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

02 June 2023, Version 2
This content is a preprint and has not undergone peer review at the time of posting.


Kinetic models parameterised 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 modelling 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 minimisation problem, leading to significantly improved convergence in solving micro-kinetic models and thus enabling the efficient study of more complex catalytic reactions.


Micro-kinetic modelling
Heterogeneous catalysis
Surface chemistry
Reaction networks

Supplementary materials

Supporting Information
Supporting information to the main text: Number of sites based solver for determining coverages from steady-state mean-field micro-kinetic models


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