Density functionals for the strong-interaction limit

摘要: The strong-interaction limit of density-functional (DF) theory is simple and provides information required for an accurate resummation DF perturbation theory. Here we derive the point-charge-plus-continuum (PC) model that limit, its gradient expansion. exchange-correlation (xc) energy ${E}_{\mathrm{xc}}[\ensuremath{\rho}]\ensuremath{\equiv}{\ensuremath{\int}}_{0}^{1}d\ensuremath{\alpha}{W}_{\ensuremath{\alpha}}[\ensuremath{\rho}]$ follows from xc potential energies ${W}_{\ensuremath{\alpha}}$ at different interaction strengths $\ensuremath{\alpha}g~0$ [but fixed density $\ensuremath{\rho}(\mathbf{r})].$ For small $\ensuremath{\alpha}\ensuremath{\approx}0,$ integrand obtained accurately theory, but expansion requires moderate large $\ensuremath{\alpha}.$ purpose, present functionals coefficients in asymptotic ${W}_{\ensuremath{\alpha}}\ensuremath{\rightarrow}{W}_{\ensuremath{\infty}}{+W}_{\ensuremath{\infty}}^{\ensuremath{'}}{\ensuremath{\alpha}}^{\ensuremath{-}1/2}$ $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\alpha}}\ensuremath{\infty}$ PC model. ${W}_{\ensuremath{\infty}}^{\mathrm{PC}}$ arises strict correlation, ${W}_{\ensuremath{\infty}}^{\ensuremath{'}\mathrm{PC}}$ zero-point vibration electrons around their strictly correlated distributions. values ${W}_{\ensuremath{\infty}}$ ${W}_{\ensuremath{\infty}}^{\ensuremath{'}}$ agree with those a self-correlation-free meta-generalized approximation, both atoms atomization molecules. We also (i) explain difference between cell hole, (ii) measure correlation strength, (iii) describe electron localization spin polarization highly stretched ${\mathrm{H}}_{2}$ molecule, (iv) discuss soft-plasmon instability low-density uniform gas.