Catalytic hydrolysis of carbonyl sulphide and carbon disulphide over Fe2O3 cluster: Competitive adsorption and reaction mechanism

The competitive adsorption and reaction mechanism for the catalytic hydrolysis of carbonyl sulphide (COS) and carbon disulphide (CS2) over Fe2O3 cluster was investigated. Compared with experimental results, the theoretical study was used to further investigate the competitive adsorption and effect of H2S in the hydrolysis reaction of COS and CS2. Experimental results showed that Fe2O3 cluster enhanced the catalytic hydrolysis effect. Meanwhile, H2S was not conducive to the hydrolysis of COS and CS2. Theoretical calculations indicated that the order of competitive adsorption on Fe2O3 is as follows: H2O (strong) >CS2 (medium) >COS (weak). In the hydrolysis process, the C=S bond cleavage occurs easier than C=O bond cleavage. The hydrolysis reaction is initiated via the migration of an H-atom, which triggers C=S bond cleavage and S–H bond formation. Additionally, we find the first step of CS2 hydrolysis to be rate limiting. The presence of H2S increases the reaction energy barrier, which is not favourable for COS hydrolysis. Fe2O3 can greatly decrease the maximum energy barrier, which decreases the minimum energy required for hydrolysis, making it relatively facile to occur. In general, the theoretical results were consistent with experimental results, which proved that the theoretical study was reliable.

. In our previous study, different active components (such as Fe, Cu, Zn, Cr, Co, Ni) supported on AC were investigated for catalytic hydrolysis of COS and CS 2 13 . The results showed that Fe 2 O 3 /AC had the highest catalytic hydrolysis performance for COS and CS 2 , yielding a 100% removal rate of CS 2 and COS after 330 min and 240 min respectively. For Fe 2 O 3 /AC, AC played a role of adsorbent and Fe 2 O 3 played a role of active component. Furthermore, nano-Fe 2 O 3 /AC showed higher catalytic ability for CS 2 , which prolonged 100% removal rate of CS 2 to 480 min 18 . However, the detailed reaction mechanisms are different for different catalysts and reaction paths. For instance, Guo et al. and Zhang et al. reported the COS hydrolysis mechanism without the use of a catalyst 19,20 . The results indicated that OH and H in H 2 O first attack the C=O and C=S bonds in COS. Li et al. also investigated the COS hydrolysis mechanism. The results indicated that the nucleophilic additions of water across the C=O or C=S bonds of COS were competitive 21 . Additionally, the mechanism of CS 2 hydrolysis is identical to that of COS, and COS is an intermediate the hydrolysis of CS 2 .
Currently, little research has focused on the reaction mechanism for the simultaneous removal of COS and CS 2 . Although Fe 2 O 3 was suitable for catalytic hydrolysis of COS and CS 2 , the corresponding reaction mechanism remains unknown. Determining the detailed steps of the reaction mechanism is necessary because they can provide a theoretical foundation for the future application and development. Therefore, this work performed theoretical study to investigate the reaction mechanism and reaction routes of the simultaneous removal of COS

Results and Discussion
Experimental study analysis. To provide the catalytic hydrolysis effect of Fe 2 O 3 , the desulphurization experiments for COS and CS 2 over Fe 2 O 3 /AC and pure AC were performed. The catalytic hydrolysis activities were showed in Fig. 1. From Fig. 1, the removal efficiency of COS and CS 2 over Fe 2 O 3 /AC were higher than that over pure AC. Addition of Fe 2 O 3 cluster prolonged the 100% COS and CS 2 removal rate from 90 min to 210 min and 150 min to 300 min respectively. The effluent H 2 S and CO 2 content over time was showed in Supplementary  Fig. S1. As shown in Supplementary Fig. S1, the effluent H 2 S content over Fe 2 O 3 /AC firstly increased and then decreased over time. Firstly, the hydrolysis reaction rate was fast. The generation rate of H 2 S was higher than the adsorption rate, which led to the increase of H 2 S. With the increase of reaction time, H 2 S was gradually adsorbed on the surface of catalyst, which covered the active site of Fe 2 O 3 cluster and adsorptive site of AC. As a result, it led to the deactivation of catalyst and the H 2 S content decreased. Compared with Fe 2 O 3 /AC, the effluent H 2 S content over pure AC was almost 0. Meanwhile, the CO 2 content over Fe 2 O 3 /AC was firstly almost stable and then decreased over time. The decrease of CO 2 content was attributed to the decrease of catalytic activity, which was caused by deactivation of catalyst. Compared with Fe 2 O 3 /AC, the effluent CO 2 content over pure AC was almost 0. These results indicated that the removal of CS 2 and COS over pure AC was mainly an adsorption process. Therefore, the removal of CS 2 and COS over Fe 2 O 3 cluster was a catalytic hydrolysis process. It indicated that Fe 2 O 3 cluster provide the catalytic hydrolysis effect and sharply enhanced the catalytic activity.
To investigate the effect of H 2 S, the desulphurization experiments for COS and CS 2 over Fe 2 O 3 /AC were performed. The catalytic hydrolysis activities of Fe 2 O 3 /AC at different inlet H 2 S content were shown in Fig. 2. From  Fig. 2, when the content of H 2 S in the inlet was 0%, the removal efficiency of COS and CS 2 over Fe 2 O 3 /AC was highest. Meanwhile, the removal efficiency of COS and CS 2 decreased with increasing H 2 S content. It indicated that H 2 S is not conducive to the hydrolysis of COS and CS 2 .  To further investigate the effect of Fe 2 O 3 and H 2 S for the catalytic hydrolysis of COS and CS 2 . The adsorption of COS and CS 2 on Fe 2 O 3 /AC and hydrolysis reaction mechanism were studied by theoretical calculation.
Theoretical study analysis. Competitive adsorption analysis. Because the size of nano-Fe 2 O 3 structure was less than 10 nm and it had the cluster structure, the (Fe 2 O 3 ) 2 cluster was used in the calculation study to represent the catalyst tested in experiments. To determine the relative (competitive) adsorption of H 2 S, COS, CS 2 and H 2 O, their corresponding optimized geometries and adsorption energies have been calculated (Fig. 3). As shown in Supplementary Fig. S2, when the O atom in COS pointed to surface Fe, the absolute value of the adsorption energy was lower. It might be attributed to that the adsorption effect of C-O…Fe was more stable than C-S…Fe. As shown in Fig. 3, for reactants, the absolute value of the adsorption energy of H 2 O + Fe 2 O 3 is the highest and that of COS + Fe 2 O 3 is the lowest. These results indicate that H 2 O is more easily adsorbed on the Fe 2 O 3 cluster than COS and CS 2 , which suggests that H 2 O firstly adsorbs on the catalyst and then reacts with COS and CS 2 . Meanwhile, the absolute value of the adsorption energy of CS 2 + Fe 2 O 3 is the higher than that of COS + Fe 2 O 3 , which suggests that the adsorption of CS 2 on the surface of the catalyst occurs first. For the product H 2 S, H 2 S + Fe 2 O 3 has higher absolute value of the adsorption energy than CS 2 , COS and H 2 O. It indicated that H 2 S will be firstly adsorbed on the Fe 2 O 3 , which will gradually decrease the catalytic hydrolysis activity of catalyst.
Reaction mechanism of COS hydrolysis over Fe 2 O 3 cluster. The reaction channels for the hydrolysis of COS and CS 2 are given in Fig. 4. The bond-lengths of transition states, reaction energies and energy barriers of various reaction steps were showed in Supplementary Table S1, Supplementary Table S2, Supplementary Table S3 and  Supplementary Table S4. As seen in Fig. 4 and Supplementary Table S4, the energy barrier of COS hydrolysis (60.19 kcal/mol) over Fe 2 O 3 is lower than that of CS 2 hydrolysis (97.21 kcal/mol), suggesting that the hydrolysis of COS occurs more easily than the hydrolysis of CS 2 . Therefore, the hydrolysis of COS occurs preferentially for the simultaneous removal of COS and CS 2 .  (1) C-O channel for COS hydrolysis. In reaction channel I (i.e., Reactant → IM1 → TS1 → IM2 → TS2 → IM3 → TS4 → IM4), H 2 O first adsorbs on the surface of Fe 2 O 3 , forming IM1. The C5-O1 bond length decreases and the H3-O1 bond breaks. At the same time, the C5-O1 and H3-O6 bonds are formed with the change from a C5=O6 double bond to a C5-O6 single bond to generate IM2 via TS1 (with just one imaginary frequency of -906.47 cm -1 ). As seen in Fig. 5 and Supplementary Table S1, H3 moves from its position in IM1 to O6 in IM2 with an energy barrier of 133.24 kcal/ mol. In effect, H3 and H2-O1 in H 2 O attack the O6 and C5 atoms in COS, respectively.
The H3-O6 bond length then becomes longer as the H3-S4 bond length becomes shorter. Meanwhile, the H3-O6 bond breaks and the C5=O6 bond forms from the C5-O6 bond. Then, H3 migrated from the H3-O6 bond in IM2 to the H3-S4 bond in IM3. As the result, IM3 is generated via TS2 (with just one imaginary frequency of -1528.43 cm −1 ) with an energy barrier of 46.75 kcal/mol. For TS2, Fe 2 O 3 had an adsorption effect on O9 and H2, which led to that the migration of H3 from O6 to S4 was easier than H2 from O1 to S4.
Concomitantly, the bond lengths of H2-O1 and C5-S4 become longer and the H2-S4 bond length becomes shorter. Additionally, the H2-O1 and C5-S4 bonds become broken, the H2-S4 bond forms, and the C5=O1 bond forms from the C5-O1 bond. Subsequently, the products (IM4) are formed via TS4 (with just one imaginary (2) C-S channel for COS hydrolysis In reaction channel II (i.e., Reactant → IM1 → TS3 → IM3 → TS4 → IM4), H 2 O first adsorbs on the surface of Fe 2 O 3 to generate IM1. Then, the C5-O1 bond length decreases and the H3-O1 bond breaks. At the same time, the C5-O1 and H3-S4 bonds form with the change from a C5=S4 double bond to a C5-S4 single bond, forming IM3 via TS3 (with just one imaginary frequency of −755.33 cm -1 ). H3 moves from its position in IM1 to S4 in IM3 with an energy barrier of 38.49 kcal/mol. More specifically, H3 and H2-O1 in H 2 O attack the S4 and C5 atoms in COS, respectively. For TS3, the adsorption effect of Fe7 and O1-H2 led to that the migration of H3 from O1 to H4 was easier than H2 from O1 to S4. The subsequent steps are identical to those in reaction channel I (i.e., IM3 → TS4 → IM4).
On the basis of these results, it is clear that the migration of H3 from the H3-O1 bond in IM1 to the H3-S4 bond in IM3 is easier than the migration of H3 from H3-O1 bond to the H3-O6 bond. Thus, the H-S bond forms more easily than the H-O bond, and reaction channel II is likely to occur more readily than reaction channel I.
Reaction mechanism of CS2 hydrolysis over Fe2O3 cluster. As seen in Fig. 4, the hydrolysis of CS 2 can be divided into two steps: CS 2 → COS and COS → H 2 S. The optimized geometries for the step 1 of hydrolysis of CS 2 are presented in Fig. 6, and the imaginary frequencies of the transition states for COS hydrolysis are shown in Supplementary Table S2. The optimized geometries for the step 2 of hydrolysis of CS 2 are presented in Fig. 7, and the imaginary frequencies of the transition states for COS hydrolysis are shown in Supplementary Table S3. (1) Double H-S channel for step 1 of CS 2 hydrolysis. In reaction channel III (i.e., the first step of CS 2 hydrolysis: IM4 → TS5 → IM5 → TS6 → IM6 → TS7 → IM7), the C17-O13 bond length decreases and the H14-O13 bond breaks. As a result, the C17-O13 and H14-S16 bonds form with the change from a C17=S16 double bond to a C17-S16 single bond to generate IM5 via TS5, which has only one imaginary frequency of −703.92 cm −1 . As seen in Fig. 6 and Supplementary Table S2, H14 moves from its position in IM4 to S16 in IM5 with an energy barrier of 97.21 kcal/mol. Thus, H14 and H14-O13 in H 2 O attack the S16 and C17 atoms in CS 2 , respectively.
Consequently, the H15-O13 bond length becomes longer and the H15-S18 bond length becomes smaller. Meanwhile, the H15-O13 bond breaks and the C17=O13 bond forms from the C17-O13 bond. As a result, IM6 is generated via TS6 (with just one imaginary frequency of −1045.81 cm −1 ) with an energy barrier of 36.76 kcal/ mol. H15 migrated from the H15-O13 bond in IM5 to the H15-S18 bond in IM6.
(2) Single H-S channel for step 1 of CS 2 hydrolysis. In reaction channel IV (i.e., the first step of CS 2 hydrolysis: IM4 → TS5 → IM5 → TS8 → IM7), IM5 is formed via TS5 causing the H15-O13 bond length to become longer and the H15-S16 bond length to become shorter. Meanwhile, the H15-O13 bond breaks and the C17=O13 bond forms from the C17-O13 bond. These changes lead to IM7, which is generated via TS8 (with just one imaginary frequency of −1546.07 cm −1 ) with an energy barrier of 48.57 kcal/mol. H15 migrated from the H15-O13 bond in IM5 to the H15-S16 bond in IM7.
Based on these results, the migration of H15 from the H15-O13 bond to the H15-O18 bond in IM6 occurs more easily than the migration of H15 from the H15-O13 bond in IM5 to the H15-S16 bond in IM7. Overall, these results suggest that the H atom more easily forms an H-S bond with the C=S bond than the C-S bond and that reaction channel III occurs more easily than reaction channel IV.
(3) C-O channel for step 2 of CS 2 hydrolysis. As seen in Fig. 7, in reaction channel V (i.e., the second step of CS 2 hydrolysis: IM7 → TS9 → IM8 → TS10 → IM9 → TS12 → Product), the C17-O21 bond length decreases and the H23-O21 bond breaks. At the same time, the C17-O21 and H23-O13 bonds are formed with the change from C17=O13 to C17-O13, forming IM8 via TS9 (with just one imaginary frequency of −1624.81 cm −1 ). As seen in Fig. 7 and Supplementary Table S3, H23 moves from its position in IM7 to O13 in IM8 with an energy barrier of 80.67 kcal/mol, and H23 and H23-O21 in H 2 O attack the O13 and C17 atoms in COS, respectively.
The H23-O13 bond length then becomes longer while the H23-S18 bond length becomes shorter. Meanwhile, the H23-O13 bond breaks and the C17=O13 bond forms from the C17-O13 bond. Then, H23 migrated from the H23-O13 bond in IM8 to the H23-S18 bond in IM9. As the result, IM9 is generated via TS10 (with just one imaginary frequency of −1325.24 cm −1 ) with an energy barrier of 97.76 kcal/mol.
Concomitantly, the H22-O21 and S18-C17 bond lengths become longer while the H22-S18 bond length becomes shorter. Additionally, the H22-O21 and C17-S18 bonds break, the H22-S18 bond forms, and the C17=O21 bond forms from the C17-O21 bond. Subsequently, the products are formed via TS12 (with just one imaginary frequency of −1495.37 cm −1 ) with an energy barrier of 43.71 kcal/mol. H22 migrated from the H22-O21 bond in IM9 to the H22-S18 bond in the product.
(4) C-S channel for step 2 of CS 2 hydrolysis. In reaction channel VI (i.e., the second step of CS 2 hydrolysis: IM7 → TS11 → IM9 → TS12 → Product), the C17-O21 bond length decreases and the H23-O21 bond breaks. At the same time, the C17-O21 and H23-O18 bonds are formed with the change from C17=S18 to C17-S18, forming IM9 via TS11 (with just one imaginary frequency of −1172.61 cm −1 ). As seen, H23 moves from its position in IM7 to S18 in IM9 with an energy barrier of 66.17 kcal/mol, and H23 and H22-O21 in H 2 O attack the S18 and C17 atoms in COS, respectively. The subsequent steps are then identical to those in reaction channel V (IM9 → TS12 → Product).
Overall, it is clear that the migration of H23 from the H23-O21 bond in IM7 to the H23-S18 bond in IM9 occurs more easily than the migration of H23 from the H23-O21 bond to the H23-O13 bond. The results also indicate that the H-S bond forms more easily than the H-O bond, which agrees with the above results. Therefore, reaction channel VI is likely to occur more easily than reaction channel V. In the hydrolysis, the C=S bond cleavage occurs easier than C=O bond cleavage. The presence of H 2 S increases the maximum energy barrier for COS hydrolysis (from 60.19 kcal/mol to 66.17 kcal/mol), which was attributed to the competitive adsorption effect. As the result, it covered the active sites and was not favourable for COS hydrolysis. Meanwhile, the first step of CS 2 hydrolysis has a higher energy barrier than the second step, which indicates that the first step is rate-limiting. The energy barriers of gas-phase reaction were showed in Supplementary Table S5. Compared with gas-phase reaction without catalyst, all the maximum energy barriers of surface reaction were lower. The addition of Fe 2 O 3 can greatly decrease the maximum energy barrier (159.74 kcal/mol and 182.71 kcal/ mol for COS and CS 2 , respectively), which decreases the minimum energy required for the hydrolysis reaction. It was attributed to the adsorption effect between Fe 2 O 3 and H 2 O, and H migration. From the experimental results, nano-Fe 2 O 3 cluster promoted the catalytic hydrolysis reaction of CS 2 and COS. It might be attributed to the interaction effect Fe 2 O 3 and COS/CS 2 , and high catalytic hydrolysis activity of Fe 2 O 3 . As a product, H 2 S decreased the removal efficiency of COS and CS 2 when it was on the surface of catalyst. It indicated that H 2 S was not conducive to the hydrolysis of COS and CS 2 . The results demonstrate that Fe 2 O 3 is a good catalyst for the hydrolysis of COS and CS 2 . In general, theoretical results were consistent with experimental results, which proved that the theoretical study was reliable. Combined with theoretical and experimental results, it can be found that the influence mechanism of Fe 2 O 3 and H 2 S for catalytic hydrolysis of COS and CS 2 .

Conclusions
The competitive adsorption and reaction mechanism for the catalytic hydrolysis reaction mechanism of carbonyl sulphide (COS) and carbon disulphide (CS 2 ) over Fe 2 O 3 cluster was investigated in this work. The experimental results showed that Fe 2 O 3 cluster enhanced the catalytic hydrolysis effect. Meanwhile, H 2 S was not conducive to the hydrolysis of COS and CS 2 . On the basis of the calculation results, the order of competitive adsorption on Fe 2 O 3 is: H 2 O (strong) > CS 2 (medium) > COS (weak). In the hydrolysis process, the C=S bond cleavage occurs easier than C=O bond cleavage. The presence of H 2 S increases the reaction energy barrier, which is not favourable for COS hydrolysis. Meanwhile, Fe 2 O 3 can greatly decrease the maximum energy barrier, which decreases the minimum energy required for hydrolysis, making it relatively facile to occur. Combined with theoretical and experimental results, it can be found that the influence mechanism of Fe 2 O 3 and H 2 S for catalytic hydrolysis of COS and CS 2 .

Experimental and Theoretical Methods
Experimental Methods. To investigate the effect of nano-Fe 2 O 3 cluster for catalytic hydrolysis of COS and CS 2 , AC (activated carbon) and nano-Fe 2 O 3 cluster/AC were used in this work. Nano-Fe 2 O 3 cluster was synthesized by hydro-thermal method 22 . 4.40 g FeCl 3 and 4.0 g urea were added into 100 mL distilled water. 50 mL NH 3 ·H 2 O was added dropwise into the solution with continuous magnetic stirring. The solution was poured into a Teflon-lined container and then it was heated at 150 °C for 12 h. The solution was cooled under room temperature. The obtained precipitates were washed by ethanol and distilled water for three times. Finally, the precipitates were calcinated at 450 °C for 3 h. The size of nano-Fe 2 O 3 structure was less than 10 nm and it had the cluster structure. Nano-Fe 2 O 3 cluster/AC (activated carbon) was synthesized by dipping method according to our previous study 13,14 . 5% mass content of nano-Fe 2 O 3 cluster and AC were added into 50 mL distilled water. The solution was placed in an ultrasonic bath for 30 min. Finally, the solution was dried at 120 °C for 20 h and nano-Fe 2 O 3 cluster/ AC was prepared.
The desulphurization tests were performed in a fixed-bed quartz reactor under atmospheric pressure 13,14 . CS 2 and COS from the gas cylinder (0.3% CS 2 in N 2 ; 1% COS in N 2 ) were diluted with N 2 (99.99%) to the required concentration (CS 2 : 20 ppm; COS: 500 ppm). The overall gas hourly space velocity (GHSV) was 10000 h -1 . Water was obtained from a saturator system, which set the temperature and corresponding relative humidity (RH) to 5 °C and 49%, respectively. The temperature of the reactor was maintained at 70 °C using a water bath. The CS 2 , COS and H 2 S (hydrolysis product) concentration of the gas feed and effluent from the reactor were analysed using a HC-6 sulphur phosphorus microscale analyser. The removal rate of CS 2 and COS were determined by calculating the inlet and outlet concentration of CS 2 and COS, and it was shown in Eq. 1: , and products were calculated and optimized using the GGA/PBE method from density functional theory (DFT) 24,25 . A density functional semi-core pseudopotential method was used for the core electrons of Fe, and the all-electron method was used for the core electrons of H, C, O and S. A double-numeric quality basis set with polarization functions (i.e., DNP, version 3.5) was used [25][26][27] . The tolerances of the SCF, energy, gradient and displacement convergence were 1.0 × 10 -6 hartree (Ha), 1.0 × 10 -5 Ha, 2.0 × 10 -3 Ha/Å and 5.0 × 10 -3 Å, respectively. All calculations using spin-polarized set were performed considering the antiferromagnetic properties. In previous study, electronic self-interaction error played an important role in DFT 28,29 . Therefore, the electron self-interaction error had been consideration in this work. Self-consistent field convergence was declared when at least two of the above criteria were satisfied. Electronic energies and zero point vibration energies (ZPVE) were calculated at the same level of theory. Linear synchronous transit/quadratic synchronous transit/conjugate gradient (LST/QST/CG) calculations were used to ensure that all of the transition states connected to the intended reactants and products. Transition states were identified by the presence of a single imaginary frequency, which corresponded to the reaction mode. The adsorption energy was defined as Eq. 2. E (adsorbate+cluster) is the total energy of adsorbate/cluster system after gas molecule being adsorbed on Fe 2 O 3 cluster. E adsorbate is the single-point energy of gas molecule and E cluster is the single-point energy of Fe 2 O 3 cluster.