Hamiltonian chemical kinetics for studying roaming in formaldehyde dissociation: Linear and nonlinear models

Abstract

A recently developed theory for formulating chemical kinetics with a Hamiltonian theory similar to classical mechanics is applied to study linear and nonlinear kinetic models for the photodissociation of formaldehyde ( H 2 CO ) via roaming pathways. Chemical kinetic equations are proposed by mapping time invariant phase space structures, such as stationary points of the potential energy surface and periodic orbits, to relevant intermediate chemical species. Solving kinetic equations in the Hamiltonian framework, we calculate reaction paths to asymptotically stable equilibria for closed reactions and varying the initial concentration of H2CO at constant temperature and pressure. The reaction paths may be classified by defining a thermodynamic distance between initial and equilibrium states, as well as the entropy production. A brusselator-type nonlinear model is proposed as the phenomenological equivalent to the periodic orbit description of roaming mechanism given before. Treating the photodissociation of formaldehyde as an open system and properly selecting the rate coefficients of the reactions and the initial concentration of formaldehyde, a periodic orbit emanates as the result of a Hamiltonian Hopf bifurcation. This yields an oscillatory reaction between the two long-range metastable intermediates, { H…CHO } and { H…HCO }, which lead to radical and molecular products.