Master equation lumping for multi-well potential energy surfaces: A bridge between ab initio based rate constant calculations and large kinetic mechanisms

Ab initio transition state theory-based master equation methodologies for the calculation of rate constants have gained enormous popularity in the past decades. Nevertheless, introducing these rate constants into large kinetic schemes is a non-trivial task when large potential energy surfaces (PESs) are investigated. To determine proper phenomenological rate constants it is in fact necessary to account for the formation of all the thermodynamically stable wells considered in the master equation (ME), even if most wells do not exhibit significant secondary reactivity. Moreover, reactions involving intermediates with lifetimes comparable to the rovibrational relaxation timescale can exhibit discontinuities both in the rate constants and in the number of thermodynamically stable wells across the investigated temperature and pressure ranges. In this work, we address these problems with a “master equation-based lumping” (MEL) approach specifically designed to process the output of ME calculations of multi-well PESs. Simple kinetic simulations allow identifying both intermediate wells with limited lifetime and isomers with similar reactivity. Then, equivalent rate constants for a smaller set of pseudospecies are derived so as to reproduce the kinetics of the detailed mechanism. Our methodology is independent of any experimental data or experience-based assumptions. The power of MEL is demonstrated with three case studies of increasing complexity, namely the PES for CH3COOH decomposition, and the portions of the C5H5OH and C10H10/C10H9 PESs accessed from C5H5 + OH and C5H5 + C5H5 recombination. This work constitutes the first systematic step addressing the robust integration of rate constants derived from ME simulations into global kinetic schemes and provides a useful approach for the entire chemical kinetics community filling the gap between detailed theoretical investigations of complex PESs and the development of detailed kinetic models.