Phase space bottlenecks and rates of no-barrier fragmentation reactions into polyatomic molecules

Abstract

An expression of the microcanonical unimolecular rate for an arbitrary transition state surface in phase space is derived and applied to fragmentation reactions into polyatomic molecules without potential barrier. The transition state which has a ‘‘point of no return’’ property in unimolecular dissociation is defined as an interfragment bottleneck in phase space. The fragmentation rate based on the interfragment bottleneck in phase space is compared with the rate based on the transition state defined in configuration space. The rate derived from the flux which crosses the interfragment bottleneck by intermode energy transfer is found to be smaller than the rate derived from the Rice–Ramsperger–Kassel–Marcus or phase space theory by an approximate factor (s+r/2)|W̃|/E, where E is the total energy and |W̃| is the magnitude of the coupling energy between the reaction coordinate and the s-dimensional vibrational and r-dimensional rotational modes of the fragments. Phase space theory grossly overestimates the rate of fragmentation of small molecules with small |W̃| in the high energy range, because the theory does not take into account the slow process of intramolecular energy redistribution.