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J. Phys. Chem. A 2010, 114, 2164–2170

Mechanism of Aqueous-Phase Ozonation of S(IV) Tara F. Kahan,† Diego Ardura,† and D. J. Donaldson*,†,‡ Department of Chemistry, UniVersity of Toronto, 80 Saint George Street, Toronto, Ontario, Canada M5S 3H6, and Department of Physical and EnVironmental Sciences, UniVersity of Toronto Scarborough Campus, Toronto, Ontario, Canada M1C 1A4 ReceiVed: September 3, 2009; ReVised Manuscript ReceiVed: December 18, 2009

The ozonation of dissolved sulfur dioxide is an important route for sulfate formation, especially in fog and cloud droplets of high pH. However, little is known about the detailed chemical mechanism of this process. We have mapped out the fate of aqueous SO2 in the presence of ozone by use of density functional theory (DFT) calculations in solution (via the polarized continuum model, PCM), including up to two explicit water molecules. The calculations predict that the hydrolysis of SO2 · H2O, although possessing a barrier, is still more energetically favorable than its ozonation. The ozonation of HOSO2- and SO32- proceeds without barriers and gives S(VI) products that are more stable than the reagents by 77.1 and 88.6 kcal/mol, respectively. By comparing our calculated pH dependence of the ozonation kinetics to those determined experimentally, we conclude that, despite a high calculated energy barrier to the ozonation of sulfonate (HSO3-), it is the dominant form of S(IV) in solutions of neutral pH and is the species through which ozonation occurs. SCHEME 1

Introduction Sulfate is an important constituent of atmospheric aerosols, comprising up to 95% of the mass (see ref 1 and references therein). Sulfate aerosols can reduce visibility and have adverse health effects; they also affect climate through both the direct effect (scattering incoming light) and the indirect effect (acting as cloud condensation nuclei). Sulfate is not emitted directly in large quantities; rather, it is generally formed through the oxidation of SO2, which is one of the principal forms of sulfur released into the atmosphere.1 In the gas phase, oxidation of SO2 by hydroxyl radicals is the major formation route of sulfate compounds. In aqueous aerosols, sulfate formation through SO2 oxidation can take many paths, including direct or metalcatalyzed photolysis, reaction with halogens, and reaction with nitric oxides. In the condensed phase, especially in fogs and clouds, H2O2 is acknowledged to be the most important oxidant at pH levels below 4 (ref 1 and references therein), with ozonation becoming important at higher pH.2-5 Ozonation rates of solvated SO2 are highly pH-dependent, because its different ionic states in solution are thought to display different reaction kinetics with ozone.1,6 These species are collectively termed S(IV), in reference to their oxidation state; the equilibria are displayed in Scheme 1. Similarly, oxidized products are often referred to collectively as S(VI). The reactivity of ozone is thought to vary considerably depending on the form of S(IV) present (e.g., refs 1 and 6). At very low pH, S(IV) is primarily in the form of the monohydrate SO2 · H2O, but as the pH increases, the tautomers bisulfite (HOSO2-) and sulfonate (HSO3-) dominate, and at pH > 7, SO32- becomes most important. These equilibria make S(IV) ozonation complex, as ozone could react with any of these species. Measured kinetics of aqueous S(IV) ozonation show a strong positive correlation between rate and pH. This pH dependence * Author to whom correspondence should be addressed: e-mail [email protected]. † Department of Chemistry, University of Toronto. ‡ Department of Physical and Environmental Sciences, University of Toronto Scarborough Campus.

is best explained by a multiterm rate law that includes separate rate constants for SO2 · H2O and for the singly and doubly ionized forms of S(IV), as is discussed in ref 6. The mechanism remains contentious, however, with two issues in particular still to be satisfactorily resolved. The first is whether SO2 · H2O undergoes ozonation or whether it is only the ionized forms of S(IV) that react. The second unresolved issue is which tautomer, bisulfite or sulfonate, participates in the reaction. The structural difference between bisulfite and sulfonate is the location of the proton: In bisulfite it is bonded to an oxygen atom, while in sulfonate it is bonded to the sulfur atom. This difference can result in different reactivities of the two tautomers. Although bisulfite is expected to be much more reactive toward ozone than sulfonate,6 the relative concentrations of the tautomers in aqueous solution are unclear. As summarized in ref 7, while the majority of studies suggest that sulfonate is the dominant species in solution by up to a factor of 200, some experimental8,9 and theoretical10 studies suggest that bisulfite may in fact dominate. In this study we attempt to resolve some of the uncertainty surrounding the ozonation mechanism of aqueous S(IV). We investigate the energetics of the ozonation mechanisms leading from SO2 · H2O, HOSO2-, HSO3-, and SO32- to determine which pathways are energetically feasible. The importance of the various S(IV) species to this reaction is discussed in the context of experimentally derived kinetics.

10.1021/jp9085156  2010 American Chemical Society Published on Web 01/19/2010

Mechanism of Aqueous-Phase Ozonation of S(IV) Methods Quantum chemical computations were performed with the Gaussian 03 series of programs.11 The geometries of the stable species and transition states were fully optimized in the gas phase with hybrid density functional theory (DFT).12-15 The hybridfunctionalemployedwasMPW1K16 (modifiedPerdew-Wang one-parameter for kinetics), which compromises well between accuracy and computational cost when tested against kinetic data. The system studied in this paper contains a sulfur atom, which needs a basis set large enough to properly describe its electronic structure. For this reason the M3GS17 basis set was used in this investigation. This basis set is identical to 6-311+G(2df) for oxygen and 6-311G(2p) for hydrogen and very similar to 6-311+G(3d,2f) for sulfur, which includes tight d functions (the tightest d function for sulfur has an exponent of 2.6).18 The nature of the stationary points was determined by analysis of the number of imaginary frequencies at the MPW1K/MG3S level of theory. The polarized continuum model19-22 (PCM) was used to include solvent effects in the electronic energy. Since it is well known that the solvent plays an important role in the mechanisms of the reaction under study, up to two water molecules were explicitly considered in our model. Although the explicit inclusion of more than two waters would better describe the first solvation shell of the solute molecules, the increase in computation time associated with including further explicit water molecules is significant. On the basis of previous studies,23 we believe that including two explicit water molecules is sufficient to account for the assistance of water molecules in the reactions modeled in this paper. Given the size of the basis set employed in the present work, singlepoint calculations on the optimized geometries in the gas phase at the MPW1K/MG3S level of theory were carried out to take solvent effects into account. This procedure is supported by the results of Voegele et al.23 in a similar system. These authors reported a difference between the PCM optimized energies and PCM energies on the DFT gas-phase geometries of less than 0.8 kcal/mol and a maximum variation in bond length of approximately 0.02 Å. Since we are using a cluster approach to model reactions in solution, we believe that solution-phase electronic energies will be more accurate than Gibbs free energies. Clusters are heavily penalized by the entropic component of Gibbs free energy. This is reasonable in modeling gas-phase reactions, but in solution, the dissipation of entropy by surrounding solvent molecules is not taken into account. Therefore, energy barriers for bimolecular reactions in solution are often overpenalized by Gibbs free energies. Moreover, the usual scheme employed to take solvent effects into account adds the increment in the Gibbs free energy of solvation to the increment of the Gibbs free energy in the gas phase; this results in an overestimation of energy barriers in solution.24 In order to benchmark the level of theory employed in the present work, we selected four reactions (Scheme 2) to compare the experimental heats of reaction with results obtained at different levels of theory [B3LYP/6-31+G(d), B3LYP/MG3S, MP1KW/MG3S, CCSD/MG3S, CCSD(T)/MG3S, and G3B3]. Table 1 summarizes the relative electronic energies in the gas SCHEME 2

J. Phys. Chem. A, Vol. 114, No. 5, 2010 2165 phase for all the reactions as well as the experimental heats of reaction. MPW1K/MG3S yields overall better agreement with the experimental values than do the other DFT methods in terms of the relative stability of the reactants and products. We have found that our DFT method predicts slightly lower barriers than does G3B325,26 (see Supporting Information). However, both methods yield the same qualitative trend; we therefore determined the most favorable pathway at the DFT level of theory. The addition of thermal corrections were computed by use of the MP1KW/MG3S frequencies within the ideal gas, rigid rotor, and harmonic oscillator approximations27 at 1 atm and 298.15 K. These corrections do not improve the agreement between the calculated energies and the enthalpies of reaction displayed in Table 1; therefore, we report the uncorrected energies. See Supporting Information for details. Results and Discussion Competition between Hydrolysis and Ozonation. The SO2 · nH2O complex that is formed upon dissolution of SO2 in aqueous solution can undergo several processes in the presence of ozone, as illustrated in Scheme 3 for n ) 1. It can hydrolyze to sulfurous and sulfonic acid (pathways A and B, respectively), which will be rapidly ionized in solution to bisulfite and sulfonate, or it can react immediately with ozone (pathway C). Comparing the energy barriers for hydrolysis with the energy barrier for ozonation of aqueous SO2 allows us to determine whether ozonation can occur before equilibrium between the various S(IV) species is established. Table 2 shows the relative energies of the reagents, products, and transition states for the hydrolysis of SO2 · nH2O for n ) 1 and n ) 2. All energies are listed in the gas phase and in solution. In reactions such as hydrolysis, where water plays an assisting role in the mechanism, calculated energy barriers might be artificially high if explicit water molecules are not included in the calculations (see, for example, the results of refs 23 and 28). Additionally, results obtained from a continuum solvation model should better approximate an aqueous environment than results performed in a gas-phase model. Therefore, we focus on energies predicted by use of a solvation model in the presence of two explicit water molecules. The hydrolysis reactions leading to sulfurous and sulfonic acids (pathways A and B, respectively) have energy barriers of 12.8 and 26.6 kcal/mol. Tunneling could reduce the kinetic significance of these barriers, as discussed in ref 29. Our predicted energy barriers are lower than those predicted by Voegele et al.,23 but we predict similar differences in the energy barriers of formation of the two acids. Voegele et al.23 report a difference in energy of 15.0 kcal/mol in favor of pathway A in the presence of two explicit water molecules in solution, while we predict a difference of 13.8 kcal/mol in favor of pathway A. Neither sulfurous acid [SO(OH)2] nor sulfonic acid (HSO2OH) has been detected in solution; if they exist, it is likely only as transient intermediates that undergo rapid ionization to form the bisulfite and sulfonate ions. Here, we report the barriers for their formation as a means to determine the electronic energy barrier for hydrolysis of SO2 · H2O in solution. The ozonation of SO2 can follow several pathways. Here we discuss only the most energetically favorable pathway we found; the profile is shown in Figure 1 in the presence of two assisting water molecules. This reaction begins with the addition of ozone to SO2: both of ozone’s terminal oxygen atoms add to sulfur to form the cyclic intermediate C1, which is more stable than the reagents by 26.1 kcal/mol. The energy barrier presented by the

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TABLE 1: Experimental Heats of Reaction and Relative Electronic Energies in the Gas Phase at Different Levels of Theory for the Benchmark Reactionsa rxn

B3LYP/6-31+G(d)

B3LYP/MG3S

MP1KW/MG3S

CCSD/MG3S

CCSD(T)/MG3S

G3B3

∆Hcorr

expb

1 2 3 4

-24.9 -12.6 -12.3 +68.4

-39.2 -13.7 -25.5 +68.9

-67.8 -28.8 -39.0 +37.9

-63.0 -24.5 -38.4 +55.8

-53.8 -22.8 -30.9 +67.3

-52.6 -25.4 -27.2 +68.3

-0.9 5.9 -6.8 -4.0

-72.1 -10.0 -62.1 +51.1

a Values are given in kilocalories per mole. Thermal correction increments are also indicated. b All experimental enthalpies of formation were taken from ref 30 except the enthalpy of formation of H2SO4 in the gas phase, which was taken from ref 37.

SCHEME 3

TABLE 2: Electronic Energy Barriers and ∆E (Products Reagents) for Hydrolysis of SO2 · H2O in the Presence of One and Two Explicit Water Molecules energy barrier (kcal/mol) gas phase

solution

∆E (kcal/mol) gas phase

solution

n)0 n)1

SO2 · H2O + nH2O f SO(OH)2 + nH2O 33.7 34.1 0.7 16.6 12.8 1.8

-0.2 -1.3

n)0 n)1

SO2 · H2O + nH2O f HSO2OH + nH2O 65.9 63.4 5.8 40.6 26.6 10.9

1.8 4.4

transition state TSC1 is 18.7 kcal/mol. The next step involves the formation of an S-O bond and a water-assisted hydrogen transfer to one of the oxygen atoms of SO2. This transition state, TSC2, presents an energy barrier of 16.2 kcal/mol. The resulting intermediate, C2, is more stable than the reagents by 18.7 kcal/ mol. In the next step of the reaction, the ring structure between ozone and sulfur opens, and the second water molecule acts as a proton shuttle as ozone forms a bond with a hydrogen atom, and one of the oxygen atoms of SO2 loses a proton. This transition state, TSC3, presents an energy barrier of 3.0 kcal/ mol, and C3, the intermediate that is formed, is more stable than the reagents by 61.7 kcal/mol. The final step in this mechanism involves the extrusion of molecular oxygen from ozone and the transfer of a hydrogen atom from ozone back to the sulfur complex with a water molecule once again acting as a proton shuttle. The transition state TSC4 presents an energy

barrier of 8.2 kcal/mol, and the resulting product, H2SO4 · H2O, is more stable than the reagents by 69.5 kcal/mol. This is in very good agreement with the experimental reaction enthalpy, which is -72.1 kcal/mol.30 The first step of this process, the addition of ozone to SO2, is the rate-determining step. Since the hydrolysis of SO2 to sulfurous acid has a lower energy barrier than the rate-determining step of ozonation (12.8 vs 18.7 kcal/mol), we predict that hydrolysis should precede ozonation and that equilibrium between the various S(IV) species will be established before ozonation occurs, regardless of the ozone concentration. It is worth noting the different results obtained when solvation is not considered, as well as when only one explicit water molecule is included in the calculation. If solvation is not considered, ozonation is more energetically favorable than hydrolysis. Although not shown in the above profile, the energy barrier to ozonation in the presence of one water molecule in solution is 15.2 kcal/mol; this is lower than the energy of hydrolysis under the same conditions (34.1 kcal/mol). Hydrolysis is energetically favorable only when extra water molecules are included both explicitly and implicitly through the PCM. This observation highlights the importance of including both implicit and explicit water molecules for modeling of reactions in which water is involved in the mechanism. It also suggests that in conditions where available water is scarce (e.g., on mineral dust), ozonation of SO2 · H2O might compete with hydrolysis. Ozonation of Ionized Forms of S(IV). Figure 2 shows the reaction profile of the ozonation of SO32- (pathway D). The

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Figure 1. MPWB1K/M3GS electronic energy profile (kilocalories per mole) for the ozonation of SO2 · H2O. The numbers given are those corresponding to the process assisted with two water molecules in solution (no parentheses) and in the gas phase (parentheses).

Figure 2. MPWB1K/M3GS electronic energy profile (kilocalories per mole) for ozonation of the sulfite anion. The numbers given are those corresponding to the process assisted with one water molecule in solution (no brackets) and in the gas phase (brackets).

reaction begins with the addition of ozone to sulfur; this barrierless process leads to the open intermediate D1, which is more stable than the reagents by 79.6 kcal/mol. The loss of

molecular oxygen leads to SO42-. In the gas phase, SO42- is higher in energy than D1 by 16.5 kcal/mol. However, when solvation effects are included, SO42- becomes more stable than D1, meaning that it will be the final product. In solution, the formation of SO42- is barrierless and D1 is a transient intermediate. The difference in electronic energy between reagents and the SO42- product is 88.6 kcal/mol, in reasonable agreement with the experimental enthalpy of reaction of -95.5 kcal/mol.30 Figure 3 shows the reaction profiles of the ozonation of HOSO2- and HSO3- (pathways E and F, respectively). The ozonation of HOSO2- is also a barrierless process. The addition of ozone to sulfur leads to the intermediate E1, which is a fourmembered ring adduct with energy 28.3 kcal/mol below that of the reagents in solution. The next step in the oxidation involves a ring-opening reaction in which two of the oxygen atoms from ozone separate from the compound to form the complex E2, which is more stable than the separate reactants by 75.8 kcal/mol. The transition state connecting these species, TSE1, presents a barrier of 3.5 kcal/mol in the gas phase but this disappears when effects of solvation are included, causing E2 to become a transient intermediate. The final step in the oxidation of HOSO2- is the barrierless extrusion of molecular oxygen to form HOSO3-, which is more stable than the reagents by 77.1 kcal/mol. This is in excellent agreement with the experimental enthalpy, calculated with values from refs 30 and 31, of -76.6 kcal/mol. The first step in the ozonation of HSO3- involves a hydrogen transfer from sulfur to ozone and the formation of a bond between ozone and sulfur. The structure that is formed, F1, is more stable than the reactants by 67.2 kcal/mol. The energy barrier corresponding to the transition state TSF1 is 22.5 kcal/

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Figure 3. MPWB1K/M3GS electronic energy profile (kilocalories per mole) for ozonation of the bisulfite (pathway E) and sulfonate (pathway F) anions. The numbers given are those corresponding to the process assisted with one water molecule in solution (no brackets) and in the gas phase (brackets).

mol in solution; interestingly, in the gas phase it is only 3.3 kcal/mol. The next step in this mechanism involves a transfer of the hydrogen atom back to the oxygen atom to which it was originally bonded, accompanied by the loss of molecular oxygen from ozone. This step, passing through TSF2, leads to HSO4-. The associated energy barrier is 21.5 kcal/mol. The energy difference between reagents and products is 67.1 kcal/mol. We were unable to find an experimental enthalpy of formation for the HSO3-(aq) tautomer. Role of Bisulfite and Sulfonate in S(IV) Ozonation. As discussed in the Introduction, it is not clear which form of S(IV) is most important to ozonation at intermediate pH. Of particular interest, the relative importance of the tautomers HOSO2- and HSO3- to the ozonation reaction is not known. To explore this issue, we estimated relative rate constants for the various ozonation reactions on the basis of our calculated energy barriers, using the Eyring-Polanyi equation.32,33 The calculated rate constants did not vary significantly whether ∆Esolv or ∆Gsolv was used. We calculated the relative rate constant for each form of S(IV) and plotted the overall rate constant as a function of pH based on the relative equilibrium concentrations of each species. Figure 4 shows predicted relative ozonation rates of S(IV) as a function of pH with varying ratios of bisulfate to sulfonate. The relative measured rate constant for S(IV) ozonation6 as a function of pH is also shown. It is clear that our data best match the shape of the experimental kinetics when sulfonate dominates bisulfite by a factor of approximately 200. This makes sense, as the measured rate constant6 for singly ionized S(IV) is 3.7 × 105 L mol-1 s-1, which is much lower than the near-diffusion-limited rate of 1.5 × 109 L mol-1 s-1 measured for SO32- and indicates a

barrier to the reaction. If reaction proceeded primarily through HOSO2-, we would expect the rate at intermediate pH to be the same as that at high pH, since ozonation of both HOSO2and SO32- are barrierless processes. We therefore conclude that ozonation at intermediate pH proceeds primarily through HSO3-; this pathway has an associated energy barrier of 22.5 kcal/mol. This suggests that HSO3- must be the dominant tautomer in solution. Our calculations support this; we predict that sulfonate is more stable than bisulfite in solution by 10.8 kcal/mol in the presence of two water molecules. Previous theoretical studies have predicted the opposite stability order in the gas phase,31,34,35 but calculations that include solvation predict either very similar energies for the isomers10,35 or an energy difference of several kilocalories per mole in favor of the sulfonate ion.23,36 Although theoretical studies largely support the dominance of the HSO3- tautomer in solution, the ratio of the two species in solution remains contentious, as some experimental studies8,9 suggest that bisulfite is the dominant species in solution. Further, the pathway leading to sulfonate formation has a higher energy barrier than the pathway leading to bisulfite. As illustrated in Table 2, the formation of sulfurous acid, which leads to bisulfite, has an energy barrier of 12.8 kcal/mol in solution in the presence of an explicit water molecule. The energy barrier to the formation of sulfonic acid, which leads to the sulfonate ion, is 26.6 kcal/mol. This suggests that, despite the greater stability of sulfonate, bisulfite is more readily formed. The formation of sulfonate through tautomerization is also energetically unfavorable, as shown in Table 3. In solution, in the presence of two assisting water molecules, tautomerization of bisulfite to sulfonate presents an energy barrier of 22.1 kcal/mol.

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Figure 4. Relative rate constants of S(IV) ozonation in aqueous solution as a function of pH, predicted by our calculated energy barriers with varying ratios of bisulfite to sulfonate. Measured rate constants (normalized to the maximum) for the reaction from ref 6 are also shown. The solid and dashed traces are spline fits to the data. (Inset) Magnification of the graph below pH 6.

TABLE 3: Electronic Energy Barriers and ∆E (Products - Reagents) for Tautomerization of HSO3- to HOSO2- in the Presence of One and Two Explicit Water Molecules ∆Eq(kcal/mol) [∆Gq(kcal/mol)] gas phase n)0 n)1 n)2

60.4 [57.0] 39.9 [38.1] 34.2 [32.7]

∆E (kcal/mol) [∆G(kcal/mol)]

solution HSO3- + nH2O f HOSO2- + nH2O 63.9 [56.8] 39.0 [37.2] 32.9 [28.5]

Although there is no consensus in the literature regarding the stability order of the two tautomers, our predicted energies and kinetics strongly suggest that HSO3- must exist in vast excess. However, it is unclear how this tautomer forms. Since the barriers to its formation are in excess of 20 kcal/mol, we might expect bisulfite, which has much lower barriers to formation, to undergo rapid ozonation before being converted to sulfonate. It therefore seems likely that HOSO3- is formed by some other pathway that has a much lower energy barrier. A mechanism has been suggested7 in which bisulfite is deprotonated to form SO32-, which is then reprotonated to form sulfonate. If this mechanism is important to sulfonate formation, we would expect the ratio of sulfonate to bisulfite to increase with pH, as the species deprotonate more readily. We are unaware of any studies that investigate the pH dependence of this ratio, however. Conclusions We have explored the fate of dissolved SO2 in aqueous solutions containing ozone using a theoretical approach. Our calculations show that hydrolysis will precede ozonation and that both neutral and ionized forms of S(IV) can undergo ozonation. Comparison of our calculated energy barriers with experimentally derived rate constants suggests that sulfonate is in excess of bisulfite in aqueous solution and is the form of S(IV) species most important to ozonation under most pH regimes, despite the high energy barrier for this reaction. Acknowledgment. D.A. acknowledges a postdoctoral fellowship (POST07-25) from the Consejerı´a de Educacio´n y

gas phase

solution

8.5 [7.1] 8.3 [7.0] 8.0 [7.5]

13.4 [8.6] 7.9 [7.2] 10.8 [4.9]

Ciencia of the Principado de Asturias. T.F.K. acknowledges NSERC for a CGS doctoral scholarship. D.J.D. acknowledges ongoing support for this work from NSERC. Supporting Information Available: A table showing benchmark of methods; eight tables showing energetic data (absolute electronic energies in the gas phase and in solution, ZPVEs, and imaginary frequencies for transition states of all critical structures located along the reaction paths); and a table showing structural data (Cartesian coordinates for all structures). This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Finlayson-Pitts, B.; Pitts, J. J. Chemistry of the Upper and Lower Atmosphere; Academic Press: New York, 2000. (2) Lagrange, J.; Pallares, C.; Lagrange, P. J. Geophys. Res., [Atmos.] 1994, 99, 14595. (3) Maahs, H. G. J. Geophys. Res., [Oceans Atmos.] 1983, 88, 721. (4) Savarino, J.; Lee, C. C. W.; Thiemens, M. H. J. Geophys. Res., [Atmos.] 2000, 105, 29079. (5) Reilly, J. E.; Rattigan, O. V.; Moore, K. F.; Judd, C.; Sherman, D. E.; Dutkiewicz, V. A.; Kreidenweis, S. M.; Husain, L.; Collett, J. L. J. Atmos. EnViron. 2001, 35, 5717. (6) Hoffmann, M. R. Atmos. EnViron. 1986, 20, 1145. (7) Ermakov, A. N.; Poskrebyshev, G. A.; Purmal, A. P. Kinetics Catal. 1997, 38, 295. (8) Horner, D. A.; Connick, R. E. Inorg. Chem. 1986, 25, 2414. (9) Risberg, E. D.; Eriksson, L.; Mink, J.; Pettersson, L. G. M.; Skripkin, M. Y.; Sandstrom, M. Inorg. Chem. 2007, 46, 8332. (10) Steudel, R.; Steudel, Y. Eur. J. Inorg. Chem. 2009, 1393. (11) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.;

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