Number of sites-based solver for determining coverages from steady-state mean-field micro-kinetic models

Kinetic models parameterized by ab-initio calculations have led to significant improvements in understanding chemical reactions in heterogeneous catalysis. These studies have been facilitated by implementations which determine steady-state coverages and rates of mean-field micro-kinetic models. As implemented in the open-source kinetic modeling program, CatMAP, the conventional solution strategy is to use a root-finding algorithm to determine the coverage of all intermediates through the steady-state expressions, constraining all coverages to be non-negative and to properly sum to unity. Though intuitive, this root-finding strategy causes issues with convergence to solution due to these imposed constraints. In this work, we avoid explicitly imposing these constraints, solving the mean-field steady-state micro-kinetic model in the space of number of sites instead of solving it in the space of coverages. We transform the constrained root-finding problem to an unconstrained least-squares minimization problem, leading to significantly improved convergence in solving micro-kinetic models and thus enabling the efficient study of more complex catalytic reactions. We have developed a constraint-free solver for determining surface coverages from steady-state mean-field micro-kinetic models, which are a crucial component for developing a mechanistic understanding of heterogeneous catalytic processes. This implementation leads to a more stable convergence in the iterative solution of such models, as depicted by the green symbols, while an approach employing constraints on coverages, as indicated by the red symbols, can fail to find the solution. image