Binomial Uncertainty in Molecular Dynamics-Based Reactions Analysis

Molecular Dynamics-based reaction analysis is an indispensable tool for studying processes defying the transition-state theory (TST), where the product ratios do not follow energies of transition states. The main class of such processes is ambimodal reactions, which have a post-transition-state bifurcation, so that several products form via a single transition state. Multiple runs of molecular dynamics allow one to sample the space of possibilities and ultimately predict the product ratio without relying on TST; however, no techniques for estimating the reliability of the prediction were proposed so far. Here we show that dynamics runs follow the same rules as die rolls, which paves a simple way for estimating their uncertainty and, accordingly, the number of runs necessary to achieve the required accuracy. Remarkably, we find that the majority of such studies carried out in the last 5 years use far too few runs, so that the product ratios predicted in them can be off by >50% in more than 50% of cases.