Differential Cross Sections and Product Rovibrational Distributions for

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Differential Cross Sections and Product Rovibrational Distributions for O+ O and O+ O Collisions 16

32

2

18

36

2

Tammineni Rajagopala Rao, Gregoire Guillon, Susanta Mahapatra, and Pascal Honvault J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.5b08638 • Publication Date (Web): 02 Nov 2015 Downloaded from http://pubs.acs.org on November 4, 2015

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The Journal of Physical Chemistry

Differential Cross Sections and Product 16

Rovibrational Distributions for 18

O+32O2 and

O+36O2 Collisions

Tammineni Rajagopala Rao,† Grégoire Guillon ,‡ Susanta Mahapatra ,∗,¶ and Pascal Honvault∗,‡,§ †Department of Chemistry, National Institute of Technology Meghalaya, Shillong 793003, India ‡Laboratoire ICB, UMR 6303, CNRS-Université de Bourgogne Franche-Comté, 21078 Dijon cedex, France ¶School of Chemistry, University of Hyderabad, Hyderabad, 500 046, India § UFR Sciences et Techniques, Université de Franche-Comté, 25030 Besan¸con Cedex, France E-mail: [email protected]; [email protected]

Abstract We report rotationally resolved opacity functions, product rotational distributions and differential cross sections for the 16 O

and

18 O

+

18 O18 O

16 O

(v=0,j=1) →

+

16 O16 O

18 O18 O

(v=0,j=1) →

(v ′ =0,j ′ ) +

18 O

16 O16 O

(v ′ =0,j ′ ) +

collisions calculated by

a time-independent quantum mechanical method employing one of the latest potential energy surface of ozone [Dawes et al., J. Chem. Phys. 139, 201103 (2013)]. The results obtained for both collisional systems in the energy range of 0.001 - 0.2 eV are examined and interesting mass scaling effects have been discovered. The shapes of product

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angular distributions suggest a transition from an indirect to a direct scattering, via an osculating intermediate complex.

Introduction Ozone formation reaction, O + O2 + M → O∗3 + M → O3 + M (where M is a stabilizer) and oxygen exchange reactions, O + O2 → O∗3 → O2 + O, have attracted a lot of attention in the recent past. 1–5 The first reaction is well known for its unusual mass fractionation. Indeed, an equal and significant enrichment of ozone in 17 O and 18 O is observed in the stratosphere 6 and also in laboratory experiments. 3,7 It is defined as mass-independent fractionation (MIF). During the past decades several theoretical and experimental studies have been performed to understand the origin of the MIF. 1–5 However, until now this puzzle is not solved completely. But it is now theoretically well established that MIF is due to a significant isotopic effect observed in the ozone formation reaction. The latter originates from the difference in the lifetimes of the intermediate complexes, O∗3 , and in the zero point energy difference (∆ZPE) of O2 fragments to which the intermediate can dissociate. 8,9 Both ozone formation reaction and oxygen exchange reaction proceeds through the same metastable intermediate O∗3 and thus these two processes compete in the stratosphere. The oxygen exchange reactions also show significant isotopic effects. 5,10,11 Recently, an accurate potential energy surface (PES) for the ground electronic state of ozone was reported by Dawes et al. 12 (hereafter abbreviated as DLLJG PES). The PES is smoothly switched to an analytical form 13 in the asymptotic region that accurately describes the long range interactions of O and O2 . In addition, the DLLJG PES takes the spin-orbit couplings into account. The most striking feature of the DLLJG PES that distinguishes it from the preceding PESs appeared in the literature is the absence of a reef-like structure in the asymptotic channel. Recent dynamical, 14,15,18–20 spectroscopic and electronic structure studies 21 confirmed that such a disputed topological feature in the earlier PESs is an artifact. 2 ACS Paragon Plus Environment

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In a recent work 19 we have obtained integral cross sections (ICSs) and thermal rate constants of 18 O + 16 O16 O (say 8+66) and 16 O + 18 O18 O (say 6+88) reactions using a time independent quantum mechanical (TIQM) method. Our results showed that the rate constants obtained for these reactions decrease with an increase in temperature which is qualitatively in accord with the experimental measurements. 5,10,11 But the theoretically obtained thermal rate constants are lower than that of experiments. More recently, using the DLLJG PES Sun et al 20 obtained the ICSs and thermal rate constants of the 6+88 and 8+66 reactions employing a time-dependent wave packet (TDWP) method. We found that their results are in good agreement with our TIQM results. 19

More recently, we have studied the quantum dynamics of the

16

O+

16

O16 O (say 6+66)

collision using the DLLJG PES and established a quantum permutation symmetry effect. 15 For this symmetric

48

O3 system, the TIQM calculations are carried out including the re-

quired nuclear spin statistics. In case of the 6+66 collision, as well as the 8 +88 system also studied here, rovibrationally excited O2 products can form via reactive collisions or inelastic collisions. Hence we classified the 6+66 collision as energetically elastic or nonelastic ones. 15 The collisions in which the scattered O2 has the rovibrational states different from that of reagent O2 are termed as the nonelastic collisions and the collisions in which the rovibrational states of both reagent and scattered O2 are the same are called as elastic collisions. ICSs and thermal rate constants are calculated for both the nonelastic and elastic processes. The results showed that the thermal rate constant computed in the temperature range between 100 and 350 K, relevant to the stratospheric conditions, is only mildly temperature dependent. 15 Furthermore, the computed ICSs and thermal rate constants for nonelastic processes are 7 to 10 times larger than earlier theoretical results 12,14,22–24 that neglected the nuclear spin statistics. In our previous studies on O + O2 , 15,19 we reported ICSs and rate constants, as well as their dependence on the collision energy or temperature, respectively. The present work is 3 ACS Paragon Plus Environment


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focused on the differential cross sections (DCSs). Only two experiments have measured the DCSs for the 18 O + 32 O2 → 18 O16 O + 16 O exchange reaction at two collision energies, 0.247 eV and 0.316 eV. 16,17 This exchange reaction was also studied by a TDWP method 16–18,24 and in the most recent study 18 DCSs up to the collision energy of 0.35 eV were obtained. A good agreement between experiment and theory has been found especially about the nonstatistical dynamics due to a forward bias in the angular distributions. However, the forward scattering is overestimated by the theoretical calculations. Moreover, no measurements exist on the title collisional systems. Only the DCSs of the 6+66 collisions were computed by a TDWP approach 24 and we will compare below our findings with these earlier results.

In the following, we report the rotationally state-resolved opacity functions, product rotational distributions and DCSs in a wide energy range up to 0.2 eV for the 6+66 and 18

18

O+

O18 O (say, 8+88) collisions using the DLLJG PES and a TIQM method described in the

next section. The results are examined for the possible mass scaling effects and compared with earlier theoretical results when possible.

Theory A hyperspherical coordinate based TIQM formalism 25,26 is used in the present calculations. The method is well tested for many atom + diatom reactions (see for instance Refs. 27–29 ) and is suited to include the quantum effects due to the nuclear spin symmetry. 30,31 Relevant details of the method and parameters used in the present work are presented in the supporting information of our previous article 15 on the 6+66 collision. Hence, only a brief description of the method is presented here.

The scattering coordinate, i.e. the hyperradius ρ, is divided into segments and at midpoint of each segment the two dimensional hypersurface Schrödinger equation is variationally solved to obtain the ρ-dependent adiabatic basis. In case of 4 ACS Paragon Plus Environment

48

O3 or

54

O3 isotopomers of

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ozone, the three nuclei have zero nuclear spin. Thus the total wavefunction for this bosonic system should be symmetric with respect to binary atomic permutations. To attain this, it can be easily shown that the nuclear spatial wave function (excluding the nuclear spin) should belong to the A2 irreducible representation of the P3 symmetry group. This is done by a proper choice of hyperspherical harmonics that form the adiabatic basis on which the scattering wave function is expanded. The total scattering wave function in each segment is expanded in the adiabatic basis and substituted into the time-independent Schrödinger equation to obtain the coupled differential equations. The latter are solved using the JohnsonManolopoulos log-derivative propagator 32 leading to the coefficients of expansion. At the asymptotic region, numerically integrated wave function is mapped onto a set of regular and irregular asymptotic functions to obtain the K and T-matrices. From them, the rotationally and vibrationally state resolved opacity functions, ICSs and DCSs are obtained using the standard equations. For convenience, we recall here that the state-to-state magnetically averaged DCS is given by 2 ∑ ∑ 1 σvj→v′ j ′ (θcm ) = 2 (2J + 1)dJΩ′ ,Ω (π − θcm )TvJ′ j ′ Ω′ ,vjΩ 4kvj (2j + 1) Ω,Ω′ J

(1)

where kvj is the initial wave vector, J is the total angular momentum, dJΩ′ ,Ω is a Wigner reduced rotation matrix element and θcm is the scattering angle in the center-of-mass (CM) coordinate system. The scattering angle θcm = 0◦ is defined as the direction of the CM velocity vector of initial O atoms and corresponds to forward scattering for the O2 products and backward scattering for the O products. Ω and Ω′ are, respectively, the reagent and product helicity quantum numbers. We found that a maximum value of Ω equal to 40 is sufficient to get converged DCSs.



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Results and discussion In this section we present the rotationally state resolved opacity functions, product rotational distributions and DCSs for the 6+66 and 8+88 collisions with the reagent O2 in the v = 0, j =1 rovibrational state. We note that in the considered energy range of 0.001 to 0.2 eV, the v ′ = 1 vibrational state of product O2 is closed, except at few energies equal to or greater than 0.19 eV. Therefore, the current discussions are confined to products formed in the ground v ′ = 0 vibrational state.

Opacity function Degeneracy weighted opacity functions for the 6+66 and 8+88 collisions are shown, respectively, in the left and right panels of Figure 1, for a few selected values of the collision energies, 0.005 eV, 0.01 eV, 0.05 eV, 0.1 eV and 0.2 eV. Let us first examine the opacity functions corresponding to the nonelastic collisions (top panels of Figure 1). At a given collision energy, the magnitude of the opacity function increases almost linearly (especially for higher J) with J and reaches a maximum value. Beyond this point the collision energy is insufficient to cross the centrifugal barrier arising due to J and hence the opacity function rapidly falls to zero. In addition, prominent resonance structures can be seen at low collision energies (for instance at 0.005 eV and at 0.01 eV) which indicates that the intermediate collision complexes may be relatively long-lived at the lowest energies. In contrast, the magnitude of the opacity function for elastic collisions (lower panels) behaves differently and acquires a bimodal structure at larger values of J where the centrifugal barrier forbids the nonelastic collisions but not the elastic collision. For instance, in case of the 6+66 collision (panels a and b) and at collision energy of 0.1 eV (green colour), the magnitude of opacity function for nonelastic collisions reaches a maximum value of ∼ 127 at J ∼ 68 and then falls to zero at J ∼ 110. This indicates that from J = 69, the centrifugal barrier starts to demote the nonelastic collisions and completely quenches them at J = 110. Now, if we


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consider the opacity functions for the elastic collision at 0.1 eV, we see that the magnitude is of similar order to that obtained for nonelastic collisions up to J = 62, then it reaches to a first maximum of 217 at J = 72. This is followed by a dip at J = 80 and then reaches a second maximum of 718 at J = 92. From here the magnitude falls again and reaches zero at J = 145. This infers that the bimodal structure is due to different barrier limits that are needed to hinder the nonelastic collisions. With regard to the mass scaling effect, the opacity functions obtained for the 8+88 collision (right panel) show a similar behavior qualitatively. However, at a given collision energy, we observe that the maximum of the opacity function shifts to relatively higher values of J for 8+88. In addition, the magnitude at the maximum is relatively larger for the 8+88 collision. As the 8+88 system has a slightly higher reduced mass than the 6+66 one, larger values of J are needed to hinder the elastic and nonelastic collisions when compared with the 6+66 collision.

Product rotational distributions In Figure 2, the product rotational distributions, i.e. the rotationally state resolved ICSs as a function of the rotational quantum number j ′ of O2 , for both the nonelastic 6+66 (upper panel) and 8+88 (lower panel) collisions are presented for a few selected values of collision energy. We recall that the results shown in Figure 2 are for the product diatom formed in its ground v ′ = 0 vibrational state. The results for the j ′ = 1 rotational state of O2 products are not shown as they correspond to elastic collisions. Further, given the nuclear spin statistics of

32

O2 or

36

O2 molecules, only odd rotational states are allowed. It is clear

from Figure 2 that the rotationally state resolved ICSs decrease with increasing collision energy. This is because more product rotational states are accessible when the collision energy becomes higher. We can also see that the ICSs obtained for both the 6+66 and 8+88 collisions are very close. In addition, at the three highest collision energies shown in Figure 2, the shapes of the product rotational distributions imply a nonstatistical behavior in the collision dynamics, the most populated rotational states being the smallest ones. This is in 7 ACS Paragon Plus Environment


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contrast to, for instance, the statistical distributions obtained in the insertion O(1 D) + H2 reaction. 33 At the lowest collision energy, 0.01 eV, too few product rotational states are open to conclude on the dynamical behavior.

Differential Cross sections Elastic and nonelastic DCSs Differential cross sections (DCSs) for the 6+66 and 8+88 collisions are shown in left and right panels of Figure 3, respectively. Here the elastic DCS (v=0,j=1 → v ′ =0,j ′ = 1) and the nonelastic DCS (v=0,j = 1 → v ′ =0,Σj ′ with j ′ ̸= 1) are plotted, respectively, in the top and bottom panels and for selected values of collision energies. Let us first compare the elastic and nonelastic DCSs. The elastic DCS is dominated by forward scattering at all five collision energies considered in Figure 3. On the contrary, we see that at the collision energies of 0.005 eV and 0.01 eV the nonelastic DCS presents a quasi forward-backward symmetry. For example, in the case of 6+66 collision at 0.005 eV, the ratio of DCSs obtained at scattering angles of 0◦ (forward scattering) and 180◦ (backward scattering) is 1.6 and 178, respectively, for the nonelastic and elastic processes. It can also be seen that the magnitude of DCSs for the forward scattering increases rapidly with an increase of collision energy for both the elastic and nonelastic processes. As expected, the elastic DCSs for the forward scattering are higher than that of nonelastic DCSs. However, for the sideways scattering, the magnitude of the elastic DCS falls rapidly with increasing the collision energy and is almost negligible (∼ 0.1 a20 /sr) at high collision energies (0.1 - 0.2 eV). Furthermore, both the 6+66 and 8+88 collisions have similar elastic and nonelastic DCSs qualitatively, even if quantitatively some differences still exist.

Dependence of DCSs on the collision energy Figure 4 shows the effect of the collision energy on the forward, backward or sideways scattering (θcm = 0◦ , 180◦ and 90◦ respectively) for the nonelastic collisions. Here the top and 8 ACS Paragon Plus Environment

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bottom panels, respectively, correspond to the 6+66 and 8+88 collisions. In the energy range of 0.002 - 0.02 eV both forward and backward scatterings are equally prominent yielding a quasi forward-backward symmetry for the angular distributions, that is consistent with the results shown in Figure 3. This indicates that the collision certainly proceeds via a complex that exists for several rotational periods in this energy range. When the collisional energy increases above 0.02 eV, the angular distributions loose their symmetry and the intensity of the forward peak dramatically increases while the backward peak becomes very small. This is consistent with the lifetime of the intermediate complex which is less than its rotational period. The osculating complex model, 36,37 which has already been suggested in two earlier studies on O + O2 18,24 to explain the dominant forward scattering, relates the ratio of the forward and backward peak intensities to the lifetime of the complex, τ , in terms of its rotational period, τrot , following the equation, σ(θcm = 180◦ ) / σ(θcm = 0◦ ) = exp−(τrot /2τ ). Assuming that the osculating complex model is valid in a wide energy range, we found that in the low energy regime, for instance at 0.01 eV, the ratio τ /τrot is 21.8 which is consistent with an indirect mechanism. In contrast, in the high energy regime, for instance at 0.1 eV, this ratio is 0.15 only suggesting a direct mechanism. The lifetime of the O∗3 intermediate which can be very long at low collision energy therefore decreases as the collision energy increases. The reaction therefore goes from a long lived intermediate to direct scattering dynamics involving a stripping mechanism, via a shorter-lived osculating complex showing a deviation from the statistical case. Of course, these findings should be confirmed by a future study entirely devoted to an accurate quantum-mechanical calculation of the lifetimes of O∗3 complexes. Another reason for the relatively small backward peak and thus for the absence of statistical nature for the title collisions above 0.02 eV may be due to the too shallow well corresponding to the intermediate complex (1.13 eV only relative to the O + O2 channel) to allow multiple rotations before the dissociation of the complex.



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Contribution of partial waves to the DCSs To continue the analysis of the dominance of forward scattering in the high collision energy range, we have computed the nonelastic DCSs with different choices of Jmax , the maximum of total angular momentum J that is included in the partial wave expansion of the DCS (See Eq. (1)). Figure 5a presents the DCSs for the 6+66 collision for different choices of Jmax and at the high collision energy of 0.1 eV. It is clear that only the highest values of Jmax (> 60) contribute to the dominant forward scattering observed in the DCS at this collision energy. For large total angular momentum J, the collision complexes are highly unstable and hence the direct mechanism seems to be more dominant than the insertion or rebound mechanisms. This conclusion is consistent with a direct reaction where the forward scattering is associated with large angular momenta J (or classically with large impact parameters). Further, the large magnitude for the forward scattering is also due to the 2J+1 weighting factor in the partial wave expansion of the DCSs. For an indirect reaction, the correlation small/large impact parameters - backward/forward scattering is not as valid as for a direct reaction. As a matter of fact, all the impact parameters (and consequently all values of J) contribute to generate intensity in the whole angular range. Such a case is found for instance in the low energy regime at 0.01 eV as shown in Figure 5b.

Rotationally state resolved DCSs Rotationally state resolved DCSs obtained for the nonelastic 6+66 and 8+88 collisions are shown in Figure 6 at the collision energy of 0.1 eV. The magnitude of DCSs decreases with increasing product rotational state, j ′ . This can be attributed to the increase of the difference between rovibrational energies of reactant and product diatoms with increasing j ′ . As expected at this high collision energy of 0.1 eV, the DCSs for all the product states presented here are prominently forward biased but in different ways. Indeed, we observe a shift in the maximum of DCSs obtained for different product states. For instance, the maximum of the DCSs for j ′ = 3, 7, 11, 15 are observed, respectively, at the scattering angles 10 ACS Paragon Plus Environment

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of 0, 6, 9, 12 degrees for the 6+66 collision. Figure 6 shows therefore that the prominent forward peak observed in Figure 3 at 0.1 eV is due to the j ′ = 3 (and in a less extent to j ′ = 5, not shown here) rotational state of the O2 products. At other high collision energies, we found similar features, i.e. contribution of the lowest product rotational states to the forward peak. In addition, a detailed analysis at 0.1 eV, but valid for other high collision energies, revealed that the forward and backward peaks come in part from the Ω′ = 0, Ω = 0 term in Equation 1, as expected. 34,35 However, the main contribution to the high forward peak is due to the Ω′ = 1, Ω = 1 term. As regard to the mass scaling effects, both the 6+66 and 8+88 collisions show similar rotationally state resolved DCSs, even if quantitatively, significant differences are observed at higher values of j ′ and in the forward scattering region where DCSs reach the maximum value. This can be attributed to the fact that for higher j ′ , the 36 O2 diatom has a relatively lower energy difference with respect to the reagent rotational state j = 1, when compared with

32

O2 .

Comparison with the earlier studies We note that there were no experiments reported for the 6+66 and 8+88 collisions. There exists only one earlier study on the 6+66 system where the DCSs were calculated using a TDWP method. 24 At 0.05 eV, the results obtained using both methods show a forward scattering larger than the backward scattering. But in terms of magnitude, the TIQM forward peak for the nonelastic DCS is almost 10 times higher than that obtained using the TDWP method. The reason for this difference is twofold. Firstly, the PES used in the TDWP method is not the same that we have used here and it possesses artificial reef-like structure in the asymptotic region. Secondly, the nuclear spin statistics effects for

48

O3 are neglected in

the TDWP method employed in Ref. 24 Consequently, this TDWP calculation considered the 6+66 collision as a pure reactive system, yielding a smaller magnitude than that obtained for the TIQM nonelastic process, as expected. Finally, previous TDWP results 18,24 on the 8+66 collision also showed a forward bias in the DCSs and the authors also explained that



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by the existence of a short-lived osculating complex. However, in their results the forward scattering is clearly less dominant than in the present case at the highest collision energies where a direct mechanism may be involved.

Summary and conclusions In continuation to our earlier work 15 on the 6+66 collisions focusing on the dependence of ICSs and rate constants on collision energy and temperature, we reported here the rotationally state resolved opacity functions, product rotational distributions and DCSs for 6+66 and 8+88 collisions in the energy range of 0.001 - 0.2 eV. To this effort, we have used a TIQM method which includes appropriate nuclear spin symmetry and a recent ab initio PES, the DLLJG PES.

The calculations have been performed for both the elastic and nonelastic processes in both collisional systems. As expected, the scattering attributes for the elastic process, at any given collision energy, is found to be much larger than those of the nonelastic ones. In the high collision energy range (> 0.02 eV), the opacity functions show a maximum at a high value of the total angular momentum J, very close to Jmax for which the opacity function falls to zero. Below 0.02 eV, the situation is less clear with important contributions of several J values. Product rotational distributions obtained for the nonelastic processes showed a clear nonstatistical behavior at the highest collision energies, that is consistent with a relatively short-lived O∗3 intermediate complex. Angular distributions confirm this conclusion. Indeed, in the high energy regime (0.02 - 0.2 eV), the nonelastic DCS presents a prominent forward scattering with a strong forward peak, while the backward scattering is very small. An analysis of the partial wave contribution to the total nonelastic DCS revealed that this dominant forward scattering is due only to very large values of J. Below 0.02 eV, the DCS sometimes shows a forward-backward symmetry at some collision energies, indicating the existence of a long-lived intermediate complex in the low energy regime. The observed 12 ACS Paragon Plus Environment

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preference of the forward scattering with the increasing collision energy is explained by the osculating complex model except at the highest collision energies where a direct stripping mechanism may be involved.

Opacity functions, product rotational distributions and DCSs obtained for 6+66 and 8+88 collisions are compared to explore the effect of the change of mass. The qualitative features observed for both collisional processes are quite similar, even if in terms of magnitude we can see some differences. For instance, the heavier

36

O2 has relatively lower rotational spacings,

that results in higher magnitudes of rotationally state resolved ICSs observed for the 8+88 collision. This is translated, in case of rotationally state resolved DCSs, as a shift in the scattering angle at which the maximum is observed. Finally, the nonelastic DCSs obtained at 0.05 eV are compared with the only available TDWP results which are found to be about 10 times smaller. This difference is due to the neglect of nuclear spin symmetry of O3 and use of relatively less accurate PES in the TDWP calculations. Hence we hope that the present results will motivate future experiments on the 6+66 and 8+88 collisional processes. In addition, these results may help in understanding the relatively lower rate constants for the ozone formation reactions with symmetric 48 O3 or 54

O3 isotopomers as products, 38 that could be directly linked to the MIF observed in ozone.

Acknowledgment TRR thanks Department of Science and technology, New Delhi for the RA fellowship (Project No. SB/S1/PC-052/2013). TIQM computations have been done on the cluster of the Centre de Calcul de l’ Université de Bourgogne (Dijon, France).



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O with NO and O2 at 298 K. J. Chem. Phys. 1985, 83, 1648-1656.

(11) Wiegell, M. R.; Larsen, N. W.; Pedersen, T. ; Egsgaard, H. The Temperature Dependence of the Exchange Reaction between Oxygen Atoms and Dioxygen Molecules Studied by Means of Isotopes and Spectroscopy. Int. J. Chem. Kinet. 1997, 29, 745-753. (12) Dawes, R.; Lolur, P.; Li, A.; Jiang, B.; Guo, H. An Accurate Global Potential Energy Surface for the Ground Electronic State of Ozone. J. Chem. Phys. 2013, 139, 201103/1201103/4. (13) Lepers, M.; Bussery-Honvault, B.; Dulieu, O. Long-Range Interactions in the Ozone Molecule: Spectroscopic and Dynamical Points of View. J. Chem. Phys. 2012, 137, 234305/1-234305/12. (14) Li, Y.; Sun, Z.; Jiang, B.; Xie, D.; Dawes, R.; Guo, H. Rigorous Quantum Dynamics of O + O2 Exchange Reactions on an Ab Initio Potential Energy Surface Substantiate the Negative Temperature Dependence of Rate Coefficients. J. Chem. Phys. 2014, 141, 081102/1-081102/4. (15) Rajagopala Rao, T.; Guillon, G.; Mahapatra, S.; Honvault, P. Huge Quantum Symmetry Effect in the O + O2 Exchange Reaction. J. Phys. Chem. Lett. 2015, 6, 633-636. (16) Van Wyngarden, A.L.; Mar, K.A.; Boering, K.A.; Lin, J.J.; Lee, Y.T.; Lin, S.-Y.; Guo, H.; Lendvay, G. Nonstatistical Behavior of Reactive Scattering in the 18 O + 32 O2 Isotope Exchange Reaction. J. Am. Chem. Soc. 2007, 129, 2866-2870. (17) Van Wyngarden, A.L.; Mar, K.A.; Quach, J.; Nguyen, A.P.Q.; Wiegel, A.A.; Lin, S.Y.; Kendvay, G.; Guo, H.; Lin, J.J.; Lee, Boering, K.A. The Nonstatistical Dynamics 15 ACS Paragon Plus Environment


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of the

18

O+

32

O2 Isotope Exchange Reaction at Two Energies. J. Chem. Phys. 2014,

141, 064311-1/064311-12. (18) Xie, W.; Liu, L.; Sun, Z.; Guo, H.; Dawes, R. State-to-State Reaction Dynamics of 18 O +

32

O2 Studied by a Time-Dependent Quantum Wavepacket Method. J. Chem. Phys.

2015, 142, 064308/1-064308/10. (19) Rajagopala Rao, T.; Guillon, G.; Mahapatra, S.; Honvault, P. Quantum Dynamics of 16

O + 36 O2 and 18 O + 32 O2 Exchange Reactions. J. Chem. Phys. 2015, 142, 174311/1-

174311/7. (20) Sun, Z.; Yu, D.; Xie, W.; Hou, J.; Dawes, R.; Guo, H. Kinetic Isotope Effect of the 16

O+

36

O2 and

18

O+

32

O2 Isotope Exchange Reactions: Dominant Role of Reactive

Resonances Revealed by an Accurate Time-Dependent Quantum Wavepacket Study. J. Chem. Phys. 2015, 142, 174312/1-174312/12. (21) Tyuterev, Vl. G.; Kochanov, R.; Campargue, A.; Kassi, S.; Mondelain, D.; Barbe, A.; Starikova, E.; De Backer, M.R.; Szalay, P.G.; Tashkun S. Does the “Reef Structure” at the Ozone Transition State towards the Dissociation Exist? New Insight from Calculations and Ultrasensitive Spectroscopy Experiments. Physical Review Letters 2014, 113, 143002/1-143002-5. (22) Yeh, K.-L.; Xie, D.; Zhang, D. H.; Lee, S.-Y.; Schinke R. Time-Dependent Wave Packet Study of the O + O2 (v = 0, j = 0) Exchange Reaction. J. Phys. Chem. A 2003, 107, 7215-7219. (23) Lin, S. Y.; Guo, H. Quantum Statistical Study of O + O2 Isotopic Exchange Reactions: Cross Sections and Rate Constant. J. Phys. Chem. A 2006, 110, 5305-5311. (24) Sun, Z.; Liu, L.; Lin, S. Y.; Schinke, R.; Guo, H.; Zhang, D. H. State-to-State Quantum Dynamics of O + O2 Isotope Exchange Reactions Reveals Non-Statistical Behavior at Atmospheric Conditions. Proc. Natl. Acad. Sci. USA 2010, 107, 555-558. 16 ACS Paragon Plus Environment

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(25) Launay, J. -M.; Dourneuf, L. M.; Hyperspherical Close-Coupling Calculation of Integral Cross Sections for the Reaction H + H2 → H2 + H. Chem. Phys. Lett 1989, 163, 178188. (26) Honvault, P.; Launay, J.-M.; Quantum Dynamics of Insertion Reactions. In Theory of Chemical Reaction Dynamics, Lagana, A.; Lendvay, G.; Kluwer: The Netherlands, 2004; pp 187-215. (27) Aoiz, F. J.; Banares, L.; Castillo, J. F.; Brouard, M.; Denzer, W.; Vallance, C.; Honvault, P.; Launay, J. -M.; Dobbyn, A. J.; Knowles, P. J. Insertion and Abstraction Pathways in the Reaction O(1 D) + H2 → OH + H. Phys. Rev. Lett. 2001, 86, 17291732. (28) Daranlot, J.; Jorfi, M.; Xie, C.; Bergeat, A.; Costes, M.; Caubet, P.; Xie, D.; Guo, H.; Honvault, P.; Hickson, K. M. Revealing Atom-Radical Reactivity at Low Temperature Through the N + OH Reaction. Science 2011, 334, 1538-1541. (29) Rajagopala Rao, T.; Goswami, S.; Mahapatra, S.; Bussery-Honvault, B.; Honvault, P. Time-Dependent Quantum Wave Packet Dynamics of the C + OH Reaction on the First Excited Electronic State. J. Chem. Phys. 2013, 138, 094318/1-094318/10. (30) Honvault, P.; Jorfi, M.; Gonzalez-Lezana, T.; Faure, A.; Pagani, L. Ortho-Para H2 Conversion by Proton Exchange at Low Temperature: an Accurate Quantum Mechanical Study. Phys. Rev. Lett. 2011, 107, 023201/1-023201/4. (31) Rajagopala Rao, T.; Mahapatra, S.; Honvault, P. A Comparative Account of Quantum Dynamics of the H+ + H2 Reaction at Low Temperature on Two Different Potential Energy Surfaces. J. Chem. Phys. 2014, 141, 064306/1-064306/7. (32) Manolopoulos, D. E. An Improved Log Derivative Method for Inelastic Scattering. J. Chem. Phys 1986, 85, 6425-6429.



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0.005 eV 0.010 eV 0.050 eV 0.100 eV 0.200 eV

Figure 1: Degeneracy weighted opacity functions obtained for the 6+66 (left) and 8+88 (right) collisions at selected values of collision energies. Top and bottom panels, respectively, show the curves obtained for the nonelastic and elastic collisions.

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Page 19 of 26 The Journal of Physical Chemistry


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ICS (a0 )

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Figure 2: Product rotational distributions obtained for the nonelastic 6+66 (top) and 8+88 (bottom) collisions at four collision energies.



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Figure 3: DCSs obtained for the 6+66 (left) and 8+88 (right) collisions at selected values of collision energies. Top and bottom panels, respectively, show the curves obtained for the nonelastic and elastic collisional processes.

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Page 21 of 26 The Journal of Physical Chemistry


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Page 22 of 26

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0.01 Collision Energy (eV)

Figure 4: Effect of forward (black), sideways (blue) and backward (red) scatterings with the collision energy obtained for the nonelastic 6+66 (top) and 8+88 (bottom) collisions.


Page 23 of 26

J max =30

DCS (a o2 /sr)

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Figure 5: DCSs as a function of Jmax obtained at the collision energies of 0.1 eV (top) and 0.01 eV (bottom) for the nonelastic 6+66 collision. 23 ACS Paragon Plus Environment

DCS (a0 sr )

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Figure 6: Rotationally state resolved DCSs obtained for the nonelastic 6+66 (black) and 8+88 (red) collisions for selected values of rotational quantum number j ′ at the collision energy of 0.1 eV.

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The Journal of Physical Chemistry Page 24 of 26

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Differential cross section (au)

Page 25 of 26

Collision energy (eV)



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194x151mm (150 x 150 DPI)


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Differential Cross Sections and Product Rovibrational Distributions for

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