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

Ion-atom-atom three-body recombination: From the cold to the thermal regime

We present a study on ion-atom-atom reaction A + A + B⁺ in a wide range of systems and collision energies ranging from 100 μK to 10⁵ K, analyzing two possible products: molecules and molecular ions. The dynamics is performed via a direct three-body formalism based on a classical trajectory method in hyperspherical coordinates developed in Pérez-Ríos et al. [J. Chem. Phys. 140, 044307 (2014)]. Our chief finding is that the dissociation energy of the molecular ion product acts as a threshold energy, separating the low- and high-energy regimes. In the low-energy regime, the long-range tail of the three-body potential dictates the fate of the reaction and the main reaction product. On the contrary, in the high-energy regime, the short-range of atom-atom and atom-ion interaction potential dominate the dynamics, enhancing molecular formation.

Ozone Formation in Ternary Collisions: Theory and Experiment Reconciled

The present Letter shows that the formation of ozone in ternary collisions O+O_{2}+M-the primary mechanism of ozone formation in the stratosphere-at temperatures below 200 K (for M=Ar) proceeds through a formation of a temporary complex MO_{2}, while at temperatures above ∼700  K, the reaction proceeds mainly through a formation of long-lived vibrational resonances of O_{3}^{*}. At intermediate temperatures 200-700 K, the process cannot be viewed as a two-step mechanism, often used to simplify and approximate collisions of three atoms or molecules. The developed theoretical approach is applied to the reaction O+O_{2}+Ar because of extensive experimental data available. The rate coefficients for the formation of O_{3} in ternary collisions O+O_{2}+Ar without using two-step approximations were computed for the first time as a function of collision energy. Thermally averaged coefficients were derived for temperatures 5-900 K. It is found that the majority of O_{3} molecules formed initially are weakly bound. Accounting for the process of vibrational quenching of the nascent population, a good agreement with available experimental data for temperatures 100-900 K is obtained.

High Resolution Infrared Spectroscopy in Support of Ozone Atmospheric Monitoring and Validation of the Potential Energy Function

The first part of this review is a brief reminder of general information concerning atmospheric ozone, particularly related to its formation, destruction, observations of its decrease in the stratosphere, and its increase in the troposphere as a result of anthropogenic actions and solutions. A few words are said about the abandonment of the Airbus project Alliance, which was expected to be the substitute of the supersonic Concorde. This project is over due to the theoretical evaluation of the impact of a fleet in the stratosphere and has been replaced by the A380, which is now operating. The largest part is devoted to calculations and observations of the transitions in the infrared range and their applications for the atmosphere based both on effective models (Hamiltonian, symmetry rules, and dipole moments) and ab initio calculations. The complementarities of the two approaches are clearly demonstrated, particularly for the creation of an exhaustive line list consisting of more than 300,000 lines reaching experimental accuracies (from 0.00004 to 0.001 cm-1) for positions and a sub percent for the intensities in the 10 microns region. This contributes to definitively resolving the issue of the observed discrepancies between line intensity data in different spectral regions: between the infrared and ultraviolet ranges, on the one hand, and between 10 and 5 microns on the other hand. The following section is devoted to the application of recent work to improve the knowledge about the behavior of potential function at high energies. A controversial issue related to the shape of the potential function in the transition state range near the dissociation is discussed.

Ab initio study of the O3-N2 complex: Potential energy surface and rovibrational states

The formation and destruction of O₃ within the Chapman cycle occurs as a result of inelastic collisions with a third body. Since N₂ is the most abundant atmospheric molecule, it can be considered as the most typical candidate when modeling energy-transfer dynamics. We report a new ab initio potential energy surface (PES) of the O₃-N₂ van der Waals complex. The interaction energies were calculated using the explicitly correlated single- and double-excitation coupled cluster method with a perturbative treatment of triple excitations [CCSD(T)-F12a] with the augmented correlation-consistent triple-zeta aug-cc-pVTZ basis set. The five-dimensional PES was analytically represented by an expansion in spherical harmonics up to eighth order inclusive. Along with the global minimum of the complex (D_e = 348.88 cm^-1), with N₂ being perpendicular to the O₃ plane, six stable configurations were found with a smaller binding energy. This PES was employed to calculate the bound states of the O₃-N₂ complex with both ortho- and para-N₂ for total angular momentum J = 0 and 1, as well as dipole transition probabilities. The nature of the bound states of the O₃-oN₂ and O₃-pN₂ species is discussed based on their rovibrational wave functions.

Direct time delay computation applied to the O + O2 exchange reaction at low energy: Lifetime spectrum of O3 * species

We report full quantum dynamical calculations for lifetimes of scattering resonances, among which are true metastable states, of the intermediate heavy ozone complex ⁵⁰O₃ ^* of the ¹⁸O + ¹⁶O¹⁶O reaction, for any value of the total angular momentum quantum number J. We show that computations for nonzero values of J are mandatory in order to properly analyze resonances and time delays, with a view to establish a somewhat comprehensive eigenlife spectrum of the complex O₃ ^*. Calculations have been performed in a given low to moderate energy range, including the interval between zero-point energies (ZPEs) of reagents and product species. Quasi-bound states tend to be more numerous, and eigenlifetimes themselves are seen to increase with J, reaching unusually large values for J = 30. A very dense forest of O₃ ^* species is pictured already for J greater than 20, especially at the highest energies considered, leading to a quasi-continuum of metastable states. On the contrary, they appear as rather sparse and isolated at J = 0 and lower energies, including the domain between ¹⁸O¹⁶O and ¹⁶O¹⁶O ZPEs, embedded among many overlapping resonances that turn out to be not long-lived enough to be associated with genuine metastable states.

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.

Influence of the Coriolis effect on the properties of scattering resonances in symmetric and asymmetric isotopomers of ozone

Scattering resonances above dissociation threshold are computed for four isotopically substituted ozone species: 16O18O16O, 16O16O18O, 18O16O18O and 16O18O18O, using a variational method with accurate treatment of the rotation-vibration coupling terms (Coriolis effect) for all values of the total angular momentum J from 0 to 4. To make these calculations numerically affordable, a new approach was developed which employs one vibrational basis set optimized for a typical rotational excitation (J,Λ), to run coupled rotation-vibration calculations at several desired values of J. In order to quantify the effect of Coriolis coupling, new data are contrasted with those computed using the symmetric-top rotor approximation, where the rotation-vibration coupling terms are neglected. It is found that, overall, the major properties of scattering resonances (such as their lifetimes, the number of these states, and their cumulative partition function Q) are all influenced by the Coriolis effect and this influence grows as the angular momentum J is raised. However, it is found that the four isotopically substituted ozone molecules are affected roughly equally by the Coriolis coupling. When the ratio η of partition functions for asymmetric over symmetric ozone molecules is computed, the Coriolis effect largely cancels, and this cancelation seems to occur for all values of J. Therefore, it does not seem grounded to attribute any appreciable mass-independent symmetry-driven isotopic fractionation to the Coriolis coupling effect.

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.

Spiers Memorial Lecture : Introductory lecture: quantum dynamics of chemical reactions

This Spiers Memorial Lecture discusses quantum effects that can be calculated and observed in the chemical reactions of small molecules.

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.

A full-dimensional model of ozone forming reaction: the absolute value of the recombination rate coefficient, its pressure and temperature dependencies

Rigorous calculations of scattering resonances in ozone are carried out for a broad range of rotational excitations with a detailed analysis of their properties and contribution into recombination process.

Self-consistent quantum kinetic theory of diatomic molecule formation

A quantum kinetic theory of molecule formation is presented which includes three-body recombination and radiative association for a thermodynamically closed system which may or may not exchange energy with its surrounding at a constant temperature. The theory uses a Sturmian representation of a two-body continuum to achieve a steady-state solution of a governing master equation which is self-consistent in the sense that detailed balance between all bound and unbound states is rigorously enforced. The role of quasibound states in catalyzing the molecule formation is analyzed in complete detail. The theory is used to make three predictions which differ from conventional kinetic models. These predictions suggest significant modifications may be needed to phenomenological rate constants which are currently in wide use. Implications for models of low and high density systems are discussed.

Does the "reef structure" at the ozone transition state towards the dissociation exist? New insight from calculations and ultrasensitive spectroscopy experiments

Since the discovery of anomalies in ozone isotope enrichment, several fundamental issues in the dynamics linked to the shape of the potential energy surface in the transition state region have been raised. The role of the reeflike structure on the minimum energy path is an intricate question previously discussed in the context of chemical experiments. In this Letter, we bring strong arguments in favor of the absence of a submerged barrier from ultrasensitive laser spectroscopy experiments combined with accurate predictions of highly excited vibrations up to nearly 95% of the dissociation threshold.

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.

On molecular origin of mass-independent fractionation of oxygen isotopes in the ozone forming recombination reaction

Theoretical treatment of ozone forming reaction is developed within the framework of mixed quantum/classical dynamics. Formation and stabilization steps of the energy transfer mechanism are both studied, which allows simultaneous capture of the delta zero-point energy effect and η-effect and identification of the molecular level origin of mass-independent isotope fractionation. The central role belongs to scattering resonances; dependence of their lifetimes on rotational excitation, asymmetry; and connection of their vibrational wave functions to two different reaction channels. Calculations, performed within the dimensionally reduced model of ozone, are in semiquantitative agreement with experiment.

Collisional stabilization of van der Waals states of ozone

The mixed quantum-classical theory developed earlier [M. Ivanov and D. Babikov, J. Chem. Phys. 134, 144107 (2011)] is employed to treat the collisional energy transfer and the ro-vibrational energy flow in a recombination reaction that forms ozone. Assumption is that the van der Waals states of ozone are formed in the O + O(2) collisions, and then stabilized into the states of covalent well by collisions with bath gas. Cross sections for collision induced dissociation of van der Waals states of ozone, for their stabilization into the covalent well, and for their survival in the van der Waals well are computed. The role these states may play in the kinetics of ozone formation is discussed.

Mixed quantum-classical theory for the collisional energy transfer and the rovibrational energy flow: application to ozone stabilization

A mixed quantum-classical approach to the description of collisional energy transfer is proposed in which the vibrational motion of an energized molecule is treated quantum mechanically using wave packets, while the collisional motion of the molecule and quencher and the rotational motion of the molecule are treated using classical trajectories. This accounts rigorously for quantization of vibrational states, zero-point energy, scattering resonances, and permutation symmetry of identical atoms, while advantage is taken of the classical scattering regime. Energy is exchanged between vibrational, rotational, and translational degrees of freedom while the total energy is conserved. Application of this method to stabilization of the van der Waals states in ozone is presented. Examples of mixed quantum-classical trajectories are discussed, including an interesting example of supercollision. When combined with an efficient grid mapping procedure and the reduced dimensionality approximation, the method becomes very affordable computationally.

Semiclassical wave packet treatment of scattering resonances: application to the delta zero-point energy effect in recombination reactions

For the first time Feshbach-type resonances important in recombination reactions are characterized using the semiclassical wave packet method. This approximation allows us to determine the energies, lifetimes, and wave functions of the resonances and also to observe a very interesting correlation between them. Most important is that this approach permits description of a quantum delta-zero-point energy effect in recombination reactions and reproduces the anomalous rates of ozone formation.

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.

Alternative Low-Energy Mechanisms for Isotopic Exchange in Gas-Phase D2O-H+(H2O)nReactions

Molecular-dynamics (MD) trajectories and high-level ab initio methods have been used to study the low-energy mechanism for D(2)O-H(+)(H(2)O)(n) reactions. At low collisional energies, MD simulations show that the collisional complexes are long-lived and undergo fast monomolecular isomerization, converting between different isomers within 50-500 ps. Such processes, primarily involving water-molecule shifts along a water chain, require the surmounting of very-low-energy barriers and present sizable non- Rice-Ramsperger-Kassel-Marcus (RRKM) effects, which are interpreted as a lack of randomization of the internal kinetic energy. Interestingly, the rate of water shifts was found to increase upon increasing the size of the cluster. Based on these findings, we propose to incorporate the following steps into the mechanism for low-energy isotopic scrambling these D(2)O-H(+)(H(2)O)(n) reactions: a) formation of the collisional complex [H(+)(H(2)O)(n)D(2)O]* in a vibro-rotational excited state; b) incorporation of the heavy-water molecule in the cluster core as HD(2)O(+) by means of isomerization involving molecular shifts; c) displacement of solvation molecules from the first shell of HD(2)O(+) inducing de-deuteration (shift of a D(+) to a neighbor water molecule); d) reorganization of the clusters and/or expulsion of one of the isotopic variants of water (H(2)O, HDO or D(2)O) from the periphery of the complex.

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.

Temperature dependent energy transfer in Ar–O3 collisions

The energy transfer between argon atoms and ozone complexes O3*, excited in the region of the dissociation threshold, is calculated for fixed temperatures (100 K< or =T < or =2500 K) using classical trajectories. The internal energy of ozone is resolved in terms of vibrational and rotational energies. For all temperatures, energy flows from O3* to Ar. The vibrational energy transfer, relative to k(B)T, is very small below 500 K, but gradually increases towards high temperatures. The relative rotational energy transfer, on the other hand, monotonously decreases with T; around 1100 K it falls below the relative vibrational energy transfer. Thermally averaged cross sections for vibrational and rotational energy transfers are also calculated. The implications for the stabilization of ozone complexes in the energy transfer model are discussed.

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.

Intra- and intermolecular energy transfer in highly excited ozone complexes

The energy transfer of highly excited ozone molecules is investigated by means of classical trajectories. Both intramolecular energy redistribution and the intermolecular energy transfer in collisions with argon atoms are considered. The sign and magnitude of the intramolecular energy flow between the vibrational and the rotational degrees of freedom crucially depend on the projection K(a) of the total angular momentum of ozone on the body-fixed a axis. The intermolecular energy transfer in single collisions between O(3) and Ar is dominated by transfer of the rotational energy. In accordance with previous theoretical predictions, the direct vibrational de-excitation is exceedingly small. Vibration-rotation relaxation in multiple Ar+O(3) collisions is also studied. It is found that the relaxation proceeds in two clearly distinguishable steps: (1) During the time between collisions, the vibrational degrees of freedom are "cooled" by transfer of energy to rotation; even at low pressure equilibration of the internal energy is slow compared to the time between collisions. (2) In collisions, mainly the rotational modes are "cool" by energy transfer to argon.

Mass-independent isotope effect in the earliest processed solids in the solar system: A possible chemical mechanism

A major constraint is described for a possible chemical origin for the "mass-independent" oxygen isotope phenomenon in calcium-aluminum rich inclusions (CAIs) in meteorites at high temperatures ( approximately 1500-2000 K). A symmetry-based dynamical eta effect is postulated for O atom-monoxide recombination on the surface of growing CAIs. It is the surface analog of the volume-based eta effect occurring in a similar phenomenon for ozone in the gas phase [Y. Q. Gao, W. C. Chen, and R. A. Marcus, J. Chem. Phys. 117, 1536 (2002), and references cited therein]: In the growth of CAI grains an equilibrium is postulated between adsorbed species XO (ads)+O (ads) <==>XO*(2)(ads), where XO*(2)(ads) is a vibrationally excited adsorbed dioxide molecule and X can be Si, Al, Ti, or other metals and can be C for minerals less refractory than the CAIs. The surface of a growing grain has an entropic effect of many order of magnitude on the position of this monoxide-dioxide equilibrium relative to its volume-based position by acting as a concentrator. The volume-based eta effect for ozone in the earlier study is not applicable to gas phase precursors of CAIs, due to the rarity of three-body recombination collisions at very low pressures and because of the high H(2) and H concentration in solar gas, which reduces gaseous O and gaseous dioxides and prevents the latter from acting as storage reservoirs for the two heavier oxygen isotopes. A surface eta effect yields XO*(2)(ads) that is mass-independently rich in (17)O and (18)O, and yields XO (ads)+O (ads) that is mass-independently poor in the two heavier oxygen isotopes. When the XO*(2)(ads) is deactivated by vibrational energy loss to the grain, it has only one subsequent fate, evaporation, and so undergoes no further isotopic fractionation. After evaporation the XO(2) again has only one fate, which is to react rapidly with H and ultimately form (16)O-poor H(2)O. The other species, O (ads)+XO (ads), are (16)O rich and react with Ca (ads) and other adsorbed metal atoms or metallic monoxides to form CAIs. The latter are thereby mass-independently poor in (17)O and (18)O. Some O (ads) used to form the minerals are necessarily in excess of the XO (ads), because of the stoichiometry of the mineral, and modify the fractionation pattern. This effect is incorporated into the mechanistic and mathematical scheme. A merit of this chemical mechanism for the oxygen isotope anomaly is that only one oxygen reservoir is required in the solar nebula. It also does not require a sequestering of intermediate products which could undergo isotopic exchange, hence undoing the original isotopic fractionations. The gas phase source of adsorbed O atoms in this environment is either O or H(2)O. As inferred from data on the evaporation of Mg(2)SiO(4) taken as an example, the source of O (ads) is primarily H(2)O rather than O and is accompanied by the evolution of H(2). Nonisotopic kinetic experiments can determine more sharply the mechanism of condensed phase growth of these minerals. Laboratory tests are proposed to test the existence of a surface eta effect on the growing CAI surfaces at these high temperatures.