Strong Correlation in Kohn-Sham Density Functional Theory

Abstract

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 nonlocal density functional whose functional derivative can be easily constructed, thus transforming exactly, in a physically transparent way, an important part of the electron-electron interaction into an effective local one-body potential. We test our approach on quasi-one-dimensional systems, showing that it captures essential features of strong correlation that restricted Kohn-Sham calculations using the currently available approximations cannot describe. DOI: 10.1103/PhysRevLett.109.246402 PACS numbers: 71.15.Mb, 31.15.ec, 73.21.Hb In principle, Kohn-Sham (KS) density functional theory (DFT) [1,2] should yield the exact ground-state density and energy of any many-electron system, including physical situations in which electronic correlation is very strong, representing them in terms of noninteracting electrons. Currently available approximations for KS DFT, however, fail at properly describing systems approaching the Mott insulating regime [3], the breaking of the chemical bond [4,5], and localization in low-density nanodevices [6][7][8], to name a few examples (for a recent review, see Ref.[9]). Artificially breaking the spin (or other) symmetry can mimic some (but not all) strong-correlation effects, at the price of a wrong characterization of several properties and of a partial loosening of the rigorous KS DFT framework.Indeed, it is very counterintuitive that strongly correlated systems, in which the electron-electron repulsion plays a prominent role, can be exactly represented in terms of noninteracting electrons. For this reason, several authors [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] have used accurate many-body solutions of prototypical strongly correlated systems to obtain (by inversion) and characterize the exact noninteracting KS system. The exact properties needed to describe strong correlation in KS DFT have also been set in a transparent framework [5,26]. These works made it all the more evident how difficult it is to find adequate approximations of the exact KS system, so that, albeit theoretically possible, it may seem unrealistic to describe strongly correlated systems with KS DFT [9].Here, we address this skepticism by showing that the strong-interaction limit of the Hohenberg-Kohn (HK) energy density functional yields approximations capturing strong-correlation effects within the noninteracting restricted self-consistent KS scheme.The Letter is organized as follows. First, we introduce the formalism, using the strong-interaction limit of the HK functional to transform exactly an important part of the manybody interaction into an effective local one-body potential, in a physically transparent way. We then present pilot self-consistent Kohn-Sham calculations, showing that this potential is indeed able to capture strong-correlation effects way beyond t...

Exchange–correlation functionals from the strong interaction limit of DFT: applications to model chemical systems

“…When the confining potential is harmonic, as in the quantum wires and quantum dots studied in Ref. [14][15][16] , the barriers remain finite in the KS SCE potential also at very low density. In LDA we see that at large R H−H there is a barrier localized on the atoms rather than in the midbond, leading to overestimation of the charge in the bond.…”

“…The starting point is the so-called strictly-correlated-electrons (SCE) reference system, introduced by Seidl and coworkers, [11][12][13] which has the same density as the real interacting one, but in which the electrons are infinitely correlated instead of non-interacting. The SCE functional has a highly non-local dependence on the density, but its functional derivative can be easily constructed, 14,15 yielding a local one-body potential which can be used in the Kohn-Sham scheme to approximate the exchange-correlation term. The SCE functional tends asymptotically to the exact Hartree-exchange-correlation functional in the extreme infinite correlation (or low-density) limit.…”

Kinetic‐energy‐density dependent semilocal exchange‐correlation functionals

“…[225][226][227][228][229][230][231][232][233][234][235][236][237][238] In this case, the electrons are kept apart by the Coulomb repulsion. Thus, the XC energy becomes independent on the relative spin-polarization f (Equation A7).…”

Kantorovich dual solution for strictly correlated electrons in atoms and molecules

“…b. Quantum wire. Next we study a model quantum wire system in 1D, for which the co-motion formulation can also be solved semi-analytically 14 . The system consists of N = 4 electrons and the Hamiltonian reads…”

“…Recently, the behavior of the exchange-correlation functional has been revealed in the limit of strictly correlated electrons (SCE) [12][13][14][15] . The many-body Coulomb repulsive energy of SCE determines the exact exchangecorrelation functional in the strong interaction limit, without artificially breaking any symmetry of the system or introducing any tunable parameters.…”