The Degree of Rate Control: A Powerful Tool for Catalysis Research

The degree of rate control (DRC) is a mathematical approach for analyzing multistep reaction mechanisms that has proven very useful in catalysis research. It identifies the rate-controlling transition states and intermediates (i.e., those whose DRCs are large in magnitude). Even in mechanisms with over 30 intermediates and transition states, these are generally just a few distinct chemical species whose energies, if they could be independently changed, would achieve a faster net reaction rate to the product of interest. For example, when there is a single rate-determining step, the DRC for its transition state (TS) is 1, which means (by definition) that if this TS's energy could be decreased by kBT (where kB is Boltzmann's constant and 7' is temperature), the net rate would increase by a factor of e. Because the (relative) energies of these key adsorbed intermediates and transition states can be adjusted by modifying the catalyst or solvent, or even a reactant's molecular structure, the DRC values provide important ideas for catalyst improvement. The species with large DRCs are also the ones whose energetics must be most accurately measured or calculated to achieve an accurate kinetic model for any reaction mechanism. A tutorial on DRC analysis, the calculation of DRCs, and examples of the applications of DRCs in catalysis research is presented here. Applications of DRC analysis include the following: clarifying reaction kinetics, improving the accuracy of computational models, improving reaction conditions, improving choice of oxidant in selective oxidation, incorporation in algorithms which calculate net reaction rates of multistep mechanisms without solving the differential equations involved, and high-throughput computational screening of catalyst materials. Because DRC values can be determined experimentally, a full microkinetic model is not required to take advantage of DRC analysis.