We use the exact strong-interaction limit of the Hohenberg-Kohn energy density functional to construct an approximation for the exchange-correlation term of the Kohn-Sham approach. The resulting exchange-correlation potential is able to capture the features of the strongly correlated regime without breaking the spin or any other symmetry. In particular, it shows "bumps" (or barriers) that give rise to charge localization at low densities and that are a well-known key feature of the exact Kohn-Sham potential for strongly correlated systems. Here, we illustrate this approach for the study of both weakly and strongly correlated model quantum wires, comparing our results with those obtained with the configuration interaction method and with the usual Kohn-Sham local density approximation.

We discuss energy densities in the strong-interaction limit of density functional theory, deriving an exact expression within the definition (gauge) of the electrostatic potential of the exchange-correlation hole. Exact results for small atoms and small model quantum dots (Hooke's atoms) are compared with available approximations defined in the same gauge. The idea of a local interpolation along the adiabatic connection is discussed, comparing the energy densities of the Kohn−Sham, the physical, and the strong-interacting systems. We also use our results to analyze the local version of the Lieb−Oxford bound, widely used in the construction of approximate exchange-correlation functionals.

Using the dual Kantorovich formulation, we compute the strictly correlated electrons (SCE) functional (corresponding to the exact strong-interaction limit of density functional theory) for the hydrogen molecule along the dissociation curve. We use an exact relation between the Kantorovich potential and the optimal map to compute the comotion function, exploring corrections based on it. In particular, we analyze how the SCE functional transforms in an exact way the electron-electron distance into a one-body quantity, a feature that can be exploited to build new approximate functionals. We also show that the dual Kantorovich formulation provides in a natural way the constant in the Kohn-Sham potential recently introduced by Levy and Zahariev [Phys. Rev. Lett. 2014, 113, 113002] for finite systems.

We study model one-dimensional chemical systems (representative of their three-dimensional counterparts) using the strictly-correlated electrons (SCE) functional, which, by construction, becomes asymptotically exact in the limit of infinite coupling strength. The SCE functional has a highly non-local dependence on the density and is able to capture strong correlation within KohnSham theory without introducing any symmetry breaking. Chemical systems, however, are not close enough to the strong-interaction limit so that, while ionization energies and the stretched H2 molecule are accurately described, total energies are in general way too low. A correction based on the exact next leading order in the expansion at infinite coupling strength of the Hohenberg-Kohn functional largely improves the results.

In order to investigate charge resonance situations in molecular complexes, Wu et al. (J. Chem. Phys. 2007, 127, 164119) recently proposed a configuration interaction method with a valence bond-like multiconfigurational basis obtained from constrained DFT calculations. We adapt this method to the Self-Consistent Charge Density-Functional-based Tight Binding (SCC-DFTB) approach and provide expressions for the gradients of the energy with respect to the nuclear coordinates. It is shown that the method corrects the wrong SCC-DFTB behavior of the potential energy surface in the dissociation regions. This scheme is applied to determine the structural and stability properties of positively charged molecular dimers with full structural optimization, namely, the benzene dimer cation and the water dimer cation. The method yields binding energies in good agreement with experimental data and high-level reference calculations.

We generalize the exact strong-interaction limit of the exchange-correlation energy of Kohn-Sham density functional theory to open systems with fluctuating particle numbers. When used in the self-consistent Kohn-Sham procedure on strongly-interacting systems, this functional yields exact features crucial for important applications such as quantum transport. In particular, the steplike structure of the highest-occupied Kohn-Sham eigenvalue is very well captured, with accurate quantitative agreement with exact many-body chemical potentials. Whilst it can be shown that a sharp derivative discontinuity is only present in the infinitely strongly-correlated limit, at finite correlation regimes we observe a slightly-smoothened discontinuity, with qualitative and quantitative features that improve with increasing correlation. From the fundamental point of view, our results obtain the derivative discontinuity without making the assumptions used in its standard derivation, offering independent support for its existence.First-principles calculations of many-electron systems such as solids, molecules, and nanostructures are based, to a very large extent, on Kohn-Sham (KS) [1] density functional theory (DFT) [2]. KS DFT is, in principle, an exact theory, in which the ground-state energy and density of an interacting many-electron system are mapped into a problem of non-interacting electrons moving in the effective one-body KS potential. In practice, KS DFT relies on approximations for the exchange-correlation energy that, although successful in very many cases, have still deficiencies that hamper its overall usefulness [3].Exact KS DFT has many weird and counterintuitive features often missed by the available approximations. One of the weirdest and most elusive of these features is the derivative discontinuity of the exact exchangecorrelation energy functional at integer particle numbers N [4], which has been an incredibly long-debated issue [5][6][7][8][9][10][11][12][13][14][15] because its formal derivation relies on some (very reasonable) assumptions. This discontinuity makes the exact KS potential "jump" by a constant ∆ xc when we add to an N -electron system even a very tiny fraction η of an electron, aligning the chemical potential of the non-interacting KS system to the exact, interacting, one, as schematically illustrated in Fig. 1. The derivative discontinuity has crucial physical consequences. For example, it accounts for the difference between the KS and the physical fundamental gaps [16][17][18], it allows a correct KS DFT description of molecular dissociation [4,19], and it should improve charge-transfer excitations in timedependent DFT [20][21][22]. It also plays a fundamental role in quantum transport, especially to capture the physics of the Coulomb blockade and the Kondo effect [23][24][25][26][27]. These are all cases in which the standard approximations, which miss this discontinuity, work poorly. Corrections based on the explicit enforcement of the discontinuity have been often proposed as a practical so...

Anions and radicals are important for many applications including environmental chemistry, semiconductors, and charge transfer, but are poorly described by the available approximate energy density functionals. Here we test an approximate exchangecorrelation functional based on the exact strong-coupling limit of the HohenbergKohn functional on the prototypical case of the He isoelectronic series with varying nuclear charge Z < 2, which includes weakly bound negative ions and a quantum phase transition at a critical value of Z, representing a big challenge for density functional theory. We use accurate wavefunction calculations to validate our results, comparing energies and Kohn-Sham potentials, thus also providing useful reference data close to and at the quantum phase transition. We show that our functional is able to bind H − and to capture in general the physics of loosely bound anions, with a tendency to strongly overbind that can be proven mathematically. We also include corrections based on the uniform electron gas which improve the results.

We introduce a density functional formalism to study the ground-state properties of stronglycorrelated dipolar and ionic ultracold bosonic and fermionic gases, based on the self-consistent combination of the weak and the strong coupling limits. Contrary to conventional density functional approaches, our formalism does not require a previous calculation of the interacting homogeneous gas, and it is thus very suitable to treat systems with tunable long-range interactions. Due to its asymptotic exactness in the regime of strong correlation, the formalism works for systems in which standard mean-field theories fail.Introduction -In contrast with its widespread use and success in areas as diverse as quantum chemistry [1], materials science [2] or semiconductor nanostructures [3], Density Functional Theory (DFT) has received relatively little attention in the very active field of ultracold atomic gases. It is well known that the Hohenberg-Kohn theorems, originally formulated in terms of the electron gas [4,5], hold for both fermionic and bosonic systems, as well as for interactions different than the Coulomb one. However, the lack of adequate density functionals has hindered the role of DFT in the study of ultracold atomic gases in favour of other well-established approaches, such as the widely used Gross-Pitaevskii (GP) method in the case of Bose gases. The latter is a mean-field approach and does not allow treating the effect of correlations, which play a crucial role in many different phenomena occurring in ultracold quantum gases [6]. One then often turns to configuration-interaction (CI), quantum Monte Carlo (QMC) or Green's-function methods (for recent reviews, see, e.g., Refs. 6-8).