BH9, a New Comprehensive Benchmark Dataset for Barrier Heights and Reaction Energies: Assessment of Density Functional Approximations and Basis Set Incompleteness Potentials

Abstract

The calculation of accurate reaction energies and barrier heights is essential in computational studies of reaction mechanisms and thermochemistry. In order to assess methods regarding their ability to predict these two properties, high-quality benchmark sets are required that comprise a reasonably large and diverse set of organic reactions. Due to the time-consuming nature of both locating transition states and computing accurate reference energies for reactions involving large molecules, previous benchmark sets have been limited in scope, the number of reactions considered, and the size of the reactant and product molecules. Recent advances in coupled-cluster theory, in particular local correlation methods like DLPNO-CCSD(T), now allow the calculation of reaction energies and barrier heights for relatively large systems. In this work, we present a comprehensive, and diverse benchmark set of barrier heights and reaction energies based on DLPNO-CCSD(T)/CBS, called BH9. BH9 comprises 449 chemical reactions belonging to nine types common in organic chemistry and biochemistry. We examine the accuracy of DLPNO-CCSD(T) vis-a-vis canonical CCSD(T) for a subset of BH9 and conclude that, although there is a penalty in using the DLPNO approximation, the reference data are accurate enough to serve as benchmark for density-functional theory (DFT) methods. We then present two applications of the BH9 set. First, we examine the performance of several density functional approximations commonly used in thermochemical and mechanistic studies. Second, we assess our basis set incompleteness potentials regarding their ability to mitigate basis set incompleteness error. The number of data points, the diversity of the reactions considered, and the relatively large size of the reactant molecules make BH9 the most comprehensive thermochemical benchmark set to date, and a useful tool for the development and assessment of computational methods.

Azulene–Naphthalene, Naphthalene–Naphthalene, and Azulene–Azulene Rearrangements

“…This selection was based on the extensive benchmark data and reliability revealed by thermochemical studies on reaction energies and barrier heights of similar systems including radicals. 61,62 In addition, single-point calculations of transition state energies using CCSD(T) 63 and employing the same basis set were performed for the sake of comparison and evaluation of the accuracy. The differences between UM06−2X and UCCSD-(T) energies were mostly small and insignificant, but in a few cases, as much as 5−7 kcal/mol (Supporting Information, Table S1).…”

Small-Basis Set Density-Functional Theory Methods Corrected with Atom-Centered Potentials

“…This improvement originates mostly from the good performance of ACPs (MAE reductions by 13−52%) on the four main BH data sets: Grambow2020-B97D3 (32722 data points), Grambow2020-ωB97XD3 (23922 data points), BH9 (898), and E2SN2 (418). Note that the BH9 data set was designed recently 74 to be used for the particular purpose of developing the ACPs in this work and For the other BH data sets in the training set besides BH9, E2SN2, and the two Grambow2020 subsets, the performance of ACPs is also quite good. ACPs mostly bring down the MAEs for the other subsets by about 22−94%.…”

“…Covalent properties such as reaction energies, barrier heights, and bond separation energies are mostly underestimated (positive MSEs) with a substantial error spread. In the particular case of barrier heights and the BLYP functional, this may be attributed to delocalization error, 74 which is partially remedied by the application of ACPs. For the covalent properties, application of the ACPs also decreases both the MSE and SDs substantially.…”