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

Abstract

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 + SO(2) 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 HSO(2) and HOSO from the source H + SO(2), 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 C(3)H(6) + C(2)H(5) and C(2)H(4) + C(3)H(7). 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 C(3)H(6) + C(2)H(5) 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 approximately 1000 K; the consequences of this convergence are discussed.

Unimolecular Reactions of Peroxy Radicals in Atmospheric Chemistry and Combustion

“…[15,16] The aim is to provide a kinetic description of the reaction system at a macroscopic, or phenomenological, level formulated in terms of the behaviour of each of the isomers at an energy resolved, or microcanonical, level. The ME partitions the rotational and vibrational energy levels of each intermediate into grains with an energy width no larger than a few kJ mol…”

On the nucleation of dust in oxygen-rich stellar outflows

“…All RRKM and ME calculations reported in this study were carried out with the open-source ME program, master equation solver for multi-well energy reactions (MESMER; [31]). MESMER determines the temperature-and pressure-dependent rate coefficient from the full microcanonical description of the system time evolution by performing an eigenvector/eigenvalue analysis similar to that described by [26,27,32].…”

“…For this study, a multi-well energy-grained ME was used [26][27][28]. The internal energies of the intermediates on the PES were divided into a contiguous set of grains (width, 200 cm −1 ), each containing a bundle of rovibrational states.…”

Communication: Thermal unimolecular decomposition of syn-CH3CHOO: A kinetic study

“…Using the calculated PES properties, anharmonic constants, and rovibrational parameters obtained with mHEAT (see above), a simplified two-dimensional-(E,J)-grained master equation was solved using an eigenvalue-eigenvector matrix technique [51][52][53][54][55][56][57][58][59][60][61] to obtain the time evolution of various intermediates as well as phenomenological rate constants as functions of pressure (P = 10 −3 to 10 4 Torr) and temperature (T = 200-400 K) that cover atmospheric conditions. Figure 2 displays the time evolution of various species as a function of pressure at 300 K, while Figure 3 shows the time evolution of various species as a function of temperature at 1 atm.…”