  Given the omnipresence of non-covalent interactions (NCIs), their accurate
simulations are of crucial importance across various scientific disciplines.
Here we construct accurate models for the description of NCIs by an
interpolation along the M{\o}ller-Plesset adiabatic connection (MP AC). Our
interpolation approximates the correlation energy, by recovering MP2 at small
coupling strengths and the correct large-coupling strength expansion of the MP
AC, recently shown to be a functional of the Hartree-Fock density. Our models
are size consistent for fragments with non-degenerate ground states, have the
same cost as double hybrids and require no dispersion corrections to capture
NCIs accurately. These interpolations greatly reduce large MP2 errors for
typical $\pi$-stacking complexes (e.g., benzene-pyridine dimers) and for the L7
dataset. They are also competitive with state-of-the-art dispersion enhanced
functionals and can even significantly outperform them for a variety of
datasets, such as CT7 and L7.
