Performance and Scope of Perturbative Corrections to Random-Phase Approximation Energies

It has been suspected since the early days of the random-phase approximation (RPA) that corrections to RPA correlation energies result mostly from short-range correlation effects and are thus amenable to perturbation theory. Here we test this hypothesis by analyzing formal and numerical results for the most common beyond-RPA perturbative corrections, including the bare second-order exchange (SOX), second-order screened exchange (SOSEX), and approximate exchange kernel (AXK) methods. Our analysis is facilitated by efficient and robust algorithms based on the resolution-of-the-identity (RI) approximation and numerical frequency integration, which enable benchmark beyond-RPA calculations on medium-and large-size molecules with size-independent accuracy. The AXK method systematically improves upon RPA, SOX, and SOSEX for reaction barrier heights, reaction energies, and noncovalent interaction energies of main-group compounds. The improved accuracy of AXK compared with SOX and SOSEX is attributed to stronger screening of bare SOX in AXK. For reactions involving transition-metal compounds, particularly 3d transition-metal dimers, the AXK correction is too small and can even have the wrong sign. These observations are rationalized by a measure (alpha) over bar of the effective coupling strength for beyond-RPA correlation. When the effective coupling strength increases beyond a critical (alpha) over bar value of approximately 0.5, the RPA errors increase rapidly and perturbative corrections become unreliable. Thus, perturbation theory can systematically correct RPA but only for systems and properties qualitatively well captured by RPA, as indicated by small (alpha) over bar values.