Reaction Kinetics of Complex Molecular Strains: The Efficiency of Mechanochemistry Under a Constant Total Energy

While the concept of mechanochemistry is not new, it is becoming significantly more prevalent in a wide variety of fundamental and industrial chemistry applications, especially in the condensed phase. However, condensed matter effects can result in complex non-linear deformations. Moreover, this highly relevant in reactions that include both thermal and mechanical influences on the reaction rate. Here we define a formalism that describes kinetic effect of molecular shape distortions as a sum over the normal modes and how those modes project onto the reactions path. By coupling this framework with a 'cost' function that defines the thermal and mechanical energy balance for a specific reaction condition, a general efficiency of the mechanochemistry is derived. We apply this concept to reactions in energetic materials where a shockwave of some energy can impart a distribution of both kinetic energy and molecular strains on the system. We derive under what conditions that mechanical energy is preferential or detrimental to local reaction rates. This workflow is general, with a proper cost function, can be applied to a wide variety of fundamental and industrial mechanochemical applications, where the cost function can define a wide range of energetic, environmental, and financial results based on changes to the reaction conditions.