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

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.

A phase diagram for energy flow-limited reactivity

Intramolecular energy flow (also known as intramolecular vibrational redistribution or IVR) is often assumed in Rice-Ramsperger-Kassel-Marcus, transition state, collisional energy transfer, and other rate calculations not to be an impediment to reaction. In contrast, experimental spectroscopy, computational results, and models based on Anderson localization have shown that ergodicity is achieved rather slowly during molecular energy flow. The statistical assumption in rate theories might easily fail due to quantum localization. Here, we develop a simple model for the interplay of IVR and energy transfer and simulate the model with near-exact quantum dynamics for a 10-degree of freedom system composed of two five-mode molecular fragments. The calculations are facilitated by applying the van Vleck transformation to local random matrix models of the vibrational Hamiltonian. We find that there is a rather sharp "phase transition" as a function of molecular anharmonicity "a" between a region of facile energy transfer and a region limited by IVR and incomplete accessibility of the state space (classically, the phase space). The very narrow transition range of the order parameter a happens to lie right in the middle of the range expected for molecular torsion, bending, and stretching vibrations, thus demonstrating that reactive energy transfer dynamics several k_BT above the thermal energy occurs not far from the localization boundary, with implications for controllability of reactions.

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.

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.

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.

Three sources of errors in the Ehrenfest treatment of inelastic scattering and possible ways of resolving them

In order to identify the origin of possible errors in the mixed quantum/classical approach to inelastic scattering [A. Semenov and D. Babikov, J. Chem. Phys. 140, 044306 (2014) and A. Semenov, M.-L. Dubernet, and D. Babikov, J. Chem. Phys. 141, 114304 (2014)], a simplified model is considered that consists of one intermolecular degree of freedom and two intramolecular states, coupled by a simple potential. For this system, analytic derivations are carried out to determine (i) the exact quantum mechanical solution of the inelastic scattering problem, (ii) a simplified version of it with all oscillatory terms neglected, and (iii) the Ehrenfest solution in which the translational motion is described by the mean-field trajectory while the internal molecular motion is treated by the time-dependent Schrodinger equation. It is shown that the appropriate choice of velocity for the mean-field trajectory permits to enforce microscopic reversibility and gives results in excellent agreement with full-quantum results. The average velocity method of Billing is rigorously derived as a limiting case (of this more general approach), when reversibility is enforced locally, at the initial moment of time only. It is demonstrated that errors of state-to-state transition probabilities in the Ehrenfest approach occur at lower values of total energy E if the magnitudes of excitation energy ΔE, potential energy difference between the two states ΔV, and coupling of two states V₁₂ are large. Possible ways of applying this concept to rotational transitions in real molecules are explored, using examples from CO + CO inelastic scattering.

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.

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.

Inelastic Scattering of Identical Molecules within Framework of the Mixed Quantum/Classical Theory: Application to Rotational Excitations in H2 + H2

Theoretical foundation is laid out for description of permutation symmetry in the inelastic scattering processes that involve collisions of two identical molecules, within the framework of the mixed quantum/classical theory (MQCT). In this approach, the rotational (and vibrational) states of two molecules are treated quantum-mechanically, whereas their translational motion (responsible for scattering) is treated classically. This theory is applied to H2 + H2 system, and the state-to-state transition cross sections are compared versus those obtained from the full-quantum calculations and experimental results from the literature. Good agreement is found in all cases. It is also found that results of MQCT, where the Coriolis coupling is included classically, are somewhat closer to exact full-quantum results than results of the other approximate quantum methods, where those coupling terms are neglected. These new developments allow applications of MQCT to a broad variety of molecular systems and processes.

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.

Huge Quantum Symmetry Effect in the O + O2 Exchange Reaction

We report extensive, full quantum-mechanical calculations for the (16)O + (16)O(16)O → (16)O(16)O + (16)O collisions, for both inelastic and atom exchange processes, using a time-independent method based on hyperspherical coordinates. The rates obtained in the present study are much larger than the previously reported ones for this system. The discrepancy is attributed to a huge symmetry effect that was missing in the studies so far. This effect differs from the well-known isotope effect. Importance of this quantum effect is further confirmed by comparison with results for the (16)O + (18)O(18)O → (16)O(18)O + (18)O, exchange reaction.

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.

Rotational quenching of H2O by He: mixed quantum/classical theory and comparison with quantum results

The mixed quantum/classical theory (MQCT) formulated in the space-fixed reference frame is used to compute quenching cross sections of several rotationally excited states of water molecule by impact of He atom in a broad range of collision energies, and is tested against the full-quantum calculations on the same potential energy surface. In current implementation of MQCT method, there are two major sources of errors: one affects results at energies below 10 cm(-1), while the other shows up at energies above 500 cm(-1). Namely, when the collision energy E is below the state-to-state transition energy ΔE the MQCT method becomes less accurate due to its intrinsic classical approximation, although employment of the average-velocity principle (scaling of collision energy in order to satisfy microscopic reversibility) helps dramatically. At higher energies, MQCT is expected to be accurate but in current implementation, in order to make calculations computationally affordable, we had to cut off the basis set size. This can be avoided by using a more efficient body-fixed formulation of MQCT. Overall, the errors of MQCT method are within 20% of the full-quantum results almost everywhere through four-orders-of-magnitude range of collision energies, except near resonances, where the errors are somewhat larger.

Accurate Calculations of Rotationally Inelastic Scattering Cross Sections Using Mixed Quantum/Classical Theory

For computational treatment of rotationally inelastic scattering of molecules, we propose to use the mixed quantum/classical theory, MQCT. The old idea of treating translational motion classically, while quantum mechanics is used for rotational degrees of freedom, is developed to the new level and is applied to Na + N2 collisions in a broad range of energies. Comparison with full-quantum calculations shows that MQCT accurately reproduces all, even minor, features of energy dependence of cross sections, except scattering resonances at very low energies. The remarkable success of MQCT opens up wide opportunities for computational predictions of inelastic scattering cross sections at higher temperatures and/or for polyatomic molecules and heavier quenchers, which is computationally close to impossible within the full-quantum framework.

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.

Mass-independent oxygen isotopic partitioning during gas-phase SiO2 formation

Meteorites contain a wide range of oxygen isotopic compositions that are interpreted as heterogeneity in solar nebula. The anomalous oxygen isotopic compositions of refractory mineral phases may reflect a chemical fractionation process in the nebula, but there are no experiments to demonstrate this isotope effect during particle formation through gas-phase reactions. We report experimental results of gas-to-particle conversion during oxidation of silicon monoxide that define a mass-independent line (slope one) in oxygen three-isotope space of (18)O/(16)O versus (17)O/(16)O. This mass-independent chemical reaction is a potentially initiating step in nebular meteorite formation, which would be capable of producing silicate reservoirs with anomalous oxygen isotopic compositions.

Vibronic origin of sulfur mass-independent isotope effect in photoexcitation of SO2 and the implications to the early earth's atmosphere

Signatures of mass-independent isotope fractionation (MIF) are found in the oxygen ((16)O,(17)O,(18)O) and sulfur ((32)S, (33)S, (34)S, (36)S) isotope systems and serve as important tracers of past and present atmospheric processes. These unique isotope signatures signify the breakdown of the traditional theory of isotope fractionation, but the physical chemistry of these isotope effects remains poorly understood. We report the production of large sulfur isotope MIF, with Δ(33)S up to 78‰ and Δ(36)S up to 110‰, from the broadband excitation of SO2 in the 250-350-nm absorption region. Acetylene is used to selectively trap the triplet-state SO2 ( (3)B1), which results from intersystem crossing from the excited singlet ( (1)A2/ (1)B1) states. The observed MIF signature differs considerably from that predicted by isotopologue-specific absorption cross-sections of SO2 and is insensitive to the wavelength region of excitation (above or below 300 nm), suggesting that the MIF originates not from the initial excitation of SO2 to the singlet states but from an isotope selective spin-orbit interaction between the singlet ( (1)A2/ (1)B1) and triplet ( (3)B1) manifolds. Calculations based on high-level potential energy surfaces of the multiple excited states show a considerable lifetime anomaly for (33)SO2 and (36)SO2 for the low vibrational levels of the (1)A2 state. These results demonstrate that the isotope selectivity of accidental near-resonance interactions between states is of critical importance in understanding the origin of MIF in photochemical systems.

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.