Multiple transition states in unimolecular reactions: A transition state switching model. Application to the C4H8 +⋅ system

Abstract

A transition state switching model is developed for use in systems where more than one transition state occurs along the reaction coordinate. The model is cast in the perspective of both the unified statistical theory (UST) of Miller and of variational transition state theory. The basic assumptions are those common to transition state theory and RRKM–QET. A reaction branching analysis leads to reaction probabilities for a number of potential surfaces and appropriate expressions are delineated for both unimolecular and bimolecular reactions. The theory is developed from a microcanonical viewpoint and rigorously conserves both energy E and angular momentum J. Comparison is made with experimental data for the C4H8 +⋅ system where absolute unimolecular rate constants and branching ratios have been measured as a function of energy, bimolecular rate constants, and branching ratios measured at room temperature (the ethylene ion–molecule reaction), the lifetime of C4H8 +⋅ measured when formed by the ethylene ion–molecule reaction, and product kinetic energy distributions measured. The principal conclusions of the work are (i) a multiple transition state switching mechanism is required if the experimental data is to be adequetely fit by theory; (ii) at least two transition states (i.e., dividing surfaces at points of minimum flux along the reaction coordinate) naturally occur in unimolecular reactions, one a tight (i.e., configurational) TS occuring near the unimolecular reactant and the second an orbiting (i.e., centrifugal) TS occuring near the bimolecular products; (iii) tight transition states naturally occur at energies E‡ less than the threshold energy for reaction E0 when the system energy E is significantly greater than E0; (iv) the relative abundance of the three product channels C2H4 +⋅+C2H4, C3H5 ++CH3⋅, and C4H+7+H⋅ are strong functions of both energy and angular momentum in the reactant C4H8 +⋅ ion.