An intramolecular theory of the mass-independent isotope effect for ozone. I

Abstract

An intramolecular theory of the unusual mass-independent isotope effect for ozone formation and dissociation is described. The experiments include the enrichment factor, its dependence on the ambient pressure, the ratio of the formation rates of symmetric and asymmetric ozone isotopomers, the enrichment of ozone formed from heavily enriched oxygen isotopes, the comparison of that enrichment to that when the heavy isotopes are present in trace amounts, the isotopic exchange rate constant, and the large mass-dependent effect when individual rate constants are measured, in contrast with the mass-independent effect observed for scrambled mixtures. To explain the results it is suggested that apart from the usual symmetry number ratio of a factor of 2, the asymmetric ozone isotopomers have a larger density of reactive (coupled) quantum states, compared with that for the symmetric isotopomers (about 10%), due to being more “RRKM-like” (Rice–Ramsperger–Kessel–Marcus): Symmetry restricts the number of intramolecular resonances and coupling terms in the Hamiltonian which are responsible for making the motion increasingly chaotic and, thereby, increasingly statistical. As a result the behavior occurs regardless of whether the nuclei are bosons (16O, 18O) or fermions (17O). Two alternative mechanisms are also considered, one invoking excited electronic states and the other invoking symmetry control in the entrance channel. Arguments against each are given. An expression is given relating the mass-independent rates of the scrambled systems to the mass-dependent rates of the unscrambled ones, and the role played by a partitioning term in the latter is described. Different definitions for the enrichment factor for heavily enriched isotopic systems are also considered. In the present paper attention is focused on setting up theoretical expressions and discussing relationships. They provide a basis for future detailed calculations.