H₂O-catalyzed formation of O₃ in the self-reaction of HO₂: a computational study on the effect of nH₂O (n = 1–3)

Abstract

The effect of nH₂O (n = 1–3) on the association energies of H₂O complexes and on the barriers for the formation of O₃ in the self-reaction of HO₂ reaction has been investigated by ab initio molecular orbital calculations at the modified Gaussian-2 (G2M) level of theory. The results show that H₂O can affect the complex and O₃ formation processes: the more H₂O molecules participating in the reaction, the higher stability of the association complexes and the greater the lowering of the O₃ elimination barrier becomes. For the isomers of the reactions, more hydrogen bonds being formed in the complexes enhances their stabilities. A preliminary kinetic calculation shows that below room temperature, H₂O may enhance the formation of O₃ noticeably.

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1. Introduction

The kinetics of the self-reaction of HO₂ is very relevant to the chemistry of the Earth's troposphere and stratosphere. The reaction has been shown experimentally^1–9 and computationally¹⁰ to be dominated by the formation of H₂O₂ and O₂. In a recent computational study, we have demonstrated that H₂O enhances the formation of all product channels significantly; in particular, the barrier for the formation of O₃via the singlet (HO₂)₂ intermediate, HOOOOH, was found to be lowered by as much as 4–8 kcal mol⁻¹ depending on its transition states, rendering the production of O₃ quite competitive to the formation of H₂O₂.¹¹

In view of the significant role played by HO₂ radical reactions in clouds,^12–14 we have examined quantum-chemically the catalytic effects of multiple H₂O molecules in the self-reaction of HO₂ specifically on the formation of O₃, a key reactive intermediate involved in the chemistry of troposphere. We compare the barriers for the formation of O₃ and the association energies of nH₂O–HO₄H clusters for the following four reactions:

n H₂O + HO₂ + HO₂ → (H₂O)_n–HOOOOH → (H₂O)_n+1 + O₃, n = 0–3

The result of this study briefly summarized in this article reveals for the first time an interesting linear decrease with n in both the transition state energies for the formation of O₃ and the association energies of the clusters from the reactants as well.

2. Computational methods

The geometries of the species involved in the reactions have been fully optimized with the hybrid density functional B3LYP method (Becke's three-parameter nonlocal exchange functional^15–17 with the correlation functional of Lee, Yang, and Parr¹⁸ with the 6-311G (d, p) basis set. Vibrational frequencies employed to characterize stationary points, zero-point energy (ZPE) corrections have also been calculated at this level of theory. Intrinsic reaction coordinate (IRC) calculations¹⁹ have been performed at the same level to confirm the connection of each transition state with designated intermediates.

The total G2M energy with ZPE corrections is calculated as follows:²⁰

E[G2M(CC5)] = E[CCSD(T)/6-311G(d, p)] + ΔE(+3df, 2p) + ΔE(HLC) + ZPE[B3LYP/6-311G(d, p)].

ΔE(+3df, 2p) = E[MP2/6-311 + G(3df, 2p)] − E[MP2/6-311G(d, p)].

ΔE(HLC) = −0.00530 n_β − 0.00019 n_α

where n_α and n_β are the numbers of valence electrons, n_α ≥ n_β. All calculations were carried out with Gaussian 98.²¹

3. Results and discussion

The equilibrium geometries of the selected association complexes and the transition states (TSs) for the formation of O₃ in the reactions of 2 HO₂ + n H₂O (n = 0–2) are drawn in Fig. 1, the corresponding structures for the reaction of 2 HO₂ + 3 H₂O are shown in Fig. 2. The association enthalpy (ΔH₀) for the most stable complex and the related O₃ elimination barrier (ΔE_a) for the reactions are presented in Figs. 3(a) and (b), respectively. Here, we define ΔH₀ = E(complex, n H₂O–2 HO₂) − E(n H₂O + 2 HO₂) and ΔE_a = E(TS) − E(n H₂O + 2 HO₂). The reference energy for the reactions involved is assigned to be the energy of the reactants, n H₂O + 2 HO₂ (n = 0–3), at the infinite separation. The energies cited in the text are obtained at the G2M (CC5) level of theory.

Fig. 1 Optimized geometries of the most stable intermediates and the transition sates for O₃ formation computed at the B3LYP/6-311G (d, p) level for the nH₂O-catalyzed HO₂ self-reaction (n = 1–2).

Fig. 2 Selected complex and transition state geometries optimized at the B3LYP/6-311G (d, p) level for the 3 H₂O-catalyzed HO₂ self-reaction.

Fig. 3 (a) The association enthalpies of the reaction of n H₂O + 2 HO₂ → n H₂O·(HO₂)₂; (b) O₃ formation barrier for the reactions of n H₂O + 2 HO₂ → (H₂O)_n+1 + O₃.

2 HO₂ reaction

As discussed in ref. 10, although there are 11 open-chain and cyclic dimers, only one of them, indicated as LM1 in Fig. 1 can produce O₃via a H₂O elimination transition state (TS1) with a barrier above the reactants by 5.2 kcal mol⁻¹. LM1 lies below the reactants by 19.1 kcal mol⁻¹.

2 HO₂ + H₂O reaction

In the reaction of two HO₂s with one H₂O,¹¹ 15 isomers (including optical isomers) were identified to lie below the reactants by 23.5–25.8 kcal mol⁻¹ at the G2M level. Among these isomers, the most stable one is a seven-member-ring minimum with two hydrogen bonds, in which the water molecule acts both as proton donor and acceptor (see Fig. 1). This phenomenon is similar to that found in water clusters.^22,23 The structures of the most stable intermediate and corresponding transition state producing O₃ are shown in Fig. 1 as LM2 and TS2, respectively. The relative energies of LM2 and TS2 are −25.8 and −3.1 kcal mol⁻¹, respectively. Comparing with the reaction without H₂O, one can see that the participation of one water molecule can enhance the stability of the association complex by 6.7 kcal mol⁻¹ and lower the O₃ formation barrier by 8.3 kcal mol⁻¹, respectively.

2 HO₂ + 2 H₂O reaction

In this reaction, only the complex with two water molecules acting as proton donors and acceptors to their neighbors is presented; it is expected to have the lowest energy.^22,23 This expectation will be discussed in the following 3 H₂O participating reaction also. In the nine-member-ring complex, LM3, three hydrogen bonds are formed as shown in Fig. 1. The first one is the hydrogen bond between the two H₂Os, 1.780 Å, which is shorter than that in the H₂O dimer, 1.928 Å, at the same level;¹¹ the second hydrogen bond is formed by the terminal H of the HOOOOH moiety in LM3 with the O atom of one of the H₂O molecules, the bond length 1.681 Å is shorter than the similar hydrogen bond, 1.790 Å in LM2; the third one is formed by the H atom in the other H₂O molecule with one of the O atom in HO₄H (see Fig. 1), the value of this bond, 1.904 Å, is also shorter than the similar one, 2.117 Å in LM2; the structural parameters in the HOOOOH moiety of LM3 are similar to those in the isolated HO₄H molecule (LM1). This complex lies below the reactants by 31.4 kcal mol⁻¹. The transition state (TS3) for O₃ formation from LM3 is predicted to lie below the reactants by 5.8 kcal mol⁻¹, which is 11 and 2.7 kcal mol⁻¹ lower than those values without H₂O and with one H₂O participating reactions, respectively.

2 HO₂ + 3 H₂O reaction

The rotation of HO and HO₂ groups in HOOOOH¹⁰ as well as the different arrangement of the three H₂Os may result in many isomers. Here we present only four typical isomers for this reaction, LM4 (a)–LM4 (d), as shown in Fig. 2.

LM4 (a). In this complex, three H₂Os and one of the OH group in HO₄H are proton donor–acceptors with the three H₂Os in the same ring; in addition, the other OH group in the HO₄H moiety acts as a proton donor in the forming hydrogen bond. There are five hydrogen bonds in this complex. The predicted association energy of LM4 (a) is 41.8 kcal mol⁻¹ below the reactants.

LM4 (b). There are also three H₂Os and one of the OH group in HO₄H acting as proton donors and acceptors; similarly, both H atoms in the HO₂ group participate in forming hydrogen bonds; however, only two H₂Os exist in the same ring, the third one is separated by the HO₄H group. Five hydrogen bonds are formed in this complex. The association energy for this complex is 39.9 kcal mol⁻¹.

LM4 (c). In this complex, three H₂Os and one of the OH group in the HO₄H moiety lie in the same ring and form hydrogen bonds among one another, but the other OH group in the HO₄H part is not involved in hydrogen bond formation. Four hydrogen bonds are formed in this isomer. The association energy is slightly smaller, 39.3 kcal mol⁻¹.

LM4 (d). In this isomer, two of the H₂Os lie in the same nine-member-ring and act as both proton donors and acceptors, but one of the H₂O acts only as a “spectator”, there are four hydrogen bonds in the complex. The combination of the above factors leads to a reduction of the association energy by 4.5 kcal mol⁻¹ comparing with that of LM4 (a).

Comparing the structures and the association energies of complexes LM4 (a) to LM4 (d), we can find the trend that the more hydrogen bonds that are formed with more H₂O molecules lying in the same ring, then the more stable the complex will be. Therefore, the expectation of LM4 (a) being the most stable complex in the reaction 3 H₂O + 2 HO₂ is reasonable.

For the O₃ formation, we only investigate the decomposition of the most stable LM4 (a). TS4 corresponds to the dissociation of LM4 (a), lying 15.4 kcal mol⁻¹ below the reactants. Comparing with the reaction without water, i.e. the 2HO₂ reaction, participation of three H₂O molecules in the reaction can reduce the O₃ elimination barrier by more than 20 kcal mol⁻¹.

It is readily seen from Figs. 3(a) and (b) that the more H₂O molecules are participating in the reaction, the greater the stability of the association complex and the lowering of the O₃ elimination barrier become. Approximately (within ±2.0 kcal mol⁻¹), we can express the association enthalpy for the reaction of 2 HO₂ + n H₂O (n = 0–3) by: ΔH₀ = −7.4 n − 19.0 kcal mol⁻¹, and the barrier for the O₃ elimination by ΔE_a = − 6.4 n + 5.0 kcal mol⁻¹. Whether these equations are valid for more than three H₂O molecules for the stabilization the association complex and the lowering of the O₃ elimination barrier needs to be explored further experimentally or theoretically.

Kinetically, H₂O, aside from the physical quenching of the excited H₂O₄, can enhance the formation of O₃ by the following four mechanisms, taking the one H₂O case, for example:

1. Complexation with HO₂ (the chaperon effect):

H₂O + HO₂ ⇌ H₂O–HO₂

H₂O–HO₂ + HO₂ → H₂O–H₂O₄* → TS1 → O₃ + 2 H₂O

2. Reaction with H₂O₄*:

HO₂ + HO₂ → H₂O₄*

H₂O + H₂O₄* → TS1 → O₃ + 2 H₂O

3. Direct termolecular reaction:

H₂O + 2 HO₂ → H₂O–H₂O₄* → TS1 → O₃ + 2 H₂O

4. Reaction with the quenched H₂O₄:

H₂O + H₂O₄ → H₂O–H₂O₄ → TS1 → O₃ + 2 H₂O.

Among the four possibilities, mechanism (4) is not expected to significantly enhance the O₃ formation because the barriers for the decomposition of the stabilized n H₂O–H₂O₄ complexes, although greatly lowered from the reactants, remain approximately the same. In solution, these complexes may undergo decomposition by quantum-mechanical tunneling to form exothermically O₃ + (n + 1) H₂O, however. Mechanisms (1)–(3) are expected to enhance O₃ formation by chemical activation with the lowered barriers relative to the reactants. A quantitative prediction of the rate constants for these three cases is computationally complex, because of the great difficulty for the variational transition state searches, particularly for case (3). Nevertheless, we have attempted to estimate the extent of enhancement by H₂O based on case (1), assuming the establishment of the equilibrium, H₂O + HO₂ ⇌ H₂O–HO₂, with K₁ = 1.38 × 10⁻³⁰T^1.52 exp (3728/T) cm³ molecule⁻¹ using the structural parameters and energetics of all species predicted in refs. 10 and 11. The result of our preliminary calculation employing two predicted association potential energy curves (by B3LYP/6-311+G(d, p)) for the HO₂ + HO₂ and HO₂ + H₂O–HO₂ processes shows that the effect depends on the temperature and the pressure of H₂O. For example, at 200 K with 100 Torr H₂O, the rate is enhanced by 2.5 times, and with 1 atm H₂O the rate is predicted to increase by more than 1 order of magnitude, comparing with that without water. At room temperature, however, the rate is not enhanced by H₂O below 1 atm. Intuitively, mechanisms (2) and (3) may lead to larger effects. We hope to examine these three cases in a greater detail in the near future.

4. Conclusion

The effect of nH₂O (with n = 1–3) on the association energy and the barrier for O₃ formation in the self-reaction of HO₂ reaction has been investigated at the G2M(CC5) level. The results indicate that H₂O molecules can enhance the stability of the association complex and reduce the O₃ elimination barrier of the three reactions. Comparing with the self-reaction reaction of HO₂ without H₂O, the association energy and the O₃ formation barrier are increased and decreased, respectively, by 22.7 and 20.5 kcal mol⁻¹, when three H₂O molecules participate in the reaction catalytically. A preliminary kinetic calculation based on one of the four possible mechanisms shows that H₂O can have an enhancement effect on the O₃ formation in the self-reaction of HO₂, depending on the temperature and the pressure of H₂O.

Acknowledgements

This work is sponsored by the Office of Naval Research under contract no. N00014-02-1-0133, Dr. J. Goldwasser program manager.

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