  We recently introduced an efficient methodology to perform density-corrected
Hartree-Fock density functional theory (DC(HF)-DFT) calculations and an
extension to it we called "corrected" HF DFT (C(HF)-DFT). In this work, we take
a further step and combine C(HF)-DFT, augmented with a straightforward orbital
energy correction, with the random phase approximation (RPA). We refer to the
resulting methodology as corrected HF RPA (C(HF)-RPA). We evaluate the proposed
methodology across various RPA methods: direct RPA (dRPA), RPA with an
approximate exchange kernel (RPA-AXK), and RPA with second-order screened
exchange (RPA-SOSEX). C(HF)-dRPA, in particular, demonstrates very promising
performance; for RPA with exchange methods we find over-corrections for certain
chemical problems.
