Joonho Lee working with Martin Head-Gordon developed and added an implementation of RI-MP3 with only cubic-storage requirement.651 The resulting code can be applied to larger systems than what is possible in CCMAN2 (6.10) due to the improved storage scaling. To use this method, one can set METHOD = RIMP3 along with AUXBASIS. In essence, it applies the RI approximation in Eq. 8.4 to the MP3 correlation energy evaluation. Interested readers are referred to Section 6.3 for further details on the Møller-Plesset perturbation theory.
In addition to RI-MP3 one can incorporate scaled RI-MP2 and RI-MP3 correlation energy contributions and alternative reference molecular orbitals (DFT and OOMP2) as seen in recent works by Bertels et al.94 and Rettig et al.958 The use of non-HF orbital references requires a composite job where the first calculation generates the orbital reference and the second first recomputes the SCF energy and Fock with HF on the fixed orbital reference and then proceeds with the correlated calculation.