Molecular dynamics simulations and machine-learning assisted study of the reaction path bifurcation: Application to the intramolecular Diels–Alder cycloaddition between cyclobutadiene and butadiene

The intramolecular Diels–Alder cycloaddition between cyclobutadiene and butadiene, which involves post-transition-state bifurcation (PTSB), has been investigated using the ring-polymer molecular dynamics (RPMD), classical MD and quasi-classical trajectory (QCT) simulations, and supervised machine-learning (ML) technique. The branching fraction of this reaction strongly depends on the simulation temperature. While QCT, classical MD and RPMD simulations performed at room temperature, starting from the ambimodal transition state (TS), showed the similar dynamics, QCT overestimated the minor branching fraction at low temperature. The supervised machine-learning analysis revealed that the initial coordinates and momenta for low frequency modes at the ambimodal TS contribute to the branching dynamics.The classical MD and RPMD methods follow similar conditions to quantum Boltzmann distributions, whereas the artificially localized phase distribution, considering that the zero-point energy is wedged into the classical particles. As a result, the QCT method can provide inadequate bifurcation dynamics, such as the overestimation of the minor product.