Hierarchies of methods towards the exact Kohn-Sham correlation energy based on the adiabatic-connection fluctuation-dissipation theorem

A hierarchy of universally applicable density functional methods based on the adiabatic-connection fluctuation-dissipation theorem is introduced that can be systematically improved to treat electronic structures with increasing accuracy. Methods at the first rank of the hierarchy already can compete with established high-level wave-function methods and exhibit an attractive ratio of accuracy to computational effort. Strong correlation can be treated in a black-box manner based on a single Slater determinant: the Kohn-Sham determinant.