Bin Wang1, Si-Yuan Zhang1, Ling-Hong Ye2, Xiao-Fei Zhang1, Yong-Fan Zhang1, Wen-Jie Chen2. 1. College of Chemistry, Fuzhou University, Fuzhou, Fujian 350108, P. R. China. 2. Department of Material Chemistry, College of Chemical Engineering and Material, Quanzhou Normal University, Quanzhou, Fujian 362000, P. R. China.
Abstract
H2S is abundantly available in nature, and it is a common byproduct in industries. Molybdenum sulfides have been proved to be active in the catalytic decomposition of hydrogen sulfide (H2S) to produce hydrogen. In this study, density functional theory (DFT) calculations are carried out to explore the reaction mechanisms of H2S with MS3 (M = Mo, W) clusters. The reaction mechanism of H2S with MoS3 is roughly the same as that of the reaction with WS3, and the free-energy profile of the reaction with MoS3 is slightly higher than that of the reaction with WS3. The overall driving forces (-ΔG) are positive, and the overall reaction barriers (ΔG b) are rather small, indicating that such H2 productions are product-favored. MS3 (M = Mo, W) clusters have clawlike structures, which have electrophilic metal sites to receive the approaching H2S molecule. After several hydrogen-atom transfer (HAT) processes, the final MS4·H2 (IM-4) complexes are formed, which could desorb H2 at a relatively low temperature. The singlet product MS4 clusters contain the singlet S2 moiety, similar to the adsorbed singlet S2 on the surface of sulfide catalysts. The theoretical results are compared with the experiments of heterogeneous catalytic decomposition of H2S by MoS2 catalysts. Our work may provide some insights into the optimal design of the relevant catalysts.
H2S is abundantly available in nature, and it is a common byproduct in industries. Molybdenum sulfides have been proved to be active in the catalytic decomposition of hydrogen sulfide (H2S) to produce hydrogen. In this study, density functional theory (DFT) calculations are carried out to explore the reaction mechanisms of H2S with MS3 (M = Mo, W) clusters. The reaction mechanism of H2S with MoS3 is roughly the same as that of the reaction with WS3, and the free-energy profile of the reaction with MoS3 is slightly higher than that of the reaction with WS3. The overall driving forces (-ΔG) are positive, and the overall reaction barriers (ΔG b) are rather small, indicating that such H2 productions are product-favored. MS3 (M = Mo, W) clusters have clawlike structures, which have electrophilic metal sites to receive the approaching H2S molecule. After several hydrogen-atom transfer (HAT) processes, the final MS4·H2 (IM-4) complexes are formed, which could desorb H2 at a relatively low temperature. The singlet product MS4 clusters contain the singlet S2 moiety, similar to the adsorbed singlet S2 on the surface of sulfide catalysts. The theoretical results are compared with the experiments of heterogeneous catalytic decomposition of H2S by MoS2 catalysts. Our work may provide some insights into the optimal design of the relevant catalysts.
Hydrogen sulfide (H2S) is a colorless, toxic, corrosive,
and flammable gas. It is abundantly available in nature and also obtained
from industries. It is known that hydrogen sulfide is an important
raw material that can be converted into elemental sulfur and water
via the Claus process.[1,2] But it seems a pity to only convert
H2S to water as the end-product. From the thermodynamic
point of view, the dissociation of H2S into hydrogen and
elemental sulfur is much easier than the splitting of H2O.[3,4] Therefore, hydrogen sulfide is also the potential
source for hydrogen energy.[3] To improve
the H2S conversion into H2 and to reduce the
operating temperature, many methods have been proposed.[2−5] For example, removing the products continuously from the reaction
system was an effective way that could shift the chemical equilibrium
toward the product side.[6] At the same time,
with the help of thermal catalysis, photocatalysis, electrolysis,
and other technologies like microwave, plasma, etc., the operating
temperature of H2S decomposition has been greatly reduced.[7] With concerted effort, nearly 100% conversion
could be achieved at a relatively low temperature.[2,8,9] Despite great progress, the hydrogen recovery
from H2S decomposition still faces several challenges,
such as cost and durability, which hinder its large-scale use in industries.[2,10]Various materials including noble metals, metal oxides, metal
sulfides,
and perovskites have been studied as promising catalysts for low-temperature
H2S decomposition.[2,11−13] Among them, metal sulfides have received great interest due to their
low price and sulfur tolerance. It is known that the gas-phase direct
pyrolysis of H2S is an endothermic process that limits
the thermodynamic conversion at low temperature.[3] But interestingly, if the H2S decomposition
occurred on the surface of metal sulfide catalysts, the process will
become an exothermic process.[3,9,10] The reaction mechanism of H2S decomposition over metalsulfide catalysts has been extensively studied.[8−10,14−16] It is accepted that the overall
decomposition process can be generally divided into two stages.[10] In the first stage, H2S interacts
with “low-sulfur” metal sulfides to form “high-sulfur”
metal sulfides and to release H2. Then, the high-sulfurmetal sulfides would revert to the initial low-sulfur species and
give off the redundant elemental sulfur. Although the composition
of elemental sulfur (S, i = 1–8) depends on the reaction temperature and the pressure
of sulfur vapors, the adsorbed elemental sulfur on the surface of
sulfide catalysts is the singlet diatomic sulfur (S2).[9] To form the adsorbed singlet S2, the
absorbed disulfane molecule (H2S2) is an important
surface intermediate.[9,10] H2S2 is
formed via the H2S bimolecular reaction in which two H2S molecules are adsorbed on two adjacent metal atoms; then,
the S–S bond is formed between two adsorbed H2S
molecules, releasing the redundant H2 molecule (21H2S → 1H2S2 + 1H2↑).[9,10] H2S2 would further desorb the molecular hydrogen at a relatively
low temperature and remain the singlet S2 in the absorbed
state up to a relatively high temperature.[9] With the formation of the S–S bond in H2S2, the metal–sulfur bond would weaken, which facilitates
the subsequent departure of elemental sulfur. Although the free diatomic
sulfur (S2) is most stable in the triplet state (3∑g–) at room temperature, the
singlet S2 (1Δg) is reasonably
stable at high temperature.[9,17] With reducing the temperature,
the absorbed singlet S2 would recombine together to form
the thermodynamically stable cyclo-octasulfur (S8) molecule.[3,9]We have been interested in increasing the application of the
gas-phase
cluster model.[18−23] Studying the reaction mechanism using the gas-phase cluster may
help us deepen the understanding of the reactions at the molecular
level and help us design catalysts with tailored performance.[24−27] It may be interesting to answer the questions: whether the small
sulfide clusters with particular size and stoichiometry have the potential
to be better catalysts, especially when the studies of single-cluster
catalysts (SCC) and gas-phase cluster catalysts have attracted much
attention.[28−32] In our early work, theoretical studies on the geometric and electronic
structures of MoS–/0 (n = 1–5) clusters have been carried out.[23] In this study, we carried out the theoretical
calculations of the H2S decomposition reaction with MS3 (M = Mo, W) clusters. According to our calculations, MS3 clusters (C31A1) have clawlike structures, which have the
electrophilic metal sites to receive the approaching H2S molecule. H2S reacts with the low-sulfurMS3 clusters to form the high-sulfurMS4 clusters and release
H2. The high-sulfurMS4 (M = Mo, W) clusters
contain the singlet S2 moiety, analogous to the adsorbed
singlet S2 on the surface of sulfide catalysts. The overall
driving forces (−ΔG) are positive, and
the overall energy barriers (ΔGb) are relatively low, indicating the reaction is product-favored.
The dissociation energies of the H2 and S2 molecules
required in the decomposition reactions were estimated as well. The
initial MS3 clusters may be regenerated via the subsequent
sulfidation of MS2 clusters with H2S.
Results
and Discussion
For the gas-phase decomposition reaction of
H2S with
MS3 (M = Mo, W) clusters, it should be noted that only
the reaction paths with the lowest overall energy barriers are discussed
here. Other pathways are given in the Supporting Information (Figures S1 and S2). The lowest-barrier reaction
paths are divided into several elementary reactions (labeled as no.
1–5 in Table and no. 1–7 in Table ). The free-energy changes (ΔG) and
the free-energy barriers (ΔGb) in
reactions are also listed in Tables and 2. The ΔG and ΔGb values of elementary steps
are the free-energy changes with respect to the respective reactants,
and the overall ΔG and overall ΔGb are the relative free energies of the final
products (MS4 + H2) and the highest-energy transition
states in the overall reactions with respect to the total energies
of the separated initial reactants (MS3 + H2S), respectively. For concision, the relevant reactants, products,
intermediates, and transition states are denoted as R, P, IM-n, and TS-n, respectively. The superscripts (m) represent
their spin multiplicities, and the postfix numbers (n) denote the sequence numbers in the reaction paths. The free-energy
(ΔG) profiles are displayed in Figures and 6, together with the corresponding energy changes (ΔE) estimated by CCSD(T) single-point calculations. Overall,
the reaction pathways of H2S with MoS3 resemble
the reaction with WS3. Moreover, all of the local minima
and transition states in the singlet states are more stable than those
in the triplet states (Figures and S5). Therefore, we mainly
discuss the energy profile of the H2S decomposition reaction
with MoS3 on the singlet potential energy surfaces.
Table 1
Relative Free Energies (ΔG)
and the Corresponding Energy Barriers (ΔGb) of H2S Reactions with MS3 (M = Mo,
W) Clusters on the Singlet-State Potential Energy Surfaces
at the B3LYP Level (Including Zero-Point Vibration Correction and
DFT-D3 Dispersion Correction)a
M = Mo
M = W
no.
reactions
(singlet state)
ΔG
ΔGb
ΔG
ΔGb
1
MS3 + H2S → MS3·H2S
–28.60
–31.37
2
MS3·H2S → MS2(SH)2
–18.43
10.97
–21.64
9.78
3
MS2(SH)2 → MS(S2)(SH)H
24.74
61.94
26.52
64.17
4
MS(S2)(SH)H → MS2(S2)·H2
9.85
14.97
12.03
16.18
5
MS2(S2)·H2 → MS2(S2) + H2
4.28
5.93
overall
MS3 + H2S → MS2(S2) + H2
–8.16
14.91
–8.53
11.16
All energies are
in kcal/mol.
Table 2
Relative Free Energies (ΔG) and the Corresponding
Energy Barriers (ΔGb) of H2S Reactions with MS3 (M = Mo, W) Clusters on the Triplet-state
Potential Energy Surfaces
at the B3LYP Level (Including Zero-Point Vibration Correction and
DFT-D3 Dispersion Correction)a
M = Mo
M = W
no.
reactions
(triplet state)
ΔG
ΔGb
ΔG
ΔGb
1
MS3 + H2S → MS3·H2S
–7.24
–4.30
2
MS3·H2S → MS2(SH)2
–16.10
6.98
–17.37
7.62
3
MS2(SH)2 isomerization
–0.34
5.35
0.81
22.06
4
MS2(SH)2 → MS(S2)(SH)H
8.03
36.67
8.47
25.85
5
MS(S2)(SH)H isomerization
–0.07
4.08
15.02
15.04
6
MS(S2)(SH)H → MS2(S2)·H2
10.32
17.70
–1.97
0.57
7
MS2(S2)·H2 → MS2(S2) + H2
–11.66
–14.42
overall
MS3 + H2S → MS2(S2) + H2
–8.50
21.55
–5.55
13.20
All energies are
in kcal/mol.
Figure 3
Lowest-barrier free-energy
paths (T = 298.15 K)
for the reaction of H2S with MoS3 (m = 1, 3). The relative free energies
(including zero-point vibration corrections and dispersion corrections)
are given in parentheses. The relative energies obtained by single-point
CCSD(T) calculations are also given in square brackets.
Figure 6
Lowest-barrier
free-energy paths (T = 298.15 K)
for the reaction of H2S with 1MS3 (M = Mo, W). The relative free energies (including zero-point vibration
corrections and dispersion corrections) are given in parentheses.
The relative energies obtained by single-point CCSD(T) calculations
are also given in square brackets.
All energies are
in kcal/mol.All energies are
in kcal/mol.
Reactants and Products
The molecular structures of
H2, S2, H2S, and MS (M = Mo, W; n = 2–4) are displayed
in Figure . The H–H
bond length in the H2 molecule (D∞1∑g+) is calculated to be 0.743 Å. The ground state of S2 is the triplet-state (D∞3∑g–) with a S–S bond length of 1.912 Å. The H2S molecule is an obtuse triangle (C21A1) with the a S–H
bond length of 1.344 Å. The most stable structures of MoS (n = 1–5) have been
studied in our early work.[23] In the current
work, these structures were reoptimized at the same level of theory
but considered the dispersion effects on the geometry optimizations
and the energy evaluations. It is obvious that the optimized geometries
of MoS (n = 2–4)
and their relative energies (Figure ) are consistent with our early work.[23] Specifically, MoS2 is an obtuse triangle with C2 (3B1) symmetry. Its singlet isomer (C21A1) is 14.73 kcal/mol less stable. The
MoS3 has a triangular pyramid structure with C3 (1A1) symmetry,
and the only Mo atom is located at the vertex of the pyramid. Its
triplet analogue C3 (3A2) is 10.71 kcal/mol less stable (Figure ). As for MoS4,
it has several isomers with nearly degenerate energies. At the DFT/B3LYP
level, the most stable structure is a triplet-state (C23A2) with a S2 group. But its singlet isomer (C21A) is only 0.27 kcal/mol (ca. 0.01 eV) less stable. Another
triplet-state isomer (D23A1) with four equivalent terminal S atoms
is 6.22 kcal/mol less stable. Similar results were found for the WS (n = 2–4) clusters.
For the WS4 species, the most stable structure is the triplet
isomer (D23A1) with four equivalent terminal S atoms. The singlet
isomer (C11A) with a S2 group is only 0.98 kcal/mol less stable. Its triplet counterpart
(C23A2) is 3.99 kcal/mol less stable. The relative energies of MS4 (M = Mo, W) are so close that higher-level CCSD(T) single-point
and full-optimization calculations were performed to further distinguish
their relative stabilities. According to the results of CCSD(T) calculations
(Figure ), the singlet
isomers with the S2 group are more likely to be the ground
states for both MoS4 and WS4. In addition, as
shown in Figure ,
the lengths of the metal–sulfur bonds and the S–S bond
in the WS (n = 2–4)
clusters are slightly longer than those in the MoS analogues, and the S–W–S bond angles are slightly
smaller than the angles in the Mo counterparts.
Figure 1
Optimized ground-state
structures of S2, H2, H2S, and MS (M = Mo, W; n = 2–4).
Figure 2
Optimized structures of selected low-lying MS (M = Mo, W; n = 2–4) isomers
and their
relative energies (ΔE) at the DFT/B3LYP level.
The ΔE values calculated by single-point and
full-optimization CCSD(T) calculations are shown in brackets and braces,
respectively.
Optimized ground-state
structures of S2, H2, H2S, and MS (M = Mo, W; n = 2–4).Optimized structures of selected low-lying MS (M = Mo, W; n = 2–4) isomers
and their
relative energies (ΔE) at the DFT/B3LYP level.
The ΔE values calculated by single-point and
full-optimization CCSD(T) calculations are shown in brackets and braces,
respectively.
Initial Complexes
The decomposition reactions were
initiated by the Lewis acid–base addition process of the H2S molecule to the MoS3 (C31A1) cluster. Sterically,
the MoS3 (C31A1) cluster has an open Mo(VI) coordination
site. The electron-rich sulfur atom of H2S attacks the
electron-deficient Mo(VI) site of MoS3, leading to the
formation of an initial complex MoS3·H2S (1IM-1). As shown in Figure , this step releases
energy by 28.60 kcal/mol. In the 1IM-1 complex, the distance
between the sulfur atom of H2S and the Mo(VI) atom is 2.508
Å, which is much longer than the other Mo–S bond lengths,
and the S–H bond lengths (1.349 Å) in the H2S moiety are very close to the S–H bond length (1.344 Å)
in the free H2S molecule (Figure ). Thus, the initial
complex 1IM-1 can be seen as the H2S molecule
adsorbed on the Mo(VI) site of MoS3.
Figure 4
Optimized structures of singlet-state species involved in the decomposition
reaction of H2S with 1MoS3 cluster.
Lowest-barrier free-energy
paths (T = 298.15 K)
for the reaction of H2S with MoS3 (m = 1, 3). The relative free energies
(including zero-point vibration corrections and dispersion corrections)
are given in parentheses. The relative energies obtained by single-point
CCSD(T) calculations are also given in square brackets.Optimized structures of singlet-state species involved in the decomposition
reaction of H2S with 1MoS3 cluster.
Sequential Hydrogen-Atom Transfer (HAT) Process
After
H2S adsorbs on the MoS3 cluster, two hydrogen
atoms of H2S would sequentially transfer to the MoS3 cluster. Specifically, with the H2S gradually
approaching the Mo(VI) atom, the H2S···Mo(VI)
distance changes from 2.508 to 2.322 Å (Figure ), together with the breaking of one S–H
bond in H2S and the hydrogen-atom transfers to the terminal
sulfur of MoS3. As shown in Figure , this step needs to overcome a small free-energy
barrier via the transition state 1TS-1 by 10.97 kcal/mol.
After that, the intermediate MoS2(SH)2 (1IM-2) is produced, whose energy is 47.03 kcal/mol lower than
those of the initial reactants (Figure ). In the intermediate 1IM-2, the S–H
bond lengths are 1.350 Å, close to the lengths in H2S (Figure ). The
Mo–SH bond lengths are 2.322 Å, which can be regarded
as the Mo–S single bonds, and the terminal Mo–S bond
lengths are 2.107 Å, which can be seen as the Mo=S double
bonds.Subsequently, the second hydrogen atom moves from one
of the S–H bonds of 1IM-2 to the Mo(VI) atom by
the intracluster H-atom transfer process. This process needs to go
through the transition state 1TS-2, which requires a considerable
energy, 61.94 kcal/mol. Although this step requires rather high energy
(61.94 kcal/mol), the stabilization of intermediate 1IM-2
may help to overcome the high energy barrier. As shown in Figure , the overall barrier
ΔGb is only 14.91 kcal/mol. It is
the rate-determining step in the overall reaction. After 1TS-2, the intermediate MoHS(S2)(SH) (1IM-3),
which comprises a S2 unit and a Mo–H bond, is produced.
As shown in Figure , 1IM-3 is 22.29 kcal/mol lower in energy than the initial
reactants.
H2 Elimination
After
two hydrogen atoms
of H2S sequentially transfer to the MoS3, the
H atom of the SH group in 1IM-3 would move to the Mo site
and bond to another H atom located on the Mo site to form the complex
MoS4·H2 (1IM-4). This process
needs to pass through the transition state 1TS-3, which
requires the energy 14.97 kcal/mol. For the complex 1IM-4,
the structural parameters of both the H2 unit and the MoS4 moiety are close to the parameters of the free H2 molecule and MoS4 (C21A) cluster (Figure ). Therefore, it can be seen as the H2 molecule
adsorbed on the Mo(VI) site of MoS4. After that, the H2 molecule is desorbed from 1IM-4, leaving the high-sulfur
MoS4 (C21A) cluster.
The H2 desorption requires energy by only 4.28 kcal/mol.
In summary, the overall reaction of H2S with singlet MoS3 releases 8.16 kcal/mol energy. The apparent energy barrier
is 14.91 kcal/mol.
Elemental Sulfur Elimination
After
H2 is
desorbed from MoS4·H2 (1IM-4),
the MoS4 (C21A)
cluster is left comprising the S2 and MoS2 moieties.
Our previous studies suggested that the S2 moiety in MoS4 (C21A) can be seen
as the singlet S22– group.[23] There have been experiments that proved the
existence of the S22– units on the sulfur-rich
edges of MoS2 catalysts.[5,33,34] The ground-state structures of S2 (D∞3∑g–), MoS2 (C23B1), and MoS4 (C21A) are displayed
in Figure . The S–S
bond length in S2 (D∞3∑g–) is 1.912 Å. MoS2 (C23B1) is an obtuse triangle
with two Mo=S bonds of length 2.115 Å. In MoS4 (C21A), the Mo–S bond
lengths between the Mo atom and the S2 unit are 2.323 Å,
close to the lengths of Mo–S single bonds. The S–S bond
length in MoS4 (C21A) is 2.089 Å, slightly longer than that of the free S2 (D∞3∑g–) molecule. The lengths of
the Mo=S bonds in MoS4 (C21A) are 2.120 Å, close to the corresponding lengths
in the MoS2 (C23B1) cluster. It is inferred that two
unpaired electrons in the MoS2 (C23B1) transfer to the
π3p* antibonding orbitals of the S2 (D∞3∑g–), which brings about the elongation of
the S–S bond and the bonding between the Mo atom and the S2 unit. It is known that the ground state of the free S2 molecule is triplet (D∞3∑g–), and its excited singlet state (D∞1Δg) is less stable at
low temperature.[17] The MoS2 ground
state is also triplet (C23B1), and its singlet (C21A1) is much less
stable. Therefore, eliminating the singlet S2 (D∞1Δg) from the MoS4 (C21A) cluster (1MoS4 → 1MoS2 + 1S2) requires much
more energy than eliminating the triplet S2 (D∞3∑g–). The free-energy change required for eliminating
the triplet S2 from the MoS4 (C21A) cluster (1MoS4 → 3MoS2 + 3S2) is calculated
to be 64.59 kcal/mol, and the enthalpy change (ΔH) is predicted to be 75.38 kcal/mol. A comparison of the low H2 desorption energy change (ΔG = 4.28
kcal/mol) from 1IM-4 with the high S2 dissociation
energy change (ΔG = 64.59 kcal/mol) of MoS4 (C21A) corresponds
to the experimental observation that H2 is desorbed first
at a relatively low temperature and the absorbed singlet S2 is remained on the surface of sulfide catalysts even up to a relatively
high temperature.[9] The bond dissociation
energy (BDE) is defined as the enthalpy change in the dissociation
process of thee corresponding bonds. In MoS4 (C21A), the BDE of the Mo–S bond between
the MoS2 and the S2 moieties is predicted to
be 37.69 kcal/mol (dissociation enthalpy (ΔH = 75.38 kcal/mol) divided by the number of Mo–S bonds between
the MoS2 and the S2 moieties in MoS4). The BDE of the Mo–S single bond in (η5-C5Me5)(CO)3Mo–SH is predicted
to be 55 kcal/mol.[35] The experiment has
also evaluated the Mo–S bond strengths in bulk MoS2 to be 59.73 kcal/mol.[36] Both of them
are larger than our calculated BDE in MoS4 (C21A), inferring the interaction between the
MoS2 and S2 moieties in MoS4 (C21A) is weaker than the normal Mo–S
single bond. Therefore, with increasing temperature, S2 may be dissociated from the MoS4 (C21A) cluster. The product MoS2 (C2v3B1) may further react
with H2S, recovering the starting reactant MoS3 (C3v1A1) (3MoS2 + 1H2S → 1MoS3 + 1H2), and the driving
force (−ΔG) is estimated to be 24.95
kcal/mol, which is thermodynamically spontaneous. It should be noted
that the sulfidation of MoS2 (C2v3B1) to MoS3 (C3v1A1) seems to be the spin-forbidden
reactions. More detailed calculations, which may consider the spin-state
inversion in these reactions, are required in the future.On
the surface of metal sulfide catalysts, the adsorbed singlet S2 is found in the H2S decomposition reaction.[3,9] To form the adsorbed singlet S2, the disulfane molecule
(H2S2) is the key surface intermediate, and
it is absorbed on two metal sites of catalyst surface.[9,10] In our calculations, no absorbed disulfane (H2S2) but MoS4·H2 (1IM-4) was located.
After desorbing the H2 molecule, the high-sulfur MoS4 cluster also contains the absorbed singlet S2 unit.
The difference may be due to only one H2S reacting with
the mononuclear MoS3 cluster in the gas phase.
Comparisons
with Reactions on the Triplet Potential Energy Surface
The
free-energy profile and the optimized structures involved in
the reaction of H2S with triplet MoS3 (C33A2) cluster are shown in Figure and 5,
respectively. For comparison, the energies listed in Figure are unified to be the relative
energies with respect to the total energy of separated singlet reactants
(1MoS3 + H2S). Compared to the singlet
reaction, the path of the triplet reaction also starts with the Lewis
acid–base addition of the H2S molecule to the MoS3 cluster, leading to the similar initial complex MoS3·H2S (1IM-1 in Figure , 3IM-1′ in Figure ). In the following HAT process,
one of the H atoms in H2S first transfers to the terminal
S (1IM-2 in Figure , 3IM-2′ and 3IM-3′ in Figure ) and then moves
to the Mo site (1IM-3 in Figure , 3IM-4′ and 3IM-5′ in Figure ). Finally, the last H atom in the −SH group moves to the
metal site, leading to the final complex MoS4·H2 (1IM-4 in Figure , 3IM-6′ in Figure ). MoS4·H2 would
split into a H2 molecule and a MoS4 cluster.
Both the singlet and triplet MoS4 cluster have the S2 group. By contrast, two more isomerization processes of intermediates
(3IM-2′ → 3IM-3′ and 3IM-4′ → 3IM-5′) occur in the
triplet path. Both these two isomerization processes involve the rotation
of −SH groups around the Mo–SH bond, facilitating the
subsequent HAT process. The singlet reactions including these two
intermediate isomerization processes and the triplet reaction without
these two isomerization processes were also found in our calculations
(Figures S1 and S2). But their overall
energy barriers are all higher than the aforementioned reaction paths
(15.06 kcal/mol vs 14.91 kcal/mol for the singlet reaction; 24.47
kcal/mol vs 21.55 kcal/mol for the triplet reaction). Moreover, as
displayed in Figure , all of the local minima and transition states in the singlet states
are more stable than those in the triplet states. It suggests that
the reaction should take place on the singlet potential energy surfaces.
Figure 5
Optimized
structures of triplet-state species involved in the decomposition
reaction of H2S with 3MoS3 cluster.
Optimized
structures of triplet-state species involved in the decomposition
reaction of H2S with 3MoS3 cluster.
Comparisons with the Reaction by WS3
On
the whole, the reaction paths of H2S with MoS3 resemble the reaction with WS3, no matter the geometries
of substances or the trends of free-energy change (Figures , 6, 7). Taking the reaction on the singlet potential energy surface for
example (Figure ),
the reaction mechanisms of H2S with MoS3 are
essentially the same as those of the reactions with WS3. The overall energy barrier in the reactions with singlet MoS3 (14.91 kcal/mol) is higher than that in the reactions with
singlet WS3 (11.16 kcal/mol). They are all lower than the
activation energy of H2S thermal decomposition experiments
without catalysts (42.0 kcal/mol) and the activation energy of H2S decompositions with MoS2 catalysts (26.8 kcal/mol).[10,37]
Figure 7
Optimized
structures of singlet-state species involved in the decomposition
reaction of H2S with 1WS3 cluster.
Lowest-barrier
free-energy paths (T = 298.15 K)
for the reaction of H2S with 1MS3 (M = Mo, W). The relative free energies (including zero-point vibration
corrections and dispersion corrections) are given in parentheses.
The relative energies obtained by single-point CCSD(T) calculations
are also given in square brackets.Optimized
structures of singlet-state species involved in the decomposition
reaction of H2S with 1WS3 cluster.
Conclusions
Density functional theory
(DFT) calculations were performed to
explore the reaction of H2S with MS3 (M = Mo,
W) clusters. The theoretical results of gas-phase cluster reactions
were compared to the heterogeneous reaction experiments. The results
suggest that the MS3 (M = Mo, W) clusters have clawlike
structures, which have the electrophilic metal sites to receive the
approaching H2S molecule. After several hydrogen-atom transfer
(HAT) processes, the final complexes MS4·H2 (IM-4) are formed, which could yield H2 at a relatively
low temperature. The overall driving forces (−ΔG) and the overall reaction barriers (ΔGb) indicate that the H2 generation is product-favored.
Both the MoS4 (C21A) and WS4 (C11A) clusters contain the singlet S2 moiety, similar to
the adsorbed singlet S2 on the surface of sulfide catalysts.
In addition, the reaction mechanism of H2S with MoS3 is roughly the same as that of the reaction with WS3. The free-energy profile of the reaction of H2S with
MoS3 is slightly higher than that of the reaction with
WS3. We hope our work could provide some insights into
the H2 regeneration via H2S decomposition at
the molecular level and help us design catalysts with better performance.
Computational
Methods
To search for stable geometries of the substances
involved in the
reaction, numerous initial structures with different spin multiplicities
were optimized by the B3LYP functional in our density functional theory
(DFT) calculations.[38−40] Because some species involved weak interaction, the
B3LYP functional was extended with Grimme’s DFT-D3(BJ) dispersion
correction,[41−43] which is available in the Gaussian 16 suite of programs.[44] In calculations, the Stuttgart small-core relativistic
efficient core potential (RECP) and the corresponding basis sets[45−48] augmented with two f-type and one g-type polarization functions[49] were employed for the metals (Mo and W) and
the aug-cc-pVTZ basis sets for the nonmetal (H and S) elements.[50,51] The same RECP and basis sets have been used in our previous studies[23,52−56] that showed good agreement with the experimental spectra. Moreover,
early thermodynamic studies have pointed out that the direct thermal
decomposition of H2S is an endothermic process (1H2S → 1H2 + 0.5 3S2), for which the standard enthalpy change ΔrH2980 is 20.25 kcal/mol and the change of standard
Gibbs free energy ΔrG2980 is 17.5 kcal/mol.[10,57] In our DFT calculations, the corresponding energies were calculated
to be 18.50 kcal/mol (ΔH) and 15.74 kcal/mol
(ΔG). The deviations were all less than 1.80
kcal/mol, which also suggested the reliability of our chosen methods.
To verify the nature of the stationary points and to obtain the zero-point
energy (ZPE) corrections, vibrational frequencies were calculated
at the same level, which confirmed that the local minima had no imaginary
frequency and the transition states had only one. Intrinsic reaction
coordinate (IRC) calculations were performed to ensure that the transition
states connect the minima in the reaction pathways. In addition, to
better estimate the relative stabilities of the species involved in
the reaction, the coupled-cluster CCSD(T) single-point calculations
were also conducted using the same RECP and basis sets. The CCSD(T)
calculations were carried out using the MOLPRO 2010.1 package.[58]
Authors: Karen L Schuchardt; Brett T Didier; Todd Elsethagen; Lisong Sun; Vidhya Gurumoorthi; Jared Chase; Jun Li; Theresa L Windus Journal: J Chem Inf Model Date: 2007-04-12 Impact factor: 4.956