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Obtaining sub-chemical accuracy (1 kJ mol−1) for reaction energies of medium-sized gas-phase molecules is a longstanding challenge in the field of thermochemical modeling. The perturbative triples correction to coupled-cluster single double triple [CCSD(T)] constitutes an important component of all high-accuracy composite model chemistries that obtain this accuracy but can be a roadblock in the calculation of medium to large systems due to its O(N7) scaling, particularly in HEAT-like model chemistries that eschew separation of core and valence correlation. This study extends the work of Lesiuk [J. Chem. Phys. 156, 064103 (2022)] with new approximate methods and assesses the accuracy of five different approximations of (T) in the context of a subset of molecules selected from the W4-17 dataset. It is demonstrated that all of these approximate methods can achieve sub-0.1 kJ mol−1 accuracy with respect to canonical, density-fitted (T) contributions with a modest number of projectors. The approximation labeled Z̃T appears to offer the best trade-off between cost and accuracy and shows significant promise in an order-of-magnitude reduction in the computational cost of the CCSD(T) component of high-accuracy model chemistries. 

Coupled cluster theory has had a momentous impact on the ab initio prediction of molecular properties, and remains a staple ingratiate in high-accuracy thermochemical model chemistries. However, these methods require inclusion of at least some connected quadruple excitations, which generally scale at best as 𝒪(𝑁9) with the number of basis functions. It is very difficult to predict, a priori, the effect correlation of past CCSD(T) on a given reaction energy. The purpose of this work is to examine cost-effective quadruple corrections based on the factorization theorem of the many-body perturbation theory that may address these challenges. We show that the 𝒪(𝑁7) factorized CCSD(TQf) method introduces minimal error to predicted correlation and reaction energies as compared to the 𝒪(𝑁9) CCSD(TQ). Further, we examine the performance of Goodson’s continued fraction method in the estimation of CCSDT(Q)Λ contributions to reaction energies as well as a “new” method related to %TAE[(T)] that we refer to as a scaled perturbation estimator. We find that the scaled perturbation estimator based upon CCSD(TQf)/cc-pVDZ is capable of predicting CCSDT(Q)Λ/cc-pVDZ contributions to reaction energies with an average error of 0.07 kcal mol–1 and an L2D of 0.52 kcal mol–1 when applied to a test-suite of nearly 3000 reactions. This offers a means by which to reliably “ballpark” how important post-CCSD(T) contributions are to reaction energies while incurring no more than CCSD(T) formal cost and a little mental math.