This article focusses on the strong-interaction limit of DFT as the counterpart of the perturbation expansion for weak interactions. Although it is far from reality, the strong-interaction limit appears to provide just that information on correlations which is not accessible by the perturbation expansion. Useful for electronic-structure calculations on real electronic systems, this limit is at the same time mathematically simple, as is illustrated here in section 3 by the SCE concept for spherically symmetric two-electron systems. The SCE concept is a candidate for the exact quantum-mechanical solution to that limit. In the SCE state, the two electrons are dynamically connected in terms of a co-motion function f(r) which is determined uniquely by the given spherical density ρ(r). The attractive external potential αw(r), required to make two strongly repulsive electrons maintain a given smooth and finite quantum-mechanical density distribution, can be constructed explicitly. In particular, the SCE concept yields a simple functional for the asymptotic limit W_∞[ρ] of the coupling-constant integrand. A simple and accurate approximation to SCE, applicable to any N-electron system, is the PC model. The interaction-strength interpolation (ISI) of section 5 combines the PC model (employing the gradient functionals W_(PC)[ρ] and W'_(PC)[ρ]) with the leading terms of the perturbation expansion (the exchange energy E_x[ρ] and the second-order correlation energy E_c~(GL2)[ρ]) in an analytical model W_α~(ISI)[ρ] for the coupling-constant integrand W_α[ρ]. By construction, the resulting approximation E_(xc)~(ISI)[ρ] for the exchange-correlation energy shares many fundamental properties with the unknown exact functional. In particular, unlike all the other approximate correlation functionals available, the ISI functional appears to be compatible with exact exchange.
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