Effects of a Single Water Molecule on the OH + H2O2 Reaction - The

Article pubs.acs.org/JPCA

Effects of a Single Water Molecule on the OH + H2O2 Reaction Robert J. Buszek,† Miquel Torrent-Sucarrat,‡ Josep M. Anglada,*,‡ and Joseph S. Francisco*,† †

Department of Chemistry, Purdue University, West Lafayette, Indiana 47907-2084, United States Departamento de Quimica Biologica I Modelitzacio Molecular, IQAC-CSIC, Institut de Quimica Avançada de Catalunya, E-08034 Barcelona, Spain

‡

S Supporting Information *

ABSTRACT: The effect of a single water molecule on the reaction between H2O2 and HO has been investigated by employing MP2 and CCSD(T) theoretical approaches in connection with the aug-cc-PVDZ, aug-cc-PVTZ, and aug-cc-PVQZ basis sets and extrapolation to an ∞ basis set. The reaction without water has two elementary reaction paths that differ from each other in the orientation of the hydrogen atom of the hydroxyl radical moiety. Our computed rate constant, at 298 K, is 1.56 × 10−12 cm3 molecule−1 s−1, in excellent agreement with the suggested value by the NASA/JPL evaluation. The influence of water vapor has been investigated by considering either that H2O2 first forms a complex with water that reacts with hydroxyl radical or that H2O2 reacts with a previously formed H2O·OH complex. With the addition of water, the reaction mechanism becomes much more complex, yielding four different reaction paths. Two pathways do not undergo the oxidation reaction but an exchange reaction where there is an interchange between H2O2·H2O and H2O·OH complexes. The other two pathways oxidize H2O2, with a computed total rate constant of 4.09 × 10−12 cm3 molecule−1 s−1 at 298 K, 2.6 times the value of the rate constant of the unassisted reaction. However, the true effect of water vapor requires taking into account the concentration of the prereactive bimolecular complex, namely, H2O2·H2O. With this consideration, water can actually slow down the oxidation of H2O2 by OH between 1840 and 20.5 times in the 240−425 K temperature range. This is an example that demonstrates how water could be a catalyst in an atmospheric reaction in the laboratory but is slow under atmospheric conditions.

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INTRODUCTION HOx is an important species as it is a vital intermediate in combustion and is the primary oxidizer in the atmosphere, involved in the formation of carbon dioxide and HOCO1−3 as well as the catalytic destruction of ozone.4−6 Hydrogen peroxide, being a temporary reservoir, regenerates HOx via photolysis and chemical reaction with OH radical (1). H2O2 + OH → HO2 + H2O

variational transition state theory including small curvature tunneling.15 The oxidation of hydrogen peroxide via the hydroxyl radical is also seen in aqueous solutions. In advanced oxidation processes17,18 used in the treatment of wastewater H2O2 is photolyzed in solution generating OH radicals to oxidize pollutants. Reaction 1 is an important secondary reaction consuming OH radical. This reaction is also seen during the radiolysis of water,19−21 where hydrogen peroxide is formed from the recombination of two OH radicals, and reaction 1 hinders the buildup of OH radicals. The only experimental study on this reaction in solution, done by Christensen et al.,22 reports a rate constant of 4.48 × 10−14 cm3 molecule−1 s−1 at pH 7.8 in the temperature range of 287−433 K, which is

(1)

As a result, the gas phase oxidation of hydrogen peroxide via OH radical (1) has been well studied7−15 over a large range of temperatures. The rate constant exhibits a negative temperature dependence below room temperature7,8 and a positive temperature dependence at higher temperatures, up to 1200 K.7−12 It is currently suggested by the NASA/JPL evaluation16 that the rate constant between 200 and 300 K is 1.8 × 10−12 cm3 molecule−1 s−1, independent of temperature. Theoretical studies have shown this reaction to have two pathways with barriers of 1.5 and 0.9 kcal mol−1, with a total rate constant of 9.8 × 10−13 cm3 molecule−1 s−1 at 298 K using canonical © 2012 American Chemical Society

Special Issue: A. R. Ravishankara Festschrift Received: August 13, 2011 Revised: March 14, 2012 Published: March 29, 2012 5821

dx.doi.org/10.1021/jp2077825 | J. Phys. Chem. A 2012, 116, 5821−5829

The Journal of Physical Chemistry A

Article

Figure 1. Potential energy surface of the H2O2 + OH reaction along with relevant geometries. All energies in kcal mol−1, bond distances in angstroms and bond angles in degrees.

become inaccurate.41 Due to the similar hydrogen bonding characteristics of the HO2·H2O complex, the OH·H2O complex has also been studied both theoretically42−50 and experimentally.48,49,51−55 The OH·H2O complex has been identified in the gas phase utilizing both microwave49,53,55 and infrared spectroscopic50 methods. This has led to the recent studies investigating water effects on hydrogen abstraction reactions with OH radicals, including formic acid,56,57 nitric acid,58 acetaldehyde,59,60 acetone,61 HOCl,62 methane,63 glyoxal,64,65 DMS,66 and propionaldehyde.67 This study uses ab inito methods to determine the effects water has on the potential energy surface and kinetics of the oxidation of hydrogen peroxide via OH radical (4).

noticeably slower than the gas phase reaction. There have also been two theoretical studies on this system,23,24 both applying solvation models to the already well-known gas phase potential energy surface. In the more recent study by Ginovska et al.24 a charge-dependent continuum is used to model the solvation. This study shows that the reaction is slower in solution than in the gas phase with a barrier of 2.5 kcal mol−1 and a rate constant of 5.98 × 10−15 cm3 molecule−1 s−1, in agreement with previous experiments. Surprisingly, there have been no studies of the effects that water will have on the potential energy surface of this reaction. Water has been previously shown to have a catalytic effect on several radical−radical reactions, most notably the HO2 selfreaction,25−29 in which water enhances the rate by 74 times.25 The reason that water is able to catalyze this reaction is due to the ability for water to form stable hydrogen bonded complexes with the HO2 radical. It is the reaction of this complex with a subsequent HO2 molecule (3) that leads to the catalytic effects seen with the introduction of water in a mechanism first proposed by Hamilton and Lii.28 HO2 + H2O ⇌ HO2 ·H2O

(2)

HO2 ·HO2 + HO2 → H2O2 + O2 + H2O

(3)

■

H2O2 + OH( +H2O) → HO2 + H2O( +H2O)

(4)

METHODS The geometries and frequencies of all reactants, transition states, and products are optimized by using second-order Møller−Plesset perturbation theory (MP2)68 using augmented, correlation-consistent polarized double-ζ basis sets (aug-ccpVDZ).69,70 Intrinsic reaction coordinate (IRC) calculations are performed to ensure that all pre- and postreactive complexes belong to the transition states.71,72 To obtain more reliable relative energies, single point energies are calculated using coupled cluster with single, double, and perturbative triple excitations (CCSD(T))73−75 using augmented, correlation-consistent polarized double, triple, and quadruple-ζ basis sets (aug-cc-pV(D,T,Q)Z).69,70 To further converge the energy, we have calculated the CCSD(T) energies at the complete basis set limit (CBS) using the triple- and quadzeta energies and employing the extrapolation scheme by Helgaker et al.76 The zero point energies (ZPE) and the enthalpic and entropic corrections at 298 K were calculated at the MP2/aug-cc-pVDZ level of theory. Because of the large

This is one of the reasons that the water catalysis is shown to have a negative temperature dependence, as the enhancement is directly related to the amount of HO2·H2O complex formed.25 The HO2·H2O complex has been well studied30−40 and shown to form two hydrogen bonds resulting in a binding energy of 7.4 ± 1.0 kcal mol−1 38 and an equilibrium constant of 5.2 ± 3.2 × 10−19 cm3 molecule−1.39 This has led to estimations that atmospheric HO2·H2O exists in significant concentrations36 and that as much as 30% of all HO2 in the atmosphere can be complexed with water.32 In fact, it has been shown that if this complex is ignored that certain atmospheric models can 5822



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Table 1. Relative Energies, Energies plus ZPE, Enthalpies, and Free Energies (kcal•mol−1) Calculated for the H2O2 + OH and H2O2·H2O + OH Reactionsa ΔE H2O2 + OH

Δ(E +ZPE)

0.0

[H2O2·OH] (CR1) [H2O2·OH]‡ (TS1) [HO2·H2O] (CP1)

−5.9 2.2 −41.2

[H2O2·OH] (CR1) [H2O2·OH]‡ (TS2) [HO2·H2O] (CP2) products (OOH + OH) H2O2·H2O + OH H2O2 + H2O·OH

−5.9 2.1 −35.1 −31.9 0.0 1.5

[H2O2·H2O·OH] (CR1w) [H2O2·H2O·OH]‡ (TS1w) [HO2·H2O·H2O] (CP1w)

−6.8 1.9 −45.1

[H2O2·H2O·OH] (CR2w) [H2O2·H2O·OH]‡ (TS2w) [HO2·H2O·H2O] (CP1w)

−6.7 0.6 −45.1

[H2O2·H2O·OH] (CR2w) [H2O2·H2O·OH]‡ (TS3w) [H2O2·H2O·OH] (CR3w) [H2O2·H2O·OH]‡ (TS4w) [HO2·H2O·H2O] (CP1w)

−6.7 −5.3 −8.7 1.2 −45.1

[H2O2·H2O·OH] (CR4w) [H2O2·H2O·OH]‡ (TS5w) [H2O2·H2O·OH] (CR5w) [H2O2·H2O·OH]‡ (TS6w) [H2O2·H2O·OH] (CR6w) [H2O2·H2O·OH]‡ (TS7w) [HO2·H2O·H2O] (CP1w) products (OOH + 2H2O)

−7.8 −7.8 −8.2 −8.3 −8.6 0.2 −45.1 −24.6

0.0 Pathway 1 −3.9 1.2 −38.0 Pathway 2 −3.9 1.2 −32.8 −31.4 0.0 1.2 Pathway 1 −4.9 0.6 −41.4 Pathway 2 −4.6 0.2 −41.4 Pathway 3 −4.6 −3.9 −6.6 3.0 −41.4 Pathway 4 −5.9 −6.3 −6.3 −6.7 −6.5 0.0 −41.4 −26.4

ΔH(298 K)

ΔG(298 K)

0.0

0.0

−4.6 0.1 −38.7

2.7 8.4 −31.3

−4.6 0.1 −32.9 −31.3 0.0 1.2

2.7 8.4 −27.3 −32.2 0.0 −0.5

−5.4 −0.1 −42.5

2.5 8.0 −33.1

−5.3 −1.0 −42.5

3.3 8.8 −33.1

−5.3 −4.7 −7.3 1.7 −42.5

3.3 3.8 1.1 11.6 −33.1

−6.5 −7.1 −6.8 −7.6 −7.2 −1.3 −42.5 −25.7

1.6 1.8 1.4 1.5 1.3 8.7 −33.1 −34.4

a Energies computed at CCSD(T)/CBS//MP2/aug-cc-pVDZ level of theory. The ZPE, S, enthalpic, and entropic corrections correspond to calculations at MP2/aug-cc-pVDZ level of theory.

conformers differing in the position of the free hydrogen of the hydrogen peroxide. At the infinite basis set limit these conformers are degenerate with an energy barrier of 1.2 kcal mol−1 (Table 1). This is in agreement with previous studies15 reporting energy barriers of 0.9 and 1.5 kcal mol−1 for TS1 and TS2, respectively. Going through TS1 the reaction continues on to form a postreactive complex (CP1) in which the newly formed water molecule forms a five-membered ringlike structure with the hydroperoxy radical in which the hydrogen from the hydroperoxy radical forms a hydrogen bond with water, and a single hydrogen from the water forms a weak hydrogen bond with the naked oxygen atom of the hydroperoxy radical, this complex lies 38.0 kcal mol−1 below the energy of the reactants. A different postreactive complex is formed after TS2 (CP2), in which there is only a single hydrogen bond between one of the hydrogens of the water molecule and the naked oxygen of the hydroperoxy radical, and lies 32.8 kcal mol−1 below the energy of the reactants. At 298 K the reaction enthalpy is computed to be 31.3 kcal mol−1, in excellent agreement with the experimental estimate of 31.333 ± 0.078 kcal mol−1.79,80

basis sets employed, along with an extrapolation to the CBS basis set limit, the basis set superposition error (BSSE) correction is not necessary and, therefore, not taken into account. All of the geometries, frequencies and energies were calculated using the Gaussian03 suite of programs.77

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RESULTS AND DISCUSSION a. H2O2 + OH. To be able to determine the water effect on the H2O2 + OH reaction, the reaction without water is also studied. This reaction has already been investigated in the literature,15,78 and our results agree well with the reported values. The reaction first forms a prereactive complex (CR1), in which the hydroxyl radical forms a five-membered ringlike structure with the hydrogen peroxide via two hydrogen bonds, as seen in Figure 1. There is a hydrogen bond formed between the hydrogen of the hydroxyl radical and the oxygen of the hydrogen peroxide along with another between the hydrogen on the peroxide and the oxygen of the hydroxyl radical. As seen in Table 1, this complex has a binding energy of 3.9 kcal mol−1 at the infinite basis set limit. The reaction can proceed through one of two possible transition states (TS1, TS2) that are 5823



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Figure 2. Relevant structures of the H2O2·H2O + OH reaction. All bond distances in angstroms and bond angles in degrees.

Table 2. Equilibrium Constants of Relevant Pre-reactive Complexesa,b T (K) 240 250 278 288 298 308 325 375 425

[H2O·OH] 1.82 1.31 5.96 4.68 3.75 3.05 2.21 1.05 6.08

× × × × × × × × ×

10−20 10−20 10−21 10−21 10−21 10−21 10−21 10−21 10−22

[H2O2·OH] 4.60 3.25 1.42 1.10 8.69 6.99 4.99 2.27 1.28

× × × × × × × × ×

10−21 10−21 10−21 10−21 10−22 10−22 10−22 10−22 10−22

[H2O2·H2O]c 2.11 1.38 5.06 3.72 2.80 2.15 1.43 5.52 2.77

× × × × × × × × ×

[H2O2·H2O·OH] (CR1w)

10−20 10−20 10−21 10−21 10−21 10−21 10−21 10−22 10−22

8.92 5.87 2.16 1.59 1.19 9.15 6.07 2.30 1.13

× × × × × × × × ×

10−21 10−21 10−21 10−21 10−21 10−22 10−22 10−22 10−22

[H2O2·H2O·OH] (CR2w) 2.22 1.48 5.66 4.21 3.20 2.48 1.67 6.54 3.28

× × × × × × × × ×

10−21 10−21 10−22 10−22 10−22 10−22 10−22 10−23 10−23

[H2O2·H2O·OH] (CR4w) 5.98 3.61 1.08 7.44 5.27 3.82 2.32 7.13 2.97

× × × × × × × × ×

10−20 10−20 10−20 10−21 10−21 10−21 10−21 10−22 10−22

Equilibrium constants in units of cm3 molecule−1. bAll equilibrium constants were calculated by using energies computed at CCSD(T)/CBS level and partition functions obtained at MP2 level. cEquilibrium constant for both the cis and trans prereactive complexes. a

b. H2O2 + OH (+H2O). The addition of water makes the oxidation of H2O2 much more complex leading to the three following bimolecular reactions: H2O2 ·H2O + OH → HO2 + 2H2O

(5)

H2O2 + H2O·OH → HO2 + 2H2O

(6)

H2O2 ·OH + H2O → HO2 + 2H2O

(7)

computing their stability and corresponding equilibrium constants. The water−hydrogen peroxide complex forms a five-membered ringlike structure via the formation of two hydrogen bonds as seen in Figure 2 with a computed binding energy of 4.9 kcal mol−1. The binding energies of the H2O·OH and H2O2·OH complexes are 3.7 and 4.0 kcal mol−1, respectively. The equilibrium constants of these complexes at 298 K are 2.80 × 10−21, 3.75 × 10−21, and 8.69 × 10−22 cm3 molecule−1, respectively (Table 2). Taking into account typical tropospheric concentrations of 7.64 × 1017 molecules cm−3 of H2O, 106 molecules cm−3 of OH, and 109 molecules cm−3 of

The significance of these reactions depends on the extent to which the respective bimolecular complexes, H2O2·H2O, H2O·OH, and H2O2·OH exist, which can be determined by 5824



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H2O2,81 it is estimated that the atmospheric concentration of the H2O2·H2O complex to be 2.14 × 107 molecules cm−3, the concentration of the H2O·OH complex is estimated to be 2.87 × 104 molecules cm−3, which is in good agreement with previous data reported in the literature.82,83 Whereas the concentration of H2O2·OH is negligible (8.69 × 10−5 molecules cm−3), and therefore reaction 5 will not be considered, and the H2O2·H2O + OH and H2O·OH + H2O2 reactions will be the focus of the remainder of this article. i. H2O2·H2O + OH. Four pathways have been found for the OH radical attack on the H2O2·H2O complex (reaction 3) yielding the formation of hydroperoxy radical and water, and these pathways are schematized in Figure 3 and related in Table 1.

hydroperoxy radical with the hydrogen of the newly formed water molecule. From the formation of CR2w, there is an additional route (pathway 3), which involves the rearrangement of this prereactive complex into another three bodied complex (CR3w). This is done via TS3w in which the hydrogen bond between the oxygen of the water molecule and the hydrogen of the hydrogen peroxide is broken. The oxygen of the OH radical forms a hydrogen bond with the hydrogen in H2O2 that was formerly bound to the water. This rearrangement is barrierless with respect to the reactants and forms a single sevenmembered ringlike structure (CR3w), which has a larger binding energy, 6.6 kcal mol−1, than CR2w. From this structure the OH radical can abstract the hydrogen (via TS4w) and proceeds to the same postreactive complex as pathway 2, CP1w. The computed energy barrier for this elementary reaction is 9.6 kcal mol−1. The last pathway (pathway 4) is the most complex, as there are two rearrangements that occur before the hydrogen abstraction. The pathway begins with the OH radical attacking the free hydrogen of the water moiety of the H2O2·H2O complex, in which CR4w is formed, a single six-membered ringlike structure between the water, OH radical, and a single OH moiety of the hydrogen peroxide. This is very similar to CR2w, except the OH radical is interacting with the free hydrogen of the water instead of the hydrogen peroxide. There is a rearrangement via TS5w in which the hydrogen bond between the hydrogen of the hydroxyl radical is shifted to the oxygen of the hydrogen peroxide with the free hydrogen another complex with a single seven-membered ring (CR5w). This transition state is barrierless with respect to the reactants at −6.3 kcal mol−1, and the proceeding complex lies 6.3 kcal mol−1 below reactants. From this complex, another barrierless rearrangement that occurs via TS6w, to form a complex, CR6w, which is composed of a seven-membered hydrogen bound ringlike structure, in which the hydrogen of the OH radical is bound to the oxygen of the H2O2, and the oxygen of the radical is hydrogen bound to one of the hydrogens of the water molecule lying 6.5 kcal mol−1 below reactants. The reaction goes on through TS7w, where the free hydrogen of the H2O2 is abstracted via the OH radical and this transition state has an energy barrier of 6.5 kcal mol−1; that is to say, the transition state has the same energy than the H2O2·H2O + HO reactants. Similar to pathway 2, the reaction proceeds to form CP1w before the release of the HO2 + 2 H2O products. An analysis of the potential energy surface displayed in Figure 3 shows that beyond the formation of hydroperoxy radical and water, the reaction of H2O2·H2O and HO can also lead to the formation of H2O2 and H2O·HO products but this process will be discussed in more detail in the next section. ii. H2O·OH + H2O2. Figure 3 shows that the oxidation of H2O2 by the H2O·OH complex (reaction 5) can occur by the formation of the CR2w complex and the reaction goes on through reaction pathways 2 and 3, as discussed in the previous section. In addition, the CR3w complex can also be formed directly by the reactants. This complex is also an intermediate of pathway 3 and the reaction can lead to the formation of the HO2 + 2 H2O products through TS4w, as indicated in the previous section. The key difference here is that the reactants are 1.2 kcal mol−1 higher in energy than in reaction 4 and, consequently, the binding energy of the complexes and the reaction energy should be increased and energy barriers decreased by this value.

Figure 3. Potential energy surface of the H2O2 + OH (+ H2O) reaction. All energies in kcal mol−1.

The first pathway (pathway1) has the OH radical attacking from bare side of the hydrogen peroxide forming complex CR1w. This complex, as seen in Figure 2, has two fivemembered ringlike structures, one on each side of the hydrogen peroxide with a binding energy of 4.9 kcal mol−1 with respect to the reactants. The reaction proceeds through TS1w in which the OH radical abstracts the hydrogen from hydrogen peroxide with an energy barrier of 5.5 kcal mol−1 to form a postreactive complex, CP1w. This complex is composed of a single sevenmembered ring via the breaking of the hydrogen bond between the hydrogen of the original water molecule and the oxygen of the H2O2 and lies 41.4 kcal mol−1 below the energy of the reactants. The mechanism is extremely similar to the unassisted reaction, with the key difference being that the water molecule is hydrogen bound to the bare side of the hydrogen peroxide. The following three pathways all have water actively participating in the transition state. The first two of these, pathways 2 and 3, have the hydroxyl radical attacking the free hydrogen of the hydrogen peroxide moiety of the H2O2·H2O complex. The hydroxyl radical forms a three-membered complex, CR2w, in which the bonding between water and hydrogen peroxide is undisturbed, but a new six-membered ringlike structure is formed through the hydrogen of the OH radical hydrogen bonding with the oxygen of the water, and the free hydrogen of the H2O2 bonding with the oxygen of the OH radical, and has a binding energy of 4.6 kcal mol−1. In pathway 2 there is a simple hydrogen abstraction (TS2w), with an energy barrier of 4.8 kcal mol−1. This goes on to form the postreactive complex, CP1w, lying 41.4 kcal mol−1 below the energy of the reactants. This is followed by the formation of a new hydrogen bond between the free oxygen of the 5825



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state partition function, V(s*) is the potential energy, and κ is the tunneling parameter, which has been computed with the small curvature approach. The overall rate constant is computed according eq 13. For the calculations of the

These reactants share the same three bodied complexes as seen in the H2O2·H2O + OH reaction. This allows for another set of reactions aside from those leading to the oxidation products, HO2 + 2H2O, that is, the possible interchange reaction between bimolecular complexes. This is seen after the formation of CR2w in which the complex can simply dissociate to H2O2·H2O + OH as well as after formation of CR3w, going through TS3w and CR2w can also produce H2O2·H2O + OH. By the same way, starting with the H2O2·H2O + OH reactants, the H2O·OH + H2O2 can be produced by dissociation of both CR2w and CR3w complexes.

k tot =

equilibrium constants partition functions computed at the MP2/aug-cc-pVDZ level of theory and energies obtained at CCSD(T)/CBS level of theory, including ZPE are used. The rate constants using conventional transition state theory are computed with energies at CCSD(T)/CBS and CCSD(T)/ aug-cc-pVTZ levels of theory whereas the rate constants at variational transition state theory are calculated with energies obtained at CCSD(T)/aug-cc-pVTZ level of theory. In all cases, the partition functions computed at the MP2/aug-ccpVDZ level of theory were employed. The rate constant values computed at different levels have been collected in Table S4 of the Supporting Information and show that rate constants computed with conventional transition state theory using both levels of theory differ roughly by a factor of 1.2 and rate constants computed at variational transition state theory level are roughly 1.6 times smaller. More interesting is the fact that the tunneling corrections computed at zero curvature approach are overestimated by 10−30 times with respect to tunneling corrections computed with the small curvature tunneling approach. These results point out the need of using VTST calculations with small curvature tunneling to predict accurate rate constants for these reactions and the results obtained at this level will be considered hereafter. In addition, for the reaction without water we have also computed the rate constant with the hindered rotor approximation. The results are in Table S5 of the Supporting Information and are very similar to those obtained with variational transition state theory. All rate constants are computed using the polyrate program.87 The rate constants for the reaction between H2O2 and OH are displayed in Table 3 and are calculated for both reaction

KINETICS The results discussed in the previous section show that each elementary reaction begins with the formation of a barrierless reactant complex, which is formed before the hydrogen abstraction by hydroxyl radical. Thus, every process I is a complex reaction as described by eq 8, where the reactant complex is in equilibrium with the reactants, and that the rate constant for each process is given by eq 9. k uni

reactant 1 + reactant 2 HooooI reactant complex ⎯⎯⎯⎯→ products k−1 (8)

kI =

k1 k uni = K eqk uni k−1

(9)

This kinetic model is correct at the high pressure limit, where the prereactive complex can be stabilized by collisions with other atmospherics species. A more precise assessment of this assumption would include the evaluation of the intramolecular vibrational energy redistribution (IVR), which is beyond the scope of this work. The equilibrium constant Keq in the first step is given by eq 10. The rate constant kuni is computed, in a first step, following the conventional transition state theory according eq 11, K eq =

Q complex Q reactant 1Q reactant 2

e−(EC − ER )/ RT

k T QTS k uni = κ B e−(ETS − EC)/ RT h Q complex

Table 3. Bimolecular Rate Constants (cm3 molecule−1 s−1) for Reaction 1

(10)

T (K)

(11)

240 250 278 288 298 308 325 375 425

where the various Q denote the partition functions of the reactants, the prereactive complex, and the transition state; ER, EC, and ETS are the total energies of the reactants, hydrogen bond complex, and transition state, respectively, kb and h are the Boltzmann and Planck constants, respectively, and κ is the tunneling parameter that has been computed with the zero curvature approach. In this case, the unsymmetrical Eckart potential energy barrier has been used to approximate the potential energy curve. For the elementary processes playing a key role in the kinetics of the reaction, the rate constants are also computed employing variational transition state theory (VTST) according to eq 12.84−86 k T Q GT(s*) −V (s )/ kBT * kCVT = κ B e h Q complex

(13)

I

■

k1

∑ KeqIk uniI

a

kPathway 1 9.98 9.75 9.57 9.61 9.73 9.86 1.02 1.12 1.26

× × × × × × × × ×

−13

10 10−13 10−13 10−13 10−13 10−13 10−12 10−12 10−12

kv1a

kPathway 2 5.11 5.17 5.51 5.68 5.86 6.06 6.44 7.79 9.41

× × × × × × × × ×

−13

10 10−13 10−13 10−13 10−13 10−13 10−13 10−13 10−13

1.51 1.49 1.51 1.53 1.56 1.59 1.66 1.90 2.20

× × × × × × × × ×

10−12 10−12 10−12 10−12 10−12 10−12 10−12 10−12 10−12

kv1= = kPathway 1 + kPathway 2.

pathways. The total rate constant for this reaction is 1.56 × 10−12 cm3 molecule−1 s−1 at 298 K in very good agreement with 1.8 × 10−12 cm3 molecule−1 s−1 suggested by NASA/JPL.16 Moreover, our calculations predict the reaction to be independent of T in the 240−308 K range of temperatures considered, which is in agreement with the NASA/JPL suggestion, but at higher temperatures the rate constant increases up to 1.41 times at 425 K.

(12)

where s* is the free energy maximum along the reaction path at temperature T, Qcomplex is the partition function of the prereactive complex, QGT(s*) is the generalized transition 5826



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Table 4. Bimolecular Rate Constants (cm3 molecule−1 s−1) for All Reaction All Elementary Pathways of Reaction 3, Atmospheric Water Concentration (molecules cm−3), Effective Rate Constant kv2 ′ (cm3 molecule−1 s−1), and Ratio between the Rate Constant of the Bare Reaction (kv1) and kv2 ′ T (K)

kPathway 1

240 250 278 288 298 308 325 375 425

4.19 3.99 3.68 3.63 3.57 3.55 3.53 3.66 3.96

× × × × × × × × ×

10−12 10−12 10−12 10−12 10−12 10−12 10−12 10−12 10−12

kPathway 2 4.85 3.54 1.85 1.56 1.35 1.20 1.01 7.66 6.85

× × × × × × × × ×

10−12 10−12 10−12 10−12 10−12 10−12 10−12 10−13 10−13

kv2a

kPathway 4 5.14 5.26 5.29 5.24 5.20 5.17 5.12 5.31 5.64

× × × × × × × × ×

10−13 10−13 10−13 10−13 10−13 10−13 10−13 10−13 10−13

4.70 4.52 4.21 4.15 4.09 4.07 4.04 4.19 4.52

× × × × × × × × ×

10−12 10−12 10−12 10−12 10−12 10−12 10−12 10−12 10−12

kv2 ′ c

[H2O]b 8.29 2.21 2.25 4.25 7.64 1.31 3.04 2.12 8.56

× × × × × × × × ×

1015 1016 1017 1017 1017 1018 1018 1019 1019

8.23 1.38 4.79 6.57 8.75 1.15 1.76 4.90 1.07

× × × × × × × × ×

10−16 10−15 10−15 10−15 10−15 10−14 10−14 10−14 10−13

kv1/kv2 ′ d 1.84 1.08 3.15 2.33 1.78 1.39 9.45 3.87 2.05

× × × × × × × × ×

103 103 102 102 102 102 101 101 101

a kv2 = kPathway 1 + kPathway 4 (see text). bWater concentration at 100% of relative humidity.90,91 ckv2 ′ = kv2Keq2 [H2O] see text. Keq2 are taken from Table 2. dkv1 values are taken from Table 3.

not overcome the transition states but instead will favor the interchange reaction between the H2O2·H2O and H2O·HO complexes. Even in the case that, starting with the H2O2 + H2O·HO reactants, the CR3w is formed directly, the reaction will proceed through TS3w to CR2w rather than through TS4w and CP1w by more than 99.9% (at 298 K, the unimolecular rate constant for the CR3w → TS3w → CR2w is computed to be 7.2 × 1010 s−1, and the unimolecular rate constant for the CR3w → TS4w → CP1w is computed to be 1.6 × 108 s−1). Therefore, the only water assisted pathways capable of oxidizing hydrogen peroxide are pathways 1 and 4, as they are unable to undergo the interchange reaction. Thus, the total rate constant for the oxidation of H2O2 by OH with water is computed to be 4.09 × 10−12 cm3 molecule−1 s−1 at 298 K which is 2.6 times faster than the naked reaction (Table 3). The table also shows that the reaction with water has no temperature dependence in the range of temperatures considered. To determine the atmospheric impact of water on the oxidation of hydrogen peroxide by hydroxyl radical, the reaction rates instead of the rate constants must be compared. The rate for the naked reaction can be written as

For the reaction with water the corresponding potential energy surface is much more complex, as shown in Figure 3. For the reaction between H2O2·H2O and OH (reaction 3), reaction pathways 1 and 2 (through TS1w and TS2w) involve the formation of a prereactive complex before the transition state and product formation; hence the kinetic model described in eq 9 is applied. The reaction occurring through pathways 3 and 4 require a geometrical rearrangement of the prereactive complexes to allow the hydroxyl radical moiety to abstract the hydrogen atom of H2O2, and in these cases kuni is computed according the canonical unified statistical model described by eq 14.88,89

1 = k uni

∑ i

1 kTSi

(14)

In Table 4 the rate constants for the different elementary processes are displayed. The rate constants for pathways 1, 2, and 4 are of the same order of magnitude as those computed for the unassisted reaction, whereas the rate constants for pathway 3 is computed to be 3 orders of magnitude slower and therefore does not contribute to the total rate constant. To assess the impact of water vapor on the gas phase oxidation of H2O2 by OH radical, the effect of the two reaction channels (H2O2·H2O + OH and H2O2 + H2O·OH) discussed in the previous section must be considered. It is also important to compare the rates as well as the rate constants of the water assisted and unassisted reactions. As discussed in the previous section and shown in Figure 3, the two entry channels (H2O2·H2O + OH and H2O2 + H2O·OH) are connected on the potential energy surface through reaction pathways 2 and 3, and the first point to be considered is whether these two channels can compete with the oxidation of H2O2 forming HO2 and two H2O molecules. It has already been pointed out that these two channels lie very close in energy (1.2 kcal mol−1, (Δ(E+ZPE) value, Table 1) but in terms of Gibbs free energies they are quasi degenerate (0.4 kcal mol−1, Table 1), H2O2 + H2O·HO lying below H2O2·H2O + OH. In addition, the Gibbs free energy values of TS2w and TS4w (which would lead to the oxidation of H2O2 through pathways 2 and 3) lie more than 8 kcal mol−1 higher in energy than the direct dissociation of the prereactive complexes (CR2w and CR3w) into the H2O2 + H2O·OH or H2O2·H2O + OH reactants. As the rate constant depends on the exponential of the free energy barrier, we can easily conclude that the elementary reactions occurring through these pathways could

v1 = k v1[H2O2 ][OH]

(15)

whereas the rate for the water assisted reactions can be written as ′ [H2O2 ][OH] v2 = k v2[H2O2 ·H2O][OH] = k v2

(16)

where kv2 ′ = kv2 Keq2[H2O], Keq2 being the equilibrium constant for the formation of the H2O2·H2O complexes. kv2 ′ is an effective rate constant that depends parametrically on the water concentration and can be directly compared to the kv1 rate constant of the unassisted reaction. The corresponding kv2 ′ values computed at different temperatures are displayed in Table 4. Comparing the rate constant of the unassisted reaction to the effective rate constant of the water assisted reaction, a single water molecule slows down the oxidation of H2O2 by OH between 1840 and 20.5 times.

■

SUMMARY AND CONCLUSIONS The effect of a single water molecule on the reaction between H2O2 and OH has been investigated by considering the assisted and unassisted reactions. The reaction without water has been reported in the literature. It proceeds through two reaction channels that begin with a five-membered ring prereactive complex and follow a transition state barrier of 1.2 kcal mol−1 before producing HO2 + H2O products. These two reactions 5827



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(4) Solomon, S.; Garcia, R. R.; Rowland, F. S.; Wuebbles, D. J. Nature 1986, 321, 755−758. (5) Crutzen, P. J.; Arnold, F. Nature 1986, 324, 651−655. (6) Wennberg, P. O.; Cohen, R. C.; Stimpfle, R. M.; Koplow, J. P.; Anderson, J. G.; Salawitch, R. J.; Fahey, D. W.; Woodbridge, E. L.; Keim, E. R.; Gao, R. S.; et al. Science 1994, 266, 398−404. (7) Vaghjiani, G. L.; Ravishankara, A. R.; Cohen, N. J. Phys. Chem. 1989, 93, 7833−7837. (8) Lamb, J. J.; Molina, L. T.; Smith, C. A.; Molina, M. J. J. Phys. Chem. 1983, 87, 4467−4470. (9) Keyser, L. F. J. Phys. Chem. 1980, 84, 1659−1663. (10) Sridharan, U. C.; Reimann, B.; Kaufman, F. J. Chem. Phys. 1980, 73, 1286−1293. (11) Wine, P. H.; Semmes, D. H.; Ravishankara, A. R. J. Chem. Phys. 1981, 75, 4390−4395. (12) Kurylo, M. J.; Murphy, J. L.; Haller, G. S.; Cornett, K. D. Int. J. Chem. Kinet. 1982, 14, 1149−1161. (13) Vakhtin, A. B.; McCabe, D. C.; Ravishankara, A. R.; Leone, S. R. J. Phys. Chem. A 2003, 107, 10642−10647. (14) Bahri, M.; Tarchouna, Y.; Jaidane, N.; Ben Lakhdar, Z.; Flament, J. P. J. Mol. Struc. Theochem 2003, 664, 229−236. (15) Ginovska, B.; Camaioni, D. M.; Dupuis, M. J. Chem. Phys. 2007, 127, 08439. (16) Sander, S. P.; Friedl, R. R., Golden, D. M.; Kurylo, M. J.; Moortgat, G. K.; Keller-Rudek, H.; Wine P. H.; Ravishankara, A. R.; Kolb, C. E.; Molina, M. J.; et al. Chemical Kinetics and Photochemical Data for Use in Atmospheric Studies JPL publication 06−2 Jet Propulsion Laboratory, 2006. (17) Glaze, W. H.; Kang, J. W.; Chapin, D. H. Ozone Sci. Eng. 1987, 9, 335−352. (18) De Luis, A.; Lombrana, J. I.; Menendez, A. Environ. Prog. Sustainable Energy 2011, 30, 196−207. (19) Hiroki, A.; Pimblott, S. M.; LaVerne, J. A. J. Phys. Chem. A 2002, 106, 9352−9358. (20) Garrett, B. C.; Dixon, D. A.; Camaioni, D. M.; Chipman, D. M.; Johnson, M. A.; Jonah, C. D.; Kimmel, G. A.; Miller, J. H.; Rescigno, T. N.; Rossky, P. J.; et al. Chem. Rev. 2005, 105, 355−389. (21) Buxton, G. V.; Greenstock, C. L.; Helman, W. P.; Ross, A. B. J. Phys. Chem. Ref. Data 1988, 17, 513−886. (22) Christensen, L. E.; Okumura, M.; Sander, S. P.; Friedl, R. R.; Miller, C. E.; Sloan, J. J. J. Phys. Chem. A 2004, 108, 80−91. (23) Atadinc, F.; Gunaydin, H.; Ozen, A. S.; Aviyente, V. Int. J. Chem. Kinet. 2005, 37, 502−514. (24) Ginovska, B.; Camaioni, D. M.; Dupuis, M. J. Chem. Phys. 2008, 129, 014506. (25) Kircher, C. C.; Sander, S. P. J. Phys. Chem. 1984, 88, 2082− 2091. (26) Stone, D.; Rowley, D. M. Phys. Chem. Chem. Phys. 2005, 7, 2156−2163. (27) Cox, R. A.; Burrows, J. P. J. Phys. Chem. 1979, 83, 2560−2568. (28) Hamilton, E. J.; Lii, R. R. Int. J. Chem. Kinet. 1977, 9, 875−885. (29) Hamilton, E. J. J. Chem. Phys. 1975, 63, 3682−3683. (30) Sennikov, P. G.; Ignatov, S. K.; Schrems, O. Chemphyschem 2005, 6, 392−412. (31) Morita, A.; Kanaya, Y.; Francisco, J. S. J. Geophys. Res. Atmos. 2004, 109, D09201. (32) Aloisio, S.; Francisco, J. S. J. Phys. Chem. A 1998, 102, 1899− 1902. (33) Aloisio, S.; Francisco, J. S.; Friedl, R. R. J. Phys. Chem. A 2000, 104, 6597−6601. (34) Aloisio, S.; Francisco, J. S. Acc. Chem. Res. 2000, 33, 825−830. (35) Hansen, J. C.; Francisco, J. S. Chemphyschem 2002, 3, 833−840. (36) Alongi, K. S.; Dibble, T. S.; Shields, G. C.; Kirschner, K. N. J. Phys. Chem. A 2006, 110, 3686−3691. (37) Belair, S. D.; Kais, S.; Francisco, J. S. Mol. Phys. 2002, 100, 247− 253. (38) Kanno, N.; Tonokura, K.; Koshi, M. J. Geophys. Res. Atmos. 2006, 111, D20312.

channels differ in the orientation of the hydrogen atom of the hydroxyl radical and the computed rate constant, at 298 K, is 1.56 × 10−12 cm3 molecule−1 s−1, in excellent agreement with the suggested value by NASA/JPL.16 With the inclusion of water there are two significant entrance channels, namely, H2O2·H2O + OH and H2O2 + H2O·OH, that are almost degenerate. The H2O2·H2O + OH reaction yields four pathways, two of these pathways (pathways 3 and 4) undergo geometric rearrangements before the reaction can proceed. Moreover, pathways 2 and 3 also connect the two entry channels, and in these cases, the only reaction that occurs is the interchange between H 2 O 2 ·H 2 O and H 2 O·OH complexes. The only water assisted pathways capable of oxidizing hydrogen peroxide are pathways 1 and 4, and the corresponding transition states for the oxidation process (TS1w and TS7w) are nearly isoenergetic with the H2O2·H2O + OH reactants. The computed total rate constant at 298 K leading to oxidation is 4.09 × 10−12 cm3 molecule−1 s−1, a value that is 2.6 times the value of the rate constant of the bare reaction. The real impact of water on the oxidation of H2O2 by OH radical is further assessed by taking into account the concentration of the H2O2·H2O reactant, which depends on the equilibrium constant of this complex and, parametrically, water concentration. This is an example that demonstrates how water has the potential to accelerate a gas phase reaction but exhibits no enhancement under atmospheric conditions as the water assisted reaction is slower than the unassisted reaction.

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ASSOCIATED CONTENT

* Supporting Information S

Relative energies calculated at CCSD(T)/aug-cc-pVTZ and CCSD(T)/aug-cc-pVQZ levels of theory, along with the absolute energies, Cartesian coordinates, and vibrational frequencies of all structures. Rate constants for the unimolecular processes investigated in this work. This information is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: J.M.A., [email protected]; J.S.F., francisc@purdue. edu. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research has been supported by the Spanish Dirección General de Investigación Científica y Técnica (DGYCIT, grant CTQ2011-27812), the Generalitat de Catalunya (Grant 2009SGR01472), and the Research Executive Agency (Grant Agreement no. PERG05-GA-2009-249310). The calculations described in this work were carried out at the Rosen Center for Advanced Computing (RCAC), the Centre de Supercomputació de Catalunya (CESCA), and the CTI-CSIC. M.T-S. acknowledges the CSIC for the JAE-DOC contract.

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REFERENCES

(1) Fulle, D.; Hamann, H. F.; Hippler, H.; Troe, J. J. Chem. Phys. 1996, 105, 983−1000. (2) Golden, D. M.; Smith, G. P.; McEwen, A. B.; Yu, C. L.; Eiteneer, B.; Frenklach, M.; Vaghjiani, G. L.; Ravishankara, A. R.; Tully, F. P. J. Phys. Chem. A 1998, 102, 8598−8606. (3) Smith, I. W. M.; Zellner, R. J. Chem. Soc. Faraday Trans. II 1973, 69, 1617−1627. 5828



Article

(39) Kanno, N.; Tonokura, K.; Tezaki, A.; Koshi, M. J. Phys. Chem. A 2005, 109, 3153−3158. (40) Suma, K.; Sumiyoshi, Y.; Endo, Y. Science 2006, 311, 1278− 1281. (41) Stockwell, W. R. J. Geophys. Res. Atmos. 1995, 100, 11695− 11698. (42) Kim, K. S.; Kim, H. S.; Jang, J. H.; Mhin, B. J.; Xie, Y. M.; Schaefer, H. F. J. Chem. Phys. 1991, 94, 2057−2062. (43) Xie, Y. M.; Schaefer, H. F. J. Chem. Phys. 1993, 98, 8829−8834. (44) Wang, B. S.; Hou, H.; Gu, Y. S. Chem. Phys. Lett. 1999, 303, 96− 100. (45) Zhou, Z. Y.; Qu, Y. H.; Fu, A. P.; Du, B. N.; He, F. X.; Gao, H. W. Int. J. Quantum Chem. 2002, 89, 550−558. (46) Schofield, D. P.; Kjaergaard, H. G. J. Chem. Phys. 2004, 120, 6930−6934. (47) Du, S. Y.; Francisco, J. S.; Schenter, G. K.; Iordanov, T. D.; Garrett, B. C.; Dupuis, M.; Li, J. J. Chem. Phys. 2006, 124, 224318. (48) Tsuji, K.; Shibuya, K. J. Phys. Chem. A 2009, 113, 9945−9951. (49) Brauer, C. S.; Sedo, G.; Dahlke, E.; Wu, S. H.; Grumstrup, E. M.; Leopold, K. R.; Marshall, M. D.; Leung, H. O.; Truhlar, D. G. J. Chem. Phys. 2008, 129, 104304. (50) Soloveichik, P.; O’Donnell, B. A.; Lester, M. I.; Francisco, J. S.; McCoy, A. B. J. Phys. Chem. A 2010, 114, 1529−1538. (51) Engdahl, A.; Karlstrom, G.; Nelander, B. J. Chem. Phys. 2003, 118, 7797−7802. (52) Cooper, P. D.; Kjaergaard, H. G.; Langford, V. S.; McKinley, A. J.; Quickenden, T. I.; Schofield, D. P. J. Am. Chem. Soc. 2003, 125, 6048−6049. (53) Brauer, C. S.; Sedo, G.; Grumstrup, E. M.; Leopold, K. R.; Marshall, M. D.; Leung, H. O. Chem. Phys. Lett. 2005, 401, 420−425. (54) Ohshima, Y.; Sato, K.; Sumiyoshi, Y.; Endo, Y. J. Am. Chem. Soc. 2005, 127, 1108−1109. (55) Wu, S. H.; Sedo, G.; Leopold, K. R. J. Mol. Spectrosc. 2009, 253, 35−40. (56) Anglada, J. M.; Gonzalez, J. Chemphyschem 2009, 10, 3034− 3045. (57) Luo, Y.; Maeda, S.; Ohno, K. Chem. Phys. Lett. 2009, 469, 57− 61. (58) Gonzalez, J.; Anglada, J. M. J. Phys. Chem. A 2010, 114, 9151− 9162. (59) Vohringer-Martinez, E.; Hansmann, B.; Hernandez, H.; Francisco, J. S.; Troe, J.; Abel, B. Science 2007, 315, 497−501. (60) Iuga, C.; Alvarez-Idaboy, J. R.; Reyes, L.; Vivier-Bunge, A. J. Phys. Chem. Lett. 2010, 1, 3112−3115. (61) Canneaux, B.; Sokolowski-Gomez, N.; Henon, E.; Bohr, F.; Dobe, S. Phys. Chem. Chem. Phys. 2004, 6, 5172−5177. (62) Gonzalez, J.; Anglada, J. M.; Buszek, R. J.; Francisco, J. S. J. Am. Chem. Soc. 2011, 133, 3345−3353. (63) Allodi, M. A.; Dunn, M. E.; Livada, J.; Kirschner, K. N.; Shields, G. C. J. Phys. Chem. A 2006, 110, 13283−13289. (64) Iuga, C.; Alvarez-Idaboy, J. R.; Vivier-Bunge, A. Chem. Phys. Lett. 2010, 501, 11−15. (65) Long, B.; Tan, X. F.; Ren, D. S.; Zhang, W. J. J. Mol. Struc. Theochem 2010, 956, 44−49. (66) Jorgensen, S.; Kjaergaard, H. G. J. Phys. Chem. A 2010, 114, 4857−4863. (67) Vohringer-Martinez, E.; Tellbach, E.; Liessmann, M.; Abel, B. J. Phys. Chem. A 2010, 114, 9720−9724. (68) Head-Gordon, M.; Pople, J. A.; Frisch, M. J. Chem. Phys. Lett. 1988, 153, 503−506. (69) Dunning, T. H. J. J. Chem. Phys. 1989, 90, 1007−1024. (70) Kendall, R. A.; Dunning, T. H.; Harrison, R. J. J. Chem. Phys. 1992, 96, 6796−6806. (71) Ishida, K.; Morokuma, K.; Kormornicki, A. J. Chem. Phys. 1977, 66, 2153. (72) Gonzalez, C.; Schlegel, H. B. J. Phys. Chem. 1990, 94, 5523− 5527. (73) Cizek, J. Adv. Chem. Phys. 1969, 14, 35−89. (74) Barlett, R. J. J. Phys. Chem. 1989, 93, 1963−1969.

(75) Pople, J. A.; Krishnan, R.; Schlegel, H. B.; Binkley, J. S. Int. J. Quant. Chem. XIV 1978, 545−560. (76) Helgaker, T.; Klopper, W.; Halkier, A.; Bak, K. L.; Jorgensen, P.; Olsen, J. Quantum Mechanical Prediction of Thermodynamic Data; Kluwer Academic: Dordrecht, The Netherlands, 2001. (77) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J., J. A.; Vreven, T.; Kudin, K. N.; Burant, J. C.; et al. Revision C.02 ed.; Gaussian, Inc.: Wallingford CT, 2004. (78) Bahri, M.; Jaidane, N.; Lakhdar, Z. B.; Flament, J. P. Phys. Chem. News 2001, 4, 7−10. (79) Sander, S. P.; Friedl, R. R.; Golden, D. M.; Kurylo, M. J.; Huie, R. E.; Orkin, G. K.; Moortgat, G. K.; Ravishankara, A. R.; Kolb, C. E.; Molina, M. J.; et al. Chemical Kinetics and Photochemical Data for Use in Atmospheric Studies JPL Publication 02−25; Jet Propulsion Laboratory, California 2003. (80) Ruscic, B.; Pinzon, R. E.; Morton, M. L.; Srinivasan, N. K.; Su, M. C.; Sutherland, J. W.; Michael, J. V. J. Phys. Chem. A 2006, 110, 6592−6601. (81) DeMore, W. B.; Sadner, S. P.; Golden, D. M.; Hampson, R. F.; Kurylo, M. J.; Howard, C. J.; Ravishankara, A. R.; Kolb, C. E.; Molina, M. J. Chemical Kinetics and Photochemical Data for Use in Stratospheric Modeling, Jet Propulsion Laboratory, 1992. (82) Allodi, M. A.; Dunn, M. E.; Livada, J.; Kirschner, K. N.; Shields, G. C. J. Phys. Chem. A 2006, 110, 13283−13289. (83) Gonzalez, J.; Caballero, M.; Aguilar-Mogas, A.; TorrentSucarrat, M.; Crehuet, R.; Solé, A.; Giménez, X.; Olivella, S.; Bofill, J.; Anglada, J. Theor. Chem. Acc. (Theoretica Chimica Acta) 2011, 128, 579−592. (84) Garrett, B. C.; Truhlar, D. G. J. Phys. Chem. 1979, 83, 1052− 1078. (85) Truhlar, D. G.; Garrett, B. C. Acc. Chem. Res. 1980, 13, 440− 448. (86) Liu, Y. P.; Lynch, G. C.; Truong, T. N.; Lu, D. H.; Truhlar, D. G.; Garrett, B. C. J. Am. Chem. Soc. 1993, 115, 2408−2415. (87) Corchado, J. C.; Chuang, Y.-Y.; Fast, P. L.; Villà, J.; Hu, W.-P.; Liu, Y.-P.; Lynch, G. C.; Nguyen, K. A.; Jackels, C. F.; Melissas, V. S.; et al. POLYRATE-version 9.3 ed. University of Minnesota, Minneapolis, 2002. (88) Miller, W. H. J. Chem. Phys. 1976, 65, 2216−2223. (89) Hu, W. P.; Truhlar, D. G. J. Am. Chem. Soc. 1996, 118, 860−869. (90) Lemmon, E. W. in CRC Handbook of Chemistry and Physics, edited by Haynes, W. M. (CRC Press/Taylor and Francis Group LLC, Boca Raton, FL, 2010−2011), p 6−1−6-4. (91) Marti, J.; Mauersberger, K. Geophys. Res. Lett. 1993, 20, 363− 366.

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Effects of a Single Water Molecule on the OH + H2O2 Reaction - The

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