Bc. Hathorn et Ra. Marcus, An intramolecular theory of the mass-independent isotope effect for ozone.II. Numerical implementation at low pressures using a loose transition state, J CHEM PHYS, 113(21), 2000, pp. 9497-9509
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].