Differentiating the Yield of Chemical Reactions Using Parameters in First-Order Kinetic Equations to Identify Elementary Steps That Control the Reactivity from Complicated Reaction Path Networks.

The yield of a chemical reaction is obtained by solving its rate equation. This study introduces an approach for differentiating yields by utilizing the parameters of the rate equation, which is expressed as a first-order linear differential equation. The yield derivative for a specific pair of reactants and products is derived by mathematically expressing the rate constant matrix contraction method, which is a simple kinetic analysis method. The parameters of the rate equation are the Gibbs energies of the intermediates and transition states in the reaction path network used to formulate the rate equation. Thus, our approach for differentiating the yield allows a numerical evaluation of the contribution of energy variation to the yield for each intermediate and transition state in the reaction path network. In other words, a comparison of these values automatically extracts the factors affecting the yield from a complicated reaction path network consisting of numerous reaction paths and intermediates. This study verifies the behavior of the proposed approach through numerical experiments on the reaction path networks of a model system and the Rh-catalyzed hydroformylation reaction. Moreover, the possibility of using this approach for designing ligands in organometallic catalysts is discussed.