An intramolecular theory of the unusual mass-independent isotope effect for ozone formation and dissociation is described. The experiments include the enrichment factor, its dependence on the ambient pressure, the ratio of the formation rates of symmetric and asymmetric ozone isotopomers, the enrichment of ozone formed from heavily enriched oxygen isotopes, the comparison of that enrichment to that when the heavy isotopes are present in trace amounts, the isotopic exchange rate constant, and the large mass-dependent effect when individual rate constants are measured, in contrast with the mass-independent effect observed for scrambled mixtures. To explain the results it is suggested that apart from the usual symmetry number ratio of a factor of 2, the asymmetric ozone isotopomers have a larger density of reactive ͑coupled͒ quantum states, compared with that for the symmetric isotopomers ͑about 10%͒, due to being more ''RRKM-like'' ͑Rice-RamspergerKessel-Marcus͒: Symmetry restricts the number of intramolecular resonances and coupling terms in the Hamiltonian which are responsible for making the motion increasingly chaotic and, thereby, increasingly statistical. As a result the behavior occurs regardless of whether the nuclei are bosons ( . Two alternative mechanisms are also considered, one invoking excited electronic states and the other invoking symmetry control in the entrance channel. Arguments against each are given. An expression is given relating the mass-independent rates of the scrambled systems to the mass-dependent rates of the unscrambled ones, and the role played by a partitioning term in the latter is described. Different definitions for the enrichment factor for heavily enriched isotopic systems are also considered. In the present paper attention is focused on setting up theoretical expressions and discussing relationships. They provide a basis for future detailed calculations.

We calculated an overall alpha/beta-selectivity for the pyrolysis of phenethyl phenyl ether as a composite of the alpha/beta-selectivities in the hydrogen abstraction reactions by the phenoxyl and by the benzyl radical that is in excellent agreement with experiment. The difference between the individual selectivities for these radicals is explained by analyzing the electronic structure of the transition states. Spin delocalization of the single electron favors the alpha-pathways. An opposing effect occurs for polarized transition states, such as the transition states for the hydrogen abstraction by the electrophilic phenoxyl radical, where the adjacent ether oxygen in phenethyl phenyl ether stabilizes the beta-transition states. These results indicate that theory will be able to provide excellent predictions of alpha/beta-product selectivities for more complicated lignin model compounds bearing multiple substituents. We have developed a scheme to predict alpha/beta-product selectivities in the pyrolysis of model compounds for the beta-ether linkage in lignin. The approach is based on computation of the relative rate constant, which profits from error cancellation in the individual rate constants. The Arrhenius prefactors depend strongly on the description of the low-frequency modes for which anharmonic contributions are important. We use density functional theory in combination with transition-state theory in this analysis. Diagonal anharmonic effects for individual low-frequency modes are included by employing a second-order Wigner-Kirkwood expansion in a semiclassical expression for the vibrational partition function. The composite alpha/beta-product selectivity is obtained by applying quasi-steady-state kinetic analysis for the intermediate radicals.

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.

The rotational eigenvalues of isotopically substituted hydrogen molecules adsorbed into single-walled carbon nanotubes are calculated using a semiclassical method and using a model potential. The resulting eigenvalues are used to calculate the separation factors due to rotational confinement between different isotopic species as a function of temperature and nanotube size. The results show that even for small shifts in the eigenvalues, significant fractionations should occur, suggesting possible application as an isotope-separation technique.

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For use in unimolecular reactions, a simple method is introduced for obtaining the unknown vibration frequencies of the many asymmetric isotopomers of a molecule from those of the symmetric ones. The method is illustrated for a triatomic molecule XYZ, ozone. It is based on the neglect of a single G matrix element in the GF expression for XYZ, yielding for it a block-factored expression of the XYX type for the frequencies of all the isotopomers XYZ. It agrees with available data to the accuracy needed, a few cm -1 . The first-order perturbation vanishes. (The zeroth-order case is not a symmetric molecule since it contains all three masses.) A simple second-order perturbation result for the GF matrix using data for one asymmetric isotopomer then provides agreement to about 1 cm -1 . The virtues of the method are its simplicity, transparency, and novelty, though normally one would use much more general methods such as ASYM 20 or 40. The method itself is not restricted to triatomic molecules.

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