First-Principles Computed Rate Constant for the O + O2 Isotopic

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Spectroscopy and Photochemistry; General Theory 2

First-Principles Computed Rate Constant for the O + O Isotopic Exchange Reaction Now Matches Experiment

Gregoire Guillon, Pascal Honvault, Roman Kochanov, and Vladimir G Tyuterev J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b00661 • Publication Date (Web): 29 Mar 2018 Downloaded from http://pubs.acs.org on March 29, 2018

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The Journal of Physical Chemistry Letters

First-principles Computed Rate Constant for the O + O2 Isotopic Exchange Reaction Now Matches Experiment

Grégoire Guillon1, Pascal Honvault1*, Roman Kochanov2,3, and Vladimir Tyuterev4

1

Laboratoire Interdisciplinaire Carnot de Bourgogne, UMR 6303, CNRS-Université de

Bourgogne-Franche-Comté, 21078 Dijon Cedex, France 2

Laboratory of Quantum Mechanics and Radiative Processes, Tomsk State University, Tomsk,

Russia, 3

Harvard-Smithsonian Center for Astrophysics, Atomic and Molecular Physics Division,

Cambridge MA 02138, USA. 4

Groupe de Spectrométrie Moléculaire et Atmosphérique UMR CNRS 7331, UFR Sciences BP

1039, 51687 Reims Cedex 2, France

Corresponding Author *E-mail: [email protected] , [email protected] (P.H.).

ACS Paragon Plus Environment

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ABSTRACT. We show, by performing exact time independent quantum molecular scattering calculations, that the quality of the ground electronic state global potential energy surface appears to be of utmost importance in accurately obtaining even as strongly averaged quantities as kinetic rate constants. The oxygen isotope exchange reaction,

18

O+

32

O2, motivated by the

understanding of a complex long-standing problem of isotopic ozone anomalies in the stratosphere and laboratory experiments, is explored in this context. The thermal rate constant for this key reaction is now in quantitative agreement with all experimental data available to date. A significant recent progress at the frontier of three research domains, advanced electronic structure calculations, ultra-sensitive spectroscopy, and quantum scattering calculations, has therefore permitted a breakthrough in the theoretical modeling of this crucial collision process from first principles.

TOC GRAPHICS

KEYWORDS. Molecular collisions, Reaction dynamics, Quantum reactive scattering, Kinetics.


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The origin of the mass independent fractionation (MIF) in heavy oxygen isotopes 18O and 17

O of stratospheric ozone O3 has puzzled the atmospheric chemistry community for nearly four

decades1-4. The so-called three-body recombination reaction O + O2 + M → O3 + M, which is a multistep process5, has become firmly believed to be the main reaction eventually leading to this enrichment, making it a large kinetic isotope effect4,6. At low pressures and stratospheric temperatures, the energy-transfer mechanism, also known as the Lindeman mechanism, is believed to be the dominant process for ozone formation. However, the radical-complex mechanism, also known as the Chaperon mechanism, may also play an important role7,8 in ozone formation. In the Lindeman mechanism, the recombination reaction can be partitioned into two steps: the formation of O3 in a highly excited ro-vibrational state, from reaction O + O2 → O3* (step 1), and its subsequent stabilization by collision with an energy absorbing partner M (most likely N2), O3* + M → O3 + M (step 2). It thus appears clearly that the efficiency of the oxygen exchange reaction 18

O + 16O16O → 50O3* → 16O18O + 16O,

(1)

involving 18O enriched unstable ozone O3* as an intermediate and thus competing with step 2, is one of the key parameters to understand heavy ozone formation. Inaccurate theoretical modeling of this reaction results from a lack of understanding of ro-vibrationally metastable ozone O3* properties at energies near the dissociation threshold. A progress in this domain opens the door to a correct description of the ozone stabilization process (step 2). Its so called “nascent population”9 during the ozone formation is composed by about 50 % highly-excited states10. This is one of the major characteristics for the non - local thermodynamic equilibrium (LTE) models10


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that are used for interpretation of the ozone measurements in the atmosphere by ground-based and satellite instruments11. The reaction (1) constitutes the corner stone of the present work. The reported finding, especially the absence of a reef-like structure in the transition state region, relevant to the impact of ab initio calculations of spectroscopic accuracy at this region upon the reaction dynamics, could pave the way for a better understanding of other reactive systems, as well as more complex processes of molecular formation and fragmentation. Potential energy surfaces (PESs) are likely to bring much insight into the dynamics of a molecular process, but an important issue is linked to a question: “what are the most important PES topographical features for dynamical applications and what is the level of accuracy required for a proper understanding of reactivity and especially the rate constants of reactions?”. The ozone molecule is known to have quite a complicated electronic structure with several potential minima separated by barriers12,13,14. Earlier electronic structure calculations of ozone have predicted the existence of an activation barrier at the transition state (TS) on the reaction path just before the O + O2 asymptote. Several global three dimensional (3D) PESs of O3 designed for dynamical calculations have been proposed in the recent past. The first accurate global PES built by the group of Schinke13 included such a barrier, but it was claimed15 that with increasing size of the atomic basis set used, the barrier submerged below the O + O2 dissociation limit forming a “reef”-like structure. Babikov et al.16 have modified the PES of the group of Schinke13,17 by incorporating the “reef” feature with an empirical correction for the dissociation energy for kinetics calculations. However, using this PES, Lin and Guo18 concluded that the calculated thermal rate constants for O + O2 isotopic variants, including 18O + 32O2, were about three to five times smaller than the measured ones and had a wrong temperature dependence. Dawes et al.


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first showed19,20 that an optimization of orbitals including several interacting electronic states in the TS region should result in a ground PES without the “reef” feature. This new PES, denoted hereafter DLLJG, has been used in recent quantum scattering calculations of 18O + 32O2 and 16O +

36

O2 collisions20-23, that have been able to reproduce the negative temperature dependence

exhibited by the experimental thermal rate constants24,25, despite a remaining disagreement in magnitude, yielding a qualitatively correct trend for the first time. Another ab initio PES, denoted hereafter TKTHS, constructed by Tyuterev et al.26 has proved to be the most accurate for spectroscopic purposes27. This PES presents the particularity of showing no “reef” at all, even in the vicinity of the minimum energy path, that makes it topographically different from the DLLJG PES where the “reef” does not vanish at some geometries near the TS, as shown below. In the present work, we use the TKTHS PES (see the Supporting Information) to compute the thermal rate constant for the 18O + 32O2 → 34O2 + 16O reaction. For the study of a chemical reaction, all accessible space regions must be accurately described, from the reactants to products, including barriers and wells (deep or shallow). However, it is a commonly and widely shared belief in the reaction dynamics community28 that for the computation of averaged scattering observables like rate constants at room temperature, accurate topographical details, like a 3D shape of a well or a barrier, are not quantitatively determinant for the outcome of the reaction process. From the pioneering times, the celebrated Arrhenius empirical law29 made the rate depend only on the height of the barrier (neither its position nor its shape) and famous Polanyi rules30 invoked qualitative features like advanced or retarded positions for a barrier and their effect on translation-vibration energy transfer during a reaction. This is in sharp contrast to what happens for example in precision spectroscopy27, in cold collisions31 or in fine scattering observables like differential cross sections32. On the other


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side, rate constants in reaction kinetics are already very averaged quantities, and thermal rate constants even more so. As a result, numerous compensatory effects in the averaging process are likely to yield quite an acceptable agreement between theory and experiment. Only few attributes, like energies of the internal states (partitions functions) and local knowledge of the PES in the saddle point region, would be practically sufficient to obtain averaged quantities like rate constants. This is in essence the idea of statistical theories, among which the celebrated transition state theory33. So, according to this stream of thought, rate constants do not require full knowledge and precision of every part of the PES, but only a few typical features.

Figure 1. One dimensional cut through the bottleneck transition state range. From the global minimum towards the dissociation for four recent PESs: SSB13, AB37, DLLJG20, and TKTHS26.


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The other O – O bound is fixed at 2.28 a0 along the minimum energy path, and the apex angle of the triangle is 116.75°.

In this new work, we show for the first time that both the qualitative and quantitative behavior of the experimental thermal rate constant of the

18

O +

16

O16O →

16

O18O +

16

O reaction can be

obtained from the ozone PES, without any empirical adjustments, combined with a time independent full quantum dynamical approach (see the Supporting Information) that has already been proved successful in describing dynamics of other atom-diatom reactions34-35. Three possible causes for the underestimation of the theoretical thermal rate constants in the exchange O + O2 reactions have been considered in the literature15-17: the PES topology, quantum effects, and nonadiabatic transitions. Tashiro and Schinke36 have studied the effect of non-adiabatic transitions induced by the spin–orbit coupling with 27 repulsive electronic states, which correlate with the O + O2 limit by the method of wave packet propagation, and concluded that this did not solve the problem. However other sources of non-adiabaticiy (electronicCoriolis and Renner-Teller couplings) have not been taken into account. The shape of the TS was recognized as an important issue15,17,19,20, but most studies were focused on a one dimensional cut along the minimum energy path. The related differences are shown in Fig. 1 where the PES curves are matched at the dissociation limit De taken as the scale reference. The PES of Ayouz and Babikov37 possesses the “reef” feature with a submerged barrier, in contrast to earlier works12,13 where a true barrier arises (above the O + O2 asymptote). Dawes et al.19,20 have taken higher electronic states of ozone into account indirectly. They claimed that including them results in the disappearance of the “reef” structure at the TS that is replaced by a kind of “shoulder”, as shown in the orange dashed curve in Fig 1. Tyuterev et al.26 have further extended the accuracy of electronic structure


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calculations using larger atomic basis sets and applying the Dawes corrections due to the effect of the excided electronic states. They showed that both vibrational frequencies and the shape of the TKTHS PES near the TS depend on the size of the atomic basis set. As can be seen in Fig. 1, the TS “shoulder” becomes smoother and the potential decreases more rapidly while shortening the dissociation coordinate with this latter PES.

Figure 2. Two-dimensional shape of the ozone transition state region. Recent O3 PESs, DLLJG20 and TKTHS26 are plotted in orange color and blue color respectively, as function of the dissociative bond O—OO (r1) near 4 a0 and the diatomic fragment O2 bond (r2) around 2.28 a0.


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Figure 2 shows the 2D shape of the DLLJG and TKTHS PESs in the TS range. The “reef” again appears in the DLLJG PES for the O-O bond close to but different from the minimum energy path value 2.28 a0, while it remains totally absent in the TKTHS PES. This significant difference has an impact on vibrational levels supported by these surfaces and on reactivity as mentioned below.

Number of

Mean / cm-1

RMS /cm-1

mass

Symmetry of the open structure

obs bands

(obs– ab initio)

(obs – ab initio)

16O16O16O

48

C2V

86

0.27

1.05

16O18O16O

50

C2V

21

0.35

0.69

16O16O18O

50

CS

36

0.40

0.83

16O18O18O

52

CS

19

-0.33

0.61

18O16O18O

52

C2V

22

-0.17

0.91

18O18O18O

54

C2V

54

-0.01

1.15

Ozone

Total

Isotopologue

TABLE 1. Root-mean-squares (RMS) and mean deviations between observations (Barbe et al.39, Campargue et al.40 and Refs therein) and calculations using the ab initio TKTHS PES26 for vibrational band centers of ozone isotopologues.

It has been recently demonstrated38 that a purely statistical approach on the DLLJG PES is not valid for the

18

O +

32

O2 collisions that seem more likely to be controlled by a pure

dynamical behavior. A reliable description of individual quantum vibration-rotation states of the O3* intermediate complex in the relatively deep well of the PES during the collision process, from the bottom of the well to the dissociation, is thus necessary for the modelling of this


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process. The TKTHS PES has been employed to compute many vibrational levels of ozone and its

18

O enriched isotopologues, including near dissociation highly excited states. Its quality has

been comforted by an excellent comparison26,27 of these calculations with recent measurements using ultra-sensitive cavity-ring-down laser spectrometers up to 93 % of the O + O2 dissociation threshold.

The summary of (observation-calculation) deviations given in Table 1 show that this PES possesses the so called “spectroscopic accuracy”, i.e. the errors of calculations are significantly smaller than a typical distance between vibrational band centers that makes possible an unambiguous assignment of bands in observed spectra39,40. Vibrational predictions using the TKTHS PES permit obtaining levels of six

16

O and

18

O containing ozone isotopic species with

average error for the energy of about 1 cm-1 (that correspond to the relative error of about 10-4 including observed levels near the TS) without any empirically adjusted parameters. Figure 3 shows the theoretical thermal rate constant as a function of temperature. This rate is computed from the initial state selected rate constants averaged over a Boltzmann distribution of all the rotational states of the O2 reactants populated at temperatures T < 350 K. This so obtained thermal rate constant is compared with the counterpart experimental data fits. Shaded regions represent experimental uncertainties. The thermal rate constant computed on the DLLJG PES, kD (dashed black line), reproduces the negative temperature dependence observed in the experimental rates24,25. However, in terms of the magnitude, kD is still far below both experimental predictions. For instance, at 300 K, kD is smaller than the experimental rate constant by a factor of about 2. This disagreement is in contrast with the excellent accord, both in temperature dependence and in magnitude, between the rate constant computed in this work on the TKTHS PES26, kT, and the experimental rates. The difference between the two theoretical


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thermal rates comes from the non-similar behavior found in the rotationally state specific cross sections calculated on these PESs.

Figure 3. Thermal rate constant as a function of temperature for the the 18O + 32O2 → 34O2 + 16O reaction. Calculation on the TKTHS PES (this work): black solid line. Calculation on the DLLJG PES23: black dashed line. Experiment 1997a24: blue solid line. Experiment 1997b45: single green point. Experiment 200325: red solid line. Shaded regions correspond to experimental uncertainties.


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For instance, Fig. 4 shows cross sections for the rotational states j=1, 3 or 5 of the O2 reactant. In all cases, the cross section calculated on the PES that provides the spectroscopic accuracy is larger than that on the other PES in a wide collision energy range from the lowest collision energies to 0.1 eV. The same result applies for all initial rotational states of O2 considered in the calculation of the thermal rate constant. 300 18

O+

32

O2(v=0,j) -->

250

Cross section (a02)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 19

34

O2 +

16

O

j=1 (TKTHS) j=1 (DLLJG) j=3 (TKTHS) j=3 (DLLJG) j=5 (TKTHS) j=5 (DLLJG)

200 150 100 50 0 0.001

0.01

0.1

Collision energy (eV) Figure 4. Initial state specific cross sections as a function of collision energy for the 18O + 32

O2(v=0,j) → 34O2 + 16O reaction. Calculation on the TKTHS PES: black solid line for j=1; red

solid line for j=3; blue solid line for j=5. Calculation on the DLLJG PES: dashed lines, same colors.

These findings are directly related to the features of potential functions presented above. The full-dimensional shape of the PES26 that assures the best agreement with accurate


12

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spectroscopic experiments27,39,40 for highly excited states of O3* towards the O + O2 dissociation limit, plays key role for the excellent agreement of kT with observed rate values. We therefore found that a difference in a topographic characteristic of the PES in a medium range zone, namely the full-dimensional shape of the neighborhood of the TS region, results in a dramatic effect in the cross-sections, and consequently even also in the most averaged quantity which is the thermal rate constant. This is in contrast to a generally accepted idea in reaction dynamics28 that the PES need not always be very accurate in its globality, by comparison with spectroscopic studies that require a very high precision at every geometry of the complex. Of course, it is known that at very low collision energy, the long range part of the PES plays a crucial role and must be rigorously described. But the situation in this work is quite different. Collision energies are relatively high and mainly a sole 3D feature in an intermediate region of the PES is responsible for the present dynamical results. Our study therefore suggests that the full PES of some molecular systems, as ozone, should be accurate in all space regions and that the description of the nuclear motion in reactive processes could be sensitive to the quality of the PES at the level of the “spectroscopic accuracy”. This means that not only topological features of the PES play a crucial role for the dynamics (see for instance Ref. 42), but also a very accurate description of individual highly excited ro-vibrational states of ozone26,27 supported by this PES, including those above the dissociation threshold41 is important in this context. The excellent agreement between our theoretical results and the experimental thermal rate constants is an important step within the long history and controversy of O + O2 collisions that started fifty years ago43, showing that a full quantum dynamical method within the BornOppenheimer approximation combined with very accurate ab initio PES calculations confirmed


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by spectroscopic measurements at high-energy range permit a quantitative description of the dynamics of such processes for ranges of temperatures relevant to atmospheric chemistry. Of course, this result should be confirmed by a full quantum dynamical calculation taking explicit couplings between excited electronic states and other non-Born-Oppenheimer effects into account, that is still not possible today from a computational point of view. Concerning the key role played by the

18

O +

16

O16O reaction in the context of heavy

ozone formation problem in the atmosphere, the quantitative agreement between theory and experiment shown in this work, never obtained so far, is very encouraging. This gives a hope that a realistic modeling of the population of high-energy O3 levels resulting from collisions of metastable ozone with third bodies could be obtained as a next step. A progress in this field, together with improved Einstein coefficients for radiative transitions44, will be in turn, important for interpretation of satellite measurement of the stratospheric ozone in the non-LTE conditions. Finally, our findings throw a tag stone in the landscape in view of a full understanding of the MIF puzzle from first principles.


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ASSOCIATED CONTENT Supporting Information. Discussion on the ozone potential energy surface and description of the quantum dynamical method. Figures 1 – 7 (PDF)

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] (P.H.). Notes The authors declare no competing financial interests. ACKNOWLEDGMENT The authors thank Richard Dawes for sending us the O3 potential energy surface (the DLLJG PES). A support from LEFE INSU CNRS (France), French-Russian associated laboratory LIA SAMIA and from Mendeleev funding program of Tomsk State University is acknowledged. Erwan Privat is acknowledged for the plot of Figure 3. TIQM calculations were performed using HPC resources from DSI-CCUB (Université de Bourgogne).

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First-Principles Computed Rate Constant for the O + O2 Isotopic

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