Master equation methods for multiple well systems: application to the 1-,2-pentyl system

The master equation (ME) provides a powerful technique for modeling reactions that involve at least one potential energy well. It can be widely applied to reactions with several connected energy wells and multiple product channels. The application of the technique is reviewed by reference to the H + SO₂ reaction, where phenomenological rate constants for use, for example, in a combustion model can be extracted through an analysis of the eigenvalues and eigenvectors of the collision matrix, M, that describes formation of the adducts HSO₂ and HOSO from the source H + SO₂, collisional energy transfer in the adduct wells and reaction via the product channel (sink) OH + SO. The approach is extended to systems with more than one sink and it is demonstrated that macroscopic (phenomenological) rate coefficients derived from a ME obey detailed balance if the original ME is appropriately constructed. The method has been applied to the 1-, 2-pentyl radical system, that includes isomerisation and dissociation via two channels to form C₃H₆ + C₂H₅ and C₂H₄ + C₃H₇. The calculations clearly demonstrate the importance of indirect dissociation channels, in which an isomer can dissociate to form the product set to which it is not directly connected, e.g. formation of C₃H₆ + C₂H₅ from 1-pentyl, via the energized states of 2-pentyl. As in previous studies of pentyl dissociation, there is a convergence of the chemically significant eigenvalues and the internal energy relaxation eigenvalues above 1000 K; the consequences of this convergence are discussed.