The remarkable accuracy of an $O(N^6)$ perturbative correction to opposite-spin CCSD: are triples necessary for chemical accuracy in coupled cluster?

The focus of this work is OS-CCSD-SPT(2), which is a second-order similarity transformed perturbation theory correction to opposite spin coupled cluster singles doubles, where in the latter the same-spin amplitudes are removed and the opposite-spin ones are solved self consistently. We demonstrate that, for non-multireference molecules, OS-CCSD-SPT(2) produces relative energies that rival the accuracy of higher-order methods like CCSD(T). For example, using PBE0 orbitals in the reference, OS-CCSD-SPT(2) exhibits a mean absolute deviation (MAD) of 0.66 kcal/mol with respect to CCSD(2) benchmark values for the non-multireference subset of W4-08 atomization energies (c.f. a MAD > 6 kcal/mol for CCSD). OS-CCSD-SPT(2) is free of empirical parameters, has an instrinsic scaling of $O(N^6)$, and makes no use of triples. It is also naturally amenable to higher order corrections: the associated third-order correction, OS-CCSD-SPT(3), which does involve connected triples and quadruples, exhibits a MAD of 0.44 kcal/mol for the same benchmark.