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We present a renormalized second-order perturbation theory (rPT2), based on aKohn-Sham (KS) reference state, for the electron correlation energy thatincludes the random-phase approximation (RPA), second-order screened exchange(SOSEX), and renormalized single excitations (rSE). These three terms allinvolve a summation of certain types of diagrams to infinite order, and can beviewed as "renormalization" of the 2nd-order direct, exchange, and singleexcitation (SE) terms of Rayleigh-Schr\"odinger perturbation theory based on anKS reference. In this work we establish the concept of rPT2 and present thenumerical details of our SOSEX and rSE implementations. A preliminary versionof rPT2, in which the renormalized SE (rSE) contribution was treatedapproximately, has already been benchmarked for molecular atomization energiesand chemical reaction barrier heights and shows a well balanced performance[Paier et al, New J. Phys. 14, 043002 (2012)]. In this work, we present arefined version of rPT2, in which we evaluate the rSE series of diagramsrigorously. We then extend the benchmark studies to non-covalent interactions,including the rare-gas dimers, and the S22 and S66 test sets. Despite someremaining shortcomings, we conclude that rPT2 gives an overall satisfactoryperformance across different chemical environments, and is a promising steptowards a generally applicable electronic structure approach.

Renormalized Second-order Perturbation Theory for The Electron Correlation Energy: Concept, Implementation, and Benchmarks