Factorized Quadruples and a Predictor of Higher-Level Correlation in Thermochemistry.

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 $O\left(N^9\right)$ 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 $O\left(N^7\right)$ factorized CCSD(TQ_f) method introduces minimal error to predicted correlation and reaction energies as compared to the $O\left(N^9\right)$ 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(TQ_f)/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.