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 ͑coupled͒ quantum states, compared with that for the symmetric isotopomers ͑about 10%͒, due to being more ''RRKM-like'' ͑Rice-RamspergerKessel-Marcus͒: 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 ( . 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.

Coriolis coupling as a source of non-RRKM effects in triatomic near-symmetric top molecules: Diffusive intramolecular energy exchange between rotational and vibrational degrees of freedom

“…It was shown [1][2][3] that the unusual mass-independent isotope effect in ozone formation [4][5][6] can be explained by assuming some non-RRKM ͑non-Rice-Ramsperger-KasselMarcus͒ behavior of energetic ozone molecules. The reader can find a review of literature on the ozone isotope effect and the current status of theoretical investigations in Ref.…”

An approximate theory of the ozone isotopic effects: Rate constant ratios and pressure dependence

“…Accordingly, in unscrambled experiments vibrationally excited ozone isotopomers XYY are formed only from X + YY→ XYY, while in scrambled experiments they are also formed from Y +XY→ XYY. The relative importance of the two dissociation channels of XYY in the theory is determined by a "partitioning factor," 30 which in turn depends on whether the access to the dissociating XYY * was from one or both channels ͑X+YY and Y+XY͒. This difference in experimental conditions leads to a marked difference in the theoretical expressions for the two types of experiments.…”

“…where E a is the zero-point energy of the oxygen fragment in channel a, and Y a,b , the partitioning factor 30 is…”

“…[25][26][27][28][29] Rice-RamspergerKassel-Marcus ͑RRKM͒ theory with a master equation approach for the collisional deactivation of the intermediate excited ozone molecules has been applied to study both phenomena. [32][33][34] It was found that the MIF can be explained when an -effect, a non-RRKM effect, [30][31][32][33][34] which reduces dynamically the low-pressure rate constant of the recombination to form symmetric molecules by a factor of compared to that for the asymmetric ones, and a weak collision effect [32][33][34] for the deactivation of excited ozone molecules is also included in the theory. For the unusually large massdependent isotope effect, observed under very special ͑"unscrambled"͒ experimental conditions, the zero-point energy differences in the two dissociation paths of any asymmetric XYZ * isotopomer play the key role, together with the weak collision efficiency.…”

On collisional energy transfer in recombination and dissociation reactions: A Wiener–Hopf problem and the effect of a near elastic peak

“…[1][2][3][4][5] Our interest in the subject was prompted by studies of ozone whose formation and isotopic effects have been of much recent interest. [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] In general, the formation of a molecule AB is described by A + B AB ‫ء‬ , ͑1͒…”