Computational Model to Predict Reactivity under Ball-Milling Conditions

A computational model to estimate the mechanical work of activation for a chemical reaction under ball-milling conditions is developed. The model uses a simple force scheme based on isotropic compression ("wall-type forces") to mimic the effect of ball collisions. It calculates the mechanical work applied along the reaction path and predicts the variation of the activation energy. The forces are applied in all possible directions to simulate the random nature of the impacts. The model is tested on different systems including reactions with known experimental mechanochemical behavior. The model was applied to two representative Diels-Alder systems and [2 + 2] cycloaddition to test its predictive capacity. The model predictions agree with the main experimental trends and confirm that mechanical forces play a significant role in controlling the reactivity. The results bring to light the importance of mechanical work in driving selectivity under ball-milling conditions and demonstrate that such forces can differentially affect the forward and reverse directions of a chemical equilibrium. The model is simple to implement and permits the identification of whether a reaction is likely to be promoted by ball milling.