Unimolecular Reaction Dynamics from Kinetic Energy Release Distributions. 7. Average Translational Energy Release

Abstract

The relationship between the average translational energy 〈ε〉 released in a unimolecular reaction and the internal energy E measured in excess of the dissociation threshold is not necessarily linear. In a purely statistical situation, it reflects the shape of the function N(E) which expresses the way the density of vibrational−rotational states of the pair of fragments increases with E. In fact, 〈ε〉 is seen to vary as a function of E in exactly the same way as {d ln[N(E)]/dE-1. The most important feature of N(E) is a dimensionless parameter γ = E{d log10 [N(E)]/dE} evaluated at the internal energy at which the measurement of 〈ε〉 is made. The ratio 〈ε〉/E also depends on nonstatistical effects. An “ergodicity index” e-DS, where DS denotes the so-called entropy deficiency associated with incomplete energy randomization, can be extracted from experiments. It measures the efficiency of phase space sampling by the pair of fragments. In the case of unimolecular reactions that proceed without any reverse activation barrier, simple relationships can be derived to relate the value of e-DS to that of γ and 〈ε〉/E. When the average energy release is measured for a metastable dissociation in a two-sector mass spectrometer, the ratio 〈ε〉/E also depends in principle on the transmission efficiency function T(E). However, the necessary correction is small and often negligible. Applications to the halogen loss reactions from C2H5I+, C6H5Br+, and C6H5I+ are presented. Phase space appears to be sampled with an efficiency close to 100% both at very low and very high values of the internal energy. For intermediate values of E, the minimal efficiency is of the order of 75%. At higher values of the internal energy, numerous surface crossings bring about chaotic dynamics and efficient phase space sampling.