The strong-interaction functionals $W_{\infty }\left[n\right]$ and $W_{\infty }^{\prime }\left[n\right]$ 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, named the enhanced point-and-charge (ePC) model, constructed from exact constraints. In particular, the ePC restores the second-order gradient expansion of the PC model, which is relevant for the equilibrium properties of Wigner crystals, and it ensures the non-negativity of $W_{\infty }^{\prime }\left[n\right]$. We assess the ePC model for atoms and various systems: Hooke's atoms, two-electron exponential densities, $s$- and $p$-hydrogenic shells, quasi-two-dimensional infinite barrier model, perturbed uniform electron gas, $H_2$ dissociation, and conventional molecular benchmarks. We prove the good overall accuracy of the ePC model, which achieves a broader applicability than any previous semilocal models.

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• Electronic structure
• Electronic structure of atoms & molecules
• Density functional theory
• Electron-correlation calculations