Theoretical Investigation of the Reaction Mechanism of ClONO2+ HCl

Article pubs.acs.org/JPCA

Theoretical Investigation of the Reaction Mechanism of ClONO2 + HCl → HNO3 + Cl2 on (H2O)n (n = 0−3) Cluster Toshio Asada,†,* Toshiyuki Okajima,† and Shiro Koseki† †

Department of Chemistry, Faculty of Science, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531, Japan S Supporting Information *

ABSTRACT: Hydrated chlorine nitrate and hydrogen chloride ClONO2·HCl·(H2O)n (n = 0−3) clusters were investigated by using the MP2/aug-cc-pVTZ level of theory to clarify the reaction mechanism of Cl2 production. Isomeric stable structures found in n = 2 and 3 clusters have equivalent binding energies and the reaction barrier drastically decreases to be 2.1 kcal/mol at n = 3. The plausible reaction pathways were proposed according to calculated structures and energies, where the zero-point-energy corrections are important to determine the energy profiles of reactions especially for the n = 3 cluster. The kinetic analysis using the transition state theory suggested that the reaction rate constant from the original reactants to the product of n = 3 is 1.8 × 105 times larger than that of n = 2 cluster. Even though the small amount of the molar concentration of HCl(H2O)3 is obtained, the overall reaction rate of the trihydrate reaction is still 35 times faster than that of the dihydrate.

1. INTRODUCTION Chloride atoms in the Antarctic stratosphere are stored in the form of reservoir molecules, such as chlorine nitrate (ClONO2) or hydrochloric acid (HCl). They are released into the atmosphere as more active species of photolyzable chlorine (Cl2) produced by a multiproton transfer reaction,1 which influences the ozone depletion in the Antarctic stratosphere.2−6 The chemical reaction processes take place in polar stratospheric clouds (PSCs). It is known that the main reaction is the activation of ClONO2 + HCl, which produces a Cl2 molecule. ClONO2 + HCl · (H 2O)n → HNO3 ·(H 2O)n + Cl 2

for the same effect on HNO3 (when HCl is present in the complex). Recently, Nam et al.1 studied the proton transfer mechanism and rate constants using ab initio MO calculation at the MP2 method for limited structures of ClONO2·HCl·(H2O)n (n ≤ 2) clusters. The structures used in their analysis were based on previously reported few structures by McNamara et al.7 They indicated that calculated geometrical structures largely depend on the applied theoretical level of approximation, and the computed rate constants for n = 2 agree well with the experimental value11 measured on the bulk ice surface contaminated by nitric acid trihydrate (NAT). However, it appears doubtful whether the reaction in the small cluster can reproduce those on the bulk ice surface even though the rate constant at the n = 2 cluster can agree with the experimental data. Although many experimental and theoretical works have been devoted to the reaction,1,7,12−19 detailed mechanisms for the reaction of ClONO2+HCl are not fully understood in the microscopic point of view, since many isomeric structures exist in heterogeneous clusters with equivalent binding energies. Theoretical studies on finding stable and transition state (TS) structures are important to understand the experimental observations. For example, Eyet et al.20 used the isomeric structures and energies reported in our previous work21 for a NO+(H2O)n cluster, to provide new experimental insights for the temperature dependence of the intracluster reaction. Accordingly, in this manuscript, our discussion is focused on the geometries, energies, and electronic properties of ClONO2· HCl·(H2O)n (n ≤ 3) clusters. In addition, the plausible reaction

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McNamara et al.7 elucidated the reaction mechanisms for n ≤ 3 clusters and few structures with n = 4 and 5 using ab initio molecular orbital (MO) calculations by the second-order Møller−Plesset (MP2) perturbation theory for optimized structures obtained by Kohn−Sham density functional theory with a combination of Becke’s three-parameter exchange and Lee−Yang−Parr correlation functional (B3LYP) with the 6-311++G(d,p) basis set. They showed that the reaction barriers were lowered systematically by adding water molecules to the complex. The inclusion of water molecules significantly lowered the energy barrier from 42 kcal/mol to zero when the reaction was catalyzed by only two water molecules. Balci et al.8 investigated the proton transfer reaction by increasing the addition of a number of hydrated water molecules to a different kind of acid pair, HCl+HNO3, by applying the MP2/aug-cc-pVDZ level. Although an acid-to-water ratio that is smaller than 1:3 was believed to be necessary to stabilize the ionic forms for both HCl−water9 and HNO3−water clusters,10 they found that at least three water molecules are necessary to promote the ionization of HCl (when nitric acid is present) and more than three water molecules are required © XXXX American Chemical Society

Received: February 20, 2013 Revised: July 10, 2013

A

dx.doi.org/10.1021/jp406175j | J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A

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Table 1. Calculated Intermolecular Interaction Energies (ΔEint), Basis-Set Super-Position Errors (BSSE), and Interaction Energies after BSSE Correction (ΔEBSSE) for Molecular Pairs by Using Different Basis Sets and Theoretical Levels of Approximations. The Numbers of Basis Functions Are Also Listed ΔEint (kcal/mol) HF/aug-cc-pVDZ B3LYP/aug-cc-pVDZ B3LYP/aug-cc-pVTZ MP2/6-31+G(d, p) MP2/6-311++G(d, p) MP2/6-311++G(3df, 3pd) MP2/aug-cc-pVDZ MP2/aug-cc-pVTZ

−4.2 −5.8 −5.2 −7.0 −6.6 −6.0 −6.3 −6.0

HF/aug-cc-pVDZ B3LYP/aug-cc-pVDZ B3LYP/aug-cc-pVTZ MP2/6-31+G(d, p) MP2/6-311++G(d, p) MP2/6-311++G(3df, 3pd) MP2/aug-cc-pVDZ MP2/aug-cc-pVTZ

−1.6 −1.0 −1.0 −5.7 −5.5 −5.2 −5.9 −4.9

HF/aug-cc-pVDZ B3LYP/aug-cc-pVDZ B3LYP/aug-cc-pVTZ MP2/6-31+G(d, p) MP2/6-311++G(d, p) MP2/6-311++G(3df, 3pd) MP2/aug-cc-pVDZ MP2/aug-cc-pVTZ

−2.4 −1.8 −1.7 −5.6 −5.6 −5.2 −5.6 −5.0

BSSE (kcal/mol) HCl and H2O 0.2 0.3 0.1 2.0 1.8 0.9 1.0 0.5 ClONO2 and HCl 0.1 0.2 0.1 3.4 3.2 1.8 1.8 0.9 ClONO2 and H2O 0.3 0.3 0.1 2.5 2.7 1.3 1.7 0.9

mechanisms of proton transfer reactions to produce a Cl2 molecule from hydrated ClONO2+HCl clusters have been proposed on the basis of the properties of stable and TS structures calculated by applying ab initio MO calculations at the MP2/aug-cc-pVTZ levels. In these systems, zero point energy (ZPE) corrections cannot be neglected, since the quantum effects of nuclear motions play an important role for light proton transfer reactions to determine the energy profiles of reactions. When three water molecules coordinate to a ClONO2+HCl cluster, ZPE-corrected relative energies show that Cl2 molecules are easily produced with a small activation barrier. To consider the time scale of the reaction, reaction rates have been calculated from associated complexes of reactants, which are referred to as the prereactive complexes (PRCs), to products. Equilibrium constants between the reactant and the PRC in addition to the molar concentrations of component molecules have also been evaluated.

ΔEBSSE (kcal/mol)

number of basis functions

−4.0 −5.5 −5.1 −5.0 −4.8 −5.2 −5.3 −5.5

77 77 165 57 77 140 77 165

−1.5 −0.8 −0.9 −2.3 −2.3 −3.4 −4.1 −3.9

155 155 307 128 155 268 155 307

−2.1 −1.5 −1.6 −3.0 −2.9 −3.9 −3.9 −4.1

160 160 326 128 160 278 160 326

Scheme 1. Schematic Representation of Potential Energy Surface along the Reaction Pathwaya

A, B, C, and D means given molecules. ΔE is the relative energy of TS based on the bimolecular reactants. kcap and k−cap are rate constants of bimolecular association and deassociation reactions, respectively. ku and k−u are rate constants of unimolecular forward and reverse reactions from PRC to the associated complex of products C and D. a

2. METHODS OF CALCULATION The geometries of ClONO2·HCl·(H2O)n (n ≤ 3) clusters were fully optimized by using the Gaussian 09 package.22 The optimized geometries were confirmed to be the energy minima or the TSs on the adiabatic potential energy surface, by performing normal mode vibrational frequency analyses in terms of analytical second-derivative techniques. The calculated vibrational frequencies and ZPEs are known to exceed experimental values. In order to consider these properties, vibrational frequencies and ZPEs were scaled by the typical empirical factors of 0.96 and 0.92,23 respectively, for the MP2 method. Table 1 lists the intermolecular interaction energies and

basis-set superposition errors (BSSEs) for HCl···H2 O, ClONO2···HCl, and ClONO2···H2O molecular pairs calculated by applying various kinds of basis sets and theoretical levels of approximations. Although BSSEs calculated by Hartree−Fock (HF) or B3LYP with aug-cc-pVDZ basis sets are smaller than 0.3 kcal/mol for these molecular pairs, in principle, the HF method cannot include electron correlation effects and the B3LYP method underestimates the intermolecular interaction energies for both ClONO2···H2O and ClONO2···HCl pairs B



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Table 2. Calculated Electronic Energies (E), Zero Point Energies (ZPE), Relative Energies (ΔE), and ZPE Corrected Relative Energies (ΔE+ΔZPE) for n = 0, 1, and 2, at the MP2/aug-cc-pVTZ//MP2/aug-cc-pVDZ and the MP2/aug-cc-pVTZ Level of Theorya MP2/aug-cc-pVTZ//MP2/aug-cc-pVDZ b

ΔE

b

molecule

E (hartree)

ZPE

0A 0C 0D 0E* 0F*

−1199.90560 −1199.88326 −1199.88086 −1199.88055 −1199.80400

16.4 14.0 13.5 13.4 13.2

−14.0 0.0 1.5 1.7 49.7

1A 1C 1D 1E 1F 1G*

−1276.25222 −1276.22630 −1276.22360 −1276.22101 −1276.22075 −1276.20920

30.6 28.3 28.1 27.6 27.7 30.3

−16.3 0.0 1.7 3.3 3.5 10.7

2A 2B 2C 2D 2E 2F 2G 2H* 2I*

−1352.59747 −1352.59695 −1352.56809 −1352.56701 −1352.56682 −1352.56268 −1352.56220 −1352.56135 −1352.55701

44.9 45.1 42.7 42.5 42.4 41.9 42.0 43.6 43.5

−18.4 −18.1 0.0 0.7 0.8 3.4 3.7 4.2 7.0

MP2/aug-cc-pVTZ

ΔE + ΔZPE

b

n=0 −11.6 0.0 1.0 1.1 49.0 n=1 −13.9 0.0 1.5 2.6 2.9 12.8 n=2 −16.2 −15.7 0.0 0.5 0.6 2.6 3.0 5.2 7.8

E (hartree)

ZPEb

ΔEb

ΔE + ΔZPEb

−1199.90658 −1199.88451 −1199.88196 −1199.88166 −1199.80499

16.5 13.9 13.6 13.5 13.3

−13.8 0.0 1.6 1.8 49.9

−11.3 0.0 1.3 1.4 49.3

−1276.25317 −1276.22760 −1276.22467 −1276.22229 −1276.22181 −1276.20993

30.8 28.3 28.2 27.7 27.8 30.1

−16.0 0.0 1.8 3.3 3.6 11.1

−13.5 0.0 1.7 2.8 3.2 12.9

−1352.59847 −1352.59798 −1352.56946 −1352.56830 −1352.56793 −1352.56389 −1352.56340 −1352.56220 −1352.55801

45.1 45.3 42.7 42.5 42.6 42.0 42.0 44.3 44.2

−18.2 −17.9 0.0 0.7 1.0 3.5 3.8 4.6 7.2

−15.8 −15.3 0.0 0.6 0.9 2.8 3.2 6.2 8.8

a

The same letters are used to molecular labels for products (A, B), for optimized structures (C, D, E, ...) in increasing order of the relative energy, and for TSs the asterisk is added to these letters. bValues are given in kcal/mol.

when compared to extensive MP2/aug-cc-pVTZ results. Therefore, the use of a less accurate theoretical level for optimization is critical for the relevance of structure used for more extensive calculations. On the other hand, the MP2 method requires larger basis sets than HF or B3LYP methods to reduce BSSEs. Therefore, the MP2/aug-cc-pVTZ level of theory was mainly used in this paper for ClONO2·HCl·(H2O)n (n ≤ 3) clusters and the MP2/aug-cc-pVTZ//MP2/aug-cc-pVDZ level was also applied for only some TS structures of n = 3 clusters. Reaction rate constants of the unimolecular reaction from PRC to product ku(T) were obtained by the conventional TST using GAUSSRATE,24 which is an interface of POLYRATE25 with Gaussian 09. The rate constant at a given temperature T can be represented by ku(T ) = σ

kBT Q TS(T ) exp( −βV ) h Q R (T )

kcap[A][B] = k −cap[A·B]

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where kcap and k−cap mean the forward and the backward capture reaction rate constants, respectively. “Capture” means the formation of PRC. [A] is the molar concentration of a given molecule A. The molar concentration is related to the equilibrium constant Kcap which can be expressed by the calculated Gibbs free energy difference ΔG. Kcap = exp( −ΔG) =

[A·B](RT /P) [A][B]

(4)

where R means the gas constant, and P is the total pressure. Writing the overall reaction rate vP as a product of the unimolecular rate constant ku and the molar concentration of PRC denoted as [A·B], we have vP approximated as vp ≈

(2)

⎛ RT ⎞ d[C·D] ⎟[A][B] = k [A][B] = k u[A·B] = k uKcap⎜ p ⎝ P ⎠ dt (5)

where β is 1/(kBT), kB is the Boltzmann constant, V is the activation energy barrier for the reaction, h is the Planck constant, σ means the symmetry factor, and QTS(T) and QR(T) are the molecular partition functions of the TS and the reactant structures, respectively. In the molecular partition functions, vibrational partition functions are treated quantum mechanically. For the rate constant of reaction 1, two different cases of the potential energy surface illustrated in Scheme 1 should be considered. In the first case, TS energy ΔE is higher than that of bimolecular reactants. In this case, the fast-equilibrium approximation can be applied. The equilibrium condition between reactants and PRCs gives

where kp is the second-order rate constant of the bimolecular reaction. In this approximation, the associated complex consisting of the product, C·D, is regarded as the product of the Cl2 reservoir complex. In the other case, the TS energy ΔE is smaller than the energy of reactants and the reaction proceeds over a submerged TS. Then the rate law to form PRCs can be expressed as the following equation. d[A· B] = kcap[A][B] − k −cap[A· B] − k u[A· B] + k −u[C· D] dt (6) C



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Supposing ku ≫ k−u and the concentration of PRC is constant, which is known as the steady state approximation, eq 6 gives d[A·B] = kcap[A][B] − (k −cap + k u)[A·B] = 0 dt

(7)

Then [A·B] =

kcap (k −cap + k u)

[A][B] (8)

Similar to eq 5, the overall reaction rate becomes vp = k u[A·B] =

kcapk u (k −cap + k u)

[A][B] (9)

If we assume ku ≫ k−cap which means it has deeply submerged TS, eq 9 can be represented by the capture rate constant kcap.

d[C·D] = kcap[A][B] dt

(10)

The capture rate constant kcap is approximated by the hardsphere collision theory as ⎛ 8kBT ⎞1/2 kcap = σAB⎜ ⎟ ⎝ πμ ⎠

(11)

where, σAB is the collision diameter and μ means the reduced mass. In this study, the collision diameter is approximated by using both the volume of the molecule with vdW radii calculated by Winmostar program26 and the hard sphere model. To evaluate the time scale of reactions for various hydration numbers, concentrations of all component molecules should be evaluated under the polar stratospheric condition. To estimate these values, the pertaining equilibrium constants should be obtained by Gibbs free energy differences. Then, partial pressures of molecular complexes are estimated by both the equilibrium constant Kcap for the clustering reaction and experimental partial pressures of H2O, HCl, and ClONO2 as follows. PAB/P = Kcap·(PA /P) ·(PB/P)

Figure 1. Four important structures corresponding to the intracluster reaction calculated by the MP2/aug-cc-pVTZ level of theory for ClONO2·HCl clusters. The other calculated structure are shown in the Supporting Information. The same letters are used for molecular labels for products (A, B), for optimized structures (C, D, E, ...) in increasing order of the relative energy, and for TSs the asterisk is added to these letters. Values are given in angstrom.

is more negative than those of the other oxygen atoms in ClONO2. This can be explained by Pauling’s electronegativity. Since the electronegativities of chloride (3.160) and nitrogen (3.040) atoms are smaller than that of oxygen atom (3.440), chemical bonds are polarized for both O2−N3 and O2−Cl1 bonds so that the negative charges are localized dominantly on the O2 atom. Thus, the isomer 0C is more favorable than 0D, by the strong electrostatic interaction between H7 and O2 atoms. Indeed, the bond distance r(O2−H7) of 1.98 Å in the isomer 0C is shorter than r(O5−H7) of 2.28 Å in the isomer 0D. Table 2 shows that the reaction energy ΔE + ΔZPE is −11.3 kcal/mol for n = 0 in our calculation, and the TS structure 0E* (see Supporting Information figures) with one imaginary frequency (28.3i cm−1) is found for the isomerization reaction between 0C and 0D with the relative energy ΔE + ΔZPE of 1.4 kcal/mol. The energy barrier is smaller than the binding energy of 3.9 kcal/mol between ClONO2 and HCl, as listed in Table 1, indicating that the isomerization reaction for the rearrangement of hydrogen bonds between ClONO2 and HCl can be realized easily. An important TS structure for the proton transfer reaction is the isomer 0F* with one imaginary frequency of 1419.1i cm−1. However, the reaction 1 from isomer 0D to 0A has a large energy barrier (48.0 kcal/mol), which is too high to proceed at the atmospheric temperature of 200 K in PSCs. Some important isomeric structures for ClONO2·HCl·H2O are depicted in Figure 2, and others are given in the figures in the Supporting Information. Four reactant isomers are found at the MP2/aug-cc-pVTZ level. The isomer 1C is the most stable reactant and the next stable reactant 1D is higher by 1.7 kcal/mol.

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where PA/P is the partial pressure of molecule A.

3. RESULTS AND DISCUSSION 3.1. Stable and TS structures for ClONO2·HCl·(H2O)n (n ≤ 3) clusters. Relative energies based on the most stable reactant isomer of ClONO2·HCl·(H2O)n (n = 0, 1, 2) clusters, calculated at two levels of theory, are listed in Table 2. In the following discussions, for all hydration numbers of clusters n = 1, 2, and 3, the same letters are used for molecular labels for products (A, B), for optimized structures (C, D, E, ...) in increasing order of the relative energy, and for TSs the asterisk is added to these letters for the sake of convenience. Two isomeric structures are found as reactants in n = 0 cluster (Figure 1), where isomer 0D was previously found by McNamara et al.7 Although 0D was reported to be the reactant with the hydrogen bond between two atoms O5 and H7, the new reactant isomer 0C is found to be more stable than 0D with a hydrogen bond between O2 and H7. In 0C, HCl molecule coordinates to ClONO2 in the direction perpendicular to the molecular plane of ClONO2. The geometrical parameters and group natural charges (natural atomic charges with hydrogens summed into heavy atoms) are listed in the Supporting Information tables. The group natural charge of O2 D



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Figure 2. Calculated key isomers for the n = 1 cluster. Four important isomers corresponding to the intracluster reaction to form Cl2 are illustrated. The other calculated structures can be downloaded from Supporting Information. The same letters are used to molecular labels for products (A, B), for optimized structures (C, D, E, ...) in increasing order of the relative energy, and for TSs the asterisk is added to these letters. Values are given in angstrom.

The structural features in 1C and 1D are similar to those in 0C and 0D, respectively, not only by the hydrogen bonding networks but also by the group natural charges. For example, the coordinated hydrogen atom is bound with the oxygen atom O2 in ClONO2 for both 0C and 1C, in contrast to the hydrogen bond with O5 atom in ClONO2 for both 0D and 1D. The isomer 1G* is confirmed to be the TS structure from the reactant 1D to the product 1A by intrinsic reaction coordinate (IRC) calculations. While a hydrated water molecule lowers the reaction energy by ca. 2 kcal/mol to be −13.5 kcal/mol at the MP2/aug-ccpVTZ level, the reaction barrier is lowered to 12.9 kcal/mol by a coordinated water molecule. The reaction process includes the proton transfer from HCl to the bridging water molecule, to form the oxonium ion at TS. Five reactants, two TSs, and two product isomers are obtained for the n = 2 cluster, and some key structures are shown in Figure 3. The relative energies ΔE + ΔZPE for two product isomers, 2A and 2B, are very close (only 0.5 kcal/mol) despite discrepancies of coordination patterns between Cl2 and HNO3(H2O)2. It is reasonable to consider that 2B can easily isomerize to 2A by slightly displacing the Cl2 molecule with respect to the ClONO2 moiety. The most stable reactant is 2C with the arrangement of ClONO2 parallel to the molecular plane containing HCl and (H2O)2 moieties, and the characteristic features of hydrogen bonds and natural charge distributions are similar to those of the isomer 1C. The next stable isomer 2D can be generated by the insertion of a water molecule between H2O and ClONO2 in 1E. The oxygen atom O2 in these two lowest reactants accepts the hydrogen bond from the hydrated water molecule. Since the relative energy ΔE + ΔZPE among 2C, 2D, and 2E lies within 0.9 kcal/mol,

Figure 3. Calculated key isomers for the n = 2 cluster. Six important isomers corresponding to the intracluster reaction to form Cl2 are illustrated. The other calculated structures can be seen in the Supporting Information. The same letters are used for molecular labels for products (A, B), for optimized structures (C, D, E, ...) in increasing order of the relative energy, and for TSs the asterisk is added to these letters. Values are given in angstrom.

these three reactant can easily isomerize each other by flipping the ClONO2 moiety. The IRC calculation confirmed that 2H* is the TS between 2E and 2A with an energy barrier of 5.3 kcal/mol for reaction 1. Because of an energy barrier smaller than that of the n ≤ 1 cluster, the imaginary frequency of 2H* becomes much lower (82.7i cm−1) than that of 0F* (1419.1i cm−1) and of 1G*(157.0i cm−1). In addition, another TS 2I* is also obtained for the alternative reaction pathway of the reaction, which lies between reactant 2D and product 2B. Although 2D is slightly more stable than 2E, the reaction barrier (8.2 kcal/mol) of 2I* is obviously higher than the corresponding value of 2H*. Both reaction pathways require triple proton transfers to proceed. At both TSs, proton H10 is shared by two water molecules such as the cation H5O2+.27 While the proton is located nearly at the center of two water molecules, the bond distances E



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by the double proton transfer from the reactant 3G, and it isomerizes to product 3B immediately as discussed below. In this intermediate 3F, the covalent bond in the HCl molecule is completely dissociated and r(Cl1−Cl6) shows that a weak bond is formed between two Cl atoms. On the other hand, the intracluster reaction has not yet occurred in 3G, though the hydrogen bonding network in 3G is very close to that of the isomer 3F. In the structural point of view, both a contact ion pair between NO3 and H3O and a water-shared ion pair between Cl6 and H3O are considered to be formed since the group natural charges of NO3(N3,O2,O4,O5), H3O (O11,H10,H12,H13), and Cl6 moieties are −0.478e, 0.734e, and −0.430e, respectively. 3G is confirmed to be one of the most important reactant in the n = 3 cluster in the overall reaction pathways, while the relative energy ΔE + ΔZPE of 3G is 1.6 kcal/mol and the probability ratio of its appearance against the most stable reactant 3C is ca. 1.8% according to the Boltzmann distribution at 200 K. It is known that increasing the hydration number enhances the proton transfer in neutral aggregates of water and one acid (HCl, HBr, or HNO3), where at least four water molecules seem to be required to stabilize the formed ion pair.30−32 However, it is confirmed that three water molecules are necessary to stabilize the ion pair, when both HCl and ClONO2 are present in the small water cluster. The reaction pathways of the proton transfer have been analyzed for n = 3 clusters according to our calculations on five TS structures. Prior to the discussion, computational levels should be noticed for some TS structures. While TS structures 3H* and 3I* can be obtained by the MP2/aug-cc-pVDZ level of theory, they unfortunately cannot be addressed by the MP2/ aug-cc-pVTZ level due to limited computational resources, since the potential energy surfaces become very flat compared to those in n = 0−2 clusters. However, since the maximum differences in ΔE between the MP2/aug-cc-pVTZ//MP2/augcc-pVDZ and the MP2/aug-cc-pVTZ calculations for all other structures listed in Table 3 are only 0.6 kcal/mol, the following discussion on 3H* and 3I* will be made on the basis of the properties obtained using MP2/aug-cc-pVTZ//MP2/aug-cc-pVDZ level of theory. The IRC calculation from TS 3I* leads to isomers 3G and 3F on the adiabatic potential surface. The ZPE corrected energy barrier for this isomerization reaction from 3G to 3F is only 0.5 kcal/mol, suggesting that the reaction can readily proceed once 3G is formed. In the following reactions, structure 3E* was obtained as TS on the potential energy surface. While the TS structure 3E* leads to the reactant 3F and the stable product 3B by IRC calculation, ZPE corrected energy ΔE+ΔZPE shows that 3E* is not TS and the energy decreases monotonically from 3I* to 3B via 3F and 3E*. The first reaction from 3G to 3F is the double proton transfer to form the ion pair configuration, and then the following reaction from 3F to 3B is the single proton transfer to form the covalent bond between Cl1 and Cl6 atoms. Since the series of reactions proceeds with a very small energy barrier from isomer 3G for the n = 3 cluster, the addition of the ClONO2 molecule with perpendicular orientation on the HCl·(H2O)3 ring moiety makes a preferable complex for the intracluster proton transfer in reaction 1. In alternative reaction pathways, two reactants 3C and 3D can isomerize to a same intermediate structure 3J via different TSs 3L* and 3H*, respectively. However, since the TS of 3H* diminishes in ΔE + ΔZPE, the potential energy along the single proton transfer seems to increase monotonically from 3D to 3J. On the other hand, the reaction from 3C to 3J is a triple proton

Figure 4. Calculated key isomers for the n = 3 cluster. Six important isomers corresponding to the intracluster reaction to form Cl2 are illustrated. The other calculated structures can be downloaded from Supporting Information. The same letters are used for products (A, B), for optimized structures (C, D, E, ...) in increasing order of the relative energy, and for TSs the asterisk is added to these letters. Values are given in angstrom.

r(H10−O8) and r(H10−O11) clearly differ. This situation may change if the quantum effect of the proton is considered, since tunneling effects sometimes affect the TS structures and energies, especially for light proton transfer.21,28,29 Both reaction pathways still seem to be difficult to proceed in vacuum at the temperature of 200 K, although the second hydrated water molecule considerably lowered the reaction barriers. For n = 3 clusters, some calculated stable structures and TSs are illustrated in Figure 4. By increasing the number of coordinated water molecules, the number of isomers with low relative energies is increased. For example, ΔE + ΔZPE of 12 structures for n = 3 is less than only 2.9 kcal/mol including those of the TS structures as listed in Table 3. Two lowest reactants 3C and 3D are similar isomers except for the direction of the hydrogen bonding network in HCl·(H2O)3, which have stacking interactions between the ClONO2 molecule and the cyclic HCl·(H2O)3 moiety similar to the isomer 2C. The next stable structure 3F with the relative energy of 0.9 kcal/mol by the MP2/aug-cc-pVTZ is the intermediate structure produced F



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Table 3. Calculated Electronic Energies (E), Zero Point Energies (ZPE), Relative Energies (ΔE), and ZPE Corrected Relative Energies (ΔE+ΔZPE) for n = 3 at the MP2/aug-cc-pVDZ, MP2/aug-cc-pVTZ//MP2/aug-cc-pVDZ and the MP2/aug-cc-pVTZ Level of Theorya MP2/aug-cc-pVDZ

MP2/aug-cc-pVTZ//MP2/aug-cc-pVDZ

molecule

E (hartree)

ZPE

ΔE

ΔE + ΔZPE

3A 3B 3C 3D 3E* 3F 3G 3H* 3I* 3J 3K* 3L*

−1428.38372 −1428.38177 −1428.36527 −1428.36491 −1428.36318 −1428.36512 −1428.36026 −1428.36114 −1428.35980 −1428.36285 −1428.35889 −1428.35814

59.1 59.4 57.3 57.4 59.0 60.1 56.8 56.6 56.5 59.5 58.9 57.5

−12.9 −11.7 −1.3 −1.1 0.0 −1.2 1.8 1.3 2.1 0.2 2.7 3.2

−12.8 −11.3 −2.9 −2.6 0.0 −0.1 −0.3 −1.1 −0.4 0.8 2.6 1.7

b

b

b

E (hartree)

ΔE

−1428.94270 −1428.94058 −1428.91627 −1428.91609 −1428.91939 −1428.91990 −1428.91322 −1428.91431 −1428.91366 −1428.91713 −1428.91536 −1428.91297

−14.6 −13.3 2.0 2.1 0.0 −0.3 3.9 3.2 3.6 1.4 2.5 4.0

b

ΔE + ΔZPE

b

−14.5 −12.9 0.3 0.5 0.0 0.8 1.7 0.8 1.1 2.0 2.4 2.6

MP2/aug-cc-pVTZ E (hartree)

ZPEb

ΔEb

ΔE + ΔZPEb

−1428.94372 −1428.94164 −1428.91762 −1428.91743 −1428.92032 −1428.92099 −1428.91453 −1428.91431 −1428.91366 −1428.91828 −1428.91632 −1428.91403

59.6 59.3 57.3 57.4 59.6 60.3 56.9 56.9 56.9 60.0 59.4 57.9

−14.7 −13.4 1.7 1.8 0.0 −0.4 3.6 3.8 4.2 1.3 2.5 3.9

−14.7 −13.7 0.0 0.3 0.6 0.9 1.6 1.7 2.1 2.2 2.9 2.9

a

The same letters are used to molecular labels for products (A, B), for optimized structures (C, D, E, ...) in increasing order of the relative energy, and for TSs the asterisk is added to these letters. bValues are given in kcal/mol.

Table 4. ZPE Corrected Reaction Energies (ΔE + ΔZPE) and ZPE Corrected Activation Energies (ΔE⧧) for Primary Reaction Processes at the MP2/aug-cc-pVTZ Level of Theory

a

primary reactiona

ΔE⧧ + ΔZPE

ΔE + ΔZPE

(a) HCl + ClONO2 → HONO2 + Cl2 (b) HCl + ClONO2 → HCl·ClONO2 (c) HCl·(H2O) + ClONO2 → HONO2·(H2O) + Cl2 (d) HCl·(H2O) + ClONO2 → HCl·ClONO2·(H2O) (e) HCl + H2O → HCl·(H2O) (f) HCl·(H2O)2 + ClONO2 → HONO2·(H2O)2 + Cl2 (g) HCl·(H2O)2 + ClONO2 → HCl·ClONO2·(H2O)2 (h) HCl·(H2O) + H2O → HCl·(H2O)2 (i) HCl·(H2O)3+ ClONO2 → HONO2·(H2O)3 + Cl2 (j) HCl·(H2O)3+ ClONO2 → HCl·ClONO2·(H2O)3 (k) HCl·(H2O) + H2O → HCl·(H2O)3

46.1

−11.8 −3.2 −17.2 −5.9 −4.2 −17.6 −5.5 −6.4 −17.3 −6.4 −8.7

7.0

0.7

−4.7

The most stable isomer is considered for each structure listed in this table.

activation energies, it has an effect on the time scale of each reaction process. Since the atmospheric pressure in the stratosphere is known as ca. 50 hPa,33 it is a reasonable assumption that kinetic effects for clusters can be estimated under the thermal equilibrium condition. Then, reaction rate constants will be discussed in the next section using the conventional TST. 3.2. Reaction Mechanism to Produce the Cl2 Molecule. Unimolecular reaction rate coefficients ku from PRCs, such as HCl·ClONO2.(H2O)3, were evaluated by TST using the optimized structures. Since isomerization rearrangement between reactants have relatively low energy barriers, reaction pathways from the most stable reactant to the product through different TSs have been considered. While there is only one TS for reactions in n ≤ 2 clusters, an intermediate structure exists in all reaction processes for n = 3. Thus, reaction rate constants have been obtained based on the method of steady state which assumes that the concentration of any intermediate in the reaction is unchanged to make the calculation of rate expressions easier for n = 3. In this assumption, the rate constant k can be written as

transfer reaction and the reaction barrier with ZPE becomes as large as 2.9 kcal/mol at the TS 3L*. From the intermediate structure 3J, the following intracluster reaction occurs to produce the most stable product 3A through the TS 3K* with the small energy barrier of 0.7 kcal/mol. The overall reaction pathways of reaction 1 for n = 0−3 clusters are summarized in Scheme 2 on the basis of our calculated ΔE + ΔZPE. Some important ZPE corrected activation and reaction energies for the elementary processes along with the plausible stepwise reaction mechanisms that produce a Cl2 molecule are listed in Table 4. We assumed that the adapted forms of all structures are the most stable isomers in each reaction step. Although the stepwise processes for the addition of the ClONO2 molecule to HCl·(H2O)n (n ≤ 3) (reactions a, c, f, and i) are exothermic, the energy barrier is higher than that of the reactants for n ≤ 2 clusters, since the relative energies ΔE + ΔZPE at TSs based on the reactant in each elementary process, denoted as ΔE⧧ + ΔZPE, are positive for n ≤ 2. These facts indicate that the reactions a, c, and f should overcome the activation barrier to promote the reaction on the energy surface. In contrast, the direct activation reaction seems to easily occur in the n = 3 cluster because of the negative ΔE⧧ + ΔZPE for reaction i. Although chemical reactions under the thermal equilibrium condition can occur in principle even in the system with high

k=

k1·k 2 k −1 + k 2

(13)

where, k1 and k−1 represent elemental forward and backward rate constants, respectively, from PRC to the intermediate G



Article

Scheme 2. Overall Reaction Processes for ClONO2·HCl·(H2O)n Calculated by the MP2/aug-cc-pVTZ Level of Theory. The Energies Are Given in kcal/mol, (a) n = 0; (b) n = 1; (c) n = 2; (d) n = 3. Isomers 3H* and 3I* Are Calculated by the MP2/ aug-cc-pVTZ//MP2/aug-cc-pVDZ Level of Theory

very good agreement with the experimental pseudo-first-order reaction rate constant of kobs = 1.1 × 103 to 1.5 × 104 s−1 measured on the ice/NAT surface. On the other hand, the reaction through TS 2I* is an unfavorably slow reaction with ku = 1.7 s−1. It is noteworthy that the agreement of rate constants at n = 2 with the experimental value does not mean the reaction process at n = 2 can reproduce the reaction mechanism on the bulk ice/NAT surface, because unimolecular reactions do not include the information of the binding reaction from reactants to PRC, and the partial pressure of component molecules should affect the reaction rate. At n = 3 clusters the rate constant significantly increases to 4.8 × 108 s−1 in the pathway 3C→3I*→3F→3E*→3B. In alternative reaction pathways, rate constants also become 3.9 × 107 s−1 and 6.7 × 107 s−1 for 3C→3L*→3J→3K*→3A and 3C→3H*→3J→3K*→3A, respectively, which are apparently larger than those in n = 2 clusters. The large reaction rate constants for n = 3 clusters are rather reasonable, because activation energies at n = 3 are smaller than corresponding values of n = 2 clusters. To obtain more reliable reaction rate constants, more sophisticated methods such as variational TSTs are required to consider the unharmonicity around TSs and to perform multidimensional tunneling effects. Such investigations are in progress in our laboratory, but they are too time-consuming to be performed with the MP2/aug-ccpVTZ level of theory. As discussed above, the first-order ku values give no information about the time scale of overall processes. Since the reaction rate for the bimolecular reactions between the original reactants are of real practical interest, the second-order reaction rate coefficients kp through PRCs have been examined by eq 5. Molar concentrations and calculated properties of component molecules, in addition to the collision diameters σ, are summarized in Table 6. In these calculations, experimental values34,35 of the partial pressure in the lower stratospheric condition of HCl, ClONO2, and H2O were taken as 1.0 × 10−6 Torr, 1.0 × 10−7 Torr, and 1.0 × 10−4 Torr, respectively. Table 6 indicated that as increasing the hydration number, the partial pressure of complexed molecular cluster decreases, then the ratio of concentrations between HCl(H2O)2 and HCl(H2O)3, [HCl(H2O)3]/ [HCl(H2O)2] is estimated as only 1.9 × 10−4. Therefore, the bimolecular reaction rate of n = 3 cluster should be lowered by the small partial pressure of HCl(H2O)3 while the unimolecular reaction rate coefficient ku is 4.9 × 104 times larger than that in the n = 2 cluster. On the other hand, equilibrium constants Kcap for ClONO2 addition to HCl(H2O)n (n = 1−3) clusters were obtained from the calculated free energy differences ΔGcap between reactants and PRCs as shown in Table 7. Since entropies of PRCs are smaller than those of bimolecular reactants due to some additional hydrogen bonds, ΔGcap became positive in contrast to negative values in energy differences ΔE + ΔZPE for reactions b, d, g and j in Table 4. Since TSs are lying above the original reactants on the free energy surfaces for all association reactions in Table 7, reaction rate coefficients, kcap, can be obtained by solving eq 5. The important thing is that the reaction rate constants evaluated by TST also cannot exceed the capture rates kcap which are upper limits of the reactions. While capture rate constants depend on collision diameters, no significant difference can be seen for n = 0−3 clusters ranging from 2.2 × 10−10 to 2.4 × 10−10 cm3/s. As a results, the rate coefficient kcap of the trihydrate reaction is 1.8 × 105 times larger than the dihydrate reaction. Even though a

structure. Although the intermediate structure goes to the product with the elemental rate constant k2, the backward reaction from the product to the intermediate structure was neglected because of a small reaction rate. These elemental rate constants were calculated at some different temperatures. Reaction rate constants ku for the plausible reaction pathways shown in Scheme 2 have been summarized in Table 5. The largest rate constant at n = 2 is evaluated as ku = 9.7 × 103 s−1 at 200 K in the pathway 2C→2H*→2A, which is occasionally in H


1.988 4.607 9.743 1.905 3.483 9.846 2.328 4.793 8.841 3.531 7.904 1.288 1.601 1.574 8.491 2.447 4.317 5.148

103 104 104 104 105 105 105 105 106

10−17 10−16 10−14 10−13 10−12 10−11 10−9 10−8 10−7

× × × × × × × × ×

× × × × × × × × ×

9.708 1.962 3.669 6.420 1.061 2.519 5.141 9.338 1.547

3.531 7.904 1.288 1.601 1.574 8.491 2.447 4.317 5.148

180 190 200 210 220 240 260 280 300

180 190 200 210 220 240 260 280 300

× × × × × × × × ×

× × × × × × × × × × × × × × × × × ×

× × × × × × × 10−19 10−17 10−16 10−15 10−14 10−12 10−10 10−9 10−8

101 101 102 102 103 103 103

2D→2I*→2B

foward direction 103 1.988 103 8.190 103 2.222 104 5.443 104 1.221 104 4.942 105 1.583 105 4.228 105 9.773 backward direction 10−17 4.602 10−16 1.406 10−14 3.036 10−13 4.871 10−12 6.047 10−11 4.916 10−9 2.010 10−8 4.793 10−7 7.435

2C→2H*→2A

2E→2H*→2A

temperature/K

n=2

4.602 1.406 3.036 4.871 6.047 4.916 2.010 4.793 7.435

1.763 5.903 1.738 4.586 1.101 5.020 1.780 5.188 1.295 × × × × × × × × ×

× × × × × 10−19 10−17 10−16 10−15 10−14 10−12 10−10 10−9 10−8

101 101 102 102 103

× 10−1 × 10−1

2C→2I*→2B

7.534 8.261 8.966 9.649 1.031 1.155 1.270 1.376 1.473

4.677 6.612 8.963 1.172 1.488 2.223 3.069 3.989 4.948 × × × × × × × × ×

× × × × × × × × × 1011 1011 1011 1011 1012 1012 1012 1012 1012

107 107 107 108 108 108 108 108 108

3C→3L*→3J

3.809 3.556 3.354 3.189 3.054 2.850 2.709 2.612 2.547

2.364 2.847 3.352 3.875 4.407 5.484 6.547 7.575 8.554 × × × × × × × × ×

× × × × × × × × × 1013 1013 1013 1013 1013 1013 1013 1013 1013

109 109 109 109 109 109 109 109 109

3C→3H*→3J foward direction 2.995 × 108 3.811 × 108 4.713 × 108 5.688 × 108 6.723 × 108 8.926 × 108 1.123 × 109 1.357 × 109 1.587 × 109 backward direction 2.076 × 1011 2.481 × 1011 2.917 × 1011 3.380 × 1011 3.869 × 1011 4.916 × 1011 6.045 × 1011 7.244 × 1011 8.507 × 1011

3C→3I*→3F

n=3

2.076 2.481 2.917 3.380 3.869 4.916 6.045 7.244 8.507

5.305 6.075 6.873 7.695 8.536 1.026 1.202 1.381 1.559 × × × × × × × × ×

× × × × × × × × × 10−11 10−10 10−9 10−9 10−8 10−6 10−5 10−4 10−3

1011 1011 1011 1011 1011 1012 1012 1012 1012

3J→3K*→3A

6.370 4.360 2.452 1.165 4.789 5.637 4.500 2.651 1.225

5.809 5.765 5.739 5.726 5.724 5.745 5.788 5.845 5.912

× × × × × × × ×

× × × × × × × × ×

10−7 10−6 10−5 10−4 10−4 10−3 10−2 10−1

1012 1012 1012 1012 1012 1012 1012 1012 1012

3F→3E*→3B

Table 5. Calculated Reaction Rate Constants from PRCs to Products by Transition State Theory at Some Different Temperatures for n = 2 and n = 3 Clusters. Values Are Given in sec−1

The Journal of Physical Chemistry A Article

I



Article

Table 6. Gibbs Free Energies (G) Calculated at the Condition of 200 K and 50 hPa, Partial Pressures (P), Molar Concentration (C), and Collision Diameters (σ) Are Summarized for Component Molecules G/hartree

molecule HCl ClONO2 H2O HCl(H2O) HCl(H2O)2 HCl(H2O)3 ClONO2·HCl ClONO2·HCl·H2O ClONO2·HCl·(H2O)2 ClONO2·HCl·(H2O)3

C/mol−1

P/torr

−460.32147 −739.56757 −76.32116 −536.6414 −612.96231 −689.28692 −1199.88486 −1276.20609 −1352.52618 −1428.85162

1.00 1.00 1.88 1.17 6.58 1.27 3.55 3.29 5.07 3.61

× × × × × × × × × ×

−6

5.87 5.87 1.10 6.89 3.87 7.47 2.08 1.93 2.98 2.12

10 10−7 10−4 10−13 10−20 10−23 10−18 10−24 10−31 10−34

× × × × × × × × × ×

σ/pm

10−11 10−12 10−8 10−18 10−24 10−28 10−22 10−28 10−35 10−38

362.5 480.6 333.0 434.7 486.6 527.5

Table 7. Calculated Properties Related to Overall Reaction Rate Constants for the Reaction (eq 1)a n=0 −1

ΔGcap (kcal mol ) Kcap kcap (cm3 s−1) ku (sec−1) kp (cm3 sec−1)

2.6 1.33 2.23 2.04 1.50

× × × ×

10−3 10−10 10−49 10−70

n=1 1.8 1.05 2.29 8.65 5.02

× × × ×

n=2 2.3 2.89 2.35 9.70 1.55

10−2 10−10 10−6 10−26

× × × ×

10−3 10−10 103 10−17

n=3 1.8 1.06 2.40 4.80 2.82

× × × ×

10−2 10−10 108 10−12

a Included are the Gibbs free energy differences ΔG of PRC relative to the original reactants, equilibrium constants Kcap of association reaction of the reactants, capture rate constants (kcap), unimolecular reaction rate constant ku from PRC to products, and overall reaction rate constants (kp) of the most favorable reaction pathways in each size of cluster.

an n = 2 cluster because of the low TS energy. However, since the ratio of molar concentration between HCl[(H2O)3] and HCl[(H2O)2], HCl[(H2O)3]/ HCl[(H2O)2] is estimated as only 1.9 × 10−4, the overall reaction rate of the trihydrate reaction becomes small. Nevertheless, the trihydrate reaction is still 35 times faster than that of the dihydrate reaction.

small amount of the molar concentration of HCl(H2O)3 is obtained, the overall reaction rate of the trihydrate reaction is 35 times faster than that of the dihydrate for the former to outrun the latter. Apparently, it is suggesting that reaction 1 may proceeds more easily as the hydration number increases. However, it is expected that the reaction rate does not dramatically increase even if n becomes larger than three. This is because the molar concentration significantly decreases as n increases, while the capture rate constant will not decrease so much. Thus, the overall reaction rate would be suppressed by the small amount of the molar concentration of hydrated clusters at n ≥ 4 even if the TS energy diminishes at n ≥ 4 and the potential energy from PRC to products monotonically decreases.

■

ASSOCIATED CONTENT

S Supporting Information *

The isomeric structures except for those illustrated in this manuscript; tables that have structural parameters in detail. This material is available free of charge via the Internet at http://pubs.acs.org.

■

4. CONCLUSIONS The activation reactions of ClONO2 + HCl that produce a Cl2 molecule on water clusters have been investigated by means of ab initio MO calculations using the MP2/aug-cc-pVTZ level of theory. Optimized structures and their relative energies were obtained to describe the isomerization and Cl2 production reactions. Many isomeric structures exist with equivalent binding energies in the cluster and the activation barrier significantly decreases to be 2.1 kcal/mol at n = 3. ZPE corrections are essential to describe the overall energy profiles during the reaction. While there exist two TS structures from the reactant to the product in n = 3 clusters, one TS disappears with the inclusion of ZPE corrections in our calculations. Although the calculated energy profiles for plausible reaction pathways indicated that hydrated water molecules lower the reaction barriers to produce a Cl2 molecule, activation energies are rather high for n = 0−2 clusters at T = 200 K. Since chemical reactions can proceed in principle even in the system with high activation energies under the thermal equilibrium condition, the reaction rate constants have been evaluated using conventional TST. Calculated rate constants from the original reactants to the product in an n = 3 cluster are 1.8 × 105 times larger than that in

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: (+81)-722-54-9722. Fax: (+81)-722-54-9722. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported by Grant-in-Aid for Scientific Research (C) from the Japanese Ministry of Education, Culture, Sports, Science and Technology (No. 23550021). T.A. also acknowledges the financial support provided by Core Research for Evolution Science and Technology (CREST) “High Performance Computing for Multi-scale and Multi-physics Phenomena” from the Japan Science and Technology Agency.

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REFERENCES

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Theoretical Investigation of the Reaction Mechanism of ClONO2+ HCl

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