  Adiabatic connection models (ACMs), which interpolate between the limits of
weak and strong interaction, are powerful tools to build accurate
exchange-correlation functionals. If the exact weak-interaction expansion from
second-order perturbation theory is included, a self-consistent implementation
of these functionals is challenging and still absent in the literature. In this
work we fill this gap by presenting a fully self-consistent-field (SCF)
implementation of some popular ACM functionals. While using second-order
perturbation theory at weak interactions, we have also introduced new
generalised gradient approximations (GGA's), beyond the usual
point-charge-plus-continuum model, for the first two leading terms at strong
interactions, which are crucial to ensure robustness and reliability. We then
assess the SCF-ACM functionals for molecular systems and for prototypical
strong-correlation problems. We find that they perform well for both the total
energy and the electronic density and that the impact of SCF orbitals is
directly connected to the accuracy of the ACM functional form. For the H$_2$
dissociation the SCF-ACM functionals yield significant improvements with
respect to standard functionals, also thanks to the use of the new GGA's for
the strong-coupling functionals.
