An intramolecular theory of the mass-independent isotope effect for ozone. II. Numerical implementation at low pressures using a loose transition state

Abstract

A theory is described for the variation in the rate constants for formation of different ozone isotopomers from oxygen atoms and molecules at low pressures. The theory is implemented using a simplified description which treats the transition state as loose. The two principal features of the theory are a phase space partitioning of the transition states of the two exit channels after formation of the energetic molecule and a small ͑ca. 15%͒ decrease in the effective density of states, ͓a ''non-Rice-Ramsperger-Kassel-Marcus ͑RRKM͒ effect''͔, for the symmetric ozone isotopomers ͓B. C. Hathorn and R. A. Marcus, J. Chem. Phys. 111, 4087 ͑1999͔͒. This decrease is in addition to the usual statistical factor of 2 for symmetric molecules. Experimentally, the scrambled systems show a ''mass-independent'' effect for the enrichments ␦ ͑for trace͒ and E ͑for heavily͒ enriched systems, but the ratios of the individual isotopomeric rate constants for unscrambled systems show a strongly mass-dependent behavior. The contrasting behavior of scrambled and unscrambled systems is described theoretically using a ''phase space'' partitioning factor. In scrambled systems an energetic asymmetric ozone isotopomer is accessed from both entrance channels and, as shown in paper I, the partitioning factor becomes unity throughout. In unscrambled systems, access to an asymmetric ozone is only from one entrance channel, and differences in zero-point energies and other properties, such as the centrifugal potential, determine the relative contributions ͑the partitioning factors͒ of the two exit channels to the lifetime of the resulting energetic ozone molecule. They are responsible for the large differences in individual recombination rate constants at low pressures. While the decrease in for symmetric systems is attributed to a small non-RRKM effect , these calculated results are independent of the exact origin of the decrease. The calculated ''mass-independent'' enrichments, ␦ and E, in scrambled systems are relatively insensitive to the transition state ͑TS͒, because of the absence of the partitioning factor in their case ͑for a fixed non-RRKM ͒. They are compared with the data at room temperature. Calculated results for the ratios of individual isotopomeric rate constants for the strongly mass-independent behavior for unscrambled systems are quite sensitive to the nature of the TS because of the partitioning effect. The current data are available only at room temperature but the loose TS is valid only at low temperatures. Accordingly, the results calculated for the latter at 140 K represent a prediction, for any given . At present, a comparison of the 140 K results can be made only with room temperature data. They show the same trends as, and are in fortuitous agreement, with the data. Work is in progress on a description appropriate for room temperature.

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.…”

“…The non-RRKM behavior of vibrationally excited ozone molecules was suggested in several classical mechanical numerical studies and an important role of the coupling of the rotational degrees of freedom to the vibrations was emphasized. 7,8 Recently, the classical molecular dynamics ͑MD͒ simulations 9,10 of collisional ozone formation O + O 2 → O 3 ‫ء‬ showed a nonstatistical distribution of lifetimes of the vibrationally excited ozone molecules. In a series of two papers we show analytically that the observed non-RRKM effects are indeed governed by the Coriolis coupling between the rotational and vibrational degrees of freedom, which cannot be accounted for by the standard RRKM theory.…”

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

“…[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…”