  The random phase approximation (RPA) has received a considerable interest in
the field of modeling systems where noncovalent interactions are important. Its
advantages over widely used density functional theory (DFT) approximations are
the exact treatment of exchange and the description of long-range correlation.
In this work we address two open questions related to RPA. First, how
accurately RPA describes nonadditive interactions encountered in many-body
expansion of a binding energy. We consider three-body nonadditive energies in
molecular and atomic clusters. Second, how does the accuracy of RPA depend on
input provided by different DFT models, without resorting to selfconsistent RPA
procedure which is currently impractical for calculations employing periodic
boundary conditions. We find that RPA based on the SCAN0 and PBE0 models, i.e.,
hybrid DFT, achieves an overall accuracy between CCSD and MP3 on a dataset of
molecular trimers of \v{R}ez\'{a}\v{c} et al. (J. Chem. Theory. Comput. 2015,
11, 3065) Finally, many-body expansion for molecular clusters and solids often
leads to a large number of small contributions that need to be calculated with
a high precision. We therefore present a cubic-scaling (or SCF-like)
implementation of RPA in atomic basis set, which is designed for calculations
with a high numerical precision.
