A useful approach called the direct random phase
approximation (dRPA) based on the RI approximation is available. This
particular implementation was added by Joonho Lee working with Martin
J. Chem. Theory Comput.
(2020), 16, pp. 243. RI-dRPA has been applied to the thermochemistry 280 J. Chem. Theory Comput.
(2018), 14, pp. 2596. and non-covalent interaction problems 794 J. Chem. Theory Comput.
(2020), 16, pp. 2258. and often demonstrated superior performance over RI-MP2. In terms of the computational cost, RI-dRPA should be compared to the scaled-opposite-spin MP2 while theoretically it involves diagrams far beyond second-order and includes infinite-order diagrams similarly to coupled-cluster theory. In fact, one can view dRPA as a reduced coupled-cluster with doubles approach. 980 J. Chem. Phys.
(2008), 129, pp. 231101. In a nutshell, we define the dRPA energy as
where using the plasmon formula we compute
In this form, the cost of computing the dRPA correlation is quartic-scaling which is comparable to SOS-MP2. To use this method, one must set METHOD = RIDRPA along with AUXBASIS.