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

Lifetimes and decay mechanisms of isotopically substituted ozone above the dissociation threshold: matching quantum and classical dynamics

Energies and lifetimes of vibrational resonances were computed for 18O-enriched isotopologue 50O3 = {16O16O18O and 16O18O16O} of the ozone molecule using hyperspherical coordinates and the method of complex absorbing potential. Various types of scattering resonances were identified, including roaming OO-O rotational states, the series corresponding to continuation of bound vibrational resonances of highly excited bending or symmetric stretching vibrational modes. Such a series become metastable above the dissociation limit. The coupling between the vibrationally excited O2 fragment and rotational roaming gives rise to Feshbach type resonances in ozone. Different paths for the formation and decay of symmetric 16O18O16O and asymmetric species 16O16O18O were also identified. The symmetry properties of the total rovibronic wave functions of the 18O-enriched isotopologues are discussed in the context of allowed dissociation channels.

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.

Oxygen and magnesium mass-independent isotopic fractionation induced by chemical reactions in plasma

Both the physical effect and the chemical conditions at the origin of the oxygen isotope variations in the solar system have been puzzling questions for 50 y. The data reported here bring the MIF effect (the mass-independent fractionation originally identified on ozone) back to the center of the debate. Similar to Ti isotopes, we observe that the MIF effect for O and Mg is triggered by redox reactions in plasmas. These observations reinforce the idea of a universal mechanism observable in photochemical reactions when molecular collisions involving indistinguishable isotopes yield a symmetrical complex stabilized as a chemical product.

Enrichment or depletion ranging from −40 to +100% in the major isotopes ¹⁶O and ²⁴Mg were observed experimentally in solids condensed from carbonaceous plasma composed of CO₂/MgCl₂/Pentanol or N₂O/Pentanol for O and MgCl₂/Pentanol for Mg. In NanoSims imaging, isotope effects appear as micrometer-size hotspots embedded in a carbonaceous matrix showing no isotope fractionation. For Mg, these hotspots are localized in carbonaceous grains, which show positive and negative isotopic effects so that the whole grain has a standard isotope composition. For O, no specific structure was observed at hotspot locations. These results suggest that MIF (mass-independent fractionation) effects can be induced by chemical reactions taking place in plasma. The close agreement between the slopes of the linear correlations observed between δ²⁵Mg versus δ²⁶Mg and between δ¹⁷O versus δ¹⁸O and the slopes calculated using the empirical MIF factor η discovered in ozone [M. H. Thiemens, J. E. Heidenreich, III. Science 219, 1073–1075; C. Janssen, J. Guenther, K. Mauersberger, D. Krankowsky. Phys. Chem. Chem. Phys. 3, 4718–4721] attests to the ubiquity of this process. Although the chemical reactants used in the present experiments cannot be directly transposed to the protosolar nebula, a similar MIF mechanism is proposed for oxygen isotopes: at high temperature, at the surface of grains, a mass-independent isotope exchange could have taken place between condensing oxides and oxygen atoms originated form the dissociation of CO or H₂O gas.

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.

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.

Properties of Feshbach and “shape”-resonances in ozone and their role in recombination reactions and anomalous isotope effects

Three reaction pathways for formation of symmetric and asymmetric isotopologues of ozone.

Recombination reactions as a possible mechanism of mass-independent fractionation of sulfur isotopes in the Archean atmosphere of Earth

A hierarchy of isotopically substituted recombination reactions is formulated for production of sulfur allotropes in the anoxic atmosphere of Archean Earth. The corresponding system of kinetics equations is solved analytically to obtain concise expressions for isotopic enrichments, with focus on mass-independent isotope effects due to symmetry, ignoring smaller mass-dependent effects. Proper inclusion of atom-exchange processes is shown to be important. This model predicts significant and equal depletions driven by reaction stoichiometry for all rare isotopes: ³³S, ³⁴S, and ³⁶S. Interestingly, the ratio of capital [Formula: see text] values obtained within this model for ³³S and ³⁶S is -1.16, very close to the mass-independent fractionation line of the Archean rock record. This model may finally offer a mechanistic explanation for the striking mass-independent fractionation of sulfur isotopes that took place in the Archean atmosphere of Earth.

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.

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.

A periodic orbit bifurcation analysis of vibrationally excited isotopologues of sulfur dioxide and water molecules: symmetry breaking substitutions

Theoretical predictions and assignment of highly excited vibrational states and their organization is one of the most important challenges in molecular spectroscopy. A systematic procedure to investigate such problems is locating the principal families of periodic orbits that emanate from the stationary points of the molecule and then following their evolution with the total energy. This results in constructing continuation/bifurcation diagrams that assist in locating the critical bifurcation energies and to discover new types of vibrational modes. Another parameter that may influence the dynamics of a molecule is isotopic mass substitution. In this article, we investigate the effect of symmetry breaking by isotopic mass substitution of triatomic molecules with C(2v) symmetry in classical and quantum dynamics. Sulfur dioxide and water molecules in their ground electronic state are studied by employing accurate potential energy surfaces. Continuation/bifurcation diagrams of periodic orbits are constructed by varying the energy and the mass of one oxygen atom of sulfur dioxide and one hydrogen atom of a water molecule. The transition from normal-to-local mode vibrations is studied in terms of a pitchfork to a center-saddle elementary bifurcation of periodic orbits. The results presented in this article aim to help the assignment of experimentally obtained spectra.

Towards quantum mechanical description of the unconventional mass-dependent isotope effect in ozone: resonance recombination in the strong collision approximation

The dependence of ozone recombination rate on the masses of oxygen isotopes is examined in the strong collision approximation by means of quantum mechanical calculations of resonance spectra of several rotating isotopomers. The measured DeltaZPE effect and its temperature dependence can be reconstructed from partial widths of narrow nonoverlapping resonances. The effect is attributed to substantial contributions of highly rotationally excited states to recombination.

State-to-state quantum dynamics of O + O2 isotope exchange reactions reveals nonstatistical behavior at atmospheric conditions

The O + O(2) exchange reaction is a prerequisite for the formation of ozone in Earth's atmosphere. We report here state-to-state differential and integral cross sections for several O + O(2) isotope-exchange reactions obtained by dynamically exact quantum scattering calculations at collision energies relevant to atmospheric conditions. These reactions are shown to be highly nonstatistical, evidenced by dominant forward scattering and deviation of the integral cross section from the statistical limit. Mechanistic analyses revealed that the nonstatistical channel is facilitated by short-lived osculating resonances. The theoretical results provided an in-depth interpretation of a recent molecular beam experiment of the exchange reaction and shed light on the initial step of ozone recombination.

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.

Nonstatistical Behavior of Reactive Scattering in the 18O+32O2 Isotope Exchange Reaction

The recombination of oxygen atoms with oxygen molecules to form ozone exhibits several strange chemical characteristics, including unusually large differences in formation rate coefficients when different isotopes of oxygen participate. Purely statistical chemical reaction rate theories cannot describe these isotope effects, suggesting that reaction dynamics must play an important role. We investigated the dynamics of the 18O + 32O2 --> O3(*) --> 16O + 34O2 isotope exchange reaction (which proceeds on the same potential energy surface as ozone formation) using crossed atomic and molecular beams at a collision energy of 7.3 kcal mol(-1), providing the first direct experimental evidence that the dissociation of excited ozone exhibits significant nonstatistical behavior. These results are compared with quantum statistical and quasi-classical trajectory calculations in order to gain insight into the potential energy surface and the dynamics of ozone formation.

Theoretical investigation of exchange and recombination reactions in O(P3)+NO(Π2) collisions

We present a detailed dynamical study of the kinetics of O(3P)+NO(2Pi) collisions including O atom exchange reactions and the recombination of NO2. The classical trajectory calculations are performed on the lowest 2A' and 2A" potential energy surfaces, which were calculated by ab initio methods. The calculated room temperature exchange reaction rate coefficient, kex, is in very good agreement with the measured one. The high-pressure recombination rate coefficient, which is given by the formation rate coefficient and to a good approximation equals 2kex, overestimates the experimental data by merely 20%. The pressure dependence of the recombination rate, kr, is described within the strong-collision model by assigning a stabilization probability to each individual trajectory. The measured falloff curve is well reproduced over five orders of magnitude by a single parameter, i.e., the strong-collision stabilization frequency. The calculations also yield the correct temperature dependence, kr proportional, T-1.5, of the low-pressure recombination rate coefficient. The dependence of the rate coefficients on the oxygen isotopes are investigated by incorporating the difference of the zero-point energies between the reactant and product NO radicals, DeltaZPE, into the potential energy surface. Similar isotope effects as for ozone are predicted for both the exchange reaction and the recombination. Finally, we estimate that the chaperon mechanism is not important for the recombination of NO2, which is in accord with the overall T-1.4 dependence of the measured recombination rate even in the low temperature range.

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.

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.

Quantum Statistical Study of O + O2 Isotopic Exchange Reactions: Cross Sections and Rate Constants

Using a wave packet based statistical model, we compute cross sections and thermal rate constants for various isotopic variants of the O + O2 exchange reaction on a recently modified ab initio potential energy surface. The calculation predicts a highly excited rotational distribution and relatively cold vibrational distribution for the diatomic product. A small but important threshold effect was identified for the (16)O + 18O2 reaction, which is suggested to contribute to the experimentally observed negative temperature dependence of the rate ratio, k(18O + 16O2)/k(16O + 18O2). Despite reasonable agreement with quasiclassical trajectory results, however, the calculated thermal rate constants are smaller than experimental measurements by a factor from 2 to 5. The experimentally observed negative temperature dependence of the rate constants is not reproduced. Possible reasons for the theory-experiment discrepancies are discussed.

Comparison of rovibronic density of asymmetric versus symmetric NO2 isotopologues at dissociation threshold: broken symmetry effects

We have measured the rovibronic densities of four symmetric (C2v) and two asymmetric (Cs) isotopologues of nitrogen dioxide just below their photodissociation threshold. At dissociation threshold and under jet conditions the laser-induced fluorescence abruptly disappears because the dissociation into NO(2pi(1/2)) + O(3P2) is much faster than the radiative decay. As a consequence, in a narrow energy range below D0, the highest bound rovibronic energy levels of J=1/2 and J=3/2 can be observed and sorted. A statistical analysis of the corresponding rovibronic density, energy spacing, and rovibronic transition intensities has been made. The observed intensity distributions are in agreement with the Porter-Thomas distribution. This distribution allows one to estimate the number of missing levels, and therefore to determine and compare the rovibronic and the vibronic densities. The four symmetric NO2 isotopologues, 16O14N16O, 18O14N18O, 16O15N16O, and 18O15N18O, have, respectively, a sum of J=1/2 and J=3/2 rovibronic densities of 18+/-0.8, 18.3+/-1.4, 18.4+/-2.7, and 19.8+/-3.5 cm(-1), while for the two asymmetric isotopologues, 18O14N16O and 18O15N16O, the corresponding densities are 20.9+/-4.5 and 23.6+/-5.6 cm(-1). The corresponding vibronic densities are in agreement only if we include both the merging of symmetry species (from those of C2v to those of Cs) and the contribution of the long-range tail(s) of the potential-energy surface along the dissociation coordinate. The effects of isotopic substitution on dissociation rates and the possible relation to mass-independent isotopic fractionation are 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.