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We study numerically the strong-interaction limit of the exchange-correlationfunctional for neutral atoms and for Bohr atoms as the number of electronsincreases. Using a compact representation, we analyse the second-order gradientexpansion, comparing it with the one for exchange (weak interaction limit). Thetwo gradient expansions, at strong and weak interaction, turn out to be verysimilar in magnitude, but with opposite signs. We find that the point-chargeplus continuum model is surprisingly accurate for the gradient expansioncoefficient at strong coupling, while generalized gradient approximations suchas PBE and PBEsol severely underestimate it. We then use our results to analysethe Lieb-Oxford bound from the point of view of slowly-varying densities,clarifying some aspects on the bound at fixed number of electrons.

Large-Z atoms in the strong-interaction limit of DFT: Implications for gradient expansions and for the Lieb-Oxford bound