What can we learn from the adiabatic connection formalism about local hybrid functionals?

Local hybrid functionals with position-dependent exact-exchange admixture are a promising new generation of exchange-correlation functionals for a large variety of applications. So far, the local mixing functions (LMFs) determining the position dependence have been largely constructed in an ad hoc manner, albeit based on physical reasoning. Here the basic formalism of the adiabatic connection is employed to investigate the formal basis of local hybrids and to construct a priori LMFs. Both a local spin density approximation to the LMF (AC-LSDA LMF) and generalized gradient approximation approximations (AC-PW91 LMF and AC-PBE LMF) turn out to provide inferior performance when used in local hybrids to compute atomization energies and reaction barriers compared to previous semiempirical LMFs. This is rationalized by limited flexibility of these first-principles LMFs and some basic limitations of the adiabatic connection formalism in this context. Graphical analyses and formal considerations provide nevertheless important new insight into the physical background of local hybrid functionals.