Water-Assisted Dehalogenation of Thionyl Chloride in the Presence of

Mar 8, 2010 - of the dehalogenation reactions of thionyl chloride is reported, in which water ... Thionyl chloride is a very strong oxidant that is wi...
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J. Phys. Chem. A 2010, 114, 4123–4130

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Water-Assisted Dehalogenation of Thionyl Chloride in the Presence of Water Molecules Chi Shun Yeung, Ping Leung Ng, Xiangguo Guan, and David Lee Phillips* Department of Chemistry, The UniVersity of Hong Kong, Pokfulam Road, Hong Kong, People’s Repubic of China ReceiVed: NoVember 10, 2009; ReVised Manuscript ReceiVed: January 20, 2010

A second-order Møller-Plesset perturbation theory (MP2) and density functional theory (DFT) investigation of the dehalogenation reactions of thionyl chloride is reported, in which water molecules (up to seven) were explicitly involved in the reaction complex. The dehalogenation processes of thionyl chloride were found to be dramatically catalyzed by water molecules. The reaction rate became significantly faster as more water molecules became involved in the reaction complex. The dehalogenation processes can be reasonably simulated by the gas-phase water cluster models, which reveals that water molecules can help to solvate the thionyl chloride molecules and activate the release of the Cl- leaving group. The computed activation energies were used to compare the calculations to available experimental data. Introduction

Computational Details

Thionyl chloride is a very strong oxidant that is widely used in organic chemistry to convert alcohols and carboxylic acids into their corresponding chlorides. Thionyl chloride also reacts rapidly with water and has been employed to dehydrate metal chlorides.1 SOCl2 has found an important role in lithium batteries that have high energy densities and long storage lives,2,3 and this has prompted investigations of the electrochemical reduction of SOCl2 in Li/SOCl2 batteries.4 SOCl2 has also found applications for use in the end group derivatization of single-wall carbon nanotubes (SWCNTs),5-8 where this SOCl2 treatment can greatly improve the electrical conductivity and mechanical properties of the SWCNTs. Although there are diverse applications and studies of SOCl2, there are only a few reported experiments and theoretical studies on how SOCl2 reacts with water.9,10 Theoretical work on the hydrolysis of SOCl2 with one to two water molecules has been studied previously.10 Since water molecules are known to react and catalyze various reactions (CO2 and SO3 hydration, dehalogenation of CBr4 and other polyhalomethanes, hydrolysis of N,N-dimethyl-N′-(2′,3′dideoxy-3′-thiacytidine) formamidine, H2O2 formation, heme degradation by the enzyme heme oxygenase, etc.)11-17 and increasing the number of water molecules involved in the reaction system can decrease the activation barrier and hence increase the reaction rates, it would be useful to extend the previous study of the SOCl2 reaction with water to larger water cluster sizes to better understand how solvation influences the reaction. In this paper, we report the results of ab initio and DFT calculations employed to investigate the gas-phase dehalogenation reactions of SOCl2. We find that the presence of water molecules can accelerate the decomposition reaction, and the decomposition reaction can be further accelerated by introducing more water molecules into the reaction system. These ab initio studies help to elucidate the reaction mechanism that can account for the relatively easy conversion of the halogen atoms in SOCl2 to become chloride ions in the presence of water, as observed in previously reported experiments.9

Second-order Møller-Plesset perturbation theory (MP2) and density functional theory (DFT) approaches were used to investigate the gas-phase water-catalyzed reaction mechanisms of the dehalogenation of thionyl chloride (SOCl2). We considered the dehalogenation reaction to be a two-step reaction. The first reaction step involves the dehalogenation of SOCl2 to SOCl(OH) and HCl (reaction 1-1), and the second reaction step is the decomposition of SOCl(OH) to produce SO2 and HCl (reaction 1-2), as shown below

* To whom correspondence should be addressed. E-mail: phillips@ hkucc.hku.hk.

SOCl2 + nH2O f SOCl(OH) + HCl + (n - 1)H2O (n ) 1, 3, 4, 5, 6, 7)

(1-1)

SOCl(OH) + nH2O f SO2 + HCl + nH2O

(1-2)

(n ) 0, 1, 2)

These may be added together to obtain the overall reaction given below

SOCl2 + 2nH2O f SO2 + (2n - 1)H2O + 2HCl

(1) All of the reactions have been explored by optimizing the structures of the reactant complexes (RC), transition states (TS), and product complexes (PC). RCmn, TSmn, and PCmn denote the structures obtained from the calculations where m ()1 and 2) represents the step of the reaction and n ()1, 3, 4, 5, 6, 7 for m ) 1; )0, 1, 2 for m ) 2) represents the number of water molecules in the reaction. For example, RC12 is the reaction complex of reaction 1-1 with two water molecules, and TS22 is the transition state of reaction 1-2 with two water molecules. The stationary structures for all of the RC, TS, and PC were fully optimized without symmetry constraints (C1 symmetry). The 6-31+G* basis set was employed in the MP2 and DFT (B3LYP) calculations for both the optimization and frequency calculations with the Gaussian 03 program suite (C02 version). Analytical frequency calculations were performed to confirm

10.1021/jp9106926  2010 American Chemical Society Published on Web 03/08/2010

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the optimized structures to be either a minimum or a first-order saddle point and to obtain the zero-point energy correction for all of the reactions. Intrinsic reaction coordinate (IRC) calculations were performed to confirm that the optimized TS correctly connected the relevant reactants and products. To compare with the experimental gas-phase kinetics data available in the literature, the energies of the stationary structures for all of the reactions were refined by optimization at the B3LYP level of theory with a larger basis set 6-311++G(3df,3pd). Analytical frequency calculations and the zero-point energy (ZPE) correction for all of the reactions have been computed using the B3LYP/6-311++G(3df,3pd) level of theory. Results and Discussion A. Reactions of SOCl2 with H2O. Figure 1 presents the optimized structures of the RCs, TSs, and PCs obtained from MP2/6-31+G* calculations for reaction 1-1 with a different number of water molecules involved (n ) 1, 3, 4, 5, 6, 7) in the reaction system. Selected key geometry parameters (bond lengths given in Å) are also shown in the figure. Figures 2-4 display the relative energy profiles including the zero-point energy (ZPE) (in kcal/mol) obtained from MP2/6-31+G*, B3LYP/6-31+G*, and B3LYP/6-311++G(3df,3pd) calculations, respectively. For the reaction where n ) 2, we failed to locate and optimize the transition state TS12 which connects the reaction complex SOCl2 · 2(H2O) and product complex SOCl(OH) by using the theory and basis set mentioned above, and results for this reaction are thus not reported. Detailed optimized structures and energies for the reactions studied here are available in the Supporting Information. Inspection of Figure 2 shows that the activation barriers for the first reaction step are about 26.5 kcal/mol for n ) 1 and 24.3 kcal/mol for n ) 3, and they gradually decreases to 16.6 kcal/mol for n ) 4. By increasing the number of water molecules involved, the reaction barriers further decrease from 14.7 kcal/ mol for n ) 5 to 8.0 kcal/mol for n ) 7. The trend observed in the results of the calculations reveals that incorporation of additional water molecules can greatly assist the reaction. DFT calculations were done to compare with the results computed at the MP2 level of theory. The energy profiles of the B3LYP/ 6-31+G* calculations are shown in Figure 3, and a similar catalysis trend is observed by increasing the number of water molecules incorporated into the reaction system, with the exception of the reaction with n ) 6. This exception is probably due to the more incomplete basis functions used to simulate the cooperative hydrogen bonding in the reaction. Some reports suggested that diffuse functions are important to study weak hydrogen bonds.18-20 When a larger basis set (namely 6-311++G(3df,3pd)) is used, this exception disappears, and the overall trend behaves in a manner similar to the results from the MP2 calculations. The results from DFT calculations using a larger basis set are shown in Figure 4, and most of the energies computed are lower than the energies obtained from the MP2 calculations. The catalytic effect by addition of water molecules can be accounted for by the increase of hydrogen bonds between water molecules and the leaving group chloride species. Previous work on halide elimination reactions suggested that watersolvated clusters can help to stabilize the negative charge on the halide anion and spread the charge over the whole water cluster reaction system.21-25 To better understand this water solvation effect, it is helpful to investigate the structural and charge changes that take place during the reaction when an increasing number of water molecules are involved in the reaction system. With reference

Yeung et al. to previous work on water cluster calculations,14-17,26-33 various models for reaction complexes have been developed. The structures presented in Figure 1 are chosen from the ones that give the lowest activation barrier among the different reaction complex orientations with a given number of water molecules involved in the reaction system. In the reaction for n ) 1, there are great structural changes taking place. The S-Cl(1) bond change from RC11 to TS11 is 0.61 Å, and the original pyramidal structure of thionyl chloride becomes deformed to a nearly planar structure in TS11. These structural changes are consistent with the high activation energy needed for the reaction to proceed. For n ) 3, the water molecules are connected with the leaving group H · · · Cl through cyclic hydrogen bonds. The S-Cl(1) bond change from RC13 to TS13 is 0.42 Å, and there is less distortion of the pyramidal shape upon going from RC to TS compared with that for the one water reaction system case. The decrease in the change of the S-Cl(1) bond is accompanied by a smaller shape change leading to a lower activation barrier. To further increase the number of water molecules from n ) 3 to 4, the energy drops significantly from 24.3 to 16.6 kcal/mol. To account for the decrease of the activation barrier, it is worth noting the reaction mechanism between the three water and four water molecule involved reactions. The H-O1 bonds in TS13 and TS14 are 1.42 and 1.26 Å, and the H-O2 bonds are 1.08 and 1.18 Å, respectively. These values indicate that the H atom is already somewhat detached from the O1 atom in the three water assisted reaction while the H atom is partially bonded to O1 and O2 in the four water assisted reaction. Furthermore, in the latter stage of the reaction, the zwitterions H5O2+Cl- in TS13 collapse and associate to form a HCl molecule and water molecules. However, the H3O+ entity can be stabilized in TS14 so that H3O+ Cl- pairs are maintained in PC14. The partial bond cleavage and stabilization of the H3O+ entity in the four water assisted reaction may explain the lower activation energy than that of the three water assisted reaction. For the four, five, and six water involved reactions, the H-O1 bonds are all partially detached from the O1 atom. It is interesting that there is a trend of a decrease of the H-O1 bond in TS1n where n ) 4, 5, 6, with corresponding H-O1 bond lengths of 1.26 Å for TS14, 1.23 Å for TS15, and 1.19 Å for TS16, respectively. The shortening of the H-O1 bond suggests that less energy is required for the H-O1 bond cleavage during the reaction. The increase in the water molecules enhances the hydrogen bonds between the water molecules and chloride leaving group. There are two H · · · Cl(1) interactions, and cagelike water clusters are formed in the n ) 4, 5, 6 reactions. Therefore, the H3O+ ion can be stabilized and H3O+ Cl- pairs formed. These interactions also help to stabilize the leaving Cl atom by spreading the charge over the whole water cluster. The hydrogen bond interactions between water molecules also limit the flexibility of the water cluster. For the seven water molecule involved reaction, the reaction mechanism is similar to the (n ) 4, 5, 6) involved reactions and gives the lowest activation barrier. Seven water molecules were incorporated with the thionyl chloride substrate. The seven water molecules occupied seven corners of the cube, while the Cl(1) atom occupied the remaining corner. The cubic water cluster has been well-studied theoretically34-40 and experimentally,41-43 and these studies found that the cubic cluster appears to be the most stable with a large binding energy per water molecule compared with those of hexamer and heptamer water clusters.39 Two strong H · · · Cl(1) interactions (H · · · Cl(1) interactions change from RC to TS with differences of 0.75 and 0.63, Å respectively) and the shortening of the S-Cl bond (by about 0.31 Å) would help

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Figure 1. The optimized geometries (bond lengths are in Å) for all of the RC1n, TS1n, and PC1n obtained from the MP2/6-31+G* calculations for the SOCl2 + nH2O f SOCl(OH) + HCl + (n - 1)H2O (n ) 1, 3, 4, 5, 6, 7) reaction are shown.

to compensate the energy required for partial cleavage of the H-O1 bond. In addition, the extensive hydrogen bonding in the cubic structure imposes a constraint on the structural changes

that take place upon going from RC17 to TS17. This less flexible water-solvated cubic structure provides better solvation of the leaving chloride anion and spreads the charge over the water

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Figure 2. Relative energy profiles (in kcal/mol) obtained from the MP2/6-31+G* calculations for the SOCl2 + nH2O f SOCl(OH) + HCl + (n - 1)H2O (n ) 1, 3, 4, 5, 6, 7) reaction are shown.

Figure 3. Relative energy profiles (in kcal/mol) obtained from the B3LYP/6-31+G* calculations for the SOCl2 + nH2O f SOCl(OH) + HCl + (n - 1)H2O (n ) 1, 3, 4, 5, 6, 7) reaction are shown.

Figure 4. The relative energy profiles (in kcal/mol) obtained from the B3LYP/6-311++G(3df,3pd) calculations for the SOCl2 + nH2O f SOCl(OH) + HCl + (n - 1)H2O (n ) 1, 3, 4, 5, 6, 7) reaction are shown.

cluster.44 The effect of spreading the charges over the water cluster can be better understood by performing a charge distribution analysis. The results of a natural bond orbital (NBO) analysis of the RCs, TSs, and PCs are shown in Table 1. The

Yeung et al. charge on the leaving Cl(1) atom in the transition states for the n ) 3, 4, 5, 6 reaction systems remains nearly the same, but there is a decrease of the charge in TS17. This suggests that the cubic water cluster structure can help to spread the charge on the leaving Cl(1) atom into the cluster. From the charge difference between the transition states and the reaction complexes, QTS - QRC of the Cl(1) atom, there is a general trend that the charge difference becomes smaller as the number of water molecules involved in the reaction systems increase (n ) 1, 4, 5, 6, 7). A lower charge transfer is consistent with a lower activation energy being observed for the reaction system. Moreover, the charge on the Cl(1) atom in PC1n for n larger than 3 is very negative, which shows that the Cl(1) atom is anionic. This result is consistent with the formation of the H3O+ Cl- pairs in PC1n for the n ) 4, 5, 6, 7 reaction systems. For n ) 1 and 3, there is decrease of charge on Cl(1) in the product complexes. This implies that the H3O+ Cl- pairs collapse and a covalent H-Cl molecule is formed. Apart from the kinetic studies on this reaction, the energy difference between Eproduct and Ereactant is negative in the six and seven water involved reactions, which indicates that the reaction is exothermic (see Figures 2-4). Therefore, the reactions of water-assisted dissociation of chloride from the SOCl2 reaction with water molecules are both kinetically and thermodynamically favorable. B. Reactions of SOCl(OH) with H2O. Figure 5 presents the optimized structures of the RCs, TSs, and PCs obtained from the MP2/6-31+G* calculations for reaction 1-2 with a different number of water molecules involved (n ) 0, 1, 2). Selected key geometry parameters (with the bond lengths given in Å) are also shown in the figure. Figures 6-8 display the relative energy profiles including the ZPE (in kcal/mol) obtained from the MP2/6-31+G*, B3LYP/6-31+G*, and B3LYP/6311++G(3df,3pd) calculations, respectively. Detailed optimized structures and energies are available in the Supporting Information. Inspection of Figure 6 shows that the activation barrier for the second reaction step is about 16.2 kcal/mol for n ) 0, and there is a significant decrease of the reaction barrier to 6.1 kcal/ mol for n ) 1. Addition of more water molecules gradually decreases the reaction barrier by about 5 to 1.5 kcal/mol for n ) 2. This trend is similar to the results found for the first reaction step discussed in the previous section. DFT calculations were done to compare with the results computed at the MP2 level of theory. The energy profiles determined from the B3LYP/631+G* and B3LYP/6-311++G(3df,3pd) calculations are shown in Figures 7 and 8, respectively, and similar trends are observed for the reaction barriers as the number of water molecules incorporated in the reaction increases. The catalytic effect associated with addition of water molecules can be accounted for by the increase of hydrogen bonds between the water molecules and the leaving chloride species. The reaction mechanism of reaction 1-2 is simpler than that determined for reaction 1-1. The hydrogen atom in the SOCl(OH) molecule detaches from the oxygen atom, and this is accompanied by the elimination of the Cl(2) atom from the sulfur atom to form HCl. This reaction mechanism is similar to our previous study of the reaction of CH2Cl(OH) f HCl + HClO.27 Examination of Figure 5 shows that the decomposition reaction can be enhanced by a cyclic hydrogen bond system. For n ) 0, there is a large shape distortion of RC20 for the reaction to proceed, and there is also a large elongation of the S-Cl(2) bond during the reaction. By introducing one water molecule into the reaction system, the structural distortion can

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Figure 5. The optimized geometries (bond lengths are in Å) for all of the RC2n, TS2n, and PC2n obtained from the MP2/6-31+G* calculations for the SOCl(OH) + nH2O f SO2 + HCl + nH2O (n ) 0, 1, 2) reaction are shown.

TABLE 1: NBO Charges on the Leaving Cl(1) Atom for the Reaction SOCl2 + nH2O f SOCl(OH) + HCl + (n - 1)H2O (n ) 1, 3, 4, 5, 6, 7) from the MP2/6-31+G* Computations Cl(1)

n)1

n)3

n)4

n)5

n)6

n)7

reactant complex (RC) transition state (TS) product complex (PC) QTS - QRC QPC - QTS

-0.204 -0.686 -0.307 -0.482 0.379

-0.348 -0.727 -0.375 -0.379 0.353

-0.291 -0.749 -0.863 -0.458 -0.114

-0.277 -0.726 -0.855 -0.449 -0.129

-0.429 -0.758 -0.853 -0.330 -0.094

-0.503 -0.642 -0.871 -0.139 -0.229

become less severe, and the pyramidal configuration can be retained in the transition state. The smaller structural changes can reduce the energy required for the reaction to proceed. It is interesting to note that there are systematic changes upon going from the reaction complex to the corresponding transition state. The elongation of the S-Cl(2) bond in RC2n and the change in the S-Cl(2) bond upon going from RC to TS becomes smaller. For example, the S-Cl(2) bond in RC20 is 2.18 Å, and it is 2.20 Å for RC21 and 2.28 Å for RC22. The elongation of the S-Cl(2) bond is accompanied by a shortening of the S-O1 bond. For example, the bond length between the S and O1 atoms in RC20 is 1.66 Å and changes to 1.59 Å in RC22, and this indicates partial double bond character. The activation of the reaction complex can be accounted for by the hydrogen bond linkage between the leaving H atom and the Cl(2) atom in RC22. Meanwhile, the change of the bond length upon going from the RC to the TS can also account for the decrease of the activation barrier when more water molecules are involved in

the reaction system. The changes in the H-Cl(2) bond length upon going from the RC to the TS is 0.53 Å for n ) 0, 0.31 Å for n ) 1, and 0.12 Å for n ) 2. The smaller bond length changes observed upon going from the RC to the TS imply that the reaction complex has been activated toward the reaction. This is consistent with the argument stated above. The product complexes have lower energy than their corresponding reactant complexes. The negative sign of the value ∆E ) Eproduct Ereactant indicates that the reaction is exothermic. Therefore, the second reaction steps are also both kinetically and thermodynamically feasible. Apart from an investigation of the structural changes, the changes that take place for the charge on each atom can also help explain the trend observed for the reaction barriers as a function of the number of water molecules involved in the reaction system. The results of a natural bond orbital (NBO) analysis of the RCs, TSs, and PCs are shown in Table 2. The charge on the leaving Cl atom in the RCs is quite negative

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Yeung et al. TABLE 2: NBO Charges on the Leaving Cl(2) Atom for the Reaction SOCl(OH) + nH2O f SO2 + HCl + nH2O (n ) 0, 1, 2) Determined from the MP2/6-31+G* Computations Cl(2)

n)0

n)1

n)2

reactant complex (RC) transition state (TS) product complex (PC) QTS - QRC QPC - QTS

-0.337 -0.591 -0.300 -0.254 0.291

-0.352 -0.602 -0.363 -0.250 0.238

-0.444 -0.560 -0.391 -0.116 0.169

TABLE 3: MP2/6-31+G* Calculated Energies (∆E‡, kcal/mol), Enthalpies (∆H‡, kcal/mol), Free Energies (∆G‡, kcal/mol), Entropies (∆S‡, kcal/mol), Zero-Point Energies (∆ZPE, kcal/mol), and Rate Constants (k, L mol-1 s-1) for Reactions 1-1 and 1-2 reaction Figure 6. The relative energy profiles (in kcal/mol) obtained from the MP2/6-31+G* calculations for the SOCl(OH) + nH2O fSO2 + HCl + nH2O (n ) 0, 1, 2) reaction are displayed.

1-1: SOCl2 4, 5, 6, 7) 11 13 14 15 16 17

∆E‡a

∆H‡b

∆G‡

∆S‡

∆ZPEc

kd

+ nH2O f SOCl(OH) + HCl + (n - 1)H2O (n ) 1, 3, 23.6 22.3 14.4 13.9 7.2 6.2

21.8 19.1 11.7 11.0 4.5 3.3

1-2: SOCl(OH) + nH2O f 20 19.5 15.9 21 6.5 3.8 22 3.5 0.9

-0.4 -1.2 -1.0 -1.5 -0.9 -1.1

2.1 × 10-7 8.6 × 10-6 4.0 × 100 1.1 × 102 6.7 × 105 8.1 × 106

26.5 24.3 16.6 14.7 9.5 8.0

-15.9 -17.5 -16.6 -12.3 -16.8 -15.7

SO2 + 16.2 6.1 1.5

HCl + nH2O (n ) 0, 1, 2) -0.2 -3.4 8.4 × 100 -7.4 -1.7 2.0 × 108 -5.8 -1.7 4.9 × 1011

a ∆E‡: Energies of activation for the reaction. b ∆H‡, ∆G‡: Enthalpies and free energies of activation for the reaction with a ZPE correction. c ∆ZPE ) ZPE(TS) - ZPE(RC). d k: Calculated from the free energy of activation by k ) (kBT/h) exp(-∆G‡/RT).

Figure 7. The relative energy profiles (in kcal/mol) obtained from the B3LYP/6-31+G* calculations for the SOCl(OH) + nH2O f SO2 + HCl + nH2O (n ) 0, 1, 2) reaction are shown.

Figure 8. The relative energy profiles (in kcal/mol) obtained from the B3LYP/6-311++G(3df,3pd) calculations for the SOCl(OH) + nH2O f SO2 + HCl + nH2O (n ) 0, 1, 2) reaction are displayed.

(ranging from -0.34 to -0.44), and the charge becomes more negative in the corresponding TSs (ranging from -0.56 to -0.60). This suggests there is a substantial charge redistribution that occurs during the reaction. The charge on the Cl atom in the transition states for n ) 0, 1, and 2 remains nearly the same.

From the charge difference between the transition states and the reaction complexes, QTS - QRC of the Cl atom, the charge difference becomes smaller as the number of water molecules involved in the reaction increases (n ) 0, 1, 2). The sulfur atom also exhibits a similar trend. This reveals that the S-Cl bond is activated, and this bond is more ready to be cleaved as the number of water molecules involved in the reaction increases. A smaller charge transfer results in a lower activation energy. C. Comparison of the Proposed Model with the Available Experimental Kinetic Rate Constant. It is useful to compare our computed thermodynamic results, which are shown in Tables 3 and 4, to the experimental gas-phase decomposition reactions of SOCl2 + H2O f SO2 + HCl. Recently, the reaction kinetics of SOCl2 dehalogenation was studied by gas-phase IR spectroscopy in a chamber.9 To have a very rough comparison with the experimental results, the data set of the B3LYP/6311++G(3df,3pd) and MP2/6-31+G* computational results has been used to estimate the rate constant kn using Eyring’s equation. For our proposed mechanism, reaction 1-1 has smaller rate constants compared to the corresponding ones for reaction 1-2. This shows that reaction 1-1 is the rate-determining step, and we shall assume that the contribution from reaction 1-2 can be neglected. However, to compare with the experimental value, the calculated rate constants have to be convert to the “effective rate constants” Kn by the expression Kn ) kn × [(H2O)n], where [(H2O)n] represents the water cluster concentration. The chance of several water molecules colliding together to initiate the reaction is rare. Therefore, the probability of the formation of the water clusters before reacting with thionyl chloride is critical for the water-assisted reaction to proceed. The reaction was studied experimentally in the gas phase with experimental conditions of 297 K and 1 atm of pressure.9 Previous experimental studies observed that the water dimer is

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TABLE 4: B3LYP/6-31++G(3df,3pd) Calculated Energies (∆E‡, kcal/mol), Enthalpies (∆H‡, kcal/mol), Free Energies (∆G‡, kcal/mol), Entropies (∆S‡, kcal/mol), Zero-Point Energies (∆ZPE, kcal/mol), and Rate Constants (k, L mol-1 s-1) for Reactions 1-1 and 1-2 reaction 1-1: SOCl2 4, 5, 6, 7) 111 113 114 115 116 117

∆E‡a

∆H‡b

∆G‡

∆S‡

∆ZPEc

kd

+ nH2O f SOCl(OH) + HCl + (n - 1)H2O (n ) 1, 3, 24.8 21.5 14.3 7.4 6.2 5.2

23.1 17.5 11.4 4.6 3.4 2.2

28.6 23.1 18.5 10.7 9.0 6.6

-18.6 -18.9 -24.1 -20.3 -18.7 -15.0

-0.2 -1.9 -1.1 -0.7 -0.6 -1.3

6.6 × 10-9 6.5 × 10-5 1.6 × 10-1 8.9 × 104 1.5 × 106 8.5 × 107

1-2: SOCl(OH) + nH2O f SO2 + HCl + nH2O (n ) 0, 1, 2) 120 19.6 15.9 15.9 -0.8 -3.3 1.2 × 101 121 7.7 4.8 6.0 -4.4 -2.2 2.5 × 108 122 2.1 -0.1 2.6 -5.5 -1.5 7.1 × 1010 a ∆E‡: Energies of activation for the reaction. b ∆H‡, ∆G‡: Enthalpies and free energies of activation for the reaction with a ZPE correction. c ∆ZPE ) ZPE(TS) - ZPE(RC). d k: Calculated from the free energy of activation by k ) (kBT/h) exp(-∆G‡/RT).

present at 294 K, and it was speculated that larger water cluster with n ) 3-6 may also exist in quantities comparable to the aerosol background in the troposphere.45 A recent theoretical study also demonstrated that the concentrations of higher-order water trimers, tetramers, pentamer, and hexamers at 298.15 K produced from individual water molecules were estimated to be 2.6 × 1012, 5 × 1011, 2.5 × 1010, and 3 × 104 clusters/cm3.45,46 These estimated values give support for the existence of larger water clusters under 1 atm and room-temperature conditions. The estimated water cluster concentrations were quoted from refs 45 and 46. These references have been utilized by different research groups to study water cluster properties or related subjects. Therefore, we refer readers to these two references for details about the errors associated with estimating the water cluster concentrations. We note that we cannot preclude surfacecatalyzed reactions and aerosol-catalyzed reactions also being involved to some extent in the experiments reported previously.9 After consideration of the water cluster concentration, the rate constants Kn are roughly equal to 1.8 × 10-10, 3.7 × 10-14, 3.3 × 10-9, 4.5 × 10-9, and 3.3 × 10-11 s-1 based on the results from the MP2 calculations and 5.5 × 10-12, 2.8 × 10-13, 1.3 × 10-10, 3.7 × 10-6, and 7.7 × 10-11 s-1 based on the results from the DFT calculations for the n ) 1, 3, 4, 5, and 6 water involved reaction systems, respectively. A previous theoretical study has calculated the rate constant for one water molecule reacting with thionyl chloride.10 The value calculated from B3LYP/6-311++G(3df,3pd) is about k1 ) 1.4 × 10-31 cm3 s-1 molecule-1, which is equivalent to K1 ) 7 × 10-14 s-1 (using a typical experimental concentration of water of 5 × 1017 molecules/cm3). The rate constant is smaller than the value that we found in the n ) 1 case (K1 ) 5.5 × 10-12 s-1 from the same theory and basis set). The difference comes from the smaller activation barrier between RC11 and TS11. As only one water molecule is present in the system, various orientations in the RC can be obtained. The restriction of the orientation is not as large as that in the n ) 7 case, which has been mentioned in a previous section. The value of Kn from the two calculation methods indicates that the water-assisted pathway appears to be mostly dominated by the five water involved reactions. This suggests that trace amounts of water clusters can play an important role in these kinds of dehalogenation reactions. The experimental rate constant of the reaction k is 6.3 × 10-21 cm3

s-1 molecule-1.9 In order to compare the experimental value with the computational data, the concentration of water has to be estimated, and the concentration was estimated to be roughly 5 × 1017 molecules/cm3, which is a typical experimental concentration of water.9 Therefore, the rate constant is equivalent to 3.2 × 10-3 s-1. By comparing the experimental value with the value of K5 derived from the results of the MP2 and DFT calculations, the computational value are about 6 and 3 orders lower than the experimental value, respectively. This discrepancy between the calculated rate constant being too low compared to the experimental value is probably due to the interpretation of the experimental rate constant and an insufficient representation to more accurately model the actual cooperative hydrogen bond system. The experimental reaction rate reflects the overall effect of all of the reaction pathways in the system. On the basis of the calculation data from the MP2 and B3LYP methods, there are reaction pathways which give comparable reaction rates with the pathway n ) 5 (e.g., reaction pathways n ) 1 and 4 in the MP2 calculations). Therefore, the hydrolysis of thionyl chloride may react via several reaction pathways but not particularly predominated by any one particular reaction pathway. To better model the cooperative hydrogen system, a highlevel treatment of electron correlation with a large basis set is important to describe the weak hydrogen bonds between the water molecules and SOCl2. Therefore, ab initio theory, MP2, and CCSD(T) and larger basis functions with diffuse function18-20 are thought to be appropriate candidates to better describe the reaction. Previous work on the calculation of hydrolysis of thionyl chloride reported that no great improvement of the reaction rate was found by using larger basis functions and highlevel theory ranging from MP2/6-311++G(2df,2pd) to MP2/ 6-311++G(3df,3pd) and CCSD(T)/aug-cc-VTZ.10 However, the reaction that was investigated by high-level theory and extended basis sets resembles the reaction pathway for n ) 1, which is shown in Figure 1. The hydrogen bond effect in the reaction complex may make an important contribution to the activation of the reaction when more water molecules become involved in the reaction. High-level theory and large basis sets are likely required to take into account the hydrogen bonds in the system. These high-level theory calculations with extended basis functions require high computational cost. The DFT method with the BH&H-LYP functional47 was recommended in some reports for studying intramolecular hydrogen bonds and proton-transfer reactions,48-50 and those results were found to be comparable to MP2 calculations. The reaction system that we proposed here has similar characteristics. Thus, the BH&HLYP method may be an alternative way to study these water-assisted reactions to obtain more accurate values but are too computationally intensive for us to employ at this time with the resources available to us. It is interesting to note that the advantage of the low activation barrier in the n ) 6 reaction system cannot fully compensate for the low concentration of the hexamer water cluster, and hence, there is a large decrease in the estimated reaction rate associated with this reaction system. We conclude that if sufficient water is available, the decomposition reaction can take place via a cooperative mechanism in both the gas-phase and the aqueous-phase environments. In the aqueous phase, the solvation of thionyl chloride with six or seven water molecules is possible and would be expected to lead to a fast decomposition reaction on the order of 102. There are a limited number of experimental and theoretical studies of the dehalogenation of thionyl chloride reported in the literature, and it is not clear

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whether thionyl chloride interacts with other species in the reaction chamber of the recent experimental study that has been reported.9 We anticipate that it may be worthwhile to perform further experimental work to elucidate the reaction mechanism of the dehalogenation reaction as a function of the humidity in the gas phase and the water concentration in mixed aqueous solutions. Conclusion An ab initio and DFT study of the dehalogenation reactions of thionyl chloride in the presence of water molecules was presented. Up to seven water molecules were explicitly included in the reaction systems to investigate the effect of hydrogen bonding of the water molecules on the dehalogenation reactions. The decomposition reaction of thionyl chloride was found to be remarkably catalyzed by the water molecules, and the decomposition rate became faster as the number of water molecules involved in the reaction system increased. This computational study indicates that water molecules help to solvate the thionyl chloride molecules and facilitate the release of a solvated Cl- leaving group. The present results for thionyl chloride were briefly discussed in relation to previous work reported for a recent experimental study on thionyl chloride and some previous theoretical studies on water clusters and waterassisted dehalogenation reactions. Acknowledgment. This research has been supported by grants from the Research Grants Council of Hong Kong (HKU7039/07P) to D.L.P. D.L.P. thanks the Croucher Foundation for the award of a Croucher Foundation Senior Research Fellowship (2006-2007) and the University of Hong Kong for an Outstanding Researcher Award (2006). Supporting Information Available: Cartesian coordinates and total energies for the stationary points investigated. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Creary, X.; Tricker, J. J. Org. Chem. 1998, 63, 4907. (2) Levy, S. C. J. Power Sources 1993, 43, 347. (3) Wagner, C. G. Proc. Int. Power Sources Symp. 1992, 35, 125. (4) Venkatasetty, H. V. J. Electrochem. Soc. 1980, 127, 2531. (5) Skakalova, V.; Dettlaff-Weglikowska, U.; Roth, S. Diamond Relat. Mater. 2004, 13, 296. (6) Skakalova, V.; Dettlaff-Weglikowska, U.; Roth, S. Synth. Met. 2005, 152, 349. (7) Skakalova, V.; Kaiser, A. B.; Dettlaff-Weglikowska, U.; Hrncarikova, K.; Roth, S. J. Phys. Chem. B 2005, 109, 7174. (8) Dettlaff-Weglikowska, U.; Skakalova, V.; Graupner, R.; Jhang, S. H.; Kim, B. H.; Lee, H. J.; Ley, L.; Park, Y. W.; Berber, S.; Tomanek, D.; Roth, S. J. Am. Chem. Soc. 2005, 127, 5125. (9) Johnson, T. J.; Disselkamp, R. S.; Su, Y. F.; Fellows, R. J.; Alexander, M. L.; Driver, C. J. J. Phys. Chem. A 2003, 107, 6183. (10) Ignatov, S. K.; Sennikov, P. G.; Razuvaev, A. G.; Schrems, O. J. Phys. Chem. A 2004, 108, 3642. (11) Nguyen, M. T.; Raspoet, G.; Vanquickenborne, L. G.; VanDuijnen, P. T. J. Phys. Chem. A 1997, 101, 7379. (12) (a) Chu, J. W.; Trout, B. L. J. Am. Chem. Soc. 2004, 126, 900. (b) Petrie, S. Int. J. Mass Spectrom. 2006, 254, 136.

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