Classical and quasi-classical trajectory calculations of isotope exchange and ozone formation proceeding through O+O2 collision complexes

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.

Rovibrational energy transfer and dissociation in O2-O collisions

A set of state-specific transition rates for each rovibrational level is generated for the O2(X(3)Σ(g)(-))-O(3)P system using the quasi-classical trajectory method at temperatures observed in hypersonic flows. A system of master equations describes the relaxation of the rovibrational ensemble to thermal equilibrium under ideal heat bath conditions at a constant translational temperature. Vibrational and rotational relaxation times, obtained from the average internal energies, exhibit a pattern inherent in a chemically reactive collisional pair. An intrinsic feature of the O3 molecular system with a large attractive potential is a weak temperature dependence of the rovibrational transition rates. For this reason, the quasi-steady vibrational and rotational temperatures experience a maximum at increasing translational temperature. The energy rate coefficients, that characterize the average loss of internal energy due to dissociation, quickly diminish at high temperatures, compared to other molecular systems.

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.

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 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.

Some symmetry-induced isotope effects in the kinetics of recombination reactions

Symmetry-induced isotope effects in recombination and collision-induced dissociation reactions are discussed. Progress on understanding the anomalous isotope effects in ozone is reviewed. Then, calculations are performed for the simpler reaction xNe+yNe+H<-->xNeyNe+H, where x and y label either identical or different isotopes. The atomic masses in the model are chosen so that symmetry is the only difference between the systems. Starting from a single potential energy surface, the properties of the bound, quasibound, and continuum states of the neon dimer are calculated. Then, the vibration rotation infinite order sudden approximation is used to calculate cross sections for all possible inelastic and dissociative processes. A rate constant matrix that exactly satisfies detailed balance is constructed. It allows recombination to occur both via direct three-body collisions and via tunneling into the quasibound states of the energy transfer mechanism. The eigenvalue rate coefficients are determined. Significant isotope effects are clearly found, and their behavior depends on the pressure, temperature, and mechanism of the reaction. Both spin statistics and symmetry breaking produce isotope effects. Under most conditions the breaking of symmetry enhances the rates, but a wide spectrum of effects is observed; they range from isotope effects with a normal mass dependence to huge, mass-independent isotope effects to cancellation and even to reversal of the isotope effects. This is the first calculation of symmetry-induced isotope effects in recombination rates from first principles. The relevance of the present effects to ozone recombination is discussed.

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.