Reaction candidates are sampled once identified using the stochastic Monte Carlo selection scheme described in the main text. The simplest way to do so is to select one at random, without applying any physical corrections (i.e. uniformly). Alternatively, each candidate's selection probability can be weighted using the molecular rate of the template reaction path is corresponds to prior to random selection. This weighting is done using pre-calculated activation barriers based on DFT. In this study, E a values shown in Fig. were used. S-3 rected candidate sampling ('corrected/variable') reference. A value of 4 ps has been used in previous computational studies employing the MC-MD procedure, though different values have also been used. 7 out of 9 uncorrected/constant simulations (red) were terminated before reactive cycle 250, where 200 consecutive update loops were run in a single reactive cycle without a single candidate being found. These simulations in general are terminated much earlier than cycle 250 and require far more candidate searches per cycle than the corrected/constant and corrected/variable simulations (green), for which 8 out of 9 and 3 out of 3 simulations reached cycle 250, respectively. These uncorrected/constant simulations have larger computational cost by both factors i) and ii) described in the main text. There is also no significant relationship between the the number of candidate searches required and the value of τ const used.