  The random-phase approximation to the ground state correlation energy (RPA)
in combination with exact exchange (EX) has brought Kohn-Sham (KS) density
functional theory one step closer towards a universal, "general purpose first
principles method". In an effort to systematically assess the influence of
several correlation energy contributions beyond RPA, this work presents
dissociation energies of small molecules and solids, activation energies for
hydrogen transfer and non-hydrogen transfer reactions, as well as reaction
energies for a number of common test sets. We benchmark EX+RPA and several
flavors of energy functionals going beyond it: second-order screened exchange
(SOSEX), single excitation (SE) corrections, renormalized single excitation
(rSE) corrections, as well as their combinations. Both the single excitation
correction as well as the SOSEX contribution to the correlation energy
significantly improve upon the notorious tendency of EX+RPA to underbind.
Surprisingly, activation energies obtained using EX+RPA based on a KS reference
alone are remarkably accurate. RPA+SOSEX+rSE provides an equal level of
accuracy for reaction as well as activation energies and overall gives the most
balanced performance, which makes it applicable to a wide range of systems and
chemical reactions.
