3.1.1 The first step of the reaction mechanism of CS2 hydrolysis
In the first step of the mechanism for CS2 hydrolysis, two reaction paths will be discussed according to two optimized geometries (Fig. 1) and schematic potential energy surfaces. The two reaction paths are as follows:
the single C=S path: CS2+H2O→IM1→TS1→IM2-1→TS2→IM3→COS+H2S.
the double C=S path: CS2+H2O→IM1→TS1→IM2-1→TS2′→IM3′-1→TS3′→IM3→COS+H2S.
For the single C=S path, firstly, a CS2 molecule reacts with an H2O molecule and forms the intermediate (IM1), which also was called corresponding reactant complexes. IM1 is that the reactant-like intermediate during which oxygen atom on water attacks carbon atom on CS2. The energy of IM1 is slightly higher than the total energy of the reactants CS2 and H2O by 13.3 kJ/mol. As a result of van der Waals forces, these two reactant molecules could interact with each other. Meanwhile, there are also weaker electrostatic interactions between hydrogen atoms and sulfur atoms. But, it is difficult for IM1 to transfer the proton directly from the O4-atom of water to S2-atom of CS2 due to the longer C1-O4 (3.453Å) and S2-H5 (2.725Å) distances in IM1. Thus, in the reaction between CS2 and H2O, the distance between CS2 and H2O is gradually reduced under the action of van der Waals force. And the original linear CS2 molecule is distorted (∠S2-C1-S3 from 180° to 142.2°), and IM2-1 is made via TS1 with the imaginary frequency of -1573.61 i/cm. The highly strained ring TS1, with a smaller angle of hydrogen bond (113.1°), almost broken O4-H5 bond (1.216Å), and still not formed H5-S2 bond (1.716Å), is associated with the O4-C1 bond stretch and the migration of H5 from O4 to S2. Through rotation along with the C1-S2 bond, IM2-1 can be converted orderly into its isomer IM2-2 and IM2-3 accompanying a rotation barrier of 38.9 kJ/mol and -1.2 kJ/mol, respectively; subsequently, through rotation along with the C1-O4 bond, IM2-3 can also be converted orderly into its isomer IM2-4 and IM2-5 accompanying a rotation barrier of 49.9 kJ/mol and 26.7 kJ/mol, respectively. Finally, H6 migrates from O4 to S2 to form IM3, and the O4-H6 bond is 2.401A, indicating that H2S is separated from the initial complex to form COS. So the stretching of O4-C1 bond, H6 migrates from O4 to S2, forming a transitional state of quaternary ring TS2 with an imaginary frequency of -1712.30 i/cm.
For the double C=S path, the formation of IM2-1 remains unchanged for the single C=S path. However, H6 may also first transfer to S3 atom through another four-membered ring TS2′, its imaginary frequency is -1755.11 i/cm, showing the stretching pattern of S3-C1 and also the migration of H6 from O4 to S3, to form IM3′-1. Subsequently, through rotation along with the C1-S3 bond, IM3′-1 can be converted orderly into its isomer IM3′-2 and IM3′-3 accompanying a rotation barrier of 28.6 kJ/mol and 4.8 kJ/mol, respectively. Its last step refers to the formation of H2S via a four-membered ring TS structure TS3′, its imaginary frequency is -1317.63 i/cm, showing the stretching pattern of S2-C1 and the migration of H6 from S3 to S2, the by-product IM3 formed. Similarly, in IM3, H2S and COS are formed.
Table 1
Imaginary frequency of each transition state and the bonds corresponding to relative normal vibrations for the hydrolysis of CS2
Transition state
|
Imaginary frequency (i/cm)
|
Bonds corresponding to normal vibrations
|
TS1
|
-1573.61
|
H5-O4-S2; O4-C1
|
TS2
|
-1712.30
|
H6-O4-S2; S2-C1
|
TS2′
|
-1755.11
|
H6-O4-S3; S3-C1
|
TS3′
|
-1317.63
|
S3-S2-H6; S2-C1
|
According to the analysis of two reaction paths in the first step reaction mechanism of CS2 hydrolysis, It pinpoints that H migration is crucial in the first step reaction mechanism of CS2 hydrolysis. By exploring the reaction path, the reaction energy barriers of the single C=S path and double C=S path are shown in Fig. 2. The results show that the two paths, (IM1→IM2-1) are the rate-determining steps, its energy barrier is 182.7 kJ/mol. However, the energy barrier of the step (IM2-1→TS2) (146.287 kJ/mol) in single C=S path is higher than those for the step (IM2-1→TS2′) (107 kJ/mol) and the step (IM3′-1→TS3′) (122.4 kJ/mol) in double C=S path. Therefore, it’s not surprising that the double C=S path is better.
To further explore the first step reaction of CS2 hydrolysis, NBO analysis of transition states TS2 and TS2 was carried out using the Second-order Perturbation theory. the second-order stabilization energy is a measure for the strength of the electron donor-acceptor interaction [44-48]. Fig.3 shows the NBO overlap of electron donating from the lone pair of S2 to the antibonding acceptor of σ* (O4-H6) in TS2, and from the lone pair of S3 to the antibonding acceptor of σ* (S2-H6) in TS2′. The second-order stabilization energy, also shown in Fig.3, is 717.2 kJ/mol for the LP(S3) →σ*(S2-H6) in TS2′, which is larger than LP(S2) →σ*(O4-H6) in TS2 (481.2 kJ/mol). It indicates [IMAGE-C:\Workspace\ACDC\ImageHandler\adthat the TS2′ is formed easier than TS2, namely the double C=S path is better.
3.1.2 The second step of the reaction mechanism of CS2 hydrolysis
In the second step of the mechanism for CS2 hydrolysis, three reaction paths will be discussed according to two the optimized geometries and schematic potential energy surfaces. The three reaction paths are as follows:
the C=S path: COS+H2O→IM4→TS4→IM5-1→TS5→IM6→CO2+H2S
the O=C path: COS+H2O→IM4→TS4′→IM5′-1→TS5′→IM5-5→TS5→IM6→CO2+H2S
the C=S path and the O O=C path: COS+H2O→IM4→TS4→IM5-1→TS5′′→IM5-5→TS5→IM6
→CO2+H2S
For the C=S path (Fig. 4), the attack of H2O on the C1 atom of COS leads to the formation of the pre-coordination complex IM4 because of the van der Waals forces between H2O and COS. And the original linear COS molecule is gradually distorted. IM4 is 13.7 kJ/mol more active than the original reactants COS and H2O. At the first, the addition of H2O to COS is completed upon full H5 transfer from H2O to S on COS to form the thiocarbonic acid IM5-1 via TS4, its imaginary frequency is -1592.47 i/cm showing O2-C1 stretching and H5 migration from O4 to S2. In TS4, the length of the O4-H5 bond that is almost broken is 1.257 Å, and the angle O3-C1-S2 changes from
180.0° to 144.2°. Meanwhile, the H5-S2 and O4-C1 bonds are almost formed have lengths of 1.664 and 1.633 Å, respectively. The O4-C1 bond shortens from 2.834 to 1.633 Å. The energy barrier height of TS4 relative to IM4 is 195.1 kJ/mol. Then, through rotation along with the S2-C1 bond, IM5-1 can be converted orderly into its isomer IM5-2 and IM5-3 accompanying a rotation barrier of 33.8 kJ/mol and -3.3kJ/mol, respectively. Similarly, through also rotation along with the O4-C1 bond, IM5-3 can be converted orderly into its isomer IM5-4 and IM5-5 accompanying a rotation barrier of 45.5kJ/mol and 20.3 kJ/mol, respectively. Finally, H6 migrates to S2 to form IM6, and the S2-C1 bond is 3.352A. The stretch of O4-C1 bond and the migration of H6 to S2 form the transition state TS5, whose imaginary frequency is -1752.28 i/cm. The energy of TS5 is 136.9 kJ/mol higher than that of IM5-1.
In the O=C path (Fig. 4), a COS molecule reacts with an H2O molecule and leads to form the pre-coordination complex IM4, whose interaction energy of13.7 kJ/mol. After the pre-complex IM4 between COS and H2O is formed, the following nucleophilic attack of H2O leads to the four-membered TS4′ with the energy barrier of 260.0 kJ/mol, which H6 transfer from H2O to O-atom of COS. The imaginary frequency for TS4′ is -1887.88 i/cm, associating with the O4-C1 bond and the migration of H6 to O3. After the reaction surmounted TS4′, intermediate IM5′-1 is formed. For IM5′-1 with an energy barrier of 91.9 kJ/mol, C1-O4 and C1-O3 are 1.347 Å and 1.328 Å, respectively. Then the tautomerization of IM5′-1 leads orderly to its isomer IM5′-2 and IM5′-3, accompanying a rotation barrier of 91.4 kJ/mol and -0.02 kJ/mol, respectively. Moreover, IM5′-3 is the most relative structure with a view to the next four-membered TS5′, its imaginary frequency of -1755.12 i/cm showing the stretching pattern of S2-C1 and the migration of H5 to S2, to form M5-5, and its energy barrier is 58.4 kJ/mol. Finally, the remaining two steps of the O=C path correspond to the C=S path.
From Fig. 4, what’s the difference between the C=S and O=C path and the C=S path is the reaction steps (IM5-1→ IM5-3). Concerning the C=S and O=C path, in brief, firstly, H5 of water transfer from H2O to S2-atom of COS to form IM5-1; and Secondly, the migration of H6 from O4 to O3 forms the intermediate IM5-3(30.3 kJ/mol). Thus, these two processes are connected with a vital transition state structure TS5″ (195.6 kJ/mol), where H6 transfers to O3. And the imaginary frequency for TS5″ is -1956.90 i/cm.
Table 2
Imaginary frequency of each transition state and the bonds corresponding to relative normal vibrations for the hydrolysis of COS.
Transition state
|
Imaginary frequency (cm−1)
|
Bonds corresponding to normal vibrations
|
TS4
|
-1592.47
|
H5-O4-S2; O4-C1
|
TS5
|
-1752.28
|
H6-O4-S2; S2-C1
|
TS4′
|
-1887.88
|
H6-O3-O4; O4-C1
|
TS5′
|
-1755.12
|
H5-O4-S2; S2-C1
|
TS5″
|
-1956.90
|
H6-O3-O4; O3-C1
|
In the mechanism of CS2 hydrolysis, the transfer of H is very important. Fig. 5 shows that IM4→ TS4 (195.1 kJ/mol) is 58.2 kJ/mol higher than IM5-1→ TS5 (136.9 kJ/mol) in terms of reaction energy barrier under the C=S path. Under the C=O path, IM4→TS4 '(260.0 kJ/mol) is 150.5 kJ/mol and 138.1 kJ/mol higher than IM5'-1→TS5'(109.5 kJ/mol) and IM5-5→TS5(121.9 kJ/mol), respectively. Meanwhile, the rate-determining steps of the two paths are IM4→IM5-1. For C=S and O=C paths, IM4→TS4 (195.1 kJ/mol) is 42.9 kJ/mol higher than IM5-1→TS5 "(152.2 kJ/mol) and 73.2 kJ/mol higher than IM5-5→TS5(121.9 kJ/mol). Therefore, we can conclude that of the three paths, the C=S path is better.
To future explore the first step reaction of CS2 hydrolysis, NBO analysis was performed for the transition states TS4, TS4′, TS5, and TS5′′. Fig. 6 shows the NBO overlap between O4 lone pair electrons in TS4 and σ* (S2-H5) antibonding receptors, and between O4 lone pair electrons in TS4 'and σ* (O3-H6) antibonding receptors. LP(O4) → σ*(S2-H5) in TS4 (527.2 kJ/mol) is greater than LP(O4) → σ*(O3-H6) in TS2 '(500.7 kJ/mol). This shows that TS4 is easier to form than TS4′, that is, the C=S path and the C=S, O=C path are more favorable than the C=O path. Similarly, the lone pair O4 donates electrons to the σ* (S2-H6) antibonding receptor in TS5 and the lone pair O3 donates electrons to the σ* (O4-H6) antibonding receptor in TS5. TS5 (594.6 kJ/mo) in LP (m1) and sigma * (S2 - H6) is greater than the TS2′ (457.5 kJ/mol) in the LP (O3) and sigma * (m1 - H6). It indicates that TS5 is easier to form than TS5 ", that is, the C=S path is superior to the other two paths.