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

The adiabatic connection that has as weak-interaction expansion the M{\o}ller-Plesset perturbation series has been recently shown to have a large coupling-strength expansion in terms of functionals of the Hartree-Fock density with a clear physical meaning. In this work we accurately evaluate these density functionals and we extract second-order gradient coefficients from the data for neutral atoms, following ideas similar to the ones used in the literature for exchange, with some modifications. These new gradient expansions will be the key ingredient for performing interpolations that have already been shown to reduce dramatically MP2 errors for large non-covalent complexes. As a byproduct, 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.