Estimating Systematic Error and Uncertainty in Ab Initio Thermochemistry: II. ATOMIC(hc) Enthalpies of Formation for a Large Set of Hydrocarbons.

Abstract

ATOMIC is a thermochemistry protocol geared toward larger molecules with first-row atoms. It implements Pople's concept of bond separation reactions in an ab initio fashion and so enhances the accuracy of midlevel composite models for atomization energies. Recently we have introduced ATOMIC(hc), a model for applications to hydrocarbons, that estimates bias and uncertainty for each of the components contributing to the ATOMIC bottom-of-the-well atomization energy ( Bakowies , D. J. Chem. Theory Comput. 2019 , 15 , 5230 - 5251 ). Here we scrutinize the remaining components of the ATOMIC protocol, including midlevel composite models to approximate the complete-basis set (CBS) limit of CCSD(T) as well as zero-point energies (ZPEs) and thermal enthalpy increments that are evaluated from scaled harmonic MP2 frequencies. Potential errors relating to imperfections in MP2 geometries and ZPEs are estimated using auxiliary information obtained from geometry optimizations and frequency calculations at the density functional (B3LYP) level. Overall corrections to and uncertainties of enthalpies of formation are obtained from summation and error propagation, respectively. The error and uncertainty model is validated with accurate data from the Active Thermochemical Tables (ATcT) and compared to earlier statistical assessments for the G3/99 benchmark. The proposed model is a welcome alternative to statistical assessment, first because it does not depend on comparison with experiment, second because it recognizes the expected scaling of error with system size, and third because it provides a detailed account of the importance of various contributions to overall error and uncertainty. The evaluation of ZPEs from scaled harmonic frequencies expectedly emerges as the leading source of uncertainty if highly accurate composite models are used to treat the electronic problem, but uncertainties are usually balanced with those arising from computationally more attractive B level (B1...B6) models to estimate the CBS limit of CCSD(T). ATOMIC(hc) enthalpies of formation, complete with uncertainty estimates, are reported for 161 hydrocarbons ranging in size from methane (CH4) to [8]circulene (C32H16) and tetra-tert-butyltetrahedrane (C20H36). Experimental data are available for 127 molecules but cannot be reconciled with theory in 37 cases. Theory helps to identify the more accurate among conflicting experimental values in 11 cases and emerges as a valuable complement to experiment also for larger molecules, provided that fair estimates of uncertainty are available.