Gradient Expansions for the Large-Coupling Strength Limit of the Møller–Plesset Adiabatic Connection

The adiabatic connection that has, as weak-interaction expansion, the Møller–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 noncovalent 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.