The strong-interaction limit of density functional theory

Abstract

This is a comprehensive review of the strong-interaction limit of density functional theory. It covers the derivation of the limiting strictly correlated electrons (SCE) functional from exact Hohenberg-Kohn DFT, basic aspects of SCE physics such as the nonlocal dependence of the SCE potential on the density, equivalent formulations and the mathematical interpretation as optimal transport with Coulomb cost, rigorous results (including exactly soluble cases), approximations, numerical methods, integration into Kohn-Sham DFT (KS SCE), and applications to molecular systems, an example being that KS SCE, unlike the local density approximation or generalized gradient approximations, dissociates H 2 correctly. We have made an effort to make this review accessible to a broad audience of physicists, chemists, and mathematicians.

A Finite Element Configuration Interaction Method For Wigner Localization

“…We finally point out that the semi-classical limit has also been investigated within the framework of density functional theory (DFT), which is highly related to this work. In particular, the semi-classical limit was derived and analyzed for the Hohenberg-Kohn functional when the single-particle density is fixed (see [23] for a comprehensive review).…”

“…In contrast to the HF approximation, we will consider the opposite α → 0 limit as the starting point, which is more appropriate for strongly correlated systems with Wigner localization [40,42]. This semi-classical limit has been studied by the SCE theory [16,23,28,45,46] within the framework of density functional theory, and we can exploit essentially the same idea to construct the initial state. More precisely, to obtain the ground state of (2.5) when α is very small, we can start from the α = 0 limit (2.8) and find the electron configurations that can minimize the interactions in the given external electric field min…”

Electronic excited states in extreme limits via ensemble density functionals

“…To make matters worse, interesting excitations often involve strong correlations which, as in all flavors of DFT, remain an outstanding challenge for approximations based on EDFT. [15] It is therefore of enormous interest if advances in understanding the strictly correlated limit of ground state DFT [16][17][18][19][20][21] could be transferred to ensemble problems. Strikingly, the present work reveals that strict correlations actually makes the ensemble problem easier, via an additional constraint:…”

“…In doing so, we shall extend to excited states concepts and core results which have previously been worked out for pure ground states only. [16][17][18][19][20][21] These works can be understood as providing a generalization of the seminal work of Wigner [24,25] to inhomogeneous systems within DFT. Our current work completes the generalization to include excited inhomogeneous systems within EDFT.…”

“…Here, f i (r) are comotion maps that preserve the density and the indistinguishability of electrons. [16,20] At large but finite λ we construct orthonormal wave functions, |κ λ , based on quantum harmonic oscillations (QHO) around the strictly-correlated distribution, P N [n]. [17,30] The QHOs act on curvilinear coordinates orthogonal to the manifold parametrized by the comotion functions; and contribute at O( √ λ) in the kinetic and potential energies.…”