Construction of a parameter-free doubly hybrid density functional from adiabatic connection

In this work, the adiabatic connection (AC) formalism, coordinate scaling relations, and the second order Görling-Levy perturbation theory (GL2) are first reviewed. Emphasis is laid upon the construction of the AC integrand (Wxc(λ)), with suitable input data {Wxc(0), Wxc'(0), Wxc(1) and the proper asymptotic behavior on λ(-1/2) as λ → ∞. This leads to a non-empirical DH functional, namely, PBE-ACDH. The PBE-ACDH functional is unique in that it explicitly considers contributions from density scaling and singles, and it utilizes density and orbital information from the PBE functional, which has a local multiplicative potential, being most compatible with the GL2 theory. Systematical tests on heats of formation, bond dissociation enthalpies, reaction barrier heights, and nonbonded interactions, using some well-established benchmarking sets, suggest that PBE-ACDH is a significant improvement over its parent functional PBE, as well as PBE0, Becke's Half-and-Half (PBE-HH), and GL2. The physical insight gained in the present work should prove useful for the further development of new functionals.