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

Inelastic scattering in isotopologues of O2-Ar: the effects of mass, symmetry, and density of states

The two species considered here, O2 (oxygen molecule) and Ar (argon-atom), are both abundant components of Earth's atmosphere and hence familiar collision partners in this medium. O2 is quite reactive and extensively involved in atmospheric chemistry, including Chapman's cycle of the formation and destruction of ozone; while Ar, like N2, typically plays the nevertheless crucial role of inert collider. Inert species can provide stabilization to metastable encounter-complexes through the energy transfer associated with inelastic collisions. The interplay of collision frequency and energy transfer efficiency, with state lifetimes and species concentrations, contributes to the rich and varied chemistry and dynamics found in diverse environments ranging from planetary atmospheres to the interstellar and circumstellar media. The nature and density of bound and resonance states, coupled electronic states, symmetry, and nuclear spin-statistics can all play a role. Here, we systematically investigate some of those factors by looking at the O2-Ar system, comparing rigorous quantum-scattering calculations for the 16O16O-40Ar, 18O16O-40Ar, and 18O18O-40Ar isotope combinations. A new accurate potential energy surface was constructed for this purpose holding the O2 bond distance at its vibrationally averaged distance.

Four Isotope-Labeled Recombination Pathways of Ozone Formation

A theoretical approach is developed for the description of all possible recombination pathways in the ozone forming reaction, without neglecting any process a priori, and without decoupling the individual pathways one from another. These pathways become physically distinct when a rare isotope of oxygen is introduced, such as ¹⁸O, which represents a sensitive probe of the ozone forming reaction. Each isotopologue of O₃ contains two types of physically distinct entrance channels and two types of physically distinct product wells, creating four recombination pathways. Calculations are done for singly and doubly substituted isotopologues of ozone, eight rate coefficients total. Two pathways for the formation of asymmetric ozone isotopomer exhibit rather different rate coefficients, indicating large isotope effect driven by ΔZPE-difference. Rate coefficient for the formation of symmetric isotopomer of ozone (third pathway) is found to be in between of those two, while the rate of insertion pathway is smaller by two orders of magnitude. These trends are in good agreement with experiments, for both singly and doubly substituted ozone. The total formation rates for asymmetric isotopomers are found to be somewhat larger than those for symmetric isotopomers, but not as much as in the experiment. Overall, the distribution of lifetimes is found to be very similar for the metastable states in symmetric and asymmetric ozone isotopomers.

The role of rotation-vibration coupling in symmetric and asymmetric isotopomers of ozone

A theoretical framework and a computer code (SpectrumSDT) are developed for accurate calculations of coupled rotational-vibrational states in triatomic molecules using hyper-spherical coordinates and taking into account the Coriolis coupling effect. Concise final formulas are derived for the construction of the Hamiltonian matrix using an efficient combination of the variational basis representation and discrete variable representation methods with locally optimized basis sets and grids. First, the new code is tested by comparing its results with those of the APH3D program of Kendrick et al. [Kendrick, Pack, Walker, and Hayes, J. Chem. Phys. 110, 6673 (1999)]. Then, accurate calculations of the rovibrational spectra are carried out for doubly substituted symmetric (¹⁸O¹⁶O¹⁸O) and asymmetric (¹⁸O¹⁸O¹⁶O) ozone isotopomers for the total angular momentum up to J = 5. Together with similar data recently reported for the singly substituted symmetric (¹⁶O¹⁸O¹⁶O) and asymmetric (¹⁶O¹⁶O¹⁸O) ozone isotopomers, these calculations quantify the role of the Coriolis coupling effect in the large mass-independent isotopic enrichment of ozone, observed in both laboratory experiments and the atmosphere of the Earth. It is found that the Coriolis effect in ozone is relatively small, as evidenced by deviations of its rotational constants from the symmetric-top-rotor behavior, magnitudes of parity splittings (Λ-doubling), and ratios of rovibrational partition functions for asymmetric vs symmetric ozone molecules. It is concluded that all of these characteristics are influenced by the isotopic masses as much as they are influenced by the overall symmetry of the molecule. It is therefore unlikely that the Coriolis coupling effect could be responsible for symmetry-driven mass-independent fractionation of oxygen isotopes in ozone.

Rotationally inelastic scattering of O3–Ar: state-to-state rates with the multiconfigurational time dependent Hartree method

The rates of state-changing collisions are compared for different isotopologues of ozone from quantum scattering calculations with the MCTDH method.

Use of Isotope Effects To Understand the Present and Past of the Atmosphere and Climate and Track the Origin of Life

Stable isotope ratio measurements have been used as a measure of a wide variety of processes, including solar system evolution, geological formational temperatures, tracking of atmospheric gas and aerosol chemical transformation, and is the only means by which past global temperatures may be determined over long time scales. Conventionally, isotope effects derive from differences of isotopically substituted molecules in isotope vibrational energy, bond strength, velocity, gravity, and evaporation/condensation. The variations in isotope ratio, such as ¹⁸ O/¹⁶ O (δ¹⁸ O) and ¹⁷ O/¹⁶ O (δ¹⁷ O) are dependent upon mass differences with δ¹⁷ O/δ¹⁸ O=0.5, due to the relative mass differences (1 amu vs. 2 amu). Relations that do not follow this are termed mass independent and are the focus of this Minireview. In chemical reactions such as ozone formation, a δ¹⁷ O/δ¹⁸ O=1 is observed. Physical chemical models capture most parameters but differ in basic approach and are reviewed. The mass independent effect is observed in atmospheric species and used to track their chemistry at the modern and ancient Earth, Mars, and the early solar system (meteorites).

Development of a potential energy surface for the O3–Ar system: rovibrational states of the complex

Collisional stabilization is an important step in the process of atmospheric formation of ozone.

Several Levels of Theory for Description of Isotope Effects in Ozone: Symmetry Effect and Mass Effect

The essential components of theory for the description of isotope effects in recombination reaction that forms ozone are presented, including the introduction of three reaction pathways for symmetric and asymmetric isotopomers, a brief review of relevant experimental data for singly- and doubly substituted isotopologues, the definitions of ζ-effect and η-effect, and the introduction of isotopic enrichment δ. Two levels of theory are developed to elucidate the role of molecular symmetry, atomic masses, vibrational zero-point energies, and rotational excitations in the recombination process. The issue of symmetry is not trivial, since the important factors, such as 1/2 and 2, appear in seven different places in the formalism. It is demonstrated that if all these effects are taken into account properly, then no anomalous isotope effects emerge. At the next level of theory, a model is considered in which one scattering resonance (sitting right at the top of centrifugal barrier) is introduced per ro-vibrational channel. It is found that this approach is equivalent to statistical treatment with partition functions at the transition state. Accurate calculations using hyper-spherical coordinates show that no isotope effects come from difference in the number of states. In contrast, differences in vibrational and rotational energies lead to significant isotope effects. However, those effects appear to be local, found for the rather extreme values of rotational quantum numbers. They largely cancel when rate coefficients are computed for the thermal distribution of rotational excitations. Although large isotope effects (observed in experiments) are not reproduced here, this level of theory can be used as a foundation for more detailed computational treatment, with accurate information about resonance energies and lifetimes computed and included.

Several levels of theory for description of isotope effects in ozone: Effect of resonance lifetimes and channel couplings

In this paper, two levels of theory are developed to determine the role of scattering resonances in the process of ozone formation. At the lower theory level, we compute resonance lifetimes in the simplest possible way, by neglecting all couplings between the diabatic vibrational channels in the problem. This permits to determine the effect of "shape" resonances, trapped behind the centrifugal barrier and populated by quantum tunneling. At the next level of theory, we include couplings between the vibrational channels, which permits to determine the role of Feshbach resonances and interaction of different reaction pathways on the global PES of ozone. Pure shape resonances are found to contribute little to the overall recombination process since they occur rather infrequently in the spectrum, in the vicinity of the top of the centrifugal barrier only. Moreover, the associated isotope effects are found to disagree with experimental data. By contrast, Feshbach-type resonances are found to make dominant contribution to the process. They occur in a broader range of spectrum, and their density of states is much higher. The properties of Feshbach resonances are studied in detail. They explain the isotopic ζ -effect, giving theoretical prediction in good agreement with experiments for both singly and doubly substituted ozone molecules. Importantly, Feshbach resonances also contribute to the isotopic η -effect, moving theoretical predictions in the right direction. Some differences with experimental data remain, which indicates that there may be another additional source of the η -effect.

On stabilization of scattering resonances in recombination reaction that forms ozone

Calculations of energy transfer in the recombination reaction that forms ozone are carried out within the framework of the mixed quantum/classical theory and using the dimensionally reduced 2D-model of ozone molecule, with bending motion neglected. Recombination rate coefficients are obtained at room temperature for symmetric and asymmetric isotopomers of singly and doubly substituted isotopologues. The processes of resonance formation, spontaneous decay, collisional dissociation, and stabilization by bath gas (Ar) are all characterized and taken into account within the steady-state approximation for kinetics. The focus is on stabilization step, where the mysterious isotopic η-effect was thought to originate from. Our results indicate no difference in cross sections for stabilization of scatteringresonances in symmetric and asymmetric isotopomers. As practical results, the general and simple analytic models for stabilization and dissociation cross sections are presented, which can be applied to resonances in any ozone molecule, symmetric or asymmetric, singly or doubly substituted. Present calculations show some isotope effect that looks similar to the experimentally observed η-effect, and the origin of this phenomenon is in the rates of formation/decay of scatteringresonances, determined by their widths, that are somewhat larger in asymmetric isotopomers than in their symmetric analogues. However, the approximate two-dimensional model used here is insufficient for consistent and reliable description of all features of the isotopic effect in ozone. Calculations using an accurate 3D model are still needed.

Introduction to chemistry and applications in nature of mass independent isotope effects special feature

Stable isotope ratio variations are regulated by physical and chemical laws. These rules depend on a relation with mass differences between isotopes. New classes of isotope variation effects that deviate from mass dependent laws, termed mass independent isotope effects, were discovered in 1983 and have a wide range of applications in basic chemistry and nature. In this special edition, new applications of these effects to physical chemistry, solar system origin models, terrestrial atmospheric and biogenic evolution, polar paleo climatology, snowball earth geology, and present day atmospheric sciences are presented.

Theory of mass-independent fractionation of isotopes, phase space accessibility, and a role of isotopic symmetry

Key experimental and theoretical features of mass-independent fractionation (MIF) of isotopes, also known as the η-effect, are summarized, including its difference from the exit channel zero-point energy difference effect. The latter exactly cancels in the MIF. One key experimental result is that the MIF for O3 formation is a low-pressure phenomenon and, moreover, that it decreases with increasing pressure of third bodies at pressures far below the "Lindemann fall-off" pressures for three-body recombination of O and O2. A possible origin of the MIF is discussed in terms of a role for isotopologue symmetry in intramolecular energy sharing. An explanation is suggested for the large difference in the fall-off pressure for recombination and the pressure for a large decrease in MIF, in terms of a difference between deactivating collisions and what we term here "symmetry-changing collisions". It is noted that the theory of the MIF involves four recombination rate constants and an equilibrium constant, for each trace isotope, seven rate constants in all and two equilibrium constants. A conceptual shortcut is noted. Experimental and computational information that may provide added insight into the MIF mechanism and tests is described.

The Physical Chemistry of Mass-Independent Isotope Effects and Their Observation in Nature

Historically, the physical chemistry of isotope effects and precise measurements in samples from nature have provided information on processes that could not have been obtained otherwise. With the discovery of a mass-independent isotopic fractionation during the formation of ozone, a new physical chemical basis for isotope effects required development. Combined theoretical and experimental developments have broadened this understanding and extended the range of chemical systems where these unique effects occur. Simultaneously, the application of mass-independent isotopic measurements to an extensive range of both terrestrial and extraterrestrial systems has furthered the understanding of events such as solar system origin and evolution and planetary atmospheric chemistry, present and past.

Coriolis coupling as a source of non-RRKM effects in triatomic near-symmetric top molecules: Diffusive intramolecular energy exchange between rotational and vibrational degrees of freedom

A classical theory is proposed to describe the non-RRKM effects in activated asymmetric top triatomic molecules observed numerically in classical molecular dynamics simulations of ozone. The Coriolis coupling is shown to result in an effective diffusive energy exchange between the rotational and vibrational degrees of freedom. A stochastic differential equation is obtained for the K-component of the rotational angular momentum that governs the diffusion.

The role of symmetry in the mass independent isotope effect in ozone

Understanding the internal distribution of "anomalous" isotope enrichments has important implications for validating theoretical postulates on the origin of these enrichments in molecules such as ozone and for understanding the transfer of these enrichments to other compounds in the atmosphere via mass transfer. Here, we present an approach, using the reaction NO(2)(-) + O(3), for assessing the internal distribution of the Delta(17)O anomaly and the delta(18)O enrichment in ozone produced by electric discharge. The Delta(17)O results strongly support the symmetry mechanism for generating mass independent fractionations, and the delta(18)O results are consistent with published data. Positional Delta(17)O and delta(18)O enrichments in ozone can now be more effectively used in photochemical models that use mass balance oxygen atom transfer mechanisms to infer atmospheric oxidation chemistry.

High-level ab initio studies of the structure, vibrational spectra, and energetics of S3

Observation of mass-dependent and non-mass-dependent sulfur isotope fractionations in elemental sulfur is providing new insight into the nature of the sulfur cycle in the atmosphere. Interpretation of the experimental isotope data requires estimation of the energetics for the reaction S+S2-->S3 (isoelectronic with O+O2-->O3). Key molecular properties of the S3 potential-energy surface, such as vibrational frequencies and isotopic shifts, are presented that can be used to assess the mass-dependent fractionation effect. Ab initio results are compared to the available experimental results for S2 to evaluate the reliability of the computational results for S3. The S-S bond dissociation energy for S3 is determined to be 60.9+/-1 kcal mol(-1).

Mass-dependent and non-mass-dependent isotope effects in ozone photolysis: Resolving theory and experiments

In addition to the anomalous (17)O and (18)O isotope effects in the three-body ozone formation reaction O+O(2)+M, isotope effects in the destruction of ozone by photolysis may also play a role in determining the isotopic composition of ozone and other trace gases in the atmosphere. While previous experiments on ozone photolysis at 254 nm were interpreted as evidence for preferential loss of light ozone that is anomalous (or "non-mass-dependent"), recent semiempirical theoretical calculations predicted a preferential loss of heavy ozone at that wavelength that is mass dependent. Through photochemical modeling results presented here, we resolve this apparent contradiction between experiment and theory. Specifically, we show that the formation of ozone during the UV photolysis experiments is not negligible, as had been assumed, and that the well-known non-mass-dependent isotope effects in ozone formation can account for the non-mass-dependent enrichment of the heavy isotopologs of ozone observed in the experiment. Thus, no unusual non-mass-dependent fractionation in ozone photolysis must be invoked to explain the experimental results. Furthermore, we show that theoretical predictions of a mass-dependent preferential loss of the heavy isotopologs of ozone during UV photolysis are not inconsistent with the experimental data, particularly if mass-dependent isotope effects in the chemical loss reactions of ozone during the photolysis experiments or experimental artifacts enrich the remaining ozone in (17)O and (18)O. Before the calculated fractionation factors can be quantitatively evaluated, however, further investigation of possible mass-dependent isotope effects in the reactions of ozone with O((1)D), O((3)P), O(2)((1)Delta), and O(2)((1)Sigma) is needed through experiments we suggest here.

Semiclassical wave packet study of ozone forming reaction

We have applied the semiclassical wave packet method (SWP) to calculate energies and lifetimes of the metastable states (scattering resonances) in a simplified model of the ozone forming reaction. All values of the total angular momentum up to J=50 were analyzed. The results are compared with numerically exact quantum mechanical wave packet propagation and with results of the time-independent WKB method. The wave functions for the metastable states in the region over the well are reproduced very accurately by the SWP; in the classically forbidden region and outside of the centrifugal barrier, the SWP wave functions are qualitatively correct. Prony's method was used to extract energies and lifetimes from the autocorrelation functions. Energies of the metastable states obtained using the SWP method are accurate to within 0.1 and 2 cm(-1) for under-the-barrier and over-the-barrier states, respectively. The SWP lifetimes in the range of 0.5<tau(n)<100 ps are accurate to within 10%. A three-level model was used to investigate accuracies of different approximations for the reaction rate constant. It was shown that the majority of the metastable states in this system are either long lived (narrow resonances) which can be treated as stable, or short lived (broad resonances) which can be treated without the knowledge of their lifetimes. Only a few metastable states fall into the intermediate range where both energies and lifetimes are needed to model the kinetics. The recombination rate constant calculated with the SWP method at room temperature and pressure is in good agreement with available experimental data.

Anomalous oxygen isotope enrichment in CO2 produced from O+CO: estimates based on experimental results and model predictions

The oxygen isotope fractionation associated with O+CO-->CO(2) reaction was investigated experimentally where the oxygen atom was derived from ozone or oxygen photolysis. The isotopic composition of the product CO(2) was analyzed by mass spectrometry. A kinetic model was used to calculate the expected CO(2) composition based on available reaction rates and their modifications for isotopic variants of the participating molecules. A comparison of the two (experimental data and model predictions) shows that the product CO(2) is endowed with an anomalous enrichment of heavy oxygen isotopes. The enrichment is similar to that observed earlier in case of O(3) produced by O+O(2) reaction and varies from 70 0/00 to 136 0/00 for (18)O and 41 0/00 to 83 0/00 for (17)O. Cross plot of delta (17)O and delta (18)O of CO(2) shows a linear relation with slope of approximately 0.90 for different experimental configurations. The enrichment observed in CO(2) does not depend on the isotopic composition of the O atom or the sources from which it is produced. A plot of Delta(delta (17)O) versus Delta(delta (18)O) (two enrichments) shows linear correlation with the best fit line having a slope of approximately 0.8. As in case of ozone, this anomalous enrichment can be explained by invoking the concept of differential randomization/stabilization time scale for two types of intermediate transition complex which forms symmetric ((16)O(12)C(16)O) molecule in one case and asymmetric ((16)O(12)C(18)O and (16)O(12)C(17)O) molecules in the other. The delta (13)C value of CO(2) is also found to be different from that of the initial CO due to the mass dependent fractionation processes that occur in the O+CO-->CO(2) reaction. Negative values of Delta(delta (13)C) ( approximately 12.1 0/00) occur due to the preference of (12)C in CO(2)* formation and stabilization. By contrast, at lower pressures (approximately 100 torr) surface induced deactivation makes Delta(delta (13)C) zero or slightly positive.

Quantum-mechanical calculations on pressure and temperature dependence of three-body recombination reactions: application to ozone formation rates

A quantum-mechanical model is designed for the calculation of termolecular association reaction rate coefficients in the low-pressure fall-off regime. The dynamics is set up within the energy transfer mechanism and the kinetic scheme is the steady-state approximation. We applied this model to the formation of ozone O + O2 + M --> O3 + M for M = Ar, making use of semiquantitative potential energy surfaces. The stabilization process is treated by means of the vibrational close-coupling infinite order sudden scattering theory. Major approximations include the neglect of the O3 vibrational bending mode and rovibrational couplings. We calculated individual isotope-specific rate constants and rate constant ratios over the temperature range 10-1000 K and the pressure fall-off region 10(-7)-10(2) bar. The present results show a qualitative and semiquantitative agreement with available experiments, particularly in the temperature region of atmospheric interest.

DYNAMICAL STUDIES OF THE OZONE ISOTOPE EFFECT: A Status Report

▪ Abstract  Dynamical studies of the recombination of O and O2 to form ozone are reviewed. The focus is the intriguing isotope dependence of the recombination rate coefficient as observed by Mauersberger and coworkers in the last decade. The key quantity for understanding of this dependence appears to be the difference of zero-point energies of the two fragmentation channels to which excited ozone can dissociate, i.e., X + YZ ← XYZ* → XY + Z, where X, Y, and Z stand for the three isotopes of oxygen. Besides the isotope dependence, the variation of the recombination rate coefficient with pressure and temperature is also addressed. Despite the numerous approaches of recent years, the recombination of ozone is far from being satisfactorily explained; there are still several essential questions to be solved by detailed theoretical analysis. We mainly discuss—and critically assess—the results of our own investigations of the ozone kinetics. The work of other research groups is also evaluated.

Recombination of ozone via the chaperon mechanism

The recombination of ozone via the chaperon mechanism, i.e., ArO+O2 --> Ar+O3 and ArO2+O --> Ar+O3, is studied by means of classical trajectories and a pairwise additive Ar-O3 potential energy surface. The recombination rate coefficient has a strong temperature dependence, which approximately can be described by T(-n) with n approximately 3. It is negligible for temperatures above 700 K or so, but it becomes important for low temperatures. The calculations unambiguously affirm the conclusions of Hippler et al. [J. Chem. Phys. 93, 6560 (1990)] and Luther et al. [Phys. Chem. Chem. Phys. 7, 2764 (2005)] that the chaperon mechanism makes a sizable contribution to the recombination of O3 at room temperature and below. The dependence of the chaperon recombination rate coefficient on the isotopomer, studied for two different isotope combinations, is only in rough qualitative agreement with the experimental data. The oxygen atom isotope exchange reaction involving ArO and ArO2 van der Waals complexes is also investigated; the weak binding of O or O2 to Ar has only a small effect.

A Quantum Dynamical Treatment of Symmetry-Induced Kinetic Isotope Effects in the Formation of He2+

Kinetic isotope effects for He(2)(+) formation are calculated quantum dynamically using high-quality Born-Oppenheimer (BO) potentials for two electronic states of He(2)(+) and an accurate treatment of all nonadiabatic BO corrections. The two potentials are coupled only when the helium isotopes are different, and the calculations reveal that this coupling is sufficient to allow the two sets of distinguishable reactants, (4)He(+) + (3)He or (3)He(+) + (4)He, to yield He(2)(+) with comparable efficiency over a wide temperature range. Consequently, the potential coupling provides a significant formation rate enhancement for the low isotopic symmetry reactants, as compared to the symmetrical cases (e.g., (4)He(+) + (4)He or (3)He(+) + (3)He). The computed symmetry-induced kinetic isotope effects (SIKIEs) are in substantial agreement with the available experimental results and represent the first theoretical demonstration of this unusual kinetic phenomenon. Possible application of SIKIE to ozone formation and other chemical systems is discussed.

The role of the radical-complex mechanism in the ozone recombination/dissociation reaction

The data bases for low-pressure rate coefficients of the dissociation of O3 and the reverse recombination of O with O2 in the bath gases M=He, Ar, N2, CO2 and SF6 are carefully analyzed. At very high temperatures, the rate constants have to correspond solely to the energy transfer (ET) mechanism. On condition that this holds for Ar and N2 near 800 K, average energies transferred per collision of -DeltaE/hc=18 and 25 cm-1 are derived, respectively. Assuming an only weak temperature dependence of DeltaE as known in similar systems, rate coefficients for the ET-mechanism are extrapolated to lower temperatures and compared with the experiments. The difference between measured and extrapolated rate coefficients is attributed to the radical complex (RC) mechanism. The derived rate coefficients for the RC-mechanism are rationalized in terms of equilibrium constants for equilibria of van der Waals complexes of O (or O2) with the bath gases and with rate coefficients for oxygen abstraction from these complexes. The latter are of similar magnitude as rate coefficients for oxygen isotope exchange which provides support for the present interpretation of the reaction in terms of a superposition of RC- and ET-mechanisms. We obtained rate coefficients for the ET-mechanism of k/[Ar]=2.3x10(-34) (T/300)(-1.5) and k/[N2]=3.5x10(-34) (T/300)(-1.5) cm6 molecule-2 s-1 and rate coefficients for the RC-mechanism of k/[Ar]=1.7x10(-34) (T/300)(-3.2) and k/[N2]=2.5x10(-34) (T/300)(-3.3) cm6 molecule-2 s-1. The data bases for M=He, CO2 and SF6 are less complete and only approximate separations of RC- and ET-mechanism were possible. The consequences of the present analysis for an analysis of isotope effects in ozone recombination are emphasized.

The effect of zero-point energy differences on the isotope dependence of the formation of ozone: A classical trajectory study

The effect of zero-point energy differences (DeltaZPE) between the possible fragmentation channels of highly excited O(3) complexes on the isotope dependence of the formation of ozone is investigated by means of classical trajectory calculations and a strong-collision model. DeltaZPE is incorporated in the calculations in a phenomenological way by adjusting the potential energy surface in the product channels so that the correct exothermicities and endothermicities are matched. The model contains two parameters, the frequency of stabilizing collisions omega and an energy dependent parameter Delta(damp), which favors the lower energies in the Maxwell-Boltzmann distribution. The stabilization frequency is used to adjust the pressure dependence of the absolute formation rate while Delta(damp) is utilized to control its isotope dependence. The calculations for several isotope combinations of oxygen atoms show a clear dependence of relative formation rates on DeltaZPE. The results are similar to those of Gao and Marcus [J. Chem. Phys. 116, 137 (2002)] obtained within a statistical model. In particular, like in the statistical approach an ad hoc parameter eta approximately 1.14, which effectively reduces the formation rates of the symmetric ABA ozone molecules, has to be introduced in order to obtain good agreement with the measured relative rates of Janssen et al. [Phys. Chem. Chem. Phys. 3, 4718 (2001)]. The temperature dependence of the recombination rate is also addressed.

The terrestrial record of stable sulphur isotopes: a review of the implications for evolution of Earth’s sulphur cycle

The observation of anomalous (non mass-dependent) sulphur isotope compositions in Archaean and early Proterozoic rocks but not in rocks younger than approximately 2 Ga has been interpreted to reflect fundamental change in the terrestrial sulphur cycle, in atmospheric chemistry, and in atmospheric oxygen content. Similar non mass-dependent sulphur isotope compositions in present-day samples (atmospheric aerosols and ice-core horizons containing remnants of stratosphere-piercing volcanic eruptions) are interpreted to carry information about modern atmospheric chemistry and transport. The interpretation of these observations hinges on our understanding of the processes that produce non mass-dependent sulphur isotope compositions, the processes that transport and transfer the isotopic signals throughout the sulphur cycle, and the processes that act to preserve or erase these isotopic signals once they are established. The growing dataset and hypotheses related to non mass-dependent sulphur are evaluated, emphasizing that which remains to be learned about the evolution of the record, the compositions of key reservoirs, and the transfer of the signal from the atmosphere to the surface and ultimately to the deep Earth.