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.