Geometric investigation of association/dissociation kinetics with an application to the master equation for CH3+CH3⇆C2H6

The dynamics of association/dissociation kinetics is studied, with an application to the titled reaction. The focus is the geometry of the phase space of the phenomenological rate law, a Lindemann mechanism, and the master equation of this reversible reaction, all of which are nonlinear. It is shown that all three systems possess similar phase space structure, including a 1-D manifold. This 1-D manifold describes asymptotic motion for either dissociation or recombination and is the analogue of the corresponding eigenvector for linear master equations describing dissociation without recombination. The 1-D manifold allows for the separation of asymptotic motion from transient behavior and together with other manifolds in phase space allows a better understanding of the dissociation and recombination processes. The 1-D manifold also allows us to test various approximations that have been used in the past to calculate association rate constants from the master equation and Lindemann mechanism and develop new methods for calculating association rate constants and generating rate laws.