  We study in detail the first three leading terms of the large
coupling-strength limit of the adiabatic connection that has as
weak-interaction expansion the M{\o}ller-Plesset perturbation theory. We first
focus on the H atom, both in the spin-polarized and the spin-unpolarized case,
reporting numerical and analytical results. In particular, we derive an
asymptotic equation that turns out to have simple analytical solutions for
certain channels. The asymptotic H atom solution for the spin-unpolarized case
is then shown to be variationally optimal for the many-electron spin-restricted
closed-shell case, providing expressions for the large coupling-strength
density functionals up to the third leading order. We also analyze the H2
molecule and the uniform electron gas.
