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(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.