Detailed balance in multiple-well chemical reactions

Chemical reactions that involve multiple, interconnected potential wells are of paramount importance in applications of chemical kinetics, particularly combustion and atmospheric chemistry. The only accurate way of determining phenomenological rate constants theoretically for this type of reaction is from the solution of a time-dependent, multiple-well master equation. In this Perspective we address the issue of whether or not (and to what extent) detailed balance is satisfied by rate constants obtained from such solutions. In addressing this issue we discuss a number of related topics, including necessary and sufficient conditions for a system of first-order rate equations to evolve to chemical equilibrium and the relationship between detailed balance and Wegscheider conditions. The assumption of a “near-Boltzmann” distribution in the wells sheds considerable light on the issue at hand. We discuss this approximation in some detail and suggest a quantitative measure of “near-Boltzmann”. It is extremely unlikely that the rate constants of interest satisfy detailed balance exactly (there is no reason to believe that they do). However, the discrepancies are expected to be vanishingly small, as observed in practice.