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

Hathorn, B. C. and Marcus, R. A. (2000) An intramolecular theory of the mass-independent isotope effect for ozone. II. Numerical implementation at low pressures using a loose transition state. Journal of Chemical Physics, 113 (21). pp. 9497-9509. ISSN 0021-9606.

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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, rho [a "non-Rice–Ramsperger–Kassel–Marcus (RRKM) effect"], for the symmetric ozone isotopomers [B. C. Hathorn and R. A. Marcus, J. Chem. Phys. 111, 4087 (1999)]. 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 delta (for trace) and E (for heavily) 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 factors) 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 rho for symmetric systems is attributed to a small non-RRKM effect eta, these calculated results are independent of the exact origin of the decrease. The calculated "mass-independent" enrichments, delta and E, in scrambled systems are relatively insensitive to the transition state (TS), because of the absence of the partitioning factor in their case (for a fixed non-RRKM eta). 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 eta. 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.

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Marcus, R. A.0000-0001-6547-1469
Additional Information:©2000 American Institute of Physics. (Received 16 March 2000; accepted 8 September 2000) It is a pleasure to acknowledge the support of this research by the National Science Foundation and the award of a James W. Glanville Postdoctoral Fellowship in Chemistry at Caltech to one of us (B.C.H.). We have enjoyed helpful discussions with Professor Konrad Mauersberger and Professor Mark Thiemens and with Dr. Jürgen Günther. It is a pleasure to dedicate this paper to our colleague Professor Jürgen Troe, on the occasion of his sixtieth birthday. This paper was presented in part at the International Conference of Stable Isotopes, Carry le Rouet, France, June 20–25, 1999.
Subject Keywords:ozone; isomerism; isotope effects; intramolecular mechanics
Issue or Number:21
Record Number:CaltechAUTHORS:HATjcp00
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2097
Deposited By: Archive Administrator
Deposited On:08 Mar 2006
Last Modified:22 Nov 2019 09:58

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