A comprehensive theoretical study on the hydrolysis of carbonyl ...
A Comprehensive Theoretical Study on the Hydrolysis of Carbonyl Sulfide in the Neutral Water CHAO DENG,1,2 QIANG-GEN LI,1,2 YI REN,1,2,3 NING-BEW WONG,3 SAN-YAN CHU,4 HUA-JIE ZHU5 1
College of Chemistry, Sichuan University, Chengdu 610064, People’s Republic of China 2 Key State Laboratory of Biotherapy, Sichuan University, Chengdu 610064, People’s Republic of China 3 Department of Biology and Chemistry, City University of Hong Kong, Kowloon, Hong Kong 4 Department of Chemistry, National Tsing Hua University, Hsinchu 30013, Taiwan 5 Organic Synthesis and Natural Product Laboratory, Kunming Institute of Botany, CAS, Kunming 650204, China Received 18 October 2006; Revised 15 June 2007; Accepted 19 June 2007 DOI 10.1002/jcc.20806 Published online 30 July 2007 in Wiley InterScience (www.interscience.wiley.com).
Abstract: The detailed hydration mechanism of carbonyl sulfide (COS) in the presence of up to five water molecules has been investigated at the level of HF and MP2 with the basis set of 6-311þþG(d, p). The nucleophilic addition of water molecule occurs in a concerted way across the C¼ ¼S bond of COS rather than across the C¼ ¼O bond. This preferential reaction mechanism could be rationalized in terms of Fukui functions for the both nucleophilic and electrophilic attacks. The activation barriers, DH6¼ 298 , for the rate-determining steps of one up to five-water hydrolyses of COS across the C¼ ¼S bond are 199.4, 144.4, 123.0, 115.5, and 107.9 kJ/mol in the gas phase, respectively. The most favorable hydrolysis path of COS involves a sort of eight-membered ring transition structure and other two water molecules near to the nonreactive oxygen atom but not involved in the proton transfer, suggesting that the hydrolysis of COS can be significantly mediated by the water molecule(s) and the cooperative effects of the water molecule(s) in the nonreactive region. The catalytic effect of water molecule(s) due to the alleviation of ring strain in the proton transfer process may result from the synergistic effects of rehybridization and charge reorganization from the precoordination complex to the rate-determining transition state structure induced by water molecule. The studies on the effect of temperature on the hydrolysis of COS show that the higher temperature is unfavorable for the hydrolysis of COS. PCM solvation models almost do not modify the calculated energy barriers in a significant way. q 2007 Wiley Periodicals, Inc.
J Comput Chem 29: 466–480, 2008
Key words: carbonyl sulfide; hydrolysis mechanism; natural population analysis; solvent effects; temperature effects
Introduction Recently, the increasingly stringent emission standards worldwide are introduced to reduce the emission of sulfur-containing compounds into the atmosphere. Carbonyl sulfide (COS or S¼ ¼C¼ ¼O), which emits from many chemical process involving in the conversion of fossil fuel, is one of the major components of organic sulfur compounds. In the methods developed for the removal of COS, including hydrogenation [eq. (1)] and hydrolysis [eq. (2)], the hydrolysis of COS was recognized as the most promising process due to the mild reaction condition and higher conversion efficiency. COS þ 4H2 ! H2 S þ CH4 þ H2 O
(1)
COS þ H2 O ! H2 S þ CO2
(2)
There have been many experimental studies of the COS hydrolysis reaction over a wide pH range in aqueous solutions1,2; with amine-
based catalysts in aqueous, alcoholic, and glycolic solutions3–9; and with numerous catalytic surfaces.10–17 There are also some theoretical studies of the COS hydrolysis mechanism, but all of them model the reaction at metal oxide surfaces.18,19 To the best of our knowledge, there have not been any theoretical studies of the COS hydrolysis in the pure water, which will be helpful to deeply understand the mechanism in the views of quantum chemistry.
This article contains supplementary material available via the Internet at http://www.interscience.wiley.com/jpages/0192-8651/suppmat Correspondence to: Y. Ren; e-mail: [email protected] or N.-B. Wong; e-mail: [email protected] or H.-J. Zhu; e-mail: hjzhu@ mail.kib.ac.cn Contract grant sponsor: Yunnan Province Science and Technology Department; contract/grant number: 2005B0048M Contract grant sponsor: Scientific Research Foundation for the Returned Chinese Scholars of Sichuan University
q 2007 Wiley Periodicals, Inc.
Hydrolysis of Carbonyl Sulfide in the Neutral Water
COS (S¼ ¼C¼ ¼O) can be thought as one of cumulenes that contain S and O as the heteroatom. There are many theoretical studies of the hydration of cumulenes, including CO2,20–24 H2C¼ ¼C¼ ¼O,25–27 CH2¼ ¼C¼ ¼NH,28 HN¼ ¼C¼ ¼O,29 and 30–32 HN¼ ¼C¼ ¼NH, showing that consideration of a second water molecule resulted in catalysis effect with respect to the single water molecule hydrolysis; similar results were also found for the hydrolysis of SO3 (ref. 33) and SO2.34 The catalysis arises in all of these cases from alleviation of steric strain on going from a four-membered to six-membered or eight-membered cyclic transition state (TS) structure. In previous studies, there are two different viewpoints for the position of third water in the threewater hydrolysis of CO2 and HN¼ ¼C¼ ¼NH. Nguyen and coworkers29 showed that the third water molecule should be added to the proton transfer ring, and catalysis proceeds via the eightmembered ring TS structure. Lewis and Glaser31,32 proposed another choice, i.e. the three-water hydrolysis with the lowest activation barrier should involve a TS structure in which only two water molecules are involved in the six-membered proton transfer ring and the third water molecule near to the nonreactive nitrogen atom, which engages in hydrogen-bonding to the alcohol H-atom and to the imine-N of the forming isourea. To complete the comprehensive theoretical study of the hydrolysis of COS, we carried out a detailed investigation for the following reactions [eq. (3)] in the presence of up to five water molecules explicitly described and bulk solvent simulation by the polarizable continuum model (PCM). COS þ nH2 O ! H2 S þ CO2 þ ðn 1ÞH2 O ðn ¼ 1 5Þ
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als, encounters some serious difficulties in constructing the minimum-energy reaction paths of some specific chemical reactions, in particular for hydrogen-transfer processes.36–40 Thermal and entropy corrections were computed by standard statistical methods. Charge distributions were obtained from the wave functions calculated at the MP2/6-311þþG(d, p) level, employing natural population analysis (NPA).41–44 The catalytic effect of water molecule(s) described in this paper is explained by the changes of geometries and charge distributions in the rate-determining step. Bulk solvent effect is described by the PCM.45 The solvent (H2O) is thereby represented by a continuum characterized by its dielectric permittivity (e 5 78.41) and the solute is embedded in a cavity. Throughout this paper, all bond lengths are in angstroms and bond angles are in degrees. All relative energies (in kJ/mol) are computed by the enthalpy and Gibbs free energy changes at 298 K, denoted as DH298 or DG298 without PCM correction and DG(sol) with PCM treatment.
Results and Discussion In similar to the hydrolysis of isocyanate (H N¼ ¼C¼ ¼O),29 there are two possible reaction pathways in the water hydrolyses of COS (S¼ ¼C¼ ¼O). The water can attack across the C¼ ¼O bond (path one) or across the C¼ ¼S bond (path two) of the carbonyl sulfide. We will discuss them separately.
(3) One-Water Hydrolysis of Carbonyl Sulfide
The number of water molecules considered is larger enough to give results converged in activation energies. The aim of our study is (i) to clear up the favorable addition of first water occur across the C¼ ¼S bond or across the C¼ ¼O bond of carbonyl sulfide; (ii) to find the most convenient path for hydrolysis of the carbonyl sulfide; (iii) to investigate the cooperative effect of water molecules in the hydrolysis COS. These studies would lead us to discover the synergistic effect of the water molecule(s) placed away from the site of proton transfer and better understand the hydrolysis mechanism of COS.
Computational Method All calculations were performed using the GAUSSIAN-98 packages35 in this work. The geometries of all species, including reactants, precoordination complexes, intermediates, TSs, and products were fully optimized at the HF/6-311þþG(d, p) level first, and then reoptimized by MP2/6-311þþG(d, p). The nature of all optimized structures was determined using frequency analysis at the HF/6-311þþG(d, p) level. A scaling factor 0.9 of the zero-point vibration energy corrections was used in the calculations of relative energies. This procedure seems to be more reliable than density functional theory (DFT) approach for the present system. Despite the great success of DFT in calculating energetic and molecular properties of equilibrium structures, it appears that this method, with the currently available function-
An exhaustive study for all of the precoordination structures between one water molecule and COS shows that there are two possible minima: M1a and M1b (Figs. 1 and 2), corresponding to two different pathways. Structure M1a is found to be more stable than M1b by DH298 5 3.2 kJ/mol, because the OH group of water is engaged in a stronger hydrogen bond with Oatom than S-atom on carbonyl sulfide. The relative energies with respect to the separated reactants for all species in the one-water hydrolysis process of COS are listed in Table S1. All of the optimized species involved in the reaction of COS þ H2O ? CO2 þ H2S are shown in Figure 1 (path one) and Figure 2 (path two), respectively. For the reaction path one, after the precoordination complex M1a is formed, the nucleophilic attack of the water molecule at the central carbon on the COS leads to a four-membered ring TS structure TS1a across the C¼ ¼O bond. The addition of H2O to COS is completed upon full proton (H2) transfers from water to oxygen on COS to form the adduct (M2a). Through rotation along the O1 H2 bond, structure M2a can be converted into its isomer M2a0 accompanying a rotation barrier of DH6¼ 298 5 32.3 kJ/mol. Structure M2a0 is not only more stable than M2a by DH298 510.0 kJ/mol, but also is the most pertinent structure with a view to the next four-membered tautomerization TS structure TS2a0 . We show structure M2a in Figure 1, because it has the geometry that naturally follows the water addition via transition state TS1a. The final product of the one-water hydrolysis of COS is a complex between CO2 and H2S that is formed
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Figure 1. MP2-optimized structures of the stationary points along the hydration path of COS with one water molecule across the C¼ ¼O bond (path one). The energy values (in kJ/mol) reported above the arrows (boldface) are DH298 values without PCM correction. Below arrows are the corresponding DGsol values at the level of PCM-MP2/6-311þþG** values (italic). The number in parentheses corresponds to the sole imaginary frequency for each TS.
via an intermediate M3 and another four-membered ring tautomerization TS structure TS3, releasing the reaction energy of DH298 5 265.3 kJ/mol. It is found from Figure 1 that the activation barriers (DH6¼ 298 ) of four steps in the one-water hydrolysis of COS across the C¼ ¼O bond are 243.7, 32.3, 113.7, and 126.1 kJ/mol, respectively, implying that the first step is rate-determining. The higher barrier (243.7 kJ/mol) results from the quite tense four-membered ring TS structure TS1a, in which the O2 H2 bond is ˚ ), whereas the O1 almost broken (1.227 A H2 bond is still not ˚ ), meanwhile the O2 formed (1.240 A H2 O1 angle is significantly small (120.08), indicating that the one-water hydrolysis of COS is unlikely to occur in the gas phase. By and large, the use
of a model involving one water molecule attacking COS leads to quite unsatisfactory results. This suggests the need for models using multiple water molecules. For the second pathway of the one-water hydrolysis of carbonyl sulfide, nucleophilic attack of the water molecule on the COS C-atom leads to TS1b across the C¼ ¼S bond. As the first step of hydrolysis, the addition of H2O to COS is completed upon full proton (H1) transfer from water to sulfur on COS to form the adduct (M2b), which has the geometry that naturally follows the water addition via TS structure TS1b. Through two rotation along the O H bond, we can get two isomers of M2b, i.e. M2b0 and M3. Even though M3 is less stable than M2b by DH298 5 16.7 kJ/mol, structure M3 is the most pertinent struc-
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Figure 2. MP2/6-311þþG** optimized structures of the stationary points along the hydration path of COS with one water molecule across the C¼ ¼S bond (path two). The energy values reported above the arrows (boldface) are DH298 values (in kJ/mol) without PCM correction. Below arrows are the corresponding DGsol values (in kJ/mol) at the level of PCM-MP2/6-311þþG** values (italic).
ture with a view to the TS3, in which the proton H2 transfers from O2 to S-atom, leading to the final product M4. The relative energies in Figure 2 shows that the activation barrier for TS1b is DH6¼ 298 5 199.4 kJ/mol, higher than TS2b, TS2b0 , and TS3 by 156.9, 191.9, and 73.3 kJ/mol, respectively, indicating that the first step is still rate-controlling, lower than that for the path one by DH6¼ 298 5 44.3 kJ/mol. This important result shows that the addition of water molecule across the C¼ ¼S bond is more favorable than across the C¼ ¼O bond and the first proton should transfer to S-atom instead of O-atom on COS. The fact that addition across C¼ ¼S is favored over that across C¼ ¼O can be rationalized in terms of the condensed Fukui functions introduced by Yang and Mortier.46 For a system of N electrons independent calculations are made corresponding to N 2 1, N, and N þ 1 electron systems with the same geometry of the N-electron system. The NPA analysis yields qk(N þ 1), qk(N), and qk(N 2 1) for all the atoms present in the molecular system, where qk(N þ 1), qk(N), and qk(N 2 1) are the gross electronic populations of the site k in neutral, cationic, and anionic systems, respectively. In a finite difference approximation,
the fk values are calculated by using Yang and Mortier procedure.44 These calculations were performed at the level of B3LYP/6-311þþG**. fkþ ¼ qk ðN þ 1Þ qk ðNÞ
fk ¼ qk ðNÞ qk ðN 1Þ 1 fk0 ¼ ðqk ðN þ 1Þ qk ðN 1ÞÞ 2
for nucleophilic attack for eletrophilic attack for radical attack
Depending on the type of attack, different sites are indicated as the most reactive site for S¼ ¼C¼ ¼O, i.e., the site for which f is largest. The distinct mechanism of hydration of COS may illustrate this: the preferred attack proceeds via a nucleophilic attack of oxygen atom on water at COS C-atom (fþ largest for C, f+C 5 0.453, f+S 5 0.427, f+O 5 0.121), while an electrophilic attack occurs by proton at sulfur (f2 largest for S and not on O, f S 5 0.706, fO 5 0.294, fC 5 0.000). This indicates that the ability of the COS S-atom to accept and distribute positive charge is of considerable importance, in such a way that attack
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Figure 3. MP2-optimized structures of the stationary points along the hydration path of COS with two water molecules across the C¼ ¼O bond (path one). The energy values reported above the arrows (boldface) are DH298 values (in kJ/mol) without PCM correction. Below arrows are the corresponding DGsol values at the level of PCM-MP2/6-311þþG** values (italic).
on S is preferred over attack on O. These explanations can also be applied in the following two-, three-, four-, and five-water hydrolysis of carbonyl sulfide. Two-Water Hydrolysis of Carbonyl Sulfide
The two-water hydrolysis of COS has a main advantage over the single-water hydrolysis, that is, the energetic stability gained from being able to assume six-membered ring proton-transfer TS structures. There are also two pathways for the two-water hydrolysis (Figs. 3 and 4). Two possible precoordination complexes are
located for the two-water hydrolysis of COS as the starting points in the hydrolysis reaction. One is M5a, in which the second water molecule forms a six-membered ring structure with oxygen atom on COS and hydrogen atom on the first water molecule, the other is M5b, in which there is a weak hydrogen bond between sulfur and the hydrogen atom. The former is slightly more stable than latter by DH298 5 5.8 kJ/mol. The relative energies with respect to the separated reactants for all species in the two-water hydrolysis process of COS are listed in Table S2. In the first path of two-water hydrolysis of COS (Fig. 3), nucleophilic attack of water leads to the six-membered ring TS
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Figure 4. MP2/6-311þþG**-optimized structures of the stationary points along the hydration path of COS with two water molecules across the C¼ ¼S bond (path two). The energy values reported above the arrows (boldface) are DH298 values (in kJ/mol) without PCM correction. Below arrows are the corresponding DGsol values at the level of PCM-MP2/6-311þþG** values (italic).
structure (TS5a) across the C¼ ¼O bond, in which proton transfers from water to O-atom of COS through water chain. The formed complex M6a has another isomer M6a0 , which is more stable than M6a by DH298 5 7.5 kJ/mol. Moreover, M6a0 is the most pertinent structure with a view to the second six-membered tautomerization TS state structure TS6a. The structure that naturally follows from TS6a is M7a, but its isomer M7a0 with higher energy is the most pertinent structure with a view to the water-assisted tautomerization TS structure TS7, involving the proton transfer from O3 to S-atom via a water chain. The final product of the two-water hydrolysis of COS is a monohydrated complex (M8).
For the second pathway of two-water hydrolysis (Fig. 4), at the first step of reaction, nucleophilic attack of water leads to a sort of six-membered ring TS structure TS5b, involving the proton transfers from water to COS S-atom along the water chain. Even though the structure that naturally follows from TS5b is M6b, much more stable isomer, M6b0 , is the most pertinent structure with a view to another water-assisted tautomerization TS structure TS6b. The final product M8 is formed through the third tautomerization transition state TS7. As shown in Figures 3 and 4, reaction barriers for the twowater hydrolysis of COS are decreased dramatically upon incorporation of a second water molecule in the reaction coordinate.
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Figure 5. MP2-optimized structures, including three possible precoordination structures (M9a, M9b, and M9c), and two TS structures TS9b0 (relative to M9b) and TS9c (relative to M9c), and DH298 (DGsol) values (in kJ/mol), relative to separated reactants for the three-water hydrolysis of carbonyl sulfide.
That can be attributed to the fact that there are less strained sixmembered ring TS structures in the two-water hydrolysis instead of the high strained four-membered ring TSs in the single-water hydrolysis of COS. The other explanations will be given later. As the one-water hydrolysis of COS, the first step in the twowater hydrolysis is still rate-determining. Compared with the single-water hydrolysis, the energy barrier of the first step for attack across C¼ ¼O via TS5a is lowered by DH298 5 76.5 kJ/ mol, whereas that across the C¼ ¼S bond via TS5b is reduced by DH298 5 55.0 kJ/mol. The calculated rate-determining barriers are 167.2 kJ/mol for the first path and 144.4 kJ/mol for the second path, respectively. These results further confirm the water addition across the C¼ ¼S bond is favored over that across the C¼ ¼O bond. The overall reaction energy for the two-water hydrolysis of COS is DH298 5 282.4 kJ/mol, lower than that in the one-water hydrolysis by 17.1 kJ/mol, showing the second water involving the hydrolysis of COS is thermodynamically and kinetically favorable in the gas-phase. Three-Water Hydrolysis of Carbonyl Sulfide
As the next logical step, the effect of a third water molecule on the hydrolysis of the parent COS is considered in this part.
However, the placement of a third water molecule is not a trivial matter. There are three possible positions for the placement of the third water molecule. Precoordination structure M9a represents van der Waals complex between COS and three water molecules. The other two options may involve placement of two water molecules at the same site of proton transfer, thus expanding the proton-transfer ring to eight atoms, in which the hydrogen bond structure involves COS O-atom (M9b) or COS S-atom (M9c) (Fig. 5). The relative energies for the three-water hydrolysis of COS in Table S3 show that the structure M9c is more stable than M9b by DH298 5 1.2 kJ/mol and than M9a by DH298 5 20.3 kJ/mol, but the reaction barriers with respect to M9c and M9b are 136.4 and 142.3 kJ/mol (DH6¼ 298 ), larger than those relative to M9a by 13.4 and 9.0 kJ/mol, respectively, showing that there is a cooperative effect of water molecule in the proton-transfer process from M9a to TS9a or TS9b when the third water molecule is near to nonreactive sulfur or oxygen atom but not involved in the proton transfer, whereas structure M9b and M9c are, in fact, insignificant, as pointed by Lewis and Giaser32 So only the two reaction pathways involving complex M9a are considered here. Structural inspections would suggest that structure M9a can lead to two possible TS structures, one is across the C¼ ¼O bond
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Figure 6. MP2/6-311þþG** optimized structures of the stationary points along the hydration path of COS with three water molecules across the C¼ ¼O bond (path one). The energy values reported above the arrows (boldface) are DH298 values (in kJ/mol) without PCM correction. Below arrows are the corresponding DGsol values at the level of PCM-MP2/6-311þþG** values (italic).
(TS9a), the other is across the C¼ ¼S bond (TS9b), corresponding to two different pathways. There are three reaction steps in the three-water hydrolysis of COS. In the first pathway (Fig. 6), the first step concerns the nucleophilic attack of the water molecule, through a six-membered ring TS structure TS9a (across C¼ ¼O), leading to dihydrated complex M10a. Then the reaction proceeds through tautomerization TS structures TS10a and TS11 to the final dihydrate H2SCO2 complex M12. It is worth noticing from Figure 6 that the structure that naturally follows from TS10a is M11a, but its isomer M11a0 with higher energy is the most pertinent structure with a view to the water-assisted tautomerization TS structure TS11.
In the second pathway (Fig. 7), the nucleophilic attack of the water molecule leads to TS9b. The proton transfers from water to COS S-atom, forming the complex M10b. The final product is formed along TS10b ? M11a ? M11a0 ? TS11 ? M12. Inspection of the energetics in Table S3 and Figures 6 and 7 shows that the three reaction barriers (DH6¼ 298 ) are 133.3, 33.6, and 97.4 kJ/mol for the first pathway, and 123.0, 45.3, and 97.4 kJ/mol for the second pathway, respectively, indicating that the first step is also rate-determining for the three hydrolysis of COS, and the second pathway involving the addition across the C¼ ¼S bond is the more energetically favored reaction route as the one- and two-water hydrolysis of COS. The overall reaction
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Figure 7. MP2-optimized structures of the stationary points along the hydration path of COS with three water molecules across the C¼ ¼S bond (path two). The energy values reported above the arrows (boldface) are DH298 values (in kJ/mol) without PCM correction. Below arrows are the corresponding DGsol values at the level of PCM-MP2/6-311þþG** values (italic).
energy for the three-water hydrolysis is 295.5 kJ/mol (DH298) and shows that the hydrolysis of COS involving three water molecules is more exothermic. Comparison with two-water hydrolysis shows that the presence of third water molecule near to the nonreactive sulfur atom or oxygen atom (second path) but not involved in the proton transfer can significantly lower the rate-determining activation barrier by 33.9 kJ/mol (first path) or 21.4 kJ/mol (second path), indicating that the cooperative effects of the third water in the mediated hydrolysis of carbonyl sulfide. These results can also be observed in the hydrolysis of carbon dioxide24 and carbodiimide32 by Lewis and Glaser, where the activation barrier can be
drastically reduced by the cooperative effect of the third water molecule from 133.4 and 122.6 kJ/mol in the two-water hydrolysis down to 100.9 and 95.8 kJ/mol for the three-water hydrolysis, respectively. Four- and Five-Water Hydrolysis of Carbonyl Sulfide
From the aforementioned studies about one- up to three-water hydrolysis of the carbonyl sulfide, we can get same conclusion, i.e. the first step is always the rate-determining. Meanwhile it is found that the barrier for the rate-determining step across the C¼ ¼S bond decreases with the addition of water molecules from
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Table 1. Energy Barriers for the First Step in the Hydrolysis of
Carbonyl Sulfide in the Gas Phase, DH6¼ 298 , and in Aqueous Solvent, DG(sol), in kJ/mol. DH6¼ 298
S¼ ¼C¼ ¼O þ H2O S¼ ¼C¼ ¼O þ 2H2O S¼ ¼C¼ ¼O þ 3H2O S¼ ¼C¼ ¼O þ 4H2O S¼ ¼C¼ ¼O þ 5H2O
DG(sol)
Across C¼ ¼O
Across C¼ ¼S
Across C¼ ¼O
Across C¼ ¼S
243.7a 167.2b 133.3b 142.3c 136.3b 118.3c 115.3c 119.2d
199.4 144.4 123.0 136.4 115.5 126.8 107.9
259.8 167.0 143.4 143.8 138.5 131.0 120.4 126.5
208.6 156.3 131.5 137.8 129.5 119.9 111.8
a
Four-membered ring TS. Six-membered ring TS. c Eight-membered ring TS. d Ten-membered ring TS. b
199.4 kJ/mol (one-water) to 144.4 kJ/mol (two-water), to 123.0 kJ/mol (three-water). So it is necessary to consider that more water is involved in the hydrolysis of COS. In this part we will discuss the hydrolysis of COS in the presence of four and five water molecules, but only concern the first step. All of the reaction barriers involved in the first step of hydrolysis of COS with one up to five water molecules are summarized in Table 1. There are two possible precoordination complexes (M13 and M14) (Fig. 8) as the starting points in the hydrolysis reaction. M14 is slightly stable than the structure M13 by DH298 5 4.3 kJ/mol. Four possible reaction pathways for the four-water hydrolysis will be considered, in which two pathways involve a sort of eight-membered ring TS structure and one water molecule near to the nonreactive sulfur or oxygen atom but not involved in the proton transfer, and other two pathways involve a sort of six-membered ring TS structure and two water molecules are not directly involved in the proton transfer. All of optimized structures, including complexes and TS structures, are presented in Figure 8, and the relative energies are listed in Table S4. Inspection of the data in Table S4 and the geometries in Figure 8 shows that the reaction barriers (DH6¼ 298 ) are 118.3 kJ/mol for the first path (M13 ? TS13) involving the nucleophilic addition of water across the C¼ ¼O bond and 126.8 kJ/mol for the second path (M14 ? TS14) across the C¼ ¼S bond with a sort of eight-membered ring TS; 115.5 kJ/mol for the third path (M13 ? TS15) involving the proton transfer across the C¼ ¼S bond and 136.3 kJ/mol for the fourth path (M14 ? TS16) involving the proton transfer across the C¼ ¼O bond with a sort of six-membered ring TS. After the PCM correction, the barriers are 131.0 kJ/mol (the first path), 119.9 kJ/mol (the second path), 129.5 kJ/mol (the third path), and 138.5 kJ/mol (the fourth path). These calculated barriers show that the proton transfer through a sort of six-membered ring TS across the C¼ ¼S bond is more favorable than across the C¼ ¼O bond, both in the gas phase and in the bulk solvent. Even though the barrier in the first path with a eight-membered ring proton transfer TS across
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the C¼ ¼O bond is lower than that in the second path across the C¼ ¼S bond in the gas-phase, the latter barrier is still lower than former by DG(sol) 511.1 kJ/mol after the PCM treatment, indicating that second pathway through a sort of eight-membered ring TS across the C¼ ¼S bond is the most favorable in the bulk solvent. The overall reaction energy for the four-water hydrolysis of COS is 2152.2 kJ/mol (DH298), lower than one up to three water cases, showing more water molecules involved in the hydrolysis of COS is thermodynamically and kinetically favorable. As the former case, only the first step is discussed in the five-water hydrolysis of carbonyl sulfide. Three possible pathways are proposed (Fig. 9). In the first reaction path, four molecules are involved in the proton transfer across the C¼ ¼O bond, leading to a TS characterized by a sort of 10-membered ring TS structure and the other one water molecule is near to the nonreacting sulfur. The similar TS structure across the C¼ ¼S bond cannot be located, despite extensive attempts. The other two pathways include a sort of eight-membered ring TS across the C¼ ¼O bond (path two) or across the C¼ ¼S bond (path three); meanwhile, two water molecules are near to the nonreacting sulfur atom (path two) or near to the nonreacting oxygen atom (path three) but not involved in the proton transfer. The MP2/6-311þþG(d, p) optimized structures for the fivewater hydrolysis of COS are collected in Figure 9, and the relative energies are listed in Table S5. Inspection of the energies in Table S5 and Figure 9 shows that the barriers (DH6¼ 298 ) are 119.2 kJ/mol for the first path, 115.3 kJ/mol for the second path, and 107.9 kJ/mol for the third path. These results indicate that (i) the 10-membered ring TS structure is less favorable than eightmembered ring TS; (ii) the addition across the C¼ ¼S bond is preferred above the one across the C¼ ¼O bond. The overall reaction energy for the five-water hydrolysis is DH298 5 2190.8 kJ/mol. Comparison between five-water hydrolysis of COS and other cases (three and four-water hydrolysis) shows that the rate-determining activation barrier in the hydrolysis of COS depends on the number (N) of cooperative water molecule(s) on the nonreactive region. Taking the eight-membered ring TSs across the C¼ ¼S bond as examples, the barrier (DH6¼ 298 ) decreases with the number of nonreactive water in the following order: 136.3 kJ/ mol (TS9c, N 5 0) [ 126.8 kJ/mol (TS16, N 5 1) [ 107.9 kJ/ mol (TS19b, N 5 2), suggesting that there are better cooperative effects of two water molecules than the one water molecule near to the nonreacting region. If we fix the one water molecule on the nonreactive region and only discuss the TSs across the C¼ ¼O bond, it is found that the barriers decrease from DH6¼ 298 5 133.3 kJ/mol (six-membered ring TS9a) to 118.3 kJ/mol (eight-membered ring TS13) and to 119.2 kJ/mol (10-membered ring TS17), showing that the hydrolysis of COS via a sort of eight-membered ring TS is the most favorable due to the better catalytic effect of the two-water chain. This interesting result can be rationalized by the comparison of intermolecular hydrogen bonds in the TS structures. Although it is difficult to detect the geometry of the hydrogen bond, a statistical analysis of X-ray crystallographic data has shown that most of hydrogen bonds in crystals are nonlinear by about 108–158. The angles of hydrogen bonds in TS13 are about 165.78–170.28, obviously better than those in the TS9a (1508) because of the larger repulsion between two heavy atoms with
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Figure 8. MP2-optimized structures for the hydrolysis of COS with four water molecules, including precoordination complexes, the corresponding TSs for the first step and product. The energy values reported near to the arrows (boldface) are DH298 values (in kJ/mol) without PCM correction and the corresponding DGsol values at the level of PCM-MP2/6-311þþG** values (italic).
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Hydrolysis of Carbonyl Sulfide in the Neutral Water
Figure 9. MP2-optimized structures for the hydrolysis of COS with five water molecules, including precoordination complexes, the corresponding TSs for the first step and product. The energy values reported near to the arrows (boldface) are DH298 values (in kJ/mol) without PCM correction and the corresponding DGsol values at the level of PCM-MP2/6-311þþG** values (italic).
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Table 2. Selected Charges and Changes in Atom Charges Determined by Natural Population Analysis.
M1a TS1a M1a?TS1 M1b TS1b M1b?TS1b M5a TS5a M5a?TS5a M5b TS5b M5b?TS5b M9a TS9a M9a?TS9a M9a TS9b M9a?TS9b M19 TS19a M19–TS19a TS19b M19?TS19b
O1
O2
O3
O4
O5
O6
H1
H2
H3
H4
S
C
H5
H6
20.589 20.756 20.167 20.537 20.6 20.063 20.61 20.798 20.188 20.535 20.667 20.132 20.585 20.798 20.213 20.585 20.719 20.134 20.617 20.83 20.213 20.785 20.168
20.929 0.876 1.805 20.921 20.883 0.038 20.963 20.872 0.091 20.961 20.876 0.085 20.989 20.869 0.12 20.989 20.877 0.112 21.026 20.883 0.143 20.884 0.142
– – – – – – 20.951 20.903 0.048 – – – 20.946 20.909 0.037 20.946 20.948 20.002 20.981 20.902 0.079 20.986 20.005
– – – – – – – – – 20.946 20.924 0.022 20.939 20.975 20.036 20.939 0.932 1.871 20.975 20.979 20.004 20.893 0.082
– – – – – – – – – – – – – – – – – – 20.963 20.959 0.004 20.987 20.024
– – – – – – – – – – – – – – – – – – 20.986 20.999 20.013 20.976 0.01
0.455 0.505 0.05 0.461 0.413 20.048 0.457 0.529 0.072 0.496 0.559 0.063 0.486 0.57 0.084 0.486 0.56 0.074 0.504 0.566 0.062 0.559 0.055
0.472 0.577 0.105 0.457 0.505 0.048 0.499 0.56 0.061 0.459 0.516 0.057 0.496 0.56 0.064 0.496 0.564 0.068 0.518 0.558 0.04 0.559 0.041
– – – – – – 0.49 0.555 0.065 – – – 0.484 0.553 0.069 0.484 0.5 0.016 0.515 0.55 0.035 0.53 0.015
– – – – – – – – – 0.48 0.482 0.002 0.476 0.508 0.032 0.476 0.481 0.005 0.508 0.529 0.021 0.551 0.043
20.016 20.049 20.033 20.071 20.174 20.103 20.019 20.252 20.233 20.114 20.332 20.218 20.067 20.338 20.271 20.067 20.357 20.29 20.001 20.419 20.418 20.436 20.435
0.606 0.598 20.008 0.612 0.738 0.126 20.629 0.674 1.303 0.649 0.737 0.088 0.651 0.715 0.064 0.651 0.747 0.096 0.62 0.756 0.136 0.777 0.157
– – – – – – – – – – – –
– – – – – – – – – – – –
0.502 0.553 0.051 0.524 0.022
0.516 0.503 20.013 0.493 20.023
higher electronegativity in TS9a, leading to less stabilization of TS and higher tautomeric barrier in the three-water hydrolysis process of COS than that in the four-water hydrolysis TS across the C¼ ¼O bond by 15.0 kJ/mol. The increment from the eightmembered ring structure TS13 to the 10-membered ring structure TS17 does not relax the strain in the geometry of the hydrogen bonds, leading to similar reaction barrier.
Further Explanations for the Water Catalysis
Lewis and Glaser24,32 proved that the variation of activation barriers could be explained by the structural and electrical relaxation associated with the formation of rate-determining TS. As addition across the C¼ ¼S bond is more favorable, the following discussions will focus on the comparison of activation processes M9a ? TS9b and M19a ? TS19b; M1b ? TS1b and M5b ? TS5b. A structural comparison of TS9b (Fig. 7) and TS19b (Fig. 9) shows that the consideration of one or two water molecules near to the nonreacting oxygen atom results in a TS structure in which bond formation between the adding water molecules and the COS C-atom has progressed more in TS19b, where the ˚ from TS9b to TS19b. C O2 distance decreases by 0.072A Note also that the rehybridization of the COS C-atom has progressed more in TS19b than in TS9b, and this is illustrated by the S C O angles of 132.98 for TS9b and 128.28 for TS19b ˚ in as well by the lengthening of the C¼ ¼S bond from 1.699 A ˚ in TS19b. Less strain is also observed in the TS9b to 1.709 A eight-membered ring TS19b, in which three hydrogen bonds exist with angles of 164.98–167.98, obviously better than those in the TS9b, where the angles of hydrogen bonds are 159.68
and 152.18, implying that more relaxed geometry in TS19b clearly favors the triple proton transfer compared with the strained TS9b. Meanwhile, these structural differences during activation have important electronic consequences. According to the concept of hybridization, we can predict the O atom in COS will be less negative in the precoordination complexes (M9a and M19) and the change in the O atomic charge in COS would be more negative for the process M19 ? TS19b than for M9a ? TS9b. This prediction was confirmed by NPA in Table 2, which revealed Dq(O1) values of 20.134 for M9a ? TS9b and 20.168 for M19 ? TS19b. Similarly, in the course of the addition reaction, a water molecule H OH is converted into an alcohol R OH, and one can expect that the OH-group in the alcohol will be overall less negative than in water. These changes in natural atomic charges should be manifested more in the process M19 ? TS19b than for M9a ? TS9b. The NPA results (Table 2) indeed show a greater loss of electron density in O2H2 for the former reaction. Moreover, this decrease of electron density occurs both for the O2-atom (Dq 5 þ0.112 for M9a ? TS9b and þ0.142 for M19 ? TS19b). The electronic Table 3. Effect of Temperature for the Five-Water Hydrolysis of
Carbonyl Sulfide. Temperature (K)
DG (kJ/mol) K x%
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298
300
400
500
600
222.28 8052.5 99.988
222.26 7512.4 99.987
220.91 537.8 99.814
219.50 108.9 99.090
218.04 37.2 97.385
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Scheme 1. Summary of this work on the favorable reaction routes in the neutral hydrolysis of COS, including precoordination complex, rate-determining structures, and final stable product.
rearrangements occurring in the activation processes M9a ? TS9b and M19 ? TS19b clearly demonstrate an increased propensity for H-bonding interactions of both the H2 and O2 in the latter case. The O2H2 group is a better H-bond donor because the negative O-charge is reduced and the positive charge on H is increased. The COS O-atom (O1) is a better H-bond acceptor because it is more negatively charged. These effects should be felt in any H-bonding environment. The earlier structural and electronic changes associated with the processes M9a ? TS9b and M19 ? TS19b are also observed in the comparison between one-water hydrolysis (M1b ? TS1b) and two-water hydrolysis of COS (M5b ? TS5b). A closer inspection of geometries in Figures 2 and 4 reveals that ˚ from TS1b to TS5b, the C O distances decreases by 0.082 A and the S C O angles become smaller from 144.38 in TS1b to 136.08 in TS5b. The electronic rearrangements during the activation processes also clearly show that in the hydrolysis of COS with two water molecules, M5b ? TS5b, the O1 atom becomes 0.069 more negative than in the hydrolysis with one water. Likewise, the O2 and H2 atoms in the process M5b ? TS5b become þ0.047 and þ0.009 more positive than in the process M1b ? TS1b. These geometry and charge changes will make the hydrolysis of COS with two water molecules more favorable than with one water molecule. Effect of Temperature
Because the five-water hydrolysis of COS is the most favorable reaction route than other cases, the total Gibbs free energy change for the reaction M19 ? M20 is calculated at a different temperature. Our study covered the temperature range 298–600 K. The calculated equilibrium constants and conversion coefficients indicate that the higher temperature is unfavorable for the hydrolysis of COS (Table 3). This trend is consistent with the experiments.14 Solvent Effect
The performance of hydrolysis of COS was studied in aqueous solution using the PCM model employing the optimized geome-
tries in the gas phase. The relative energies after correction of bulk solvent effect are listed in Tables S1–S5. One can easily observe that the PCM solvation models almost do not modify the energy barriers in a significant way. For example, the results in Table S5 show that the PCM model slightly raise the barrier for addition across C¼ ¼O by 5.1 kJ/mol in the ‘‘five-water hydrolysis case,’’ from 115.3 kJ/mol in the gas phase to 120.4 kJ/mol [DG#(sol)] in solvent. The change does not influence qualitatively the reaction path, showing invariably the preference for the addition across the C¼ ¼S bond. The latter path appears to be similarly influenced by its surroundings. The energy barrier goes from 107.9 kJ/mol in the gas phase to 111.8 kJ/mol in solvent. For the ‘‘one up to four water cases’’ the calculated rate-determining barriers for addition across the C¼ ¼S bond are 208.6, 156.3, 131.5, and 119.9 kJ/mol in solvent, respectively. These results emphasize again that the hydrolysis mediated by a water chain is a favored process.
Conclusions In the present paper, a comprehensive mechanistic investigation of the hydrolysis of COS has been undertaken by ab initio methods, both in the gas phase and in aqueous solution. In addition to one up to five water molecules explicitly described, the effect of water bulk solvent is taken into account using the PCM model. The principle conclusions from this study are as follows: 1. In all possible considered hydrolysis of COS in the presence of up to five water molecules, the first step involving proton transfer is always rate-determining, and the nucleophilic addition of water prefers to occurs across the C¼ ¼S bond of COS rather than across the C¼ ¼O bond. Such a preferential reaction mechanism could be rationalized in terms of condensed Fukui functions for both nucleophilic and electrophilic attack. 2. Calculated MP2/6-311þþG** barriers in the gas phase, DH6¼ 298 , for the rate-determining steps of the one up to fivewater hydrolyses of COS are 199.4, 144.4, 123.0, 115.5, and 107.9 kJ/mol via the water addition across the C¼ ¼S bond. It was also shown that expanding TS structure across the C¼ ¼O
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bond from eight-membered to 10-membered ring if one more water is engaged in the proton transfer process (M17 ? TS17) cannot further lower the rate-determining barrier, suggesting that the hydrolysis of COS involving five water molecules via a sort of eight-membered ring TS is a more favorable reaction route. 3. The five-water hydrolysis of COS with the lowest activation barrier involves the eight-membered ring TS structure across the C¼ ¼S bond (M19 ? TS19b), meanwhile two other water molecules are near to the nonreactive sulfur atom and construct a eight-memebered cyclic structure via a water chain but not involved in the proton transfer, suggesting that there is a better cooperative effect on the hydrolysis by a eightmemebered ring hydrogen bond structure. 4. The catalytic effect of the second up to fifth water molecule in the hydrolysis of COS can be explained by the structural and electronic rearrangements of rate-determining step. The structural and electronic changes associated with the formation of TS can greatly affect the properties of groups that are not directly involved in the bond-breaking and forming region. 5. When DH6¼ 298 values in the gas phase are compared with the DG#(sol) one after PCM treatment, it is found that the effect associated with the bulk solvent is relative small, probably due to most of solvent contribution being already taken into account by the one up to five explicit water molecules. Scheme 1 demonstrates the summary of this work on the two favorable reaction routes of neutral hydrolysis of COS, showing the optimal circuit of the hydrogen bond for ready proton transfer and the cooperative assistance of the second circuit. These important results can be applied for the hydrolysis process of other molecules, e.g. CO2 and NH¼ ¼C¼ ¼NH. The theoretical studies for these systems are being carried out.
Acknowledgments We express our gratitude to the referees for their valuable comments.
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12. Saur, O.; Bensitel, M.; Saad, A. B. M.; Lavalley, J. C.; Tripp, C. P.; Morrow, B. A. J Catal 1986, 99, 104. 13. Williams, B. P.; Young, N. C.; West, J.; Rhodes, C.; Hutchings, G. J. Catal Today 1999, 49, 99. 14. Rhodes, C.; Riddel, S. A.; West, J.; Williams, B. P.; Hutchings, G. J. Catal Today 2000, 59, 443. 15. West, J.; Williams, B. P.; Young, N. C.; Rhodes, C.; Hutchings, G. J. Catal Lett 2001, 74, 111. 16. Huang, H. M.; Young, N.; Williams, B. P.; Taylor, S. H.; Hutchings, G. Catal Lett 2005, 104, 17. 17. Zhang, Y. Q.; Xiao, Z. B.; Ma, J. X. Appl Catal B 2004, 48, 57. 18. Aboulayt, A.; Mauge´, F. Hoggan, P. E.; Lavalley, J. C. Catal Lett 1996, 39, 213. 19. Wilson, C.; Hirst, D. M. J Chem Soc Faraday Trans 1995, 91, 793. 20. Nguyen, M. T.; Raspoet, G.; Vanquickenborne, L. G.; Van Duijen P. T. J Phys Chem A 1997, 101, 7379. 21. Merz, K. M. J Am Chem Soc 1990, 112, 7973. 22. Liang, J. Y.; Lipscomb, W. N. J Am Chem Soc 1986, 108, 5051. 23. Nguyen, M. T.; Ha, T. K. J Am Chem Soc 1984, 106, 599. 24. Lewis, M.; Glaser, R. J Phys Chem A 2003, 107, 6814. 25. Tidwell, T. T. Acc Chem Res 1990, 23, 273. 26. Allen, A. D.; Tidwell, T. T. J Am Chem Soc 1987, 109, 2774. 27. Nguyen, M. T.; Hegarty, A. F. J Am Chem Soc 1984, 106, 1552. 28. Nguyen, M. T.; Hegarty, A. F. J Am Chem Soc 1983, 105, 3811. 29. Raspoet, G.; Nguyen, M. T.; McGarraghy, M.; Hegarty, A. F. J Org Chem 1998, 63, 6867. 30. Nguyen, M. T.; Raspoet, G.; Vanquickenborne, L. G. J Chem Soc Perkin Trans 2 1999, 4, 813. 31. Lewis, M.; Glaser, R. J Am Chem Soc 1998, 120, 8541. 32. Lewis, M.; Glaser, R. Chem Eur J 2002, 8, 1934. 33. Morokuma, K.; Muguruma, C. J Am Chem Soc 1994, 116, 10316. 34. Loerting, T.; Liedl, K. R. J Phys Chem A 2001, 105, 5137. 35. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A.; Stratmann, R. E., Jr.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Baboul, A. G.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Gonzalez, C.; Challacombe, M.; Gill, P.-M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Andres, J. L.; Gonzalez, C.; Head-Gordon, M.; Replogle, E. S.; Pople, J. A. Gaussian 98, Revision A.9; Gaussian: Pittsburgh, PA, 1998. 36. Baker, J.; Andzelm, J.; Muir, M.; Taylor, P. R. Chem Phys Lett 1995, 237, 53. 37. Johnson, B. G.; Gonzales, C. A.; Gill, P. M. W.; Pople, J. A. Chem Phys Lett 1994, 221, 100. 38. Zhang, Q.; Bell, R.; Truong, T. N. J Phys Chem. 1995, 99, 592. 39. Hrusak, J.; Friedrichs, H.; Schwarz, H.; Razafinjanahary, H.; Chermette, H. J Phys Chem 1996, 100, 100. 40. Baker, J.; Muir, M.; Andzelm, J. J Chem Phys 1995, 102, 2063. 41. Reed, A. E.; Weinstock, R. B.; Weinhold, F. J Chem Phys 1985, 83, 735. 42. Carpenter, J. F.; Weinhold, F. J Mol Struct (Theochem) 1988, 169, 41. 43. Reed, A. E.; Weinhold, F. Isr J Chem 1991, 21, 277. 44. Reed, A. E.; Curtiss, L. A.; Weinhold, F. Chem Rev 1988, 88, 899. 45. Tomasi, J.; Persico, M. Chem Rev 1994, 94, 2027. 46. Yang, W.; Mortier, W. J. J Am Chem Soc 1986, 108, 5708.
Journal of Computational Chemistry
DOI 10.1002/jcc
College of Chemistry, Sichuan University, Chengdu 610064, People’s Republic of China 2 Key State Laboratory of Biotherapy, Sichuan University, Chengdu 610064, People’s Republic of China 3 Department of Biology and Chemistry, City University of Hong Kong, Kowloon, Hong Kong 4 Department of Chemistry, National Tsing Hua University, Hsinchu 30013, Taiwan 5 Organic Synthesis and Natural Product Laboratory, Kunming Institute of Botany, CAS, Kunming 650204, China Received 18 October 2006; Revised 15 June 2007; Accepted 19 June 2007 DOI 10.1002/jcc.20806 Published online 30 July 2007 in Wiley InterScience (www.interscience.wiley.com).
Abstract: The detailed hydration mechanism of carbonyl sulfide (COS) in the presence of up to five water molecules has been investigated at the level of HF and MP2 with the basis set of 6-311þþG(d, p). The nucleophilic addition of water molecule occurs in a concerted way across the C¼ ¼S bond of COS rather than across the C¼ ¼O bond. This preferential reaction mechanism could be rationalized in terms of Fukui functions for the both nucleophilic and electrophilic attacks. The activation barriers, DH6¼ 298 , for the rate-determining steps of one up to five-water hydrolyses of COS across the C¼ ¼S bond are 199.4, 144.4, 123.0, 115.5, and 107.9 kJ/mol in the gas phase, respectively. The most favorable hydrolysis path of COS involves a sort of eight-membered ring transition structure and other two water molecules near to the nonreactive oxygen atom but not involved in the proton transfer, suggesting that the hydrolysis of COS can be significantly mediated by the water molecule(s) and the cooperative effects of the water molecule(s) in the nonreactive region. The catalytic effect of water molecule(s) due to the alleviation of ring strain in the proton transfer process may result from the synergistic effects of rehybridization and charge reorganization from the precoordination complex to the rate-determining transition state structure induced by water molecule. The studies on the effect of temperature on the hydrolysis of COS show that the higher temperature is unfavorable for the hydrolysis of COS. PCM solvation models almost do not modify the calculated energy barriers in a significant way. q 2007 Wiley Periodicals, Inc.
J Comput Chem 29: 466–480, 2008
Key words: carbonyl sulfide; hydrolysis mechanism; natural population analysis; solvent effects; temperature effects
Introduction Recently, the increasingly stringent emission standards worldwide are introduced to reduce the emission of sulfur-containing compounds into the atmosphere. Carbonyl sulfide (COS or S¼ ¼C¼ ¼O), which emits from many chemical process involving in the conversion of fossil fuel, is one of the major components of organic sulfur compounds. In the methods developed for the removal of COS, including hydrogenation [eq. (1)] and hydrolysis [eq. (2)], the hydrolysis of COS was recognized as the most promising process due to the mild reaction condition and higher conversion efficiency. COS þ 4H2 ! H2 S þ CH4 þ H2 O
(1)
COS þ H2 O ! H2 S þ CO2
(2)
There have been many experimental studies of the COS hydrolysis reaction over a wide pH range in aqueous solutions1,2; with amine-
based catalysts in aqueous, alcoholic, and glycolic solutions3–9; and with numerous catalytic surfaces.10–17 There are also some theoretical studies of the COS hydrolysis mechanism, but all of them model the reaction at metal oxide surfaces.18,19 To the best of our knowledge, there have not been any theoretical studies of the COS hydrolysis in the pure water, which will be helpful to deeply understand the mechanism in the views of quantum chemistry.
This article contains supplementary material available via the Internet at http://www.interscience.wiley.com/jpages/0192-8651/suppmat Correspondence to: Y. Ren; e-mail: [email protected] or N.-B. Wong; e-mail: [email protected] or H.-J. Zhu; e-mail: hjzhu@ mail.kib.ac.cn Contract grant sponsor: Yunnan Province Science and Technology Department; contract/grant number: 2005B0048M Contract grant sponsor: Scientific Research Foundation for the Returned Chinese Scholars of Sichuan University
q 2007 Wiley Periodicals, Inc.
Hydrolysis of Carbonyl Sulfide in the Neutral Water
COS (S¼ ¼C¼ ¼O) can be thought as one of cumulenes that contain S and O as the heteroatom. There are many theoretical studies of the hydration of cumulenes, including CO2,20–24 H2C¼ ¼C¼ ¼O,25–27 CH2¼ ¼C¼ ¼NH,28 HN¼ ¼C¼ ¼O,29 and 30–32 HN¼ ¼C¼ ¼NH, showing that consideration of a second water molecule resulted in catalysis effect with respect to the single water molecule hydrolysis; similar results were also found for the hydrolysis of SO3 (ref. 33) and SO2.34 The catalysis arises in all of these cases from alleviation of steric strain on going from a four-membered to six-membered or eight-membered cyclic transition state (TS) structure. In previous studies, there are two different viewpoints for the position of third water in the threewater hydrolysis of CO2 and HN¼ ¼C¼ ¼NH. Nguyen and coworkers29 showed that the third water molecule should be added to the proton transfer ring, and catalysis proceeds via the eightmembered ring TS structure. Lewis and Glaser31,32 proposed another choice, i.e. the three-water hydrolysis with the lowest activation barrier should involve a TS structure in which only two water molecules are involved in the six-membered proton transfer ring and the third water molecule near to the nonreactive nitrogen atom, which engages in hydrogen-bonding to the alcohol H-atom and to the imine-N of the forming isourea. To complete the comprehensive theoretical study of the hydrolysis of COS, we carried out a detailed investigation for the following reactions [eq. (3)] in the presence of up to five water molecules explicitly described and bulk solvent simulation by the polarizable continuum model (PCM). COS þ nH2 O ! H2 S þ CO2 þ ðn 1ÞH2 O ðn ¼ 1 5Þ
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als, encounters some serious difficulties in constructing the minimum-energy reaction paths of some specific chemical reactions, in particular for hydrogen-transfer processes.36–40 Thermal and entropy corrections were computed by standard statistical methods. Charge distributions were obtained from the wave functions calculated at the MP2/6-311þþG(d, p) level, employing natural population analysis (NPA).41–44 The catalytic effect of water molecule(s) described in this paper is explained by the changes of geometries and charge distributions in the rate-determining step. Bulk solvent effect is described by the PCM.45 The solvent (H2O) is thereby represented by a continuum characterized by its dielectric permittivity (e 5 78.41) and the solute is embedded in a cavity. Throughout this paper, all bond lengths are in angstroms and bond angles are in degrees. All relative energies (in kJ/mol) are computed by the enthalpy and Gibbs free energy changes at 298 K, denoted as DH298 or DG298 without PCM correction and DG(sol) with PCM treatment.
Results and Discussion In similar to the hydrolysis of isocyanate (H N¼ ¼C¼ ¼O),29 there are two possible reaction pathways in the water hydrolyses of COS (S¼ ¼C¼ ¼O). The water can attack across the C¼ ¼O bond (path one) or across the C¼ ¼S bond (path two) of the carbonyl sulfide. We will discuss them separately.
(3) One-Water Hydrolysis of Carbonyl Sulfide
The number of water molecules considered is larger enough to give results converged in activation energies. The aim of our study is (i) to clear up the favorable addition of first water occur across the C¼ ¼S bond or across the C¼ ¼O bond of carbonyl sulfide; (ii) to find the most convenient path for hydrolysis of the carbonyl sulfide; (iii) to investigate the cooperative effect of water molecules in the hydrolysis COS. These studies would lead us to discover the synergistic effect of the water molecule(s) placed away from the site of proton transfer and better understand the hydrolysis mechanism of COS.
Computational Method All calculations were performed using the GAUSSIAN-98 packages35 in this work. The geometries of all species, including reactants, precoordination complexes, intermediates, TSs, and products were fully optimized at the HF/6-311þþG(d, p) level first, and then reoptimized by MP2/6-311þþG(d, p). The nature of all optimized structures was determined using frequency analysis at the HF/6-311þþG(d, p) level. A scaling factor 0.9 of the zero-point vibration energy corrections was used in the calculations of relative energies. This procedure seems to be more reliable than density functional theory (DFT) approach for the present system. Despite the great success of DFT in calculating energetic and molecular properties of equilibrium structures, it appears that this method, with the currently available function-
An exhaustive study for all of the precoordination structures between one water molecule and COS shows that there are two possible minima: M1a and M1b (Figs. 1 and 2), corresponding to two different pathways. Structure M1a is found to be more stable than M1b by DH298 5 3.2 kJ/mol, because the OH group of water is engaged in a stronger hydrogen bond with Oatom than S-atom on carbonyl sulfide. The relative energies with respect to the separated reactants for all species in the one-water hydrolysis process of COS are listed in Table S1. All of the optimized species involved in the reaction of COS þ H2O ? CO2 þ H2S are shown in Figure 1 (path one) and Figure 2 (path two), respectively. For the reaction path one, after the precoordination complex M1a is formed, the nucleophilic attack of the water molecule at the central carbon on the COS leads to a four-membered ring TS structure TS1a across the C¼ ¼O bond. The addition of H2O to COS is completed upon full proton (H2) transfers from water to oxygen on COS to form the adduct (M2a). Through rotation along the O1 H2 bond, structure M2a can be converted into its isomer M2a0 accompanying a rotation barrier of DH6¼ 298 5 32.3 kJ/mol. Structure M2a0 is not only more stable than M2a by DH298 510.0 kJ/mol, but also is the most pertinent structure with a view to the next four-membered tautomerization TS structure TS2a0 . We show structure M2a in Figure 1, because it has the geometry that naturally follows the water addition via transition state TS1a. The final product of the one-water hydrolysis of COS is a complex between CO2 and H2S that is formed
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Figure 1. MP2-optimized structures of the stationary points along the hydration path of COS with one water molecule across the C¼ ¼O bond (path one). The energy values (in kJ/mol) reported above the arrows (boldface) are DH298 values without PCM correction. Below arrows are the corresponding DGsol values at the level of PCM-MP2/6-311þþG** values (italic). The number in parentheses corresponds to the sole imaginary frequency for each TS.
via an intermediate M3 and another four-membered ring tautomerization TS structure TS3, releasing the reaction energy of DH298 5 265.3 kJ/mol. It is found from Figure 1 that the activation barriers (DH6¼ 298 ) of four steps in the one-water hydrolysis of COS across the C¼ ¼O bond are 243.7, 32.3, 113.7, and 126.1 kJ/mol, respectively, implying that the first step is rate-determining. The higher barrier (243.7 kJ/mol) results from the quite tense four-membered ring TS structure TS1a, in which the O2 H2 bond is ˚ ), whereas the O1 almost broken (1.227 A H2 bond is still not ˚ ), meanwhile the O2 formed (1.240 A H2 O1 angle is significantly small (120.08), indicating that the one-water hydrolysis of COS is unlikely to occur in the gas phase. By and large, the use
of a model involving one water molecule attacking COS leads to quite unsatisfactory results. This suggests the need for models using multiple water molecules. For the second pathway of the one-water hydrolysis of carbonyl sulfide, nucleophilic attack of the water molecule on the COS C-atom leads to TS1b across the C¼ ¼S bond. As the first step of hydrolysis, the addition of H2O to COS is completed upon full proton (H1) transfer from water to sulfur on COS to form the adduct (M2b), which has the geometry that naturally follows the water addition via TS structure TS1b. Through two rotation along the O H bond, we can get two isomers of M2b, i.e. M2b0 and M3. Even though M3 is less stable than M2b by DH298 5 16.7 kJ/mol, structure M3 is the most pertinent struc-
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Figure 2. MP2/6-311þþG** optimized structures of the stationary points along the hydration path of COS with one water molecule across the C¼ ¼S bond (path two). The energy values reported above the arrows (boldface) are DH298 values (in kJ/mol) without PCM correction. Below arrows are the corresponding DGsol values (in kJ/mol) at the level of PCM-MP2/6-311þþG** values (italic).
ture with a view to the TS3, in which the proton H2 transfers from O2 to S-atom, leading to the final product M4. The relative energies in Figure 2 shows that the activation barrier for TS1b is DH6¼ 298 5 199.4 kJ/mol, higher than TS2b, TS2b0 , and TS3 by 156.9, 191.9, and 73.3 kJ/mol, respectively, indicating that the first step is still rate-controlling, lower than that for the path one by DH6¼ 298 5 44.3 kJ/mol. This important result shows that the addition of water molecule across the C¼ ¼S bond is more favorable than across the C¼ ¼O bond and the first proton should transfer to S-atom instead of O-atom on COS. The fact that addition across C¼ ¼S is favored over that across C¼ ¼O can be rationalized in terms of the condensed Fukui functions introduced by Yang and Mortier.46 For a system of N electrons independent calculations are made corresponding to N 2 1, N, and N þ 1 electron systems with the same geometry of the N-electron system. The NPA analysis yields qk(N þ 1), qk(N), and qk(N 2 1) for all the atoms present in the molecular system, where qk(N þ 1), qk(N), and qk(N 2 1) are the gross electronic populations of the site k in neutral, cationic, and anionic systems, respectively. In a finite difference approximation,
the fk values are calculated by using Yang and Mortier procedure.44 These calculations were performed at the level of B3LYP/6-311þþG**. fkþ ¼ qk ðN þ 1Þ qk ðNÞ
fk ¼ qk ðNÞ qk ðN 1Þ 1 fk0 ¼ ðqk ðN þ 1Þ qk ðN 1ÞÞ 2
for nucleophilic attack for eletrophilic attack for radical attack
Depending on the type of attack, different sites are indicated as the most reactive site for S¼ ¼C¼ ¼O, i.e., the site for which f is largest. The distinct mechanism of hydration of COS may illustrate this: the preferred attack proceeds via a nucleophilic attack of oxygen atom on water at COS C-atom (fþ largest for C, f+C 5 0.453, f+S 5 0.427, f+O 5 0.121), while an electrophilic attack occurs by proton at sulfur (f2 largest for S and not on O, f S 5 0.706, fO 5 0.294, fC 5 0.000). This indicates that the ability of the COS S-atom to accept and distribute positive charge is of considerable importance, in such a way that attack
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Figure 3. MP2-optimized structures of the stationary points along the hydration path of COS with two water molecules across the C¼ ¼O bond (path one). The energy values reported above the arrows (boldface) are DH298 values (in kJ/mol) without PCM correction. Below arrows are the corresponding DGsol values at the level of PCM-MP2/6-311þþG** values (italic).
on S is preferred over attack on O. These explanations can also be applied in the following two-, three-, four-, and five-water hydrolysis of carbonyl sulfide. Two-Water Hydrolysis of Carbonyl Sulfide
The two-water hydrolysis of COS has a main advantage over the single-water hydrolysis, that is, the energetic stability gained from being able to assume six-membered ring proton-transfer TS structures. There are also two pathways for the two-water hydrolysis (Figs. 3 and 4). Two possible precoordination complexes are
located for the two-water hydrolysis of COS as the starting points in the hydrolysis reaction. One is M5a, in which the second water molecule forms a six-membered ring structure with oxygen atom on COS and hydrogen atom on the first water molecule, the other is M5b, in which there is a weak hydrogen bond between sulfur and the hydrogen atom. The former is slightly more stable than latter by DH298 5 5.8 kJ/mol. The relative energies with respect to the separated reactants for all species in the two-water hydrolysis process of COS are listed in Table S2. In the first path of two-water hydrolysis of COS (Fig. 3), nucleophilic attack of water leads to the six-membered ring TS
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Figure 4. MP2/6-311þþG**-optimized structures of the stationary points along the hydration path of COS with two water molecules across the C¼ ¼S bond (path two). The energy values reported above the arrows (boldface) are DH298 values (in kJ/mol) without PCM correction. Below arrows are the corresponding DGsol values at the level of PCM-MP2/6-311þþG** values (italic).
structure (TS5a) across the C¼ ¼O bond, in which proton transfers from water to O-atom of COS through water chain. The formed complex M6a has another isomer M6a0 , which is more stable than M6a by DH298 5 7.5 kJ/mol. Moreover, M6a0 is the most pertinent structure with a view to the second six-membered tautomerization TS state structure TS6a. The structure that naturally follows from TS6a is M7a, but its isomer M7a0 with higher energy is the most pertinent structure with a view to the water-assisted tautomerization TS structure TS7, involving the proton transfer from O3 to S-atom via a water chain. The final product of the two-water hydrolysis of COS is a monohydrated complex (M8).
For the second pathway of two-water hydrolysis (Fig. 4), at the first step of reaction, nucleophilic attack of water leads to a sort of six-membered ring TS structure TS5b, involving the proton transfers from water to COS S-atom along the water chain. Even though the structure that naturally follows from TS5b is M6b, much more stable isomer, M6b0 , is the most pertinent structure with a view to another water-assisted tautomerization TS structure TS6b. The final product M8 is formed through the third tautomerization transition state TS7. As shown in Figures 3 and 4, reaction barriers for the twowater hydrolysis of COS are decreased dramatically upon incorporation of a second water molecule in the reaction coordinate.
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Figure 5. MP2-optimized structures, including three possible precoordination structures (M9a, M9b, and M9c), and two TS structures TS9b0 (relative to M9b) and TS9c (relative to M9c), and DH298 (DGsol) values (in kJ/mol), relative to separated reactants for the three-water hydrolysis of carbonyl sulfide.
That can be attributed to the fact that there are less strained sixmembered ring TS structures in the two-water hydrolysis instead of the high strained four-membered ring TSs in the single-water hydrolysis of COS. The other explanations will be given later. As the one-water hydrolysis of COS, the first step in the twowater hydrolysis is still rate-determining. Compared with the single-water hydrolysis, the energy barrier of the first step for attack across C¼ ¼O via TS5a is lowered by DH298 5 76.5 kJ/ mol, whereas that across the C¼ ¼S bond via TS5b is reduced by DH298 5 55.0 kJ/mol. The calculated rate-determining barriers are 167.2 kJ/mol for the first path and 144.4 kJ/mol for the second path, respectively. These results further confirm the water addition across the C¼ ¼S bond is favored over that across the C¼ ¼O bond. The overall reaction energy for the two-water hydrolysis of COS is DH298 5 282.4 kJ/mol, lower than that in the one-water hydrolysis by 17.1 kJ/mol, showing the second water involving the hydrolysis of COS is thermodynamically and kinetically favorable in the gas-phase. Three-Water Hydrolysis of Carbonyl Sulfide
As the next logical step, the effect of a third water molecule on the hydrolysis of the parent COS is considered in this part.
However, the placement of a third water molecule is not a trivial matter. There are three possible positions for the placement of the third water molecule. Precoordination structure M9a represents van der Waals complex between COS and three water molecules. The other two options may involve placement of two water molecules at the same site of proton transfer, thus expanding the proton-transfer ring to eight atoms, in which the hydrogen bond structure involves COS O-atom (M9b) or COS S-atom (M9c) (Fig. 5). The relative energies for the three-water hydrolysis of COS in Table S3 show that the structure M9c is more stable than M9b by DH298 5 1.2 kJ/mol and than M9a by DH298 5 20.3 kJ/mol, but the reaction barriers with respect to M9c and M9b are 136.4 and 142.3 kJ/mol (DH6¼ 298 ), larger than those relative to M9a by 13.4 and 9.0 kJ/mol, respectively, showing that there is a cooperative effect of water molecule in the proton-transfer process from M9a to TS9a or TS9b when the third water molecule is near to nonreactive sulfur or oxygen atom but not involved in the proton transfer, whereas structure M9b and M9c are, in fact, insignificant, as pointed by Lewis and Giaser32 So only the two reaction pathways involving complex M9a are considered here. Structural inspections would suggest that structure M9a can lead to two possible TS structures, one is across the C¼ ¼O bond
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Figure 6. MP2/6-311þþG** optimized structures of the stationary points along the hydration path of COS with three water molecules across the C¼ ¼O bond (path one). The energy values reported above the arrows (boldface) are DH298 values (in kJ/mol) without PCM correction. Below arrows are the corresponding DGsol values at the level of PCM-MP2/6-311þþG** values (italic).
(TS9a), the other is across the C¼ ¼S bond (TS9b), corresponding to two different pathways. There are three reaction steps in the three-water hydrolysis of COS. In the first pathway (Fig. 6), the first step concerns the nucleophilic attack of the water molecule, through a six-membered ring TS structure TS9a (across C¼ ¼O), leading to dihydrated complex M10a. Then the reaction proceeds through tautomerization TS structures TS10a and TS11 to the final dihydrate H2SCO2 complex M12. It is worth noticing from Figure 6 that the structure that naturally follows from TS10a is M11a, but its isomer M11a0 with higher energy is the most pertinent structure with a view to the water-assisted tautomerization TS structure TS11.
In the second pathway (Fig. 7), the nucleophilic attack of the water molecule leads to TS9b. The proton transfers from water to COS S-atom, forming the complex M10b. The final product is formed along TS10b ? M11a ? M11a0 ? TS11 ? M12. Inspection of the energetics in Table S3 and Figures 6 and 7 shows that the three reaction barriers (DH6¼ 298 ) are 133.3, 33.6, and 97.4 kJ/mol for the first pathway, and 123.0, 45.3, and 97.4 kJ/mol for the second pathway, respectively, indicating that the first step is also rate-determining for the three hydrolysis of COS, and the second pathway involving the addition across the C¼ ¼S bond is the more energetically favored reaction route as the one- and two-water hydrolysis of COS. The overall reaction
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Figure 7. MP2-optimized structures of the stationary points along the hydration path of COS with three water molecules across the C¼ ¼S bond (path two). The energy values reported above the arrows (boldface) are DH298 values (in kJ/mol) without PCM correction. Below arrows are the corresponding DGsol values at the level of PCM-MP2/6-311þþG** values (italic).
energy for the three-water hydrolysis is 295.5 kJ/mol (DH298) and shows that the hydrolysis of COS involving three water molecules is more exothermic. Comparison with two-water hydrolysis shows that the presence of third water molecule near to the nonreactive sulfur atom or oxygen atom (second path) but not involved in the proton transfer can significantly lower the rate-determining activation barrier by 33.9 kJ/mol (first path) or 21.4 kJ/mol (second path), indicating that the cooperative effects of the third water in the mediated hydrolysis of carbonyl sulfide. These results can also be observed in the hydrolysis of carbon dioxide24 and carbodiimide32 by Lewis and Glaser, where the activation barrier can be
drastically reduced by the cooperative effect of the third water molecule from 133.4 and 122.6 kJ/mol in the two-water hydrolysis down to 100.9 and 95.8 kJ/mol for the three-water hydrolysis, respectively. Four- and Five-Water Hydrolysis of Carbonyl Sulfide
From the aforementioned studies about one- up to three-water hydrolysis of the carbonyl sulfide, we can get same conclusion, i.e. the first step is always the rate-determining. Meanwhile it is found that the barrier for the rate-determining step across the C¼ ¼S bond decreases with the addition of water molecules from
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Table 1. Energy Barriers for the First Step in the Hydrolysis of
Carbonyl Sulfide in the Gas Phase, DH6¼ 298 , and in Aqueous Solvent, DG(sol), in kJ/mol. DH6¼ 298
S¼ ¼C¼ ¼O þ H2O S¼ ¼C¼ ¼O þ 2H2O S¼ ¼C¼ ¼O þ 3H2O S¼ ¼C¼ ¼O þ 4H2O S¼ ¼C¼ ¼O þ 5H2O
DG(sol)
Across C¼ ¼O
Across C¼ ¼S
Across C¼ ¼O
Across C¼ ¼S
243.7a 167.2b 133.3b 142.3c 136.3b 118.3c 115.3c 119.2d
199.4 144.4 123.0 136.4 115.5 126.8 107.9
259.8 167.0 143.4 143.8 138.5 131.0 120.4 126.5
208.6 156.3 131.5 137.8 129.5 119.9 111.8
a
Four-membered ring TS. Six-membered ring TS. c Eight-membered ring TS. d Ten-membered ring TS. b
199.4 kJ/mol (one-water) to 144.4 kJ/mol (two-water), to 123.0 kJ/mol (three-water). So it is necessary to consider that more water is involved in the hydrolysis of COS. In this part we will discuss the hydrolysis of COS in the presence of four and five water molecules, but only concern the first step. All of the reaction barriers involved in the first step of hydrolysis of COS with one up to five water molecules are summarized in Table 1. There are two possible precoordination complexes (M13 and M14) (Fig. 8) as the starting points in the hydrolysis reaction. M14 is slightly stable than the structure M13 by DH298 5 4.3 kJ/mol. Four possible reaction pathways for the four-water hydrolysis will be considered, in which two pathways involve a sort of eight-membered ring TS structure and one water molecule near to the nonreactive sulfur or oxygen atom but not involved in the proton transfer, and other two pathways involve a sort of six-membered ring TS structure and two water molecules are not directly involved in the proton transfer. All of optimized structures, including complexes and TS structures, are presented in Figure 8, and the relative energies are listed in Table S4. Inspection of the data in Table S4 and the geometries in Figure 8 shows that the reaction barriers (DH6¼ 298 ) are 118.3 kJ/mol for the first path (M13 ? TS13) involving the nucleophilic addition of water across the C¼ ¼O bond and 126.8 kJ/mol for the second path (M14 ? TS14) across the C¼ ¼S bond with a sort of eight-membered ring TS; 115.5 kJ/mol for the third path (M13 ? TS15) involving the proton transfer across the C¼ ¼S bond and 136.3 kJ/mol for the fourth path (M14 ? TS16) involving the proton transfer across the C¼ ¼O bond with a sort of six-membered ring TS. After the PCM correction, the barriers are 131.0 kJ/mol (the first path), 119.9 kJ/mol (the second path), 129.5 kJ/mol (the third path), and 138.5 kJ/mol (the fourth path). These calculated barriers show that the proton transfer through a sort of six-membered ring TS across the C¼ ¼S bond is more favorable than across the C¼ ¼O bond, both in the gas phase and in the bulk solvent. Even though the barrier in the first path with a eight-membered ring proton transfer TS across
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the C¼ ¼O bond is lower than that in the second path across the C¼ ¼S bond in the gas-phase, the latter barrier is still lower than former by DG(sol) 511.1 kJ/mol after the PCM treatment, indicating that second pathway through a sort of eight-membered ring TS across the C¼ ¼S bond is the most favorable in the bulk solvent. The overall reaction energy for the four-water hydrolysis of COS is 2152.2 kJ/mol (DH298), lower than one up to three water cases, showing more water molecules involved in the hydrolysis of COS is thermodynamically and kinetically favorable. As the former case, only the first step is discussed in the five-water hydrolysis of carbonyl sulfide. Three possible pathways are proposed (Fig. 9). In the first reaction path, four molecules are involved in the proton transfer across the C¼ ¼O bond, leading to a TS characterized by a sort of 10-membered ring TS structure and the other one water molecule is near to the nonreacting sulfur. The similar TS structure across the C¼ ¼S bond cannot be located, despite extensive attempts. The other two pathways include a sort of eight-membered ring TS across the C¼ ¼O bond (path two) or across the C¼ ¼S bond (path three); meanwhile, two water molecules are near to the nonreacting sulfur atom (path two) or near to the nonreacting oxygen atom (path three) but not involved in the proton transfer. The MP2/6-311þþG(d, p) optimized structures for the fivewater hydrolysis of COS are collected in Figure 9, and the relative energies are listed in Table S5. Inspection of the energies in Table S5 and Figure 9 shows that the barriers (DH6¼ 298 ) are 119.2 kJ/mol for the first path, 115.3 kJ/mol for the second path, and 107.9 kJ/mol for the third path. These results indicate that (i) the 10-membered ring TS structure is less favorable than eightmembered ring TS; (ii) the addition across the C¼ ¼S bond is preferred above the one across the C¼ ¼O bond. The overall reaction energy for the five-water hydrolysis is DH298 5 2190.8 kJ/mol. Comparison between five-water hydrolysis of COS and other cases (three and four-water hydrolysis) shows that the rate-determining activation barrier in the hydrolysis of COS depends on the number (N) of cooperative water molecule(s) on the nonreactive region. Taking the eight-membered ring TSs across the C¼ ¼S bond as examples, the barrier (DH6¼ 298 ) decreases with the number of nonreactive water in the following order: 136.3 kJ/ mol (TS9c, N 5 0) [ 126.8 kJ/mol (TS16, N 5 1) [ 107.9 kJ/ mol (TS19b, N 5 2), suggesting that there are better cooperative effects of two water molecules than the one water molecule near to the nonreacting region. If we fix the one water molecule on the nonreactive region and only discuss the TSs across the C¼ ¼O bond, it is found that the barriers decrease from DH6¼ 298 5 133.3 kJ/mol (six-membered ring TS9a) to 118.3 kJ/mol (eight-membered ring TS13) and to 119.2 kJ/mol (10-membered ring TS17), showing that the hydrolysis of COS via a sort of eight-membered ring TS is the most favorable due to the better catalytic effect of the two-water chain. This interesting result can be rationalized by the comparison of intermolecular hydrogen bonds in the TS structures. Although it is difficult to detect the geometry of the hydrogen bond, a statistical analysis of X-ray crystallographic data has shown that most of hydrogen bonds in crystals are nonlinear by about 108–158. The angles of hydrogen bonds in TS13 are about 165.78–170.28, obviously better than those in the TS9a (1508) because of the larger repulsion between two heavy atoms with
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Figure 8. MP2-optimized structures for the hydrolysis of COS with four water molecules, including precoordination complexes, the corresponding TSs for the first step and product. The energy values reported near to the arrows (boldface) are DH298 values (in kJ/mol) without PCM correction and the corresponding DGsol values at the level of PCM-MP2/6-311þþG** values (italic).
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Figure 9. MP2-optimized structures for the hydrolysis of COS with five water molecules, including precoordination complexes, the corresponding TSs for the first step and product. The energy values reported near to the arrows (boldface) are DH298 values (in kJ/mol) without PCM correction and the corresponding DGsol values at the level of PCM-MP2/6-311þþG** values (italic).
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Table 2. Selected Charges and Changes in Atom Charges Determined by Natural Population Analysis.
M1a TS1a M1a?TS1 M1b TS1b M1b?TS1b M5a TS5a M5a?TS5a M5b TS5b M5b?TS5b M9a TS9a M9a?TS9a M9a TS9b M9a?TS9b M19 TS19a M19–TS19a TS19b M19?TS19b
O1
O2
O3
O4
O5
O6
H1
H2
H3
H4
S
C
H5
H6
20.589 20.756 20.167 20.537 20.6 20.063 20.61 20.798 20.188 20.535 20.667 20.132 20.585 20.798 20.213 20.585 20.719 20.134 20.617 20.83 20.213 20.785 20.168
20.929 0.876 1.805 20.921 20.883 0.038 20.963 20.872 0.091 20.961 20.876 0.085 20.989 20.869 0.12 20.989 20.877 0.112 21.026 20.883 0.143 20.884 0.142
– – – – – – 20.951 20.903 0.048 – – – 20.946 20.909 0.037 20.946 20.948 20.002 20.981 20.902 0.079 20.986 20.005
– – – – – – – – – 20.946 20.924 0.022 20.939 20.975 20.036 20.939 0.932 1.871 20.975 20.979 20.004 20.893 0.082
– – – – – – – – – – – – – – – – – – 20.963 20.959 0.004 20.987 20.024
– – – – – – – – – – – – – – – – – – 20.986 20.999 20.013 20.976 0.01
0.455 0.505 0.05 0.461 0.413 20.048 0.457 0.529 0.072 0.496 0.559 0.063 0.486 0.57 0.084 0.486 0.56 0.074 0.504 0.566 0.062 0.559 0.055
0.472 0.577 0.105 0.457 0.505 0.048 0.499 0.56 0.061 0.459 0.516 0.057 0.496 0.56 0.064 0.496 0.564 0.068 0.518 0.558 0.04 0.559 0.041
– – – – – – 0.49 0.555 0.065 – – – 0.484 0.553 0.069 0.484 0.5 0.016 0.515 0.55 0.035 0.53 0.015
– – – – – – – – – 0.48 0.482 0.002 0.476 0.508 0.032 0.476 0.481 0.005 0.508 0.529 0.021 0.551 0.043
20.016 20.049 20.033 20.071 20.174 20.103 20.019 20.252 20.233 20.114 20.332 20.218 20.067 20.338 20.271 20.067 20.357 20.29 20.001 20.419 20.418 20.436 20.435
0.606 0.598 20.008 0.612 0.738 0.126 20.629 0.674 1.303 0.649 0.737 0.088 0.651 0.715 0.064 0.651 0.747 0.096 0.62 0.756 0.136 0.777 0.157
– – – – – – – – – – – –
– – – – – – – – – – – –
0.502 0.553 0.051 0.524 0.022
0.516 0.503 20.013 0.493 20.023
higher electronegativity in TS9a, leading to less stabilization of TS and higher tautomeric barrier in the three-water hydrolysis process of COS than that in the four-water hydrolysis TS across the C¼ ¼O bond by 15.0 kJ/mol. The increment from the eightmembered ring structure TS13 to the 10-membered ring structure TS17 does not relax the strain in the geometry of the hydrogen bonds, leading to similar reaction barrier.
Further Explanations for the Water Catalysis
Lewis and Glaser24,32 proved that the variation of activation barriers could be explained by the structural and electrical relaxation associated with the formation of rate-determining TS. As addition across the C¼ ¼S bond is more favorable, the following discussions will focus on the comparison of activation processes M9a ? TS9b and M19a ? TS19b; M1b ? TS1b and M5b ? TS5b. A structural comparison of TS9b (Fig. 7) and TS19b (Fig. 9) shows that the consideration of one or two water molecules near to the nonreacting oxygen atom results in a TS structure in which bond formation between the adding water molecules and the COS C-atom has progressed more in TS19b, where the ˚ from TS9b to TS19b. C O2 distance decreases by 0.072A Note also that the rehybridization of the COS C-atom has progressed more in TS19b than in TS9b, and this is illustrated by the S C O angles of 132.98 for TS9b and 128.28 for TS19b ˚ in as well by the lengthening of the C¼ ¼S bond from 1.699 A ˚ in TS19b. Less strain is also observed in the TS9b to 1.709 A eight-membered ring TS19b, in which three hydrogen bonds exist with angles of 164.98–167.98, obviously better than those in the TS9b, where the angles of hydrogen bonds are 159.68
and 152.18, implying that more relaxed geometry in TS19b clearly favors the triple proton transfer compared with the strained TS9b. Meanwhile, these structural differences during activation have important electronic consequences. According to the concept of hybridization, we can predict the O atom in COS will be less negative in the precoordination complexes (M9a and M19) and the change in the O atomic charge in COS would be more negative for the process M19 ? TS19b than for M9a ? TS9b. This prediction was confirmed by NPA in Table 2, which revealed Dq(O1) values of 20.134 for M9a ? TS9b and 20.168 for M19 ? TS19b. Similarly, in the course of the addition reaction, a water molecule H OH is converted into an alcohol R OH, and one can expect that the OH-group in the alcohol will be overall less negative than in water. These changes in natural atomic charges should be manifested more in the process M19 ? TS19b than for M9a ? TS9b. The NPA results (Table 2) indeed show a greater loss of electron density in O2H2 for the former reaction. Moreover, this decrease of electron density occurs both for the O2-atom (Dq 5 þ0.112 for M9a ? TS9b and þ0.142 for M19 ? TS19b). The electronic Table 3. Effect of Temperature for the Five-Water Hydrolysis of
Carbonyl Sulfide. Temperature (K)
DG (kJ/mol) K x%
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298
300
400
500
600
222.28 8052.5 99.988
222.26 7512.4 99.987
220.91 537.8 99.814
219.50 108.9 99.090
218.04 37.2 97.385
DOI 10.1002/jcc
Hydrolysis of Carbonyl Sulfide in the Neutral Water
479
Scheme 1. Summary of this work on the favorable reaction routes in the neutral hydrolysis of COS, including precoordination complex, rate-determining structures, and final stable product.
rearrangements occurring in the activation processes M9a ? TS9b and M19 ? TS19b clearly demonstrate an increased propensity for H-bonding interactions of both the H2 and O2 in the latter case. The O2H2 group is a better H-bond donor because the negative O-charge is reduced and the positive charge on H is increased. The COS O-atom (O1) is a better H-bond acceptor because it is more negatively charged. These effects should be felt in any H-bonding environment. The earlier structural and electronic changes associated with the processes M9a ? TS9b and M19 ? TS19b are also observed in the comparison between one-water hydrolysis (M1b ? TS1b) and two-water hydrolysis of COS (M5b ? TS5b). A closer inspection of geometries in Figures 2 and 4 reveals that ˚ from TS1b to TS5b, the C O distances decreases by 0.082 A and the S C O angles become smaller from 144.38 in TS1b to 136.08 in TS5b. The electronic rearrangements during the activation processes also clearly show that in the hydrolysis of COS with two water molecules, M5b ? TS5b, the O1 atom becomes 0.069 more negative than in the hydrolysis with one water. Likewise, the O2 and H2 atoms in the process M5b ? TS5b become þ0.047 and þ0.009 more positive than in the process M1b ? TS1b. These geometry and charge changes will make the hydrolysis of COS with two water molecules more favorable than with one water molecule. Effect of Temperature
Because the five-water hydrolysis of COS is the most favorable reaction route than other cases, the total Gibbs free energy change for the reaction M19 ? M20 is calculated at a different temperature. Our study covered the temperature range 298–600 K. The calculated equilibrium constants and conversion coefficients indicate that the higher temperature is unfavorable for the hydrolysis of COS (Table 3). This trend is consistent with the experiments.14 Solvent Effect
The performance of hydrolysis of COS was studied in aqueous solution using the PCM model employing the optimized geome-
tries in the gas phase. The relative energies after correction of bulk solvent effect are listed in Tables S1–S5. One can easily observe that the PCM solvation models almost do not modify the energy barriers in a significant way. For example, the results in Table S5 show that the PCM model slightly raise the barrier for addition across C¼ ¼O by 5.1 kJ/mol in the ‘‘five-water hydrolysis case,’’ from 115.3 kJ/mol in the gas phase to 120.4 kJ/mol [DG#(sol)] in solvent. The change does not influence qualitatively the reaction path, showing invariably the preference for the addition across the C¼ ¼S bond. The latter path appears to be similarly influenced by its surroundings. The energy barrier goes from 107.9 kJ/mol in the gas phase to 111.8 kJ/mol in solvent. For the ‘‘one up to four water cases’’ the calculated rate-determining barriers for addition across the C¼ ¼S bond are 208.6, 156.3, 131.5, and 119.9 kJ/mol in solvent, respectively. These results emphasize again that the hydrolysis mediated by a water chain is a favored process.
Conclusions In the present paper, a comprehensive mechanistic investigation of the hydrolysis of COS has been undertaken by ab initio methods, both in the gas phase and in aqueous solution. In addition to one up to five water molecules explicitly described, the effect of water bulk solvent is taken into account using the PCM model. The principle conclusions from this study are as follows: 1. In all possible considered hydrolysis of COS in the presence of up to five water molecules, the first step involving proton transfer is always rate-determining, and the nucleophilic addition of water prefers to occurs across the C¼ ¼S bond of COS rather than across the C¼ ¼O bond. Such a preferential reaction mechanism could be rationalized in terms of condensed Fukui functions for both nucleophilic and electrophilic attack. 2. Calculated MP2/6-311þþG** barriers in the gas phase, DH6¼ 298 , for the rate-determining steps of the one up to fivewater hydrolyses of COS are 199.4, 144.4, 123.0, 115.5, and 107.9 kJ/mol via the water addition across the C¼ ¼S bond. It was also shown that expanding TS structure across the C¼ ¼O
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Deng et al. • Vol. 29, No. 3 • Journal of Computational Chemistry
bond from eight-membered to 10-membered ring if one more water is engaged in the proton transfer process (M17 ? TS17) cannot further lower the rate-determining barrier, suggesting that the hydrolysis of COS involving five water molecules via a sort of eight-membered ring TS is a more favorable reaction route. 3. The five-water hydrolysis of COS with the lowest activation barrier involves the eight-membered ring TS structure across the C¼ ¼S bond (M19 ? TS19b), meanwhile two other water molecules are near to the nonreactive sulfur atom and construct a eight-memebered cyclic structure via a water chain but not involved in the proton transfer, suggesting that there is a better cooperative effect on the hydrolysis by a eightmemebered ring hydrogen bond structure. 4. The catalytic effect of the second up to fifth water molecule in the hydrolysis of COS can be explained by the structural and electronic rearrangements of rate-determining step. The structural and electronic changes associated with the formation of TS can greatly affect the properties of groups that are not directly involved in the bond-breaking and forming region. 5. When DH6¼ 298 values in the gas phase are compared with the DG#(sol) one after PCM treatment, it is found that the effect associated with the bulk solvent is relative small, probably due to most of solvent contribution being already taken into account by the one up to five explicit water molecules. Scheme 1 demonstrates the summary of this work on the two favorable reaction routes of neutral hydrolysis of COS, showing the optimal circuit of the hydrogen bond for ready proton transfer and the cooperative assistance of the second circuit. These important results can be applied for the hydrolysis process of other molecules, e.g. CO2 and NH¼ ¼C¼ ¼NH. The theoretical studies for these systems are being carried out.
Acknowledgments We express our gratitude to the referees for their valuable comments.
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