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 E-xc[rho] equivalent to integral(0)(1)d alpha W-alpha[rho] follows from the re potential energies W-alpha at different interaction strengths alpha greater than or equal to 0 [but at fixed density rho(r)]. For small alpha approximate to 0, the integrand W-alpha is obtained accurately from perturbation theory, but the perturbation expansion requires resummation for moderate and large alpha. For that purpose, we present density functionals for the coefficients in the asymptotic expansion W-alpha-->W-infinity+W'(infinity)alpha(-1/2) for alpha-->infinity in the PC model. W-infinity(PC) arises from strict correlation, and W'(PC)(infinity) from zero-point vibration of the electrons around their strictly correlated distributions. The PC values for W-infinity and W'(infinity) 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 H-2 molecule, and (iv) discuss the soft-plasmon instability of the low-density uniform electron gas.