Hybrid functionals including random phase approximation correlation and second-order screened exchange

There has been considerable recent interest in density functionals incorporating random phase approximation (RPA) ground-state correlation. By virtue of its full nonlocality, RPA correlation is compatible with exact Hartree-Fock-type exchange and describes van der Waals interactions exceptionally well [B. G. Janesko et al., J. Chem. Phys. 130, 081105 (2009); J. Chem. Phys. 131, 034110 (2009)]. One caveat is that RPA correlation contains one-electron self-interaction error, which leads to disturbingly large correlation energies in the stretched bond situation of, e.g., H(2)(+), He(2)(+), or Ne(2)(+). In the present work, we show that inclusion of second-order screened exchange rectifies the aforementioned failure of RPA correlation. We present a large number of molecular benchmark results obtained using full-range as well as long-range corrected hybrids incorporating second-order screened exchange correlation. This correction has a generally small, and sometimes undesirable, effect on RPA predictions for chemical properties, but appears to be very beneficial for the dissociation of H(2)(+), He(2)(+), and Ne(2)(+).