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

A theory is described fur the variation in the rate constants for formation of different ozone isotopomers from oxygen atoms and molecules at low pres sures. The theory is implemented using a simplified description which treat s the transition state as loose. The two principal features of the theory a re a phase space partitioning of the transition states of the two exit chan nels after formation of the energetic molecule and a small (ca. 15%) decrea se in the effective density of states, rho [a ''no n-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 ad dition to the usual statistical factor of 2 for symmetric molecules. Experi mentally, the scrambled systems show a "mass-independent'' effect for the e nrichments delta (for trace) and E (for heavily) enriched systems, but the ratios of the individual isotopomeric rate constants for unscrambled system s show a strongly mass-dependent behavior. The contrasting behavior of scra mbled and unscrambled systems is described theoretically using a ''phase sp ace'' partitioning factor. In scrambled systems an energetic asymmetric ozo ne isotopomer is accessed from both entrance channels and, as shown in pape r I, the partitioning factor becomes unity throughout. In unscrambled syste ms, access to an asymmetric ozone is only From one entrance channel, and di fferences in zero-point energies and other properties, such as the centrifu gal potential, determine the relative contributions (the partitioning facto rs) of the two exit channels to the lifetime of the resulting energetic ozo ne molecule. They are responsible for the large differences in individual r ecombination rate constants at low pressures. While the decrease in rho for symmetric systems is attributed to a small non-RRKM effect eta, these calc ulated results are independent of the exact origin of the decrease. The cal culated "mass-independent'' enrichments, delta and E, in scrambled systems are relatively insensitive to the transition state (TS), because of the abs ence of the partitioning factor in their case (for a fixed non-RRKM eta). T hey 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 nat ure of the TS because of the partitioning effect. The current data are avai lable only at room temperature but the loose TS is valid only at low temper atures. Accordingly, the results calculated for the latter at 140 K represe nt a prediction, for any given eta. At present, a comparison of the 140 K r esults can be made only with room temperature data. They show the same tren ds as, and are in fortuitous agreement, with the data. Work is in progress on a description appropriate fur room temperature. (C) 2000 American Instit ute of Physics. [S0021-960(00)01445-8].