Estimating the intrinsic limit of the Feller-Peterson-Dixon composite approach when applied to adiabatic ionization potentials in atoms and small molecules

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 ( N 9 ) 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 ( N 7 ) factorized CCSD(TQf) method introduces minimal error to predicted correlation and reaction energies as compared to the O ( N 9 ) 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.

The long road to calibrated prediction uncertainty in computational chemistry

Uncertainty quantification (UQ) in computational chemistry (CC) is still in its infancy. Very few CC methods are designed to provide a confidence level on their predictions, and most users still rely improperly on the mean absolute error as an accuracy metric. The development of reliable UQ methods is essential, notably for CC to be used confidently in industrial processes. A review of the CC-UQ literature shows that there is no common standard procedure to report or validate prediction uncertainty. I consider here analysis tools using concepts (calibration and sharpness) developed in meteorology and machine learning for the validation of probabilistic forecasters. These tools are adapted to CC-UQ and applied to datasets of prediction uncertainties provided by composite methods, Bayesian ensembles methods, and machine learning and a posteriori statistical methods.

A theoretical study of the adiabatic and vertical ionization potentials of water

Theoretical predictions of the three lowest adiabatic and vertical ionization potentials of water were obtained from the Feller-Peterson-Dixon approach. This approach combines multiple levels of coupled cluster theory with basis sets as large as aug-cc-pV8Z in some cases and various corrections up to and including full configuration interaction theory. While agreement with experiment for the adiabatic ionization potential of the lowest energy ²B₁ state was excellent, differences for other states were much larger, sometimes exceeding 10 kcal/mol (0.43 eV). Errors of this magnitude are inconsistent with previous benchmark work on 52 adiabatic ionization potentials, where a root mean square of 0.20 kcal/mol (0.009 eV) was found. Difficulties in direct comparisons between theory and experiment for vertical ionization potentials are discussed. With regard to the differences found for the ²A₁/²Π_u and ²B₂ adiabatic ionization potentials, a reinterpretation of the experimental spectrum appears justified.