Restoring the point-and-charge gradient expansion for strong interaction density functionals

The strong-interaction functionals $W_\infty[n]$ and ${W'}_\infty[n]$ play an important role in the adiabatic-connection method of Density Functional Theory. The strictly-correlated electron approach can be used to exactly compute these functionals, yet calculations are computationally very expensive even for small electronic systems, and thus semilocal approximations have been proposed. In this work we develop a meta-generalized gradient approximation (meta-GGA) model for the strong-interaction functionals, enhanced point-and-charge (ePC), constructed from exact constraints. In particular, the ePC restores the second-order gradient expansion of the PC model, that is relevant for the equilibrium properties of Wigner crystals, and ensures the non-negativity of ${W'}_\infty[n]$. We assess the ePC model for atoms and various model systems: Hooke's atoms, two-electron exponential densities, s- and p-hydrogenic shells, quasi-two-dimensional infinite barrier model, perturbed uniform electron gas and H$_2$ dissociation. We prove a good overall accuracy of the ePC model, that achieves a broader applicability than any previous semilocal models.