Chebyshev expansions and sensitivity analysis for approximating the temperature- and pressure-dependence of chemically-activated reactions

For some time now, the importance of properly treating the pressure dependence of unimolecular dissociation and bimolecular reactions involving chemical-activation has been clearly recognized. Traditional approaches which germinated from ideas originally due to Lindemann such as Troe's F_cent method work well for single-well, single-product dissociation cases. For chemically-activated reactions multi-well, multi-product cases are typical. There is thus a need to develop accurate representations of the pressure and temperature dependences of those reactions so that the simulation, optimization and control of detailed kinetic models containing chemically-activated reactions can become routine. We argue that direct approximation of the rate coefficients via Chebyshev expansions yields reliable and accurate representations of the pressure-temperature behaviour of these reactions superior to using a Lindemann approach to fit the form factor representing the fall-off-surface. Following up on an earlier study, we review the method in detail and confirm its superiority in a study of sixteen channels corresponding to four different reactions important in combustion chemistry over the ranges 300 K - 3000 K and 0.02 Atm. - 200 Atm. Additionally, rigorous theoretical methods for estimating the interpolation errors are discussed. A variational method of sensitivity analysis is reviewed and a discussion relating the sensitivity of the reaction mechanism to the accuracy of the approximations is provided.