Non-linear and non-empirical double hybrid density functional

We develop a non-linear and non-empirical (nlane) double hybrid density functional derived from an accurate interpolation of the adiabatic connection in density functional theory, incorporating the correct asymptotic expansions. By bridging the second-order perturbative weak correlation limit with the fully interacting limit from the semi-local SCAN functional, nlane-SCAN is free of fitted parameters while providing improved energetic predictions compared to SCAN for moderately and strongly correlated systems alike. It delivers accurate predictions for atomic total energies and multiple reaction datasets from the GMTKN55 benchmark while significantly outperforming traditional linear hybrids and double hybrids for non-covalent interactions without requiring dispersion corrections. Due to the exact constraints at the weak correlation limit, nlane-SCAN has reduced delocalization errors as evident through the SIE4x4 benchmark and bond dissociations of H$_2^+$ and He$_2^+$. Its proper asymptotic behavior ensures stability in strongly correlated systems, improving H$_2$ and N$_2$ bond dissociation profiles compared to conventional functionals.