Degree of Rate Control: How Much the Energies of Intermediates and Transition States Control Rates

Abstract

For many decades, the concept of a "rate-determining step" has been of central importance in understanding chemical kinetics in multistep reaction mechanisms and using that understanding to advantage. Yet a rigorous method for identifying the rate-determining step in a reaction mechanism was only recently introduced, via the "degree of rate control" of elementary steps. By extending that idea, we argue that even more useful than identifying the rate-determining step is identifying the rate-controlling transition states and the rate-controlling intermediates. These identify a few distinct chemical species whose relative energies we could adjust to achieve a faster or slower net reaction rate. Their relative energies could be adjusted by a variety of practical approaches, such as adding or modifying a catalyst, modifying the solvent, or simply modifying a reactant's molecular structure to affect electronic or steric control on the relative energies of the key species. Since these key species are the ones whose relative energies most strongly influence the net reaction rate, they also identify the species whose energetics must be most accurately measured or calculated to achieve an accurate kinetic model for any reaction mechanism. Thus, it is very important to identify these rate-controlling transition states and rate-controlling intermediates for both applied and basic research. Here, we present a method for doing that.

Bimetallic Au–Pd Alloy Catalysts for N2O Decomposition: Effects of Surface Structures on Catalytic Activity

“…Indeed, multistep reaction processes in heterogeneous catalysis are always complicated, and the degree of rate control of elementary step might experience some changes over different catalysts surface. 84,85 Therefore, a detailed investigation of the catalytic mechanism for N 2 O decomposition over Au−Pd alloy catalysts is needed. DFT calculations are further performed to provide information about the catalytic mechanism.…”

Theory of multiple proton–electron transfer reactions and its implications for electrocatalysis

“…49,50,51,52 Although the Sabatier has distinct limitations related to the fact that kinetics is not included, the thermodynamic Sabatier-type analysis is typically accurate in identifying the bottleneck in a mechanism, as has been argued at various places in the literature. 9,19,47,51 There may be fundamental restrictions why such a thermodynamically optimal situation may not be achievable, in which case we are looking for the catalyst with the lowest overpotential, which in our thermodynamic analysis corresponds to the situation where all steps are either thermodynamically neutral or downhill.…”

Analysis of electrocatalytic reaction schemes: distinction between rate-determining and potential-determining steps

“…Campbell pointed out the limitations of the analysis based on De Donder relations, and proposed the concept of "degree of rate control". 3,21 In a multi-step mechanism, with overall rate r, the degree of rate control X i of step i is defined as:…”

“…There is a relation between the degree of rate control, the Tafel slope and the volcano slope, but they do not have exactly the same meaning, as the both the TS and VS incorporate the BEP relation, whereas the definition of Eq.19 does not (for a more detailed discussion, see also ref. 21). In Campbell's analysis, the step with the degree of rate control closest to unity is the RDS.…”

“…For detailed examples, I refer to the literature. 3,4,5,21,22 Finally, the distinction between RDS and PDS is also a useful way to look at the confusion that sometimes arises in the discussion of the rate-limiting step in the oxygen reduction reaction (ORR) to water. The experimentally observed Tafel slope for the ORR on a platinum electrode is typically between 60 and 120 mV/dec.…”