Scaled Degree of Rate Control: Identifying Elementary Steps That Control Differences in Performance of Transition Metal Catalysts

Detailed mechanistic knowledge of catalytic reaction networks and identification of key parameters that control their kinetics, such as rate limiting steps, are of central importance to the fast discovery of optimum catalyst material. Microkinetic models based on Density Functional Theory (DFT) calculated kinetic and thermodynamic parameters have been used to investigate the mechanism of complex reaction systems, predict kinetic behavior of different catalytic material and identify kinetically relevant parameters. With the fast evolution of quantum chemical computational methods, it has become apparent that microkinetic analysis of heterogeneous catalytic reactions is an indispensable part of catalyst design process.

A commonly used method in the determination of a rate limiting or selectivity controlling step in a complex kinetic network is the “Degree of Rate Control” (DoRC) method, a sensitivity analysis approach first proposed by Campbell.¹ The DoRC simplifies complex reactions to identify a few steps that are crucial to performance, thereby facilitating the identification of novel catalysts. However, due to the assumption of parametric independence, the DoRC analysis is not rigorous for heterogeneous catalytic reactions where surface species and transition state energies are related through parametric correlations, such as linear scaling (LS) and Brønsted-Evans-Polanyi (BEP) relations.

Here we propose a computational approach for the identification of elementary steps that are responsible for the differences of catalytic behavior of transition metal catalysts, by implicitly incorporating inherent parametric correlations in DoRC calculations. We introduce the concept of “scaled degree of rate control”, (S-DoRC) which is closely related to Nørskov and Bligaard’s “degree of catalytic control”.² Rather than identifying all steps, which could influence the rate or selectivity of a catalytic reaction as in the DoRC analysis, the S-DoRC only identifies the relevant rate or selectivity controlling steps that are tunable within the confines of LS and BEP relations. We derive a formulation for the S-DoRC, which is simple to implement as a modification of DoRC, given the expansive and previously published parametric correlations.

1. Campbell, C. T. Finding the Rate-Determining Step in a Mechanism. J. Catal. 204, 520–524 (2001).

2. Nørskov, J. K., Bligaard, T. & Kleis, J. Rate control and reaction engineering. Science 324, 1655–6 (2009).