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 Head-Gordon.651 RI-dRPA has been applied to the thermochemistry285 and non-covalent interaction problems817 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.1012 In a nutshell, we define the dRPA energy as
where using the plasmon formula we compute310
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.