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The adiabatic connection that has as weak-interaction expansion theM{\o}ller-Plesset perturbation series has been recently shown to have a largecoupling-strength expansion in terms of functionals of the Hartree-Fock densitywith a clear physical meaning. In this work we accurately evaluate thesedensity functionals and we extract second-order gradient coefficients from thedata for neutral atoms, following ideas similar to the ones used in theliterature for exchange, with some modifications. These new gradient expansionswill be the key ingredient for performing interpolations that have already beenshown to reduce dramatically MP2 errors for large non-covalent complexes. As abyproduct, our investigation of neutral atoms with large number of electrons$N$ indicates that the second-order gradient expansion for exchange grows as$N\log(N)$ rather than as $N$ as often reported in the literature.

Gradient expansions for the large-coupling strength limit of the M{\o}ller-Plesset adiabatic connection