Dissociation and recombination of a diatomic molecules involving two states which only interact via the atomic species

Geometric Investigation of Association/Dissociation Kinetics with an Application to the Master Equation for CH3 + CH3 ↔ C2H6

“…Another reason for the investigation undertaken here is the recent work of one of us − and others − on the asymptotic dynamics of kinetic equations. Until recently, , these techniques were applied only to complex chemical kinetics, although there is a history of more rigorous approaches (i.e., beyond steady-state approximations) used to model master equations. − The techniques used in refs −28 involve the calculation of low-dimensional manifolds that describe the asymptotic dynamics of systems approaching equilibrium and are more rigorous than the steady-state approximation. For nonlinear master equations, a low-dimensional manifold is analogous to the eigenvector with least negative eigenvalue, the one used to calculate a pressure-dependent unimolecular rate constant. , In addition, low-dimensional manifolds allow for the systematic elucidation of the global phase space structure of a dynamical system that approaches an equilibrium point at long time .…”

Nonequilibrium effects in chemical kinetics. Straight-line paths for homonuclear diatomic dissociation-recombination process

“…In some cases important progress has been made by using singular-perturbation theory. [8][9][10][11] In the present article we use an iterative numerical method, similar to that employed in various contexts by previous workers, 12 the nonequilibrium distributions for non-first-order systems. This method is much simpler and more stable than the full time-dependent solution of the master equation, yet it yields both phenomenological rate constants and nonequilibrium distributions.…”