Article pubs.acs.org/JPCA
Quantum Dynamics of the
17
O+
32
O2 Collision Process
Grégoire Guillon* and Pascal Honvault Laboratoire Interdisciplinaire Carnot de Bourgogne, UMR CNRS 6303, Université de Bourgogne Franche-Comté, 21078 Dijon, France UFR Sciences et Techniques, Université de Franche-Comté, 25030 Besancon, France ABSTRACT: We report full quantum integral and differential cross sections and rate constants for the 17O + 32O2 reactive process. This constitutes the first quantum scattering study of the 17O16O16O system. We emphasize the comparison with the 18O + 32O2 collision in close connection to the mass-independent fractionation (hereafter referred to as MIF) puzzle for ozone in atmospheric chemistry. We find similar general trends in the cross sections and rate constants for both rare isotopes, but we note some singular behaviors peculiar to the use of 17O isotope, particularly at the lowest collision energies.
The pioneering in loco findings of Mauersberger have been reproduced in stratospheric ozone samples8 and in laboratory experiments (using electrical discharges in oxygen gas) designed to simulate conditions similar to those present in the stratosphere, and heavy isotope enrichments have been analyzed by varying the O2 pressure by the Heidenreich and Thiemens group in San Diego.9,10 In the last few years, many theoretical attempts, covering a wide spectrum of quantum and classical methods, have been devoted to understanding this puzzling phenomenon. It is now well accepted that the large isotope effect experimentally observed in the full recombination reaction, O + O2 + M → O3 + M (for which rate constants can differ by as much as 50%, depending on the isotopes used but without any obvious correlation with their masses) is the key mechanism responsible for the MIF.11,12 This effect is related to differences in the lifetimes of metastable states (resonances) for variously substituted xOyOzO complexes (where x, y, and z stand for 16, 17, and 18). These are themselves due to differences in zero-point energies (the so-called ΔZPE) between two O2 fragments into which metastable ozone can dissociate.13 Still, this MIF phenomenon is not totally understood, starting from first principles, despite a few attempts using classical quantum hybrid methods14,15 to describe the rovibrational relaxation (or stabilization) of O3* by a third inert body M. As the deactivation step of the recombination forming stable ozone competes with the fast exchange reaction, the first step when focusing on the role of 17O is the precise study of the latter process. We thus have performed quantum scattering calculations3 for the 17O + 32O2 process, supported by a recently developed
1. INTRODUCTION Many recent studies have been dedicated to the computation of quantum mechanical cross sections and rate constants for the 18 O + 32O2 → 34O2 + 16O atom-exchange reactive process. To this end, both time-dependent1,2 and time-independent3−5 formalims have been used, as well as classical trajectories.6 However, for some reason, none have focused on the effect of the less abundant 17O oxygen isotope instead of 18O. However, it was shown as early as 1987 by Mauersberger,7 using a spectrometer that embarked on a balloon-probe flight, that stratospheric ozone presents a significant enrichment in 17O and 18O isotopes, roughly equal for both of them and thus called the mass-independent fractionation (MIF) effect. In a recent paper,3 we have presented full quantum cross sections and rate constants for the collision involving only the most abundant rare isotope of oxygen, 18O, namely, the 18O + 16 16 O O → 18O16O + 16O exchange process, hereafter referred to as 8 + 66 → 86 + 6. At low pressure, this reaction is believed to be the initiation step 18O + 32O2 → 50O3* for 18O-enriched ozone formation, leading to highly rovibrationally excited ozone complex O3* before it decays back into O + O2 fragments. The efficiency of the O + O2 collision process, depending on which rare isotope is used, is important because it strongly competes with the subsequent deactivation process of O3* that might take place in the presence of a third body M (most likely molecular nitrogen N2, totally dominating in the whole atmosphere) carrying out the excess energy to eventually give stable ozone: O3* + M → O3 + M. Consequently, despite the lower abundance of 17O compared to that of 18O (the natural abundances of 16O, 18O, and 17O are 99.76, 0.20, and 0.04%, respectively), the study of the 7 + 66 collision process deserves as much attention as the 8 + 66 process. © XXXX American Chemical Society
Received: July 27, 2016 Revised: September 8, 2016
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DOI: 10.1021/acs.jpca.6b07547 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry A global potential energy surface (PES)16 and later referred to as the DLLJG PES after the names of the authors, whose accuracy seems to be established by different dynamical studies, despite some remaining global quantitative discrepancies with experiments.1,3 In particular, the negative temperature dependence of the ratio of thermal exchange rates for 18O + 32O2 and 16O + 36 O2 processes, k8/6, is qualitatively reproduced using this PES by different quantum methods.3,17 This is a strong argument in favor of DLLJG PES being accurate enough for the computation of dynamical observables such as cross sections and rate constants. The goal of this article is to compute integral and differential cross sections (ICSs and DCSs respectively) and rate constants for the 17O + 16O16O → 16O17O + 16O (7 + 66 → 67 + 6) reaction, using this same DLLJG PES, and to compare them to those recently obtained for the 18O + 16O16O (8 + 66) reaction, using the same quantum method. In section 2, we describe very briefly the underlying time-independent quantum mechanical (TIQM) method we use to obtain dynamical observables. In section 3, we discuss and analyze our results concerning the 17 16 16 O O O system, and we make various comparisons with its 18 16 16 O O O counterpart.
toward all accessible outcomes energetically allowed using the TIQM method discussed in the previous section. We have shown in a previous study, by performing calculations for the 8 + 66 collision for numerous initial rotational states j, that the largely dominating contribution entering the thermal rate constants comes from the first initial rotational level j = 1. Therefore, we restrict ourselves to this initial selected state in the present study. We also compare these new results with those previously computed for the 8 + 66 process. Figure 1 shows the initial j state selected ICSs for both 7 + 66 (black line) and 8 + 66 (red line), for the ground rotational
2. THEORY We perform TIQM scattering calculations in order to obtain cross sections and rate constants for the 7 + 66 collision, at temperatures relevant to atmospheric conditions, that is, between 150 and 350 K. This implies the computation of cross sections for collision energies of between 0.01 and 0.2 eV. For that purpose, we solve coupled equations arising from the time-independent Schrödinger equation (TISE) expressed in democratic hyperspherical coordinates. The method has already been described in detail in a number of papers,18,19 so we shall mention only the calculation parameters we have used in this study. Here, we found that a value of Ωmax = 40 (maximum value of the z projection of the total angular momentum on the smallest inertia axis of the O3 complex) was enough to yield converged results. Then, for each given total angular momentum J, the solution of the TISE is expanded in terms of adiabatic states obtained in a previous step (by solving the two-dimensional hypersurface Schrödinger equation). We have used 200 adiabatic states at J = 0, and the resulting coupled equations in the radial coordinate are solved using the so-called logderivative propagator.20,21 The reactance K and transition T matrices are obtained for a large value of the hyper-radius by matching the propagated solution to its asymptotic form, respecting the boundary conditions for the scattering problem. We have obtained K matrices at 120 energy grid points using a maximum total angular momentum of Jmax = 90. Finally, the integral and differential cross sections are obtained by summing appropriately the T-matrix elements. In comparison to the 866 system, the 766 system presents only a slight mass scaling. There is no quantum indistinguishability effect due to the presence of a third 16O atom,5 so what we expect here is a pure isotope effect in dynamical observables.
Figure 1. Comparison of the initial state selected integral cross sections (with units of a02) for the ground rovibrational state of O2 (v = 0, j = 1), obtained for the 7 + 66 and 8 + 66 collisions as a function of collision energy in eV.
state j = 1 of 32O2 as a function of the collision energy, Ec. We have plotted all of the ICSs for a collision energy ranging from 0.01 to 0.20 eV. These shall lead to converged rate constants for a temperature range relevant to the study of stratospheric ozone. The first thing we notice is that 7 + 66 and 8 + 66 collisions globally follow a very similar pattern. Both ICSs are, on average, close to each other in magnitude for the entire collision energy range, showing that there is no pronounced isotope effect for this system, at least for collision energies relevant to stratospheric temperatures. However, we still may note some particular features for the 7 + 66 collision in comparison to the 8 + 66 collision. First, around the lower energies, more accurately between 0.0082 and 0.0085 eV (see the left part of the inset box in Figure 1, where data are represented on a finer scale), we can see that the ICS for the 7 + 66 process seems to dominate significantly on this tiny interval. This is the energy domain where ΔZPE lies (i.e., ZPE differences between product and reactant diatoms). ΔZPE for the 7 + 66 process is a bit smaller than that for the 8 + 66 one, leading to a cross section larger in this energy range, in accordance with what we found for the first initial rotational j states for the 8 + 66 collision (Figure 1(c) in ref 3). Then if we look at middle range energies, between 0.02 and 0.10 eV, we note that both ICSs are highly structured and oscillate strongly. This is due to numerous quantum resonances corresponding to quasibound states supported by the deep potential energy well in the O3 PES, giving rise to an intermediate complex that is relatively long-lived. Because of the slight change in the reduced mass of the collision complex
3. RESULTS AND DISCUSSION In this section, we present the initial state-selected ICSs, DCSs, and rate constants obtained for the initially defined 7 + 66 reactive collision process (i.e., including 17O atom exchange) B
DOI: 10.1021/acs.jpca.6b07547 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry A when moving from an 18O atom to a 17O, the positions of the various resonance peaks are shifted in energy. Between 0.01 and 0.04 eV, ICSs for the 8 + 66 and 7 + 66 processes dominate alternately. In contrast to this, we note that on average, starting from about 0.04 eV, the ICS for the 7 + 66 process becomes slightly dominating over a wide range of collision energies until roughly 0.15 eV. Finally, at higher collision energies, that is, above 0.15 eV, ICSs for both processes tend to become extremely similar to a common value of 14.5a02 at Ec = 0.2 eV. We note that both 7 + 66 and 8 + 66 ICSs globally monotonically decrease with increasing Ec. This is due to the absence of any barrier (even submerged) in the DLLJG PES for the entrance arrangement of the O + O2 fragments. Furthermore, we do not observe any threshold in the cross sections because both the 8 + 66 and 7 + 66 processes are exothermic. We show the corresponding rate constants in Figure 2 associated with the 7 + 66 (black line) and 8 + 66 (red line)
argument in favor of the nonsensitivity of the heavy isotope mass for the MIF effect in the stratosphere. We also have to note that, in contrast to our previous study with 18O, the nuclear spin of the 17O nuclei is nonzero (I = 5/ 2). However, we specify that we have no spin-dependent term in our Hamiltonian, so we do not consider any spin-flip transition (i.e., change in the spin projection quantum number during a collision process). If such spin-dependent terms were present, we would have to perform the averaging over initial and summing over final 17O spin states in the spinflip matrix elements in order to obtain ICSs comparable to observable ones in a nonpolarized molecular beam experiment (where the various spin states are not monitored). However, given the incredibly small magnitude of the nuclear magneton, this more complete treatment would be of importance only at extremely low collision energies. At the thermal energies of this study, assuming the various spin-flip amplitudes to be the same order of magnitude and performing the above-described averaging completely amounts to simply negelecting the 17O nuclear spin as we have done in this work. In order to gain further insight into the 7 + 66 reaction, we present in Figure 3 its so-called product rotational distributions
Figure 2. Comparison of the initial state selected rate constants (in units of cm3 s−1) for the ground rovibrational state of O2 (v = 0, j = 1), computed for the 7 + 66 and 8 + 66 processes as a function of temperature in K. Figure 3. Product rotational distributions obtained for the 7 + 66 reaction at two collision energies. At 0.1 eV, the ICS has been multiplied by a factor of 2.
processes. These have been computed between between 150 and 350 K for completeness, including all temperatures relevant to stratospheric conditions, in connection with the MIF puzzle. Their behaviors are very smooth and monotonous, slowly increasing with temperature, and very close to one another. Also, in agreement with the ICS analysis, rates associated with the 8 + 66 collision remain slightly lower than their 7 + 66 counterparts for the entire temperature range. This was to be expected from the average behavior of the cross sections. Therefore, the kinetics of the 7 + 66 reaction are slightly faster than that of 8 + 66, and the corresponding rate constant increases more rapidly with temperature but the difference in magnitude is not significant. Therefore, whatever heavy isotope is used, the speed of the exchange reaction remains nearly unmodified. Accordingly, contrary to what happens with the case of three identical oxygen atoms, such as the 6 + 66 process where the reaction is very fast,5 the latter does not compete as much with the ozone stabilization process involving a third body. This fact remains true using any rare isotope, 18O or 17O. Although careful calculations of lifetimes for both rare isotopes and several J values have to be performed to confirm this hypothesis (calculations are in progress), this constitutes an
(PRDs), which are the rotationally state resolved ICSs as a function of the final rotational quantum number j′ of 33O2, which can take odd and even values. It has to be noted at this point that at 0.1 eV the ICS has been multiplied by a factor of 2 for visibility reasons. We stay in the ground vibrational state v = 0, and we show the results for two collision energies of 0.01 and 0.1 eV. At the lowest collision energy of 0.01 eV, the distribution is highly peaked with a maximum for j′ = 3 and without any further contribution for values of j′ greater than 8. At 0.1 eV, the PRD is much broader, as expected, with final rotational states contributing up to j′ = 23. Indeed, more product rotational states become accessible with higher collision energy. At this energy, products are more likely to be formed with rotational states j′ ranging from 3 to 10. We note that the results are in contrast to what happens with three identical nuclei (such as collisions 6 + 66 and 8 + 884), where only odd final rotational states are allowed and distributions are purely decreasing (due to indistinguishability, with the elastic process entering the total flux being the strongest). C
DOI: 10.1021/acs.jpca.6b07547 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry A
coordinates. They are supported by a recently developed accurate PES known as the DLLJG PES. Cross sections for this collision have been obtained for a wide range of collision energies leading to converged rate constants computed for a range of temperatures relevant to atmospheric conditions and beyond. They present behaviors very similar to those for the parent 8 + 66 collision,5 with the 7 + 66 system being formally similar from the interaction potential point of view only. In addition, product rotational distributions and DCSs have been computed and analyzed. We are not in the situation of three identical nuclei;5,22 consequently, the permuation symmetry plays no role in the reaction dynamics. We are in the presence of a pure isotope effect due to the change in mass of one atom, and we conclude that it is not significant, as we do not observe any quasi-resonant behavior due to the change in one atomic mass. Therefore, the xO + 32O2 process is roughly as fast whatever rare isotope we use for xO (with x = 17 or 18). This finding goes toward mass-independent kinetics for this exchange reaction. This suggests that lifetimes for 18O16O16O and 17O16O16O should be of the same order of magnitude. We plan to dedicate future work to an accurate quantum study of this hypothesis. The work reported here constitutes the first step in understanding, starting from first principles, the strong and almost equal enhancement of stratospheric ozone in 17O as in 18O.
Furthermore, we cannot conclude that we have a true statistical behavior for the 7 + 66 process at 0.1 eV, with the increasing in ICS with j′ at both collison energies being far from linear. Finally, to further increase our understanding of this reaction, we show in Figure 4 DCSs as a function of the center-of-mass
Figure 4. DCSs obtained for the 7 + 66 reaction at two selected values of the collision energy.
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scattering angle for the same two collision energies as chosen for PRDs discussed above. At 0.01 eV, apart from some oscillations more relevant to sideways scattering, the DCS is nearly symmetrical, the forward scattering being a little bit more pronounced than that in the backward direction. The associated forward/backward ratio is roughly 1.05, which is an indicator of the relatively well balanced mechanism between the two directions, yielding quasi-forward−backward symmetry for the angular distribution. Moreover, we note that at this low energy the sideways scattering is far from being negligible, with marked oscillating structures. All of these features may reveal the presence of a relatively long-lived collisional O3 complex including the 17O atom, which may live for several rotational periods. In sharp contrast to this, at the higher collision energy of 0.1 eV, the scattering is almost completely forward, and we see a dramatic decrease in the backward scattering, with the forward/ backward ratio increasing to 3. In addition, the sideways scattering at this collision energy becomes quasi-negligible. The polarization (which is the ratio of forward to sideways scattering) increases to nearly 17 on a large domain of sideways angles of around 90°. These facts are consistent with the lifetime of the intermediate complex, which at this higher energy becomes smaller than its rotational period. To conclude this section, the most important point we need to stress here is the striking similarity in the cross sections and rate constant profiles for the 7 + 66 and 8 + 66 processes as well as in the more detailed scattering information such as PRDs and DCSs that we have analyzed above. This reflects the similar behavior of the two 766 and 866 systems with respect to the quantum dynamical viewpoint, as opposed to what happens when three identical atoms are involved.
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS All computations have been made on the cluster of the Centre de Calcul de l’Université de Bourgogne (CCUB, Dijon, France). We thank Richard Dawes for providing us the O3 potential energy surface.
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REFERENCES
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4. CONCLUSIONS We have performed the first full quantum scattering study of the 17O + 16O16O collision. The dynamical calculations are based on a time-independent formalism using hyperspherical D
DOI: 10.1021/acs.jpca.6b07547 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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DOI: 10.1021/acs.jpca.6b07547 J. Phys. Chem. A XXXX, XXX, XXX−XXX
