We present a renormalized second-order perturbation theory (rPT2), based on a
Kohn-Sham (KS) reference state, for the electron correlation energy that
includes the random-phase approximation (RPA), second-order screened exchange
(SOSEX), and renormalized single excitations (rSE). These three terms all
involve a summation of certain types of diagrams to infinite order, and can be
viewed as "renormalization" of the 2nd-order direct, exchange, and single
excitation (SE) terms of Rayleigh-Schr\"odinger perturbation theory based on an
KS reference. In this work we establish the concept of rPT2 and present the
numerical details of our SOSEX and rSE implementations. A preliminary version
of rPT2, in which the renormalized SE (rSE) contribution was treated
approximately, has already been benchmarked for molecular atomization energies
and chemical reaction barrier heights and shows a well balanced performance
[Paier et al, New J. Phys. 14, 043002 (2012)]. In this work, we present a
refined version of rPT2, in which we evaluate the rSE series of diagrams
rigorously. We then extend the benchmark studies to non-covalent interactions,
including the rare-gas dimers, and the S22 and S66 test sets. Despite some
remaining shortcomings, we conclude that rPT2 gives an overall satisfactory
performance across different chemical environments, and is a promising step
towards a generally applicable electronic structure approach.Comment: 16 pages, 11 figure
