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Uncertainty propagation in the derivation of phenomenological rate coefficients from theory: A case study of n-propyl radical oxidation


Goldsmith,  Claude Franklin
Inorganic Chemistry, Fritz Haber Institute, Max Planck Society;

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Goldsmith, C. F., Tomlin, A. S., & Klippenstein, S. J. (2013). Uncertainty propagation in the derivation of phenomenological rate coefficients from theory: A case study of n-propyl radical oxidation. Proceedings of the Combustion Institute, 34(1), 177-185. doi:10.1016/j.proci.2012.05.091.

Global uncertainty and sensitivity analysis is used to study the propagation of uncertainties in fundamental theoretical parameters through to uncertainties in the predicted temperature and pressure dependent phenomenological rate coefficients. Predictions are obtained from ab initio transition state theory based master equation calculations. The fundamental parameters for these rate predictions include barrier heights, well depths, vibrational frequencies, collision frequency, and energy transfer parameters. A random sampling high-dimensional model representation (HDMR) approach is used to perform the global sensitivity analysis. This approach determines the predicted distributions of the phenomenological rate coefficients based on a quasi-random sample of the fundamental parameters within their uncertainty range. Sensitivity analysis then identifies the main parameters which contribute to variance in the predicted distributions. Here the approach is applied to a study of the oxidation of the propyl radical, employing the parameters derived in our recent theoretical study. We find rates at 3σ variances that typically differ from the most frequent values by factors of 4–6, with the uncertainties decreasing with increasing temperature. For the well skipping reactions there are more parameters that contribute significantly to the variance, the second-order sensitivities are greater, and the uncertainties increased with increasing pressure. For the other reactions, the uncertainties tend to decrease with increasing pressure.