Towards a barrier height benchmark set for biologically relevant systems

We have collected computed barrier heights and reaction energies (and associated model structures) for five enzymes from studies published by Himo and co-workers. Using this data, obtained at the B3LYP/6- 311+G(2d,2p)[LANL2DZ]//B3LYP/6-31G(d,p) level of theory, we then benchmark PM6, PM7, PM7-TS, and DFTB3 and discuss the influence of system size, bulk solvation, and geometry re-optimization on the error. The mean absolute differences (MADs) observed for these five enzyme model systems are similar to those observed for PM6 and PM7 for smaller systems (10-15 kcal/mol), while DFTB results in a MAD that is significantly lower (6 kcal/mol). The MADs for PMx and DFTB3 are each dominated by large errors for a single system and if the system is disregarded the MADs fall to 4-5 kcal/mol. Overall, results for the condensed phase are neither more or less accurate relative to B3LYP than those in the gas phase. With the exception of PM7-TS, the MAD for small and large structural models are very similar, with a maximum deviation of 3 kcal/mol for PM6. Geometry optimization with PM6 shows that for one system this method predicts a different mechanism compared to B3LYP/6-31G(d,p). For the remaining systems geometry optimization of the large structural model increases the MAD relative to single points, by 2.5 and 1.8 kcal/mol for barriers and reaction energies. For the small structural model the corresponding MADs decrease by 0.4 and 1.2 kcal/mol, respectively. However, despite these small changes, significant changes in the structures are observed for some systems, such as proton transfer and hydrogen bonding rearrangements. The paper represents the first step in the process of creating a benchmark set of barriers computed for systems that are relatively large and representative of enzymatic reactions, a considerable challenge for any one research group but possible through a concerted effort by the community. We end by outlining steps needed to expand and improve the data set and how other researchers can contribute to the process.