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 Formula Presented 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 Formula Presented factorized CCSD(TQ_f) method introduces minimal error to predicted correlation and reaction energies as compared to the Formula Presented 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.