Density functionals for the strong-interaction limit

The strong-interaction limit of density-functional (DF) theory is simple and provides information required for an accurate resummation of DF perturbation theory. Here we derive the point-charge-plus-continuum (PC) model for that limit, and its gradient expansion. The exchange-correlation (xc) energy Exc[ρ]≡∫₀¹dαW_α[ρ] follows from the xc potential energies W_α at different interaction strengths α>~0 [but at fixed density ρ(r)]. For small α≈0, the integrand W_α is obtained accurately from perturbation theory, but the perturbation expansion requires resummation for moderate and large α. For that purpose, we present density functionals for the coefficients in the asymptotic expansion W_α→W_∞+W_∞^'α^-1/2 for →α∞ in the PC model. W_∞PC arises from strict correlation, and W_∞^'PC from zero-point vibration of the electrons around their strictly correlated distributions. The PC values for W_∞ and W_∞^' agree with those from a self-correlation-free meta-generalized gradient approximation, both for atoms and for atomization energies of molecules. We also (i) explain the difference between the PC cell and the exchange-correlation hole, (ii) present a density-functional measure of correlation strength, (iii) describe the electron localization and spin polarization energy in a highly stretched H₂ molecule, and (iv) discuss the soft-plasmon instability of the low-density uniform electron gas.