Simplified Wave Function Models in Thermochemical Protocols Based on Bond Separation Reactions

ATOMIC-2 Protocol for Thermochemistry

ATOMIC is a midlevel thermochemistry protocol that uses Pople's concept of bond separation reactions (BSRs) as a theoretical framework to reduce computational demands in the evaluation of atomization energies and enthalpies of formation. Various composite models are available that approximate bond separation energies at the complete-basis-set limit of all-electron CCSD(T), each balancing computational cost with achievable accuracy. Evaluated energies are then combined with very high-level, precomputed atomization energies of all auxiliary molecules appearing in the BSR to obtain the atomization energy of the molecule under study. ATOMIC-2 is a new version of the protocol that retains the overall concept and all previously defined composite models but improves on ATOMIC-1 in various other ways: Geometry optimization and zero-point-energy evaluation are performed at the density functional level (PBE0-D3/6-311G(d)), which shows significant computational savings and better accuracy than the previously employed RI-MP2/cc-pVTZ. The BSR framework is improved, using more accurate complete-basis-set (CBS) extrapolations toward the Full CI limit for the atomization energies of all auxiliary molecules. Finally, and most importantly, an error and uncertainty model termed ATOMIC-2_um is added that estimates average bias and uncertainty for each of the atomization energy contributions that arise from the simplified treatment of some contributions to bond separation energies (CCSD(T)) and the neglect of others (such as higher order, scalar relativistic, or diagonal Born-Oppenheimer corrections) or from residual error in the energies of auxiliary molecules. Large and diverse benchmarks including up to 1179 molecules are used to evaluate necessary reference data and to correlate the observed error for each of the contributions with appropriate proxies that are available without additional quantum-chemical calculations for a particular molecule and represent its size and type. The implementation of ATOMIC-2 considers neutral, closed-shell molecules containing H, C, N, O, and F atoms; compared to ATOMIC-1, the framework has been extended to cover a few challenging but rare bond topologies. In comparison to highly accurate reference data for 184 molecules taken from the ATcT database (V. 1.122r), regular ATOMIC-2 shows noticeable underbinding, but the bias-corrected protocol ATOMIC-2_um is found to be more accurate than either ATOMIC-1 or standard Gaussian-4 theory, and the uncertainty model is consistent with statistics of actually observed errors. Problems arising from ambiguous or challenging Lewis-valence structures defining BSRs are discussed, and computational efficiency is demonstrated. Computer code is made available to perform ATOMIC-2_um analyses.

Density Functional Geometries and Zero-Point Energies in Ab Initio Thermochemical Treatments of Compounds with First-Row Atoms (H, C, N, O, F)

Density functionals are often used in ab initio thermochemistry to provide optimized geometries for single-point evaluations at a high level and to supply estimates of anharmonic zero-point energies (ZPEs). Their use is motivated by relatively high accuracy at a modest computational expense, but a thorough assessment of geometry-related error seems to be lacking. We have benchmarked 53 density functionals, focusing on approximations of the first four rungs and on relatively small basis sets for computational efficiency. Optimized geometries of 279 neutral first-row molecules (H, C, N, O, F) are judged by energy penalties relative to the best available geometries, using the composite model ATOMIC/B5 as energy probe. Only hybrid functionals provide good accuracy with root-mean-square errors around 0.1 kcal/mol and maximum errors below 1.0 kcal/mol, but not all of them do. Conspicuously, first-generation hybrids with few or no empirical parameters tend to perform better than highly parameterized ones. A number of them show good accuracy already with small basis sets (6-31G(d), 6-311G(d)). As is standard practice, anharmonic ZPEs are estimated from scaled harmonic values. Statistics of the latter show less performance variation among functionals than observed for geometry-related error, but they also indicate that ZPE error will generally dominate. We have selected PBE0-D3/6-311G(d) for the next version of the ATOMIC protocol (ATOMIC-2) and studied it in more detail. Empirical expressions have been calibrated to estimate bias corrections and 95% uncertainty intervals for both geometry-related error and scaled ZPEs.

A Database of Formation Enthalpies of Nitrogen Species by Compound Methods (CBS-QB3, CBS-APNO, G3, G4)

Accurate thermochemical data for compounds containing C/H/N/O are required to underpin kinetics simulation and modeling of the reactions of these species in different environments. There is a dearth of experimental data so computational quantum chemistry has stepped in to fill this breach and to verify whether particular experiments are in need of revision. A number of composite model chemistries (CBS-QB3, CBS-APNO, G3, and G4) are used to compute theoretical atomization energies and hence enthalpies of formation at 0 and 298.15 K, and these are benchmarked against the best available compendium of values, the Active Thermochemical Tables or ATcT. In general the agreement is very good for some 28 species with the only discrepancy being for hydrazine. It is shown that, although individually the methods do not perform that well, collectively the mean unsigned error is <1.7 kJ mol(-1); hence, this approach provides a useful tool to screen published values and validate new experimental results. Using multiple model chemistries does have some drawbacks but can produce good results even for challenging molecules like HOON and CN2O2. The results for these smaller validated molecules are then used as anchors for determining the formation enthalpies of larger species such as methylated hydrazines and diazenes, five- and six-membered heterocyclics via carefully chosen isodesmic working reactions with the aim of resolving some discrepancies in the literature and establishing a properly validated database. This expanded database could be useful in testing the performance of computationally less-demanding density function methods with newer functionals that have the capacity to treat much larger systems than those tested here.