Predicting Selectivity with a Bifurcating Surface: Inaccurate Model or Inaccurate Statistics of Dynamics?

Reactions on post-transition-state bifurcation (PTSB) energy surfaces are an important class of reaction in which classical rate theories, such as the transition state theory, fail to account for the selectivity. Quasiclassical trajectory molecular dynamic (QCT-MD) simulation is an important computational approach to understanding reactions mechanisms, especially for reactions that cannot be predicted from conventional rate theories. However, the applicability of direct dynamic simulations is hampered by huge computational costs for collecting a statistically meaningful set of trajectories, making it difficult to compare simulation results with theoretical or physical insights-based predictions (non-MD predictions). In this work, we examine the PTSB of Schmidt-Aubé reactions studied by Tantillo and co-workers. With machine-learning using kernel-ridge regression (KRR) to predict atomic forces, statistical reliability was enhanced by significantly increasing the number of trajectories. With KRR, the bottleneck of simulating dynamics (atomic forces in QCT-MD with density functional theory) was accelerated more than 100-fold. We found that this KRR-aided QCT-MD approach is successful in predicting branching ratios with a much larger number of trajectories. With our approach, statistical errors are greatly reduced, and hypothetical non-MD models for predicting selectivity are tested with much higher confidence. By comparison with non-MD models, dynamical properties that affect branching ratios become more clearly described.