Kinetic-quantum chemical model for catalytic cycles: The Haber-Bosch process and the effect of reagent concentration

A combined kinetic-quantum chemical model is developed with the goal of estimating in a straightforward way the turnover frequency (TOF) of catalytic cycles, based on the state energies obtained by quantum chemical calculations. We describe how the apparent activation energy of the whole cycle, so-called energetic span (delta E), is influenced by the energy levels of two species: the TOF determining transition state (TDTS) and the TOF determining intermediate (TDI). Because these key species need not be adjoining states, we conclude that for catalysis there are no rate-determining steps, only rate determining states. In addition, we add here the influence of reactants concentrations. And, finally, the model is applied to the Haber-Bosch process of ammonia synthesis, for which we show how to calculate which catalyst will be the most effective under specific reagents conditions.