Exploring Avenues Beyond Revised DSD Functionals: II. Random-Phase Approximation and scaled MP3 corrections

For revDSD double hybrids, the G\"orling-Levy second-order perturbation theory component is an Achilles' Heel when applied to systems with significant near-degeneracy ("static") correlation. We have explored its replacement by the direct random phase approximation (dRPA), inspired by the SCS-dRPA75 functional of K\'allay and coworkers. The addition to the final energy of both a D4 empirical dispersion correction, and of a semilocal correlation component lead, to significant improvements, with DSD-PBEdRPA75-D4 approaching the performance of revDSD-PBEP86-D4 and the Berkeley $\omega$B97M(2). This form appears to be fairly insensitive to the choice of semilocal functional, but does exhibit stronger basis set sensitivity than the PT2-based double hybrids (due to much larger prefactors for the nonlocal correlation). As an alternative, we explored adding an MP3-like correction term (in a medium-sized basis sets) to a range-separated $\omega$DSD-PBEP86-D4 double hybrid, and found it to have significantly lower WTMAD2 (weighted mean absolute deviation) for the large and chemically diverse GMTKN55 benchmark suite; the added computational cost can be mitigated through density fitting techniques.