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Adiabatic connection models (ACMs), which interpolate between the limits ofweak and strong interaction, are powerful tools to build accurateexchange-correlation functionals. If the exact weak-interaction expansion fromsecond-order perturbation theory is included, a self-consistent implementationof these functionals is challenging and still absent in the literature. In thiswork we fill this gap by presenting a fully self-consistent-field (SCF)implementation of some popular ACM functionals. While using second-orderperturbation theory at weak interactions, we have also introduced newgeneralised gradient approximations (GGA's), beyond the usualpoint-charge-plus-continuum model, for the first two leading terms at stronginteractions, which are crucial to ensure robustness and reliability. We thenassess the SCF-ACM functionals for molecular systems and for prototypicalstrong-correlation problems. We find that they perform well for both the totalenergy and the electronic density and that the impact of SCF orbitals isdirectly connected to the accuracy of the ACM functional form. For the H$_2$dissociation the SCF-ACM functionals yield significant improvements withrespect to standard functionals, also thanks to the use of the new GGA's forthe strong-coupling functionals.

Self-Consistent Implementation of Kohn-Sham Adiabatic Connection Models with Improved Treatment of the Strong-Interaction Limit