Article pubs.acs.org/JPCA

Concerted or Stepwise Mechanism? New Insight into the Water-Mediated Neutral Hydrolysis of Carbonyl Sulfide Xiao-Hong Li,† Si-Jia Ren,‡ Xi-Guang Wei,§ Yi Zeng,⊥ Guo-Wei Gao,† Yi Ren,*,† Jun Zhu,∥ Kai-Chung Lau,*,§ and Wai-Kee Li○ †

College of Chemistry and Key State Laboratory of Biotherapy, Sichuan University, Chengdu 610064, China West China School of Medicine, Sichuan University, Chengdu 610041, China § Department of Biology and Chemistry, City University of Hong Kong, Kowloon, Hong Kong ⊥ School of Physics and Chemistry, Research Center for Advanced Computation, Xihua University, Chengdu 610039, China ∥ State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry and Department of Chemistry, Xiamen University, Xiamen 361005, China ○ Department of Chemistry, The Chinese University of Hong Kong, Shatin, N.T. Hong Kong ‡

S Supporting Information *

ABSTRACT: The water-mediated neutral hydrolysis mechanism of carbonyl sulfide (OCS) has been re-examined using the hybrid supramolecule/continuum models with n = 2−8 explicit water cluster at the level of MP2(fc)(CPCM)/6-311++G(d,p)//MP2(fc)(CPCM) /6-31+G(d). Present calculations indicate that the potential energy surface in water solution is different from the one in the gas-phase, and only stepwise mechanism is observed in aqueous solution, i.e., monothiocarbonic acid (H2CO2S) is formed via monothiocarbonate (OCSOH−, MTC) and its counterion, protonated water cluster, (H2O)nH3O+. The predicted rate-determining step (RDS) barrier for the stepwise mechanism in water solution, about 90 kJ/mol, shows good agreement with the experimental values, 83.7−96.2 kJ/mol using six- or eightwater model including two cooperative water molecules. Moreover, two reaction pathways, the nucleophilic addition of water molecule across the CO or the CS bond of OCS are competitive. OCS + H 2O → H 2S + CO2

1. INTRODUCTION Carbonyl sulfide (OCS, OCS), one of cumulenes containing the heteroatom, XCY (X = O, and Y = S), is the most abundant sulfur compound in the atmosphere. Over the last 2 decades, it has become increasingly apparent that emissions of sulfur compounds into the atmosphere have been unacceptably high. Recently, the increasingly stringent emission standards are introduced to reduce the emission of sulfurcontaining compounds into the atmosphere.1 Currently, among various methods of carbonyl sulfide removal including hydrogenation (eq 1),2 hydrolysis (eq 2),3,4 adsorption,5 absorption (eq 3),6,7 photolysis (eq 4),8 and oxidation (eq 5),9 hydrolysis was recognized as the most promising process due to the mild reaction condition and higher conversion efficiency. There have been many experimental studies of the OCS hydrolysis reaction over a wide pH range in aqueous solutions; with amine-based catalysts in aqueous solution,10,11 alcoholic, and glycolic solutions;12−17 or with metal oxide, mixed oxides or hydrotalcite-like compounds (HTLCs) as catalysts.18−28 But so far few theoretical studies on the mechanism of the hydrolysis reaction of OCS have been reported. OCS + 4H 2 → H 2S + CH4 + H 2O © 2014 American Chemical Society

(2)

OCS + RNH 2 ⇌ RNH 2+OCS−

(3-1)

RNH 2+OCS− + RNH 2 → RNHOCS− + RNH3+

(3-2)

1

hv

1

OCS( Σ+) → CO( Σ+) + S(3P)

(4)

2OCS + 3O2 → 2SO2 + 2CO2

(5)

The hydrolysis mechanisms of OCS analogues, including CO2 ,29−34 SCS,35,36 H 2CCO,37−40 CH 2C NH,41−44 HNCO,45−47 and HNCNH,48,49 in neutral water solution have been extensively examined by the various methods. Most of the previous studies focused on the mechanism of the concerted nucleophilic addition of water across the CX bond (X = O, S, NH). In our previous paper,50 the neutral hydrolysis mechanism of OCS in the presence of up to five water molecules was investigated by using the hybrid supermolecule-continuum models, where all geometries were Received: March 2, 2014 Revised: April 22, 2014 Published: April 23, 2014

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Figure 1. MP2(fc)(CPCM)/6-31+G(d) geometries (Å) in the two-water hydration of OCS with the concerted mechanism along path 1 (upper, across CO) and path 2 (lower, across CS). The relative energies (kJ/mol) above the arrows are ΔGsol values (boldface) and below the arrows are the ΔEsol values without ZPE correction (italic) at the MP2(fc)(CPCM)/6-311++G(d,p)//MP2(fc)(CPCM)/6-31+G(d) level.

of CO2 involving 1−8 water molecules.53 All species were optimized at the B3LYP/6-311+G(2df,2p) level in the water solution by using the conductor-like polarizable continuum model (CPCM). Their results indicate that the 1−4 water hydration of CO2 follows a concerted pathway, i.e., the hydration product, H2CO3, is formed in one step. But the stepwise mechanism occurs with 5−8 water molecules engaging the hydration of CO2, where two water chains are extended from carbonyl oxygen. The predicted reaction barrier of about 20 kcal/mol for the stepwise mechanism is close to the recent experimental value of 21.8, and 18.8 kcal/mol by CPMD simulation.53 These studies suggest that it is necessary to reexamine the hydrolysis mechanism of OCS by including the solvent effect on the geometries and energetics for all of the species involved in the reactions. Considering the differences of geometries in the gas phase and in water solution, herein, we utilize the cluster-continuum model to reinvestigate the mechanism of the neutral hydrolysis of OCS in the presence of up to eight water molecules explicitly. All of the species involved in the neutral hydrolysis of OCS will be fully optimized using a hydrated cluster in conjunction with the CPCM model.54 Our previous calculations pointed out that the formation of monothiocarbonic acid is the RDS for the hydrolysis of OCS, accordingly, only the hydration of OCS is considered in the present study (see eq 6). We will consider several reaction schemes involving one and two water chains extended from the oxygen or sulfur atom on OCS, and focus on (1) the stepwise mechanism for the hydrolysis of OCS, i.e., hydration product being formed via an intermediate, monothiocarbonate (OCSOH−, MTC); (2) the cooperative effect induced by the water molecules in the nonreactive region; and (3) the comparison of potential energy surfaces (PESs) in aqueous solution with those in the gas phase. We will apply the geometrical and energetic analysis for the TSs of RDS in the hydration mechanism, and also make detailed comparisons between two reaction pathways with the different intermediate HS(HO)CO or (HO)2CS. We hope our theoretical investigation can provide more reasonable mechanistic insight into the hydrolysis mechanism of carbonyl sulfide, which could be helpful for the further studies of the hydrolysis mechanism of other cumulenes.

optimized at the level of MP2/6-311++G(d, p) in the gas phase, then the bulk solvent effect is described by the polarizable continuum model (PCM) at the same level. A concerted mechanism was proposed, i.e., the intermediate, monothiocarbonic acid, is formed by one step. The most favorable pathway involves the nucleophilic attack of the water molecule onto the central carbon atom coupled with the concerted proton transfer to the sulfur atom. Moreover the nucleophilic addition of the water molecule across the CO and CS bond is significantly facilitated by other two water ones near to the nonreactive sulfur or oxygen atom but not involved in the proton transfer through an eight-membered hydrogen-bond chain, showing the importance of the cooperative effect. The predicted Gibbs activation barrier in neutral water for the rate-determining step (RDS) is 111.8 kJ/mol, higher than the experimental value by about 20 kJ/mol. Recently, the detailed mechanisms of the hydrolysis of OCS both in the gas phase and bulk water solvent, including the reactions of OCS with a water molecule or a hydroxide ion, were studied using DFT method,51 showing that the hydrolysis of OCS by hydroxide ion is the main reaction channel from thermodynamic and kinetic perspectives with much lower barrier and more negative Gibbs free energy change for the reaction OCS + OH− = HS− + CO2 (Ea = 73.6 kJ/mol and ΔG = −198.0 kJ/mol) than the reaction OCS + H2O = H2S + CO (Ea = 178.8 kJ/mol and ΔG = −41.0 kJ/mol). In recent years, the stepwise mechanism was proposed in the studies on the neutral hydration of carbon dioxide (CO2). In such mechanism, the addition across the CO bond of CO2 is finished by two steps. In the first step, the bicarbonate anion (HCO3−) and the protonated water are formed, which resembles an ion pair (HCO3−/H3OH2O+) mentioned by Nguyen et al. in the mechanistic re-examination of the hydration of CO2 by the hybrid cluster-continuum model with 1−4 water molecules.34 Then, one proton transfers from H3O+ to the carbonyl oxygen occurs, leading to the final product, carbonic acid H2CO3. By ab initio molecular dynamics simulation, Stirling et al. found that the neutral hydration of CO2 is practically a two-step process, i.e., following the stepwise mechanism, with HCO3− and hydrated proton as the intermediates.52 More recently, Cao et al. made a detailed theoretical investigation by the cluster-continuum model on the hydration 3504

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2. COMPUTATIONAL DETAILS All species in water solution involved in the formation of monothiocarbonic acid, including reactants complex (RC), transition state (TS), and intermediate (Int), were optimized using a hydrated cluster in conjunction with the CPCM mode at the level of MP2(fc)(CPCM)/6-31+G(d) (Cartesian 6d basis functions are used), and the bulk water solution is thereby represented by a continuum characterized by its dielectric permittivity (ε = 78.36). All stationary points on PESs were identified as minima (number of imaginary frequencies NIMAG = 0) or transition state (NIMAG = 1) based on the vibrational frequency analysis at the same level. A scaling factor of 0.98 is applied to the zero-point vibration energy (ZPVE) corrections,55 and thermal and entropy corrections computed by standard statistical methods were used in the calculations of relative energies. The energies were refined by additional

Figure 2. MP2(fc)(CPCM)/6-31+G(d) geometries (Å) in the threewater hydration of OCS with the stepwise mechanism along path 1 (upper) and path 2 (lower). The energetics above and below the arrows are ΔGsol (boldface) and ΔEsol (italic) values, respectively, at the MP2(fc)(CPCM)/6-311++G(d,p)//MP2(fc)(CPCM)/ 6-31+G(d) level.

Figure 3. Geometries (Å) and relative energies (kJ/mol) of single-water chain model in the four-water hydration of OCS with the stepwise mechanism along paths 1 (upper) and 2 (lower). The energetics above and below the arrows are ΔGsol (boldface) and ΔEsol (italic) values, respectively, at the MP2(fc)(CPCM)/6-311++G(d,p)//MP2(fc)(CPCM)/6-31+G(d) level. 3505

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Figure 4. Geometries (Å) and relative energies (kJ/mol) of dual-water chain model in the four-water hydration of OCS with the stepwise mechanism along paths 1 (upper) and 2 (lower). The energetics above and below the arrows are ΔGsol (boldface) and ΔEsol (italic) values, respectively, at the MP2(fc)(CPCM)/6-311++G(d,p)//MP2(fc)(CPCM)/6-31+G(d) level.

or sulfur side (Path 2). Both in the gas phase and in aqueous solution, only a concerted six-membered ring TS is located in the two-water model. The Gibbs free energy of activation, ΔG‡sol, is 148.4 kJ/mol for TS-2w-O, and 144.3 kJ/mol for TS-2w-S (see Figure 1), showing that the addition of water across the CS bond is slightly favored over that across the CO bond. As pointed out by our previous study,50 six-membered TS is less favorable than the eight-membered TS in the water-mediated hydrolysis of COS due to the existence of more reasonable H-bonds in the latter case, leading to the higher barrier of TS-2w-X (X = O, S) than the experimental value by more than 50 kJ/mol. Accordingly, one more water molecule should be involved in the proton transfer chain for reducing the barrier. Afterward, we investigated the hydration of OCS involving three explicit water molecules without the cooperative water molecule. The hydration reaction starts with a reactants complex, RC-3w-O (path 1) or RC-3w-S (path 2) of OCS. To our surprise, the concerted transition states cannot be located for the three-water model, and only the stepwise mechanism is observed in the aqueous solution. The reaction barrier is 131.0 kJ/mol for TS1-3w-O and 132.2 kJ/mol for TS1-3w-S (Figure 2), lower than that in the two-water model by more than 10 kJ/mol, meanwhile indicating that these two pathways are competitive. Unfortunately, some stationary points on the PESs of three-water model cannot be located, but we can still make a brief discussion for the simple threewater model.

single-point calculations at the MP2(fc)(CPCM)/6-311++G(d, p) (5d) level in order to overcome any errors arising from the smaller basis sets. Charge distributions were obtained from the wave functions calculated at the MP2(fc)(CPCM)/6-311++G(d,p) level, employing natural population analysis (NPA).56−59 In order to compare the hydrolysis mechanism in water solution with that in the gas phase, we have also optimized all species in the gas phase and obtained the corresponding energetics (see Supporting Information, Figures S1−S7). Throughout this paper, all bond lengths are in Å and bond angles are in degrees. Relative energies (in kJ/mol) in the gas phase are computed by electronic energy change without ZPE correction, ΔE, or Gibbs free energy change, ΔG, the sum of MP2(fc)/6-311++G(d,p) single energy and the scaled free energy correction at MP2(fc)/6-31+G(d) at 298 K. Relative energies in water solution are denoted as ΔEsol and ΔGsol, the sum of MP2(fc)(CPCM)/6-311++G(d,p) single energy and the scaled free energy correction at MP2(fc)(CPCM)/ 6-31+G(d) at 298 K. All calculations are performed with the Gaussian 09 package.60

3. RESULTS AND DISCUSSION 3.1. Hydration of OCS without Cooperative Water Molecules. At the first place, we re-examined the hydration of OCS in the presence of two explicit water molecules without the cooperative water molecule in the nonreactive region. The hydration of OCS starts with a reactants complex, RC-2w-O or RC-2w-S, where the active region is at near the oxygen (Path 1) 3506

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Figure 5. Geometries (Å) and relative energies (kJ/mol) of dual-water chain model in the six-water hydration of OCS with the stepwise mechanism along paths 1 (upper) and 2 (lower). The energetics above and below the arrows are ΔGsol (boldface) and ΔEsol (italic) values, respectively, at the MP2(fc)(CPCM)/6-311++G(d,p)//MP2(fc)(CPCM)/6-31+G(d) level.

calculations on the hydration of the proton, showing that the first hydration shell of the proton requires at least four water molecules.61−63 Only the stepwise mechanism are obtained with the incorporation of the fourth water molecule in the active region. In the single-water chain model, the hydration of OCS starts from a reactant complex of OCS with four water molecules, RC-3+w-O or RC-3+w-S. In the first step, a water molecule attacks the central carbon of OCS, coupled with the concerted proton transfer to the adjacent water, yielding an intermediate Int1-3+w-O via TS1-3+w-O, or Int1-3+w-S via TS13+w-S. Comparison of TS1-3w-O vs TS1-3+w-O or TS1-3w-S vs TS-3+w-S shows that the distance, rC1−O1, is longer, meanwhile the distance, rO1−H1, is shorter in the latter cases, indicating the TS of the RDS for 3+w model is more reactant-like. The characteristics of earlier TS structures lead to the lower barriers of 3+w than 3w model by about 6−13 kJ/mol. The subsequent proton transfer from H3O+ to the oxygen or sulfur atom on OCS leads to more stable monothiocarbonic acid (Int2-3+w-O) via Path 1 (Int1-3+w-O → TS2-3+w-O → Int2-3+w-O), or to the isomer of monothiocarbonic acid (Int2-3+w-S) via Path 2 (Int1-3+w-S → TS2-3+w-S → Int23+w-S) assisted by a water molecule. The second step of the stepwise mechanism experiences smaller ΔE‡sol values, 12.6 or 12.1 kJ/mol, or ΔG‡sol values, 11.3 or −0.1 kJ/mol for

Comparison of TS1-3w-O or TS1-3w-S with the corresponding TSs, TS-3w-O(g) or TS-3w-S(g) in the gas phase (See Figure S1 in Supporting Information) shows that the distance between the attacking oxygen and the transferred hydrogen atom, rO1−H1, is 1.171 Å in TS1-3w-O, and 1.157 Å in TS1-3w-S, much shorter than that in TS-3w-O(g) (1.472 Å) and TS-3w-S(g) (1.516 Å). Meanwhile, the distance between central carbon on OCS and the attacking oxygen atom, rC1−O1, is 1.546 Å in TS1-3w-O, and 1.554 Å in TS1-3w-S, longer than that in TS-3w-O(g) by 0.06 Å, and that in TS-3w-S(g) by 0.071 Å. These results show that these TSs in aqueous solution are more reactant-like than those in the gas-phase, indicating the significant structural differences from the gas phase to the water solution, and the importance of optimization by using the continuum models in the mechanistic study on the hydrolysis of OCS. Then the mechanism of four-water hydration of OCS is explored, in which one water molecule is added at the active region of TS1-3w-O or TS1-3w-S. Two different reaction schemes are considered, one is single-water chain model, but one more water is connected with a free O−H bond in TS13w-O or TS1-3w-S, denoted as TS1-3+w-O or TS1-3+w-S (Figure 3); the other is the smallest dual-water chain model involving TS1-4w-O and TS1-4w-S, shown in Figure 4. Three hydrogen-bonds stabilize the hydrated proton in both of the models, which is consistent with the previous theoretical 3507

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Figure 6. Geometries (Å) and relative energies (kJ/mol) with two cooperative water molecules in the five-water hydration of OCS with the stepwise mechanism along paths 1 (upper) and 2 (lower). The energetics above and below the arrows are ΔGsol (boldface) and ΔEsol (italic) values, respectively, at the MP2(fc)(CPCM)/6-311++G(d,p)//MP2(fc)(CPCM)/6-31+G(d) level.

The addition of one more water molecule into the threewater model has reduced the RDS barrier from about 130 to 120 kJ/mol, but it still significantly exceeds the experimental value by 30 kJ/mol. It suggests that more water molecules should be incorporated into the active region of the cluster model. Introducing more H-bonds in the TS should release the strain of TSs, which is expected to reduce the barrier further. Accordingly, two additional water molecules are added into the H-bonded networks at the active region of TS1-4w (Figure 5), yielding two hydration pathways, i.e., path 1, RC-6w-O → TS1-6w-O → Int1-6w-O → TS2-6w-O → Int26w-O, or path 2, RC-6w-S → TS1-6w-S → Int1-6w-S → TS26w-S → Int2-6w-S. MP2(CPCM) calculations show that the barrier is 120.2 kJ/mol for TS1-6w-O and 115.5 kJ/mol for TS1-6w-S, lower than the corresponding value in TS1-4w-O and TS1-4w-S by 13.7 and 20.1 kJ/mol, respectively. Geometrical comparisons of TS16w-O vs TS1-4w-O, or TS1-6w-S vs TS1-4w-S, show the former ones are more reactant-like with the shorter O1−H1 and longer C1−O1 distances, and less strained with more reasonable H-bond angles, 154.3 and 156.1° with terminal oxygen, or 149.1 and 157.9° with terminal sulfur. As the 3w and 4w hydration models, the barriers of the second step for the six-water hydration are also much lower than those in the first step by more than 95 kJ/mol. 3.2. Hydration of OCS with Two Cooperative Water Molecules. Our previous studies on the neutral hydrolysis of OCS with the concerted mechanism indicated that the two additional water molecules near the nonreactive oxygen or

TS2-3+w-O or TS2-3+w-S, respectively, which is very similar to the case found in the hydration of CO2 with the stepwise mechanism.53 In the dual-water chain model involving four water molecules, monothiocarbonic acid is formed via path 1 (RC-4w-O → TS1-4w-O → Int1-4w-O → TS2-4w-O → Int2-4w-O), or via path 2 (RC-4w-S → TS1-4w-S → Int1-4w-S → TS24w-S → Int2-4w-S). The calculated ΔE‡sol of the first step is 103.5 kJ/mol for TS1-4w-O, and 101.4 kJ/mol for TS1-4w-S, higher than the one in TS-3+w-O by 7.4 kJ/mol, or in TS-3+w-S by 4.2 kJ/mol, but the ΔG‡sol value in the 4w hydration model is higher than that in the 3+w model by 8.7 kJ/mol for TS1-4w-O, and by 15.9 kJ/mol for TS1-4w-S. These results can be attributed to the highly strained TS1-4w-O and TS1-4w-S with smaller intramolecular H-bond angles with terminal oxygen (134.6 and 148.3° in TS1-4w-O), and with terminal sulfur (136.0 and 146.7° in TS1-4w-S), obviously deviating from the ideal angle of hydrogen bond, 165−170°. Meanwhile, the average H−O−H angle in the H3O+ moiety (104° in TS1-4w-O and 105.6° in TS1-4w-S) are also smaller than that in the separated H3O+ by about 5−7°. These geometrical features will lead to higher ΔG‡sol values of TS1-4w-X (X = O, S). The ΔG‡sol values of the second step, i.e., the subsequent proton transfer from H3O+ to the oxygen or sulfur atom on OCS to form more stable monothiocarbonic acid, for the 4w model are significantly lower than the first one, 18.0 kJ/mol for TS2-4w-O, and 25.7 kJ/mol for TS2-4w-S, showing the first step is the rate determining one. 3508

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Figure 7. Geometries (Å) and relative energetics with two cooperative water molecules in the six-water hydration of OCS with the stepwise mechanism along paths 1 (upper) and 2 (lower). The energetics above and below the arrows are ΔGsol (boldface) and ΔEsol (italic) values, respectively, at the MP2(fc)(CPCM)/6-311++G(d,p)//MP2(fc)(CPCM)/6-31+G(d) level.

about 21 kJ/mol, showing the important role of water molecules in the nonreactive region. The geometric changes in the dual-water chain model are different from TS1-3w-X to TS1-3+2w-X (X = O, S). The earlier TS features of TS1-n+2w-X (n = 4, 6; X = O, S) are observed with the incorporation of the cooperative water molecules in the nonactive region. Inspection of the geometries in Figures 7 and 8 shows that the C1−O1 bond distance in TS1-n+2w-X is longer than that in TS1-nw-X by 0.108 Å (n = 4, X = O), 0.109 Å (n = 4, X = S), 0.124 Å (n = 6, X = O), and 0.120 Å (n = 6, X = S). Meanwhile, the H1−O1 bond distance is reduced from 1.119 in TS1-4w-O to 1.024 Å in TS1-4+2w-O, 1.110 in TS1-4w-S to 1.025 Å in TS1-4+2w-S, 1.083 in TS1-6w-O to 1.018 Å in TS1-6+2w-O, and 1.089 in TS1-6w-S to 1.022 Å in TS1-6+2w-S, respectively. The earlier TS features have significantly reduced the barrier, ΔG‡sol, from 133.9 (TS1-4w-O) to 92.4 kJ/mol (TS1-4+2w-O), 135.6 (TS1-4w-S) to 92.4 kJ/mol (TS1-4+2w-S), 120.2 (TS1-6w-O) to 87.5 kJ/mol (TS1-6+2w-O), and 115.5 (TS1-6w-S) to 90.6 kJ/mol (TS1-6+2w-S), indicating the importance of a cooperative role of water molecules in the stepwise mechanism. Interestingly, the activation barriers without ZPE correction, ΔE‡sol, for TS1-4+2w-X (X = O, S) are only about 77 kJ/mol, even lower than that of TS1-6+2w-X by 6.3 kJ/mol (X = O) or 9.3 kJ/mol (X = S). After considering

sulfur atom, which are not involved in the proton transfer, can significantly reduce the free energy barrier by more than 23 kJ/mol.29 As seen in the above six-water hydration model, incorporation of more water molecules in the active region can reduce the strain of TSs, but the predicted barriers, 120.2 kJ/mol for TS-6w-O and 115.5 kJ/mol for TS-6w-S, are still significantly higher than the experimental results (83.7− 96.2 kJ/mol).11 Accordingly, based on our experience, two additional water molecules are added at the nonreactive region in TS1-3w-O and TS1-3w-S, TS1-4w-O and TS1-4w-S, and TS1-6w-O and TS1-6w-S, leading to TS1-3+2w-O and TS13+2w-S, TS1-4+2w-O and TS1-4+2w-S, and TS1-6+2w-O and TS-6+2w-S. Figures 6−8 present the geometries of these species at the MP2(fc)(CPCM)/6-31+G(d) level involved in the five-, six-, and eight-water neutral hydration of OCS with the stepwise mechanism and the predicted relative energetics. As pointed out in previous mechanistic studies on the neutral hydrolysis of cumulenes containing the heteroatom, the cooperative water molecules can lower the free energy of activation by reducing the bond distance C1−O1 in the RDS transition states.29,37,42,46,49 In the present study, it is also found that the C1−O1 bond distance in TS1-3+2w-O or TS13+2w-S is shorter than that in TS1-3w-O or TS1-3w-S by 0.095 Å, and the ΔG‡sol value of TS1-3+2w-O or TS1-3+2w-S is lower than that in TS1-3w-O or TS1-3w-S by more than 3509

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Figure 8. Geometries (Å) and relative energies (kJ/mol) with two cooperative water molecules in the eight-water hydration of OCS with the stepwise mechanism along paths 1 (upper) and 2 (lower). The energetics above and below the arrows are ΔGsol (boldface) and ΔEsol (italic) values at the MP2(fc)(CPCM)/6-311++G(d,p)//MP2(fc)(CPCM)/6-31+G(d) level.

the ZPE correction and entropy effect, ΔG‡sol(TS1-4+2w-X) is only higher than ΔG‡sol(TS1-6+2w-X) by less than 5 kJ/mol. Moreover, no matter the hydration of OCS involving single- or dual-water chain with the cooperative water molecules, the differences of the RDS barriers for two reaction pathways, i.e. addition of water across CO or CS bond, are very small, less than 3 kJ/mol, indicating that two reaction pathways are competitive. 3.3. Comparison of the Hydration of OCS Obtained in the Gas Phase and in Aqueous Solution. In order to show the importance of solvent effect in the structures and energetics in the hydrolysis mechanism of OCS, herein we have made a brief comparison between their PESs in aqueous solution and the ones in the gas-phase. All of the geometries in the gasphase are denoted by adding (g) at the end, e.g. RC-nw-X(g), and TS-nw-X(g). Table 1 lists the selected geometrical parameters and Gibbs free energies of activation obtained in the gas phase and in aqueous solution. All of species obtained in the gas phase are shown in the Supporting Information (Figures S1−S7). Perhaps the most obvious differences of mechanism occur in the three-water model without cooperative water molecules and five-water hydration with two cooperative water molecules, where the hydration of OCS follows the stepwise mechanism in aqueous solution rather than the concerted one in the gas-phase. Inspection of the geometries in Figure S1 and S4 shows that, in these concerted TSs, the transferred hydrogen is very close to the adjacent water

molecule, and C1−O1 distance in TS-3w-X(g) or TS-3+2wX(g) is also shorter than that in TS-3w-X or TS-3+2w-X (X = O, S) by about 0.06 or 0.03 Å, respectively, indicating that the TSs in the gas phase are more-product like, closely resembles an ion pair formed by MTC (HCO2S)− and the protonated water cluster (H2O−H−H2O)+, similar to the case observed in the hydrolysis of CO2.36 The gas-phase RDS barriers of 3w and 3+2w hydration models in the concerted mechanism are significantly higher than those followed by the stepwise mechanism in the water solution by more than 26 kJ/mol. The four-water TSs with single-water chain in the gas phase, TS-3+w-X(g), cannot be located, and only dual-water chain TSs with stepwise mechanism, TS1-4w-X(g) (X = O, S), are found. The geometrical differences between TS1-4w-X(g) and TS-4w-X are very small, and the corresponding difference of RDS barrier is less than 12 kJ/mol. Similar results are also observed in the comparison of TS-4+2w-X(g) vs TS4+2w-X, TS-6w-X(g) vs TS-6w-X, and TS-6+2w-X(g) vs TS6+2w-X, (X = O, S). Two possible reaction pathways in the hydration of OCS, i. e., the nucleophilic addition of water molecule across the CS or CO bond, is competitive in aqueous solution, that is somewhat different from the situation in the gas phase, where the addition across the CS bond is more favorable than across the CO bond. 3510

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Table 1. Selected Bond Lengths (Å), and the Gibbs Free Energies of Activation for RDS TSs in the Gas Phase, ΔG‡ (in Normal Type), and in Aqueous Solution, ΔG‡sol (in Bold Type) (kJ/mol) with Different Hydration Models for the Neutral Hydrolysis of Carbonyl Sulfide in the gas phase

in aqueous solution

species

mechanism

rC1−O1

rH1−O1

ΔG

TS-2w-O TS-2w-S TS1-3w-O TS1-3w-S TS1-3+w-O TS1-3+w-S TS1-4w-O TS1-4w-S TS1-6w-O TS1-6w-S TS1-3+2w-O TS1-3+2w-S TS1-4+2w-O TS1-4+2w-S TS1-6+2w-O TS1-6+2w-S

concerted concerted concerted concerted

1.552 1.570 1.486 1.483

1.318 1.291 1.472 1.516

191.8 172.8 168.1 167.3

stepwise stepwise stepwise stepwise concerted concerted stepwise stepwise stepwise stepwise

1.605 1.632 1.659 1.684 1.423 1.423 1.706 1.757 1.854 1.881

1.195 1.190 1.121 1.123 1.467 1.515 1.027 1.025 1.016 1.017

132.1 123.7 117.2 109.9 140.2 136.0 104.2 94.9 99.2 85.3

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4. CONCLUSION AND REMARKS

mechanism

rC1−O1

rH1−O1

ΔG‡sol

concerted concerted stepwise stepwise Stepwise Stepwise stepwise stepwise stepwise stepwise stepwise stepwise stepwise stepwise stepwise stepwise

1.480 1.495 1.546 1.554 1.617 1.628 1.609 1.632 1.650 1.661 1.451 1.459 1.717 1.741 1.774 1.781

1.325 1.273 1.171 1.157 1.120 1.118 1.119 1.110 1.083 1.089 1.188 1.167 1.024 1.025 1.018 1.022

148.4 144.3 131.0 132.2 125.2 119.7 133.9 135.6 120.2 115.5 109.3 109.8 92.4 92.4 87.5 90.6

AUTHOR INFORMATION

Corresponding Authors

In the present work, the neutral hydrolysis mechanism of carbonyl sulfide (OCS, OCS) is re-examined using the hybrid supramolecule/continuum models with n = 2−8 explicit water molecules at the level of MP2(fc)(CPCM)/ 6-311++G(d, p)//MP2(fc)(CPCM)/6-31+G(d). Our calculations show that the hydration of OCS will indeed follow a stepwise mechanism in aqueous solution via an intermediate (OCSOH−, MTC), that is different from the case in the gas phase, where the concerted mechanism is observed when only one water chain exists in the active region, and the hydration of OCS will follow the stepwise mechanism if there are two water chains extended from terminal oxygen or sulfur. Present studies suggest that the stabilization of hydrated proton and solvent effect are two important factors for the stepwise mechanism followed by the hydration of OCS in water solution. The predicted RDS barrier for the stepwise mechanism in aqueous solution, about 90 kJ/mol, using six- or eight-water model including two cooperative water molecules, shows good agreement with the experimental values, 83.7−96.2 kJ/mol. Moreover, two reaction pathways, i.e., the nucleophilic addition of water molecule across the CO or across the CS bond of OCS are competitive in water solution. Our study also show that, with more water molecules incorporated into the active region, the differences in the reaction barriers between in the gas phase and in water solution become smaller and smaller, from about 40 kJ/mol (two-water model) to about 30 kJ/mol (five-water model) to 5−10 kJ/mol (eight-water model).

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‡

*(Y.R.) E-mail: [email protected]. Telephone: +(86)-2885412290. *(K.-C.L.) E-mail: [email protected]. Telephone: +(852)34426849. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work described in this paper is supported by the Open Research Fund of State Key Laboratory of Physical Chemistry of Solid Surfaces, Xiamen University (No. 201410), the Open Research Fund of Key Laboratory of Advanced Scientific Computation, Xihua University (No. szjj2013-024), National Natural Science Foundation of China (No. 91016002), the Shenzhen Science and Technology Research Grant (JCYJ20120613115247045), and the Shenzhen Research Institute, City University of Hong Kong.

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REFERENCES

(1) Williams, B. P.; Young, N. C.; West, J.; Rhodes, C.; Hutchings, G. J. Carbonyl Sulphide Hydrolysis Using Alumina Catalysts. Catal. Today 1999, 49, 99−104. (2) Tong, S.; Dalla Lana, I. G.; Chuang, K. T. Appraisal of Catalysts for the Hydrolysis of Carbon Disulfide. Can. J. Chem. Eng. 1992, 70, 516−522. (3) Rhodes, C.; Riddel, S. A.; West, J.; Williams, B. P.; Hutchings, G. J. The Low- temperature Hydrolysis of Carbonyl Sulfide and Carbon Disulfide: a Review. Catal. Today 2000, 59, 443−464. (4) Zhao, S. Z.; Yi, H. H.; Tang, X. L.; Jiang, S. X.; Gao, F. Y.; Zhang, B. W.; Zuo, Y. R.; Wang, Z. X. The Hydrolysis of Carbonyl Sulfide at Low Temperature: a Review. Sci. World J. 2013, ID739501, 8 pages. (5) Wang, X.; Qiu, J.; Ning, P.; Ren, X.; Li, Z.; Yin, Z.; Chen, W.; Liu, W. Adsorption/ Desorption of Low Concentration of Carbonyl Sulfide by Impregnated Activated Carbon under Micro-oxygen Conditions. J. Hazard. Mater. 2012, 229−230, 128−136. (6) Amararene, F.; Bouallou, C. Kinetics of Carbonyl Sulfide (OCS) Absorption with Aqueous Solutions of Diethanolamine and Methyldiethanolamine. Ind. Eng. Chem. Res. 2004, 43, 6136−6141.

ASSOCIATED CONTENT

S Supporting Information *

MP2(fc)(CPCM)/6-31+g(d) optimized geometries and MP2(fc)(CPCM)/6-311++g(d,p)//MP2(fc)(CPCM)/6-31+g(d) energies (au) of species in the hydration of OCS, and the reaction pathways in the gas-phase hydration of carbonyl sulfide. This material is available free of charge via the Internet at http://pubs.acs.org. 3511

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(29) Nguyen, M. T.; Ha, T. K. A Theoretical Study of the Formation of Carbonic Acid from the Hydration of Carbon Dioxide: a Case of Active Solvent Catalysis. J. Am. Chem. Soc. 1984, 106, 599−602. (30) Liang, J. Y.; Lipscomb, W. N. Theoretical Study of the Uncatalyzed Hydration of Carbon Dioxide in the Gas Phase. J. Am. Chem. Soc. 1986, 108, 5051−5058. (31) Merz, K. M. Gas-phase and Solution-phase Potential Energy Surfaces for Carbon Dioxide + n-Water (n = 1, 2). J. Am. Chem. Soc. 1990, 112, 7973−7980. (32) Nguyen, M. T.; Raspoet, G.; Vanquickenborne, L. G.; Van Duijen, P. T. How Many Water Molecules Are Actively Involved in the Neutral Hydration of Carbon Dioxide? J. Phys. Chem. A 1997, 101, 7379−7388. (33) Lewis, M.; Glaser, R. Synergism of Catalysis and Reaction Center Rehybridization. A Novel Mode of Catalysis in the Hydrolysis of Carbon Dioxide. J. Phys. Chem. A 2003, 107, 6814−6818. (34) Nguyen, M. T.; Matus, M. H.; Jackson, V. E.; Ngan, V. T.; Rustad, J. R.; Dixon, D. A. Mechanism of the Hydration of Carbon Dioxide: Direct Participation of H2O versus micro- solvation. J. Phys. Chem. A 2008, 112, 10386−10398. (35) Deng, C.; Wu, X. P.; Sun, X. M.; Ren, Y.; Sheng, Y. H. Neutral Hydrolysis of Carbon Disulfide: an ab initio Study of Water Catalysis. J. Comput. Chem. 2009, 30, 285−294. (36) Ling, L. X.; Zhang, R. G.; Han, P. D.; Wang, B. J. A Theoretical Study on the Hydrolysis Mechanism of Carbon Disulfide. J. Mo. Model. 2012, 18, 1625−1632. (37) Tidwell, T. T. Ketene Chemistry: the Second Golden Age. Acc. Chem. Res. 1990, 23, 273−279. (38) Allen, A. D.; Tidwell, T. T. Kinetics and Mechanism of Hydration of Alkyl Ketenes. J. Am. Chem. Soc. 1987, 109, 2774−2780. (39) Nguyen, M. T.; Hegarty, A. F. Molecular Orbital Study on the Hydrolysis of Ketene by Water Dimer: β-Carbon vs. Oxygen Protonation? J. Am. Chem. Soc. 1984, 106, 1552−1557. (40) Wu, X. P.; Wei, X. G.; Sun, X. M.; Ren, Y.; Wong, N. B.; Li, W. K. Theoretical Study on the Role of Cooperative Solvent Molecules in the Neutral Hydrolysis of Ketene. Theor. Chem. Acc. 2010, 27, 493− 506. (41) Nguyen, M. T.; Hegarty, A. F. Ab Initio Study of the Hydration of Ketenimine (CH2CNH) by Water and Water Dimer. J. Am. Chem. Soc. 1983, 105, 3811−3815. (42) Nguyen, M. T.; Hegarty, A. F. The Reaction Pathway for the Hydration of Ketenimine by Water Dimer: An ab initio Study. J. Mol. Struct. (THEOCHEM) 1983, 93, 329−332. (43) Nguyen, M. T.; Raspoet, G.; Vanquickenborne, L. G. Necessity to Consider a Three-water Chain in Modelling the Hydration of Ketene Imines and Carbodiimides. J. Chem. Soc.,Perkin Trans. 2 1999, 813−820. (44) Sun, X. M.; Wei, X. G.; Wu, X. P.; Ren, Y.; Wong, N. B.; Li, W. K. Cooperative Effect of Solvent in the Neutral Hydrolysis of Ketenimine: an ab initio Study Using the Hybird Cluster/ Continuum Model. J. Phys. Chem. A 2010, 114, 595−602. (45) Raspoet, G.; Nguyen, M. T.; McGarraghy, M.; Hegarty, A. F. Experimental and Theoretical Evidence for a Concerted Catalysis by Water Clusters in the Hydrolysis of Isocyanates. J. Org. Chem. 1998, 63, 6867−6877. (46) Arroyo, S. T.; Garcia, A. H.; Martin, J. A. S. Theoretical Study of the Neutral Hydrolysis of Hydrogen Isocyanate in Aqueous Solution via Assisted-concerted Mechanisms. J. Phys. Chem. A 2008, 113, 1858− 1864. (47) Wei, X. G.; Sun, X. M.; Wu, X. P.; Geng, S.; Ren, Y.; Wong, N. B.; Li, W. K. Cooperative Effect of Water Molecules in the Selfcatalyzed Neutral Hydrolysis of Isocyanic Acid: a Comprehensive Theoretical Study. J. Mol. Model. 2011, 17, 2069−2082. (48) Lewis, M.; Glaser, R. Synergism of Catalysis and Reaction Center Rehybridization. An ab Initio Study of the Hydrolysis of the Parent Carbodiimide. J. Am. Chem. Soc. 1998, 120, 8541−8542. (49) Lewis, M.; Glaser, R. Synergism of Catalysis and Reaction Center Rehybridization in Nucleophilic Additions to Cumulenes: The

(7) Hinderaker, G.; Sandall, O. C. Absorption of Carbonyl Sulfide in Aqueous Diethanolamine. Chem. Eng. Sci. 2000, 55, 5813−5818. (8) Gollnick, K.; Leppin, E. Direct Photolysis of Carbonyl Sulfide in Solution. Mechanism of Singlet D and Triplet P Sulfur Atom Formation. J. Am. Chem. Soc. 1970, 92, 2217−2220. (9) Hattori, S.; Schmidt, J. A.; Mahler, D. W.; Danielache, S. O.; Johnson, M. S.; Yoshida, N. Isotope Effect in the Carbonyl Sulfide Reaction with O(3P). J. Phys. Chem. A 2012, 116, 3521−3526. (10) Thompson, H. W.; Kearton, C. F.; Lamb, S. A. The Kinetics of the Reaction between Carbonyl Sulphide and Water. J. Chem. Soc. 1935, 1033−1037. (11) Elliott, S.; Lu, E.; Rowland, F. S. Rates and Mechanisms for the Hydrolysis of Carbonyl Sulfide in Natural Waters. Environ. Sci. Technol. 1989, 23, 458−461. (12) Sharma, M. M. Kinetics of Reactions of Carbonyl Sulphide and Carbon Dioxide with Amines and Catalysis by Brönsted Bases of the Hydrolysis of OCS. Trans. Faraday Soc. 1965, 61, 681−688. (13) Ernst, W. R.; Chen, M. S. K.; Mitchell, D. L. Hydrolysis of Carbonyl Sulfide: Comparison to Reactions of Isocyanates. Can. J. Chem. Eng. 1990, 68, 319−323. (14) Littel, R. J.; Versteeg, G. F.; van Swaaij, W. P. M. Kinetic study of OCS with Tertiary Alkanolamine Solutions. 1. Experiments in an Intensely Stirred Batch Reactor. Ind. Eng. Chem. Res. 1992, 31, 1262− 1269. (15) Littel, R. J.; Versteeg, G. F.; van Swaaij, W. P. M. Kinetics of OCS with Primary and Secondary Amines in Aqueous Solutions. AIChE J. 1992, 38, 244−250. (16) Alper, E.; Al-Roweih, M.; Bouhamra, W. Reaction Kinetics of OCS with Primary and Secondary Amines in Alcoholic Solutions. Chem. Eng. J. 1994, 55, 53−59. (17) Lee, S. C.; Snodgrass, M. J.; Park, M. K.; Sandall, O. C. Kinetics of Removal of Carbonyl Sulfide by Aqueous Monoethanolamine. Environ. Sci. Technol. 2001, 35, 2352−2357. (18) Laperdix, E.; Justin, I.; Constentin, G.; Saur, O.; Lavalley, J. C.; Aboulayt, A.; Ray, J. L.; Nédez, C. Comparative Study of CS2 Hydrolysis Catalyzed by Alumina and Titania. Appl. Catal., B 1998, 17, 167−173. (19) Bachelier, J.; Aboulyat, A.; Lavalley, J. C.; Legendre, O.; Luck, F. Activity of Different Metal Oxides towards OCS Hydrolysis. Effect of SO2 and Sulfation. Catal. Today 1993, 17, 55−62. (20) Saur, O.; Bensitel, M.; Saad, A. B. M.; Lavalley, J. C.; Tripp, C. P.; Morrow, B. A. The Structure and Stability of Sulfated Alumina and Titania. J. Catal. 1986, 99, 104−110. (21) West, J.; Williams, B. P.; Young, N. C.; Rhodes, C.; Hutchings, G. J. Low Temperature Hydrolysis of Carbonyl Sulfide Using γAlumina Catalysts. Catal. Lett. 2001, 74, 111−114. (22) Huang, H. M.; Young, N.; Williams, B. P.; Taylor, S. H.; Hutchings, G. OCS Hydrolysis Using Zinc-promoted Alumina Catalysts. Catal. Lett. 2005, 104, 17−21. (23) Zhang, Y. Q.; Xiao, Z. B.; Ma, J. X. Hydrolysis of Carbonyl Sulfide over Rare Earth Oxysulfides. Appl. Catal., B 2004, 48, 57−63. (24) Aboulayt, A.; Maugé, F.; Hoggan, P. E.; Lavalley, J. C. Combined FTIR, Reactivity and Quantum Chemistry Investigation of OCS Hydrolysis at Metal Oxide Surfaces Used to Compare Hydroxyl Group Basicity. Catal. Lett. 1996, 39, 213−218. (25) Wilson, C.; Hirst, D. M. High-level ab initio Study of the Reaction of OCS with OH Radicals. J. Chem. Soc. Faraday Trans. 1995, 91, 793−798. (26) Wang, H. Y.; Yi, H. H.; Ning, P.; Tang, X. L.; Yu, L. L.; He, D.; Zhao, S. Z. Calcined Hydrotalcite-like Compounds as Catalysts for Hydrolysis Carbonyl Sulfide at Low Temperature. Chem. Eng. J. 2011, 166, 99−104. (27) Zhao, S. Z.; Yi, H. H.; Tang, X. L.; Song, C. Y. Low Temperature Hydrolysis of Carbonyl Sulfide using Zn−Al Hydrotalcite-derived Catalysts. Chem. Eng. J. 2013, 226, 161−165. (28) Yi, H. H.; Zhao, S. Z.; Tang, X. L.; Ning, P.; Wang, H. Y.; He, D. Influence of Calcination Temperature on the Hydrolysis of Carbonyl Sulfide over Hydrotalcite-derived Zn−Ni−Al Catalyst. Catal. Commun. 2011, 12, 1492−1495. 3512

dx.doi.org/10.1021/jp5021559 | J. Phys. Chem. A 2014, 118, 3503−3513

The Journal of Physical Chemistry A

Article

One-, Two- and Three-Water Hydrolyses of Carbodiimide and Methyleneimine. Chem.Eur. J. 2002, 8, 1934−1944. (50) Deng, C.; Li, Q. G.; Ren, Y.; Wong, N. B.; Chu, S. Y.; Zhu, H. J. A Comprehensive Theoretical Study on the Hydrolysis of Carbonyl Sulfide in the Neutral Water. J. Comput. Chem. 2008, 29, 466−480. (51) Zhang, R. G.; Ling, L. X.; Wang, B. J. Density Functional Theory Analysis of Carbonyl Sulfide Hydrolysis: Effect of Solvation and Nucleophile Variation. J. Mol. Model. 2012, 18, 1255−1262. (52) Stirling, A.; Pápai, I. H2CO3 Forms via HCO3− in Water. J. Phys. Chem. B 2010, 114, 16854−6859. (53) Wang, B. J.; Cao, Z. X. How Water Molecules Modulate the Hydration of CO2 in Water Solution: Insight from the ClusterContinuum Model Calculations. J. Comput. Chem. 2013, 34, 372−378. (54) Barone, V.; Cossi, M. Quantum Calculation of Molecular Energies and Energy Gradients in Solution by a Conductor Solvent Model. J. Phys. Chem. A 1998, 102, 1995−2001. (55) Mourik, T. v. On the Relative Stability of two Noradrenaline Conformers. Chem. Phys. Lett. 2005, 414, 364−368. (56) Reed, A. E.; Weinstock, R. B.; Weinhold, F. Natural Population Analysis. J. Chem. Phys. 1985, 83, 735−746. (57) Carpenter, J. F.; Weinhold, F. Analysis of the Geometry of the Hydroxymethyl Radical by the “Different Hybrids for Different Spins” Natural Bond Orbital Procedure. J. Mol. Struct. (THEOCHEM) 1988, 169, 41−62. (58) Reed, A. E.; Weinhold, F. Natural Bond Orbital Analysis of Internal Rotation Barriers and Related Phenomena. Isr. J. Chem. 1991, 31, 277−285. (59) Reed, A. E.; Curtiss, L. A.; Weinhold, F. Intermolecular Interactions from a Natural Bond Orbital, Donor-acceptor Viewpoint. Chem. Rev. 1988, 88, 899−926. (60) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A. et al. Gaussian 09, revision A.02; Gaussian, Inc.: Wallingford, CT, 2009. (61) Tawa, G. J.; Topol, I. A.; Burt, S. K.; Caldwell, R. A.; Rashin, A. A. Calculation of the Aqueous Solvation Free Energy of the Proton. J. Chem. Phys. 1998, 109, 4852−4863. (62) Zhan, C. G.; Dixon, D. A. Absolute Hydration Free Energy of the Proton from First- Principles Electronic Structure Calculations. J. Phys. Chem. A 2001, 105, 11534−11540. (63) Wang, B. J.; Cao, Z. X. Mechanism of Acid-Catalyzed Hydrolysis of Formamide from Cluster-Continuum Model Calculations: Concerted versus Stepwise Pathway. J. Phys. Chem. A 2010, 114, 12918− 12927.

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dx.doi.org/10.1021/jp5021559 | J. Phys. Chem. A 2014, 118, 3503−3513