs · Mathematics 2015-03-19 Codina Cotar , Gero Friesecke , Claudia Klüppelberg

While in principle exact, Kohn-Sham density functional theory -- the workhorse of computational chemistry -- must rely on approximations for the exchange-correlation functional. Despite staggering successes, present-day approximations still…

Density functional theory is the workhorse of modern electronic structure calculations, with wide-ranging applications in chemistry, physics, materials science, and machine learning. At its heart lies the exchange-correlation functional, a…

Chemical Physics · Physics 2026-02-20 Fabien Tran , Susi Lehtola , Stefano Pittalis , Miguel A. L. Marques

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…

Mathematical Physics · Physics 2011-03-14 Rafael D. Benguria , Gonzalo Bley , Michael Loss

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…

Strongly Correlated Electrons · Physics 2010-02-25 E. Rasanen , S. Pittalis

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…

Chemical Physics · Physics 2023-11-28 Kimberly J. Daas , Derk P. Kooi , Tarik Benyahia , Michael Seidl , Paola Gori-Giorgi

We prove that the electron density function of a real physical system can be uniquely determined by its values on any finite subsystem. This establishes the existence of a rigorous density-functional theory for any open electronic system.…

Quantum Physics · Physics 2007-05-23 Xiao Zheng , Fan Wang , GuanHua Chen

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…

Materials Science · Physics 2016-08-24 Kieron Burke , Antonio Cancio , Tim Gould , Stefano Pittalis

Knowledge of the properties of the exchange-correlation functional in the form $\frac 1\lambda v_{xc}([\rho _\lambda ],\frac{{\bf r}}\lambda )$, where $\rho _\lambda ({\bf r})=$ $\lambda ^3\rho (\lambda {\bf r}),$ is important when…

Condensed Matter · Physics 2009-10-28 Daniel Joubert , Mel Levy

In this chapter we first review the Levy-Lieb functional, which gives the lowest kinetic and interaction energy that can be reached with all possible quantum states having a given density. We discuss two possible convex generalizations of…

Mathematical Physics · Physics 2023-09-19 Mathieu Lewin , Elliott H. Lieb , Robert Seiringer

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…

Materials Science · Physics 2016-08-24 Jianmin Tao , Yuxiang Mo

We present and test a new approximation for the exchange-correlation (xc) energy of Kohn-Sham density functional theory. It combines exact exchange with a compatible non-local correlation functional. The functional is by construction free…

Chemical Physics · Physics 2014-05-23 Tobias Schmidt , Eli Kraisler , Adi Makmal , Leeor Kronik , Stephan Kümmel

The derivative discontinuity of the exchange-correlation (xc) energy at integer particle number is a property of the exact, unknown xc functional of density functional theory (DFT) which is absent in many popular local and semilocal…

Strongly Correlated Electrons · Physics 2015-06-11 Gao Xianlong , A-Hai Chen , I. V. Tokatly , S. Kurth

Density functional theory provides the most widespread framework for the realistic description of the electronic structure of solids, but the description of strongly-correlated systems has remained so far elusive. Here we consider a…

Strongly Correlated Electrons · Physics 2016-09-07 Zu-Jian Ying , Valentina Brosco , Giorgia Maria Lopez , Daniele Varsano , Paola Gori-Giorgi , José Lorenzana