Nobel Centennial Symposia
"Frontiers of Molecular Science"

December 4-7, 2001
Friiberghs Manor, Örsundsbro and Stockholm University

Unimolecular Reactions and the Strange Mass-Independent Isotope Effect in Chemistry

by Rudolph A. Marcus
Noyes Laboratory, 127-72 California Institute of Technology Pasadena, CA 91125, USA

A strange "mass-independent" isotope effect has been observed in ozone formation in the stratosphere and in the laboratory, and in the oldest material (4.6 billion years) in the solar system, namely, the calcium-aluminum rich inclusions in meteorites. Unusual isotope effects are also found in a variety of reactions in the upper atmosphere and in other environments.

In the present talk we describe the mass-independent isotope effect for the enrichment of ozone, which occurs in "scrambled systems", and a paradoxical and unconventionally large mass-dependent isotope effect for individual ratios of recombination reaction rate constants for ozone formation in "unscrambled systems". To treat the ozone phenomena, a puzzle in the geochemistry/chemical physics literature beginning two decades ago, a statistical (RRKM) based theory is used. The theory involves (1) an "eta effect" discussed below, (2) a partitioning effect arising naturally from the competition between the two exit channels of a dissociating ozone molecule, (3) a hindered-rotor transition state, and (4) weak collisions for the deactivation of the vibrationally excited ozone molecule. The partitioning between the two exit channels plays a major role in producing the large unconventional isotope effect in the unscrambled systems. The effect is shown analytically to disappear exactly in scrambled systems. The mass-independent enrichment studies in scrambled systems, on the other hand, reflect the eta effect. The two very different kinds of experiments are seen, thereby, to be complimentary.

It is shown how very small differences in zero-point energies of the two exit channels for the dissociation of an asymmetric ozone isotopomer are multiplied into substantial differences in the numbers of accessible states in the transition state. They lead thereby to an initially surprisingly large difference in the partitioning effect and to large ratios of individual recombination rate constants.

At low pressures the density of states of the vibrationally excited ozone molecule and the effective deactivation collision frequency occur as a product in the theory. The eta effect itself can either be due to a small deviation from the statistical density of states for symmetric isotopomers (fewer anharmonic and Coriolis dynamic coupling terms, for example, because of symmetry restrictions), or to a greater efficiency of energy transfer from the asymmetric molecule. An experiment which distinguishes the two factors is proposed. It is pointed out how both the partitioning and the eta effects can be regarded as "symmetry-driven" isotopic effects.

The theoretical results on low-pressure mass-independent ozone enrichments and individual rate constant ratios obtained from these calculations are consistent with the corresponding experimental data. The isotopic exchange rate constant for the reaction provides information on the nature of a variationally determined hindered-rotor transition state using experimental data at different temperatures. Pressure effects on the individual rate constant ratios, on the enrichments, and on the recombination rate constant are again consistent with the data. The temperature dependence of the enrichment and of the rate constant ratios is also discussed, and experimental tests of the theory are suggested. Pump-dump short-time laser experiments on isolated ozone molecules to study the energy dependence and the isotopic effect for the dissociation of the isolated molecules could be highly revealing. The desirability of a more accurate potential energy surface for ozone in the transition state region is also noted.

Looking to the future, besides the utility of similarly highly detailed experimental studies on isotope effects for other reactions in the upper atmosphere, there is also a real need for a new area of study: the broad interdisciplinary merging of geochemical, inorganic and chemical physics study of these problems. One of these is the mechanism of formation of early solids in the solar system, such as CAI's and the material formed slightly later, the chondrules. Much is already known about the early material from the many-faceted studies of their appearance in meteorites, but the various scenarios for their formation, chemical versus nucleosynthetic, are a largely uncharted field in chemistry which would be useful to explore in future collaborative laboratory studies. There is a need similarly, I believe, for the broad-based study of unusual isotope effects in many other systems, atmospheric, planetary, and geological.

The ozone studies are described in part in Y. Q. Gao and R. A. Marcus, Science 293, 259 (2001), J. Chem. Phys. 115 (December 2001); B. C. Hathorn and R. A. Marcus ibid. 111, 4087 (1999), 113, 9497 (2000).