The degree of rate control of catalyst-bound intermediates in catalytic reaction mechanisms: Relationship to site coverage

The degree of rate control (DRC) quantifies how much the energy of each species in a reaction mechanism (e.g., catalyst-bound intermediates and transition states) affects the net reaction rate. It thus plays an important role in understanding catalyst activity and selectivity and in efforts to find better catalysts. We show here that under steady-state reaction conditions, the DRC for any catalyst-bound intermediate n (X-n) is proportional to its fractional population of catalyst sites (theta(n)), X-n = -sigma x theta(n), where the proportionality constant sigma is given by sigma = Sigma i Xi x n(i). Here, Xi is the DRC of the transition state in step i, n(i) is the number of catalyst sites of the same type required for the elementary step i, and the sum is over all transition states (or elementary steps) i. Since only a few transition states typically have non-negligible DRCs, this simple sum (or weighted average of elementary-step site requirements) includes only a few terms (and only one term when there is a single rate-determining step). We also show that the DRCs of reactants and catalyst depend upon the choice of zero-energy reference, but simplify to zero when their standard states are used as the zero-energy references. (C) 2019 Elsevier Inc. All rights reserved.