Binary collision theory for thermal and nonisothermal relaxation and reaction of polyatomic molecules Original Research Article

Many unimolecular reactions are initiated by photoexcitation of a polyatomic molecule at room temperature from its S0 ground state to an electronically excited S1 state. This excitation will generally lead to a nonisothermal initial distribution of energy in the excited state. Collisions with a buffer gas at room temperature tend to reequilibrate the reacting molecule. The ensuing radiative and nonradiative decay will depend on the competition between the energy dependent unimolecular decay rate and the energy relaxation. In this paper we describe a Gaussian binary collision theory which includes all three aspects – radiative decay, nonradiative decay and relaxation. The Gaussian property is justified when the reacting species is large enough, i.e. it has a large enough number of degrees of freedom such that the equilibrium distribution of the molecule can be described by a Gaussian. Guided by experimental observation, we adapt a Gaussian transition probability, which is similar to Melʹnikovʹs, to describe the relaxation dynamics. An analytic solution for the Gaussian master equation is presented. We find that pressure induced decay which is faster than the initial decay rate is an experimental signature of an initial cold distribution of reactants. This signature was observed experimentally in the isomerization of trans-stilbene. Application to the decay dynamics of the trans-stilbene molecule shows that an initial temperature of 230 K for trans-stilbene in the excited S1 state suffices for good agreement between the theoretical and experimental survival probability measured at a gas temperature of 300 K.