On the theory of the strange and unconventional isotopic effects in ozone formation

Abstract

The strange mass-independent isotope effect for the enrichment of ozone and the contrastingly unconventional strong mass-dependent effect of individual reaction rate constants are studied using statistical ͑RRKM͒-based theory with a hindered-rotor transition state. Individual rate constant ratios of recombination reactions and enrichments are calculated. The theory assumes ͑1͒ an ''-effect,'' which can be interpreted as a small deviation from the statistical density of states for symmetric isotopomers, compared with the asymmetric isotopomers, and ͑2͒ weak collisions for deactivation of the vibrationally excited ozone molecules. A partitioning effect controls the recombination rate constant ratios. It arises from small differences in zero-point energies of the two exit channels of dissociation of an asymmetric ozone isotopomer, which are magnified into large differences in numbers of states in the two competing exit channel transition states. In enrichment experiments, in contrast, this partitioning factor disappears exactly ͓Hathorn and Marcus, J. Chem.Phys. 112, 9497 ͑2000͔͒, and what remains is the -effect. Both aspects can be regarded as ''symmetry driven'' isotopic effects. The two experiments, enrichments and rate constant ratios, thus reveal markedly different theoretical aspects of the phenomena. The calculated low-pressure ozone enrichments, the low-pressure recombination rate constant ratios, the effects of pressure on the enrichment, on the individual recombination rate constant ratios, and on the recombination rate constant are consistent with the experimental data. The temperature dependence of the enrichment and of the recombination rate constant ratios is discussed and a variety of experimental tests are proposed. O at 130 K and 300 K is used for testing or providing information on the nature of a variationally determined hindered-rotor transition state. The theory is not limited to ozone formation but is intended to apply to other reactions where a symmetrical stable or unstable gas phase molecule may be formed.

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

“…So that value should be much larger than that if only vibrational energy transfer were considered. If we compare the total internal down-energy transfer ͗⌬E int ↓͘ in Ivanov and Schinke's trajectory work 40 with the values in Gao and Marcus' work [11][12][13] used to fit experimental data, there is only a small difference in ͗⌬E int ↓͘.…”

“…[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…”

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

“…An origin of this -effect was discussed elsewhere. 32,33 To calculate rate constant ratios between different reactions, an approximate formalism is given in the present study. The pressure dependence of rate constant ratios and enrichments is also considered.…”

“…[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.…”

“…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. [32][33][34] Earlier the large mass-dependent effect for unscrambled systems had been empirically correlated with many properties, all functionally related, 32 including zero-point energy differences 32,37 of the two dissociation channels of an asymmetric XYZ * . The proof that of these properties it was the zero-point differences that was responsible was given in Refs.…”