where [C] is averaged over 0.2 ps windows using ReaxFF bond orders (0.3 cutoff). To sample a variety of T and △U states, reactions were incurred using constant heating and deformation rates instead of isothermal states. Simulations begin at an initial energy U i in which all energy is thermal, △U = 0. The intra-molecular deformation rates used were 0.0. 0.2, 0.8, 1.5, and 2.0 kcal/mol / ps. The three base heating rates (deformation rate = 0.0) used were 40.0, 30.0, and 20.0 K/ps. For deformation rates greater than 0.0, heating rates were lowered such that at a given simulation time, all simulations at that base heating rate would have the same total energy. For cases where N = 1, or in which an averaged 𝜙 with a total ∆𝑈 is a good approximation, all sums go away: