A Combined Kinetic−Quantum Mechanical Model for Assessment of Catalytic Cycles:  Application to Cross-Coupling and Heck Reactions

The efficiency of catalytic cycles is measured by their turnover frequency (TOF). The degree of TOF control determines which states contribute most to the rate of the cycle, and thus indicates the steps that have the highest impact on the cycle. A kinetic model developed by Christiansen (Christiansen, J. A. Adv. Catal. 1953, 5, 311) for catalytic cycles is implemented here in a form that utilizes state energies. This enables one to assess the efficiency of quantum mechanically computed catalytic cycles like the palladium-catalyzed cross-coupling and Heck reactions, to test alternative hypotheses, and to make some predictions. This implementation can also account for effects such as Sabatier's volcano curve for heterogeneous catalysis. The model leads to a dependence of the TOF for any cycle on the "corrected" energy span quantity, deltaE, whose precise expression depends on the location of the summit and trough of the cycle in the step sequence of the cycle. Thus, knowing the highest energy transition state, the most abundant reaction intermediate, and the reaction energy enables one to make quick predictions about relative efficiency of cycles. At the same time, the degree of TOF control determines which states contribute most to the rate of reaction, and thus indicates the values to be included in the calculation of the energetic span and the steps that may be tinkered with to improve the cycle.