THE JOURNAL OF CHEMICAL PHYSICS 139, 204301 (2013)

Hydrogen evolution from water through metal sulfide reactions Arjun Saha and Krishnan Raghavachari Department of Chemistry, Indiana University, Bloomington, Indiana 47405, USA

(Received 25 July 2013; accepted 30 October 2013; published online 22 November 2013) Transition metal sulfides play an important catalytic role in many chemical reactions. In this work, we have conducted a careful computational study of the structures, electronic states, and reactivity of metal sulfide cluster anions M2 SX − (M = Mo and W, X = 4–6) using density functional theory. Detailed structural analysis shows that these metal sulfide anions have ground state isomers with two bridging sulfide bonds, notably different in some cases from the corresponding oxides with the same stoichiometry. The chemical reactivity of these metal sulfide anions with water has also been carried out. After a thorough search on the reactive potential energy surface, we propose several competitive, energetically favorable, reaction pathways that lead to the evolution of hydrogen. Selectivity in the initial water addition and subsequent hydrogen migration are found to be the key steps in all the proposed reaction channels. Initial adsorption of water is most favored involving a terminal metal sulfur bond in Mo2 S4 − isomers whereas the most preferred orientation for water addition involves a bridging metal sulfur bond in the case of W2 S4 − and M2 S5 − isomers. In all the lowest energy H2 elimination steps, the interacting hydrogen atoms involve a metal hydride and a metal hydroxide (or thiol) group. We have also observed a higher energy reaction channel where the interacting hydrogen atoms in the H2 elimination step involve a thiol (–SH) and a hydroxyl (–OH) group. For all the reaction pathways, the Mo sulfide reactions involve a higher barrier than the corresponding W analogues. We observe for both metals that reactions of M2 S4 − and M2 S5 − clusters with water to liberate H2 are exothermic and involve modest free energy barriers. However, the reaction of water with M2 S6 − is highly endothermic with a considerable barrier due to saturation of the local bonding environment. © 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4830096] I. INTRODUCTION

Hydrogen, known as a high energy carrier,1, 2 can be a major replacement for conventional energy sources. The most sustainable way of obtaining hydrogen is from water, recognizing its abundance in nature. There is substantial technological interest in successful utilization of solar energy to decompose water by photolysis.3 The use of photochemical energy to decompose water needs catalysts. Semiconductorbased photocatalysts have caught much attention in this field.4 Particular attention has also been focused on platinumbased surfaces5 and different transition metal oxides,6 known for catalyzing the reaction H2 O(l) → 1/2 O2 (g) + H2 (g); G = +237 kJ/mol. Transition metal oxides (TMOs) are important candidates in this field of photochemical hydrogen evolution. Unfortunately, the band gap associated with many TMO based semiconductors is very high7 and they can only absorb in the UV region. In order to make successful utilization of solar energy, photocatalysts must absorb in the visible region. Transition metal sulfides (TMSs) are excellent candidates and they are being investigated since they have lower band gaps to drive photochemical water reduction. They have generated substantial research focus with widespread catalytic applications in coal liquefaction,8 fuel cells,9 hydrodesulfurization (HDS),10 etc. Characterization of reactive sites on surfaces and their interaction with chemisorbed molecules is one of the most important steps in understanding catalysts. A popular method of designing catalysts is based on the understanding obtained 0021-9606/2013/139(20)/204301/12/$30.00

from gas phase cluster studies. The nature of bonding of adsorbed molecules in catalytically active sites has a lot of similarity with the type of bonding that we observe in clusters. Furthermore, the bonding in crystal defects, frequently known for their adsorption properties, is a local phenomenon that is well represented in a cluster. Intense investigation on small clusters allows us to perform accurate molecular orbital calculations to understand the electronic aspects of such interactions (energies of d-orbitals, interaction due to charge transfers, etc.) that are important in bond activation.11 Although the Group VI metal oxides have been studied extensively recently,12, 13 there is a paucity of detailed information about transition metal sulfides in the literature. Available studies on structure determination of molybdenum and tungsten sulfides are inconclusive.14 In this report, we have initiated a computational investigation on binary molybdenum sulfides and tungsten sulfides. Different possible structures of Mo2 Sn − and W2 Sn − with varying n (from 4 to 6) have been taken into account. We have carried out a careful computational investigation of the electronic structures of these clusters and subsequently explored several possible mechanistic pathways for chemical reaction with water with the aim of liberating hydrogen.

II. COMPUTATIONAL DETAILS

All the calculations have been performed using the B3LYP hybrid density functional.15 The Stuttgart–Dresden

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(SDD) relativistic pseudopotentials were used to replace the 28 core electrons of molybdenum and the 60 core electrons of tungsten. The remaining 14 valence electrons were treated with a double-zeta basis set16 augmented with a set of polarization functions of l+1 angular momentum (ζ = 0.3 for f on Mo and W, ζ = 1.292 for d on O and ζ = 0.650 for d on S) along with a set of diffuse functions needed to describe the extended anionic electron density (s, p, and d functions on Mo and W; s and p functions on O and S).17 These diffuse and polarization functions were added to the SDD basis set for Mo and W, and the D95 basis set for O and S. This augmented basis set is denoted as “SDDplus.” Optimization of geometries and calculation of vibrational frequencies (and zero point energies) were carried out at the B3LYP/SDDplus level of theory. All the transition states were rigorously characterized by the presence of one (and only one) imaginary frequency. Intrinsic reaction coordinate studies have been used to confirm that the key transition states connect to the minima on either side. Single point calculations using augmented triple-ζ quality basis sets16 at the B3LYP level of theory have been performed to get more reliable relative energies. The SDD basis sets for Mo and W were augmented with diffuse s, p, and d functions, two f functions (ζ Mo = 0.338, 1.223, and ζ W = 0.256, 0.825), and 1 g function (ζ Mo = 0.744 and ζ W = 0.627). The large polarized aug-cc-pVTZ basis set was used for O, S, and H in these calculations. The calculated coordinates of all the important structures are provided in the supplementary material.27 The Gaussian program suite18 has been used for all the calculations. The spin multiplicity of the clusters can change during the reaction sequence. High spin clusters that start the reaction on the quartet surface often end up being on the doublet surface. To consider this carefully, we have used the following procedure. Each of the proposed reaction channels has been initiated with stable complexes formed between the reactants starting from the lowest energy structure of the bare cluster. For M2 S4 − , we find that the lowest energy isomers have quartet multiplicities unlike the doublet states found in M2 S5 − and M2 S6 − . All the reaction channels reported here have been considered for both doublet and quartet surfaces. For each of the stationary points in the reported reaction profiles, both the quartet and doublet electronic configuration have been investigated. Interestingly, reaction energy profiles can sometimes show multiple crossovers19 between such surfaces. We generally interpret the very first crossover point as the important one and the rest of the reaction can be thought to proceed on that resulting surface even though one may find additional crossovers. For each of the reaction pathways for M2 S4 − , the first crossover point will be pointed out and discussed in Sec. III. This factor is not important for M2 S5 − or M2 S6 − where no crossover points have been observed in any reaction channel, indicating that the whole reaction proceeds on the doublet ground state surface. Spin orbit corrections can be large for heavy elements (such as Mo or W). They are important for the gas phase atoms in orbitally degenerate states, for linear molecules in , , . . . electronic states, or in the case of a symmetric molecule such as octahedral MF6 − . However, for a larger molecule in an asymmetric environment, as in our clusters

J. Chem. Phys. 139, 204301 (2013)

containing multiple metal atoms and sulfurs, they are not expected to play a significant role. Nevertheless, we note that when the calculated energy ordering between different spin states is small (i.e., on the order of 1–2 kcal/mol as the case of M2 S4 − , vide infra), the ordering could change if more accurate methods are used. To take this into account, we have reported the entire reactive potential energy for the low-lying doublet and quartet states in all cases. III. RESULTS AND DISCUSSION A. Structure

An extensive search for low lying isomers and electronic states has been carried out for three types of clusters (M2 S4 − , M2 S5 − , and M2 S6 − ). The results are summarized in Tables I and II. Structural features of the low lying isomers are discussed in Subsections III A 1–III A 3. 1. M2 S4 −

We find that M2 S4 − clusters (for both Mo and W) have quartet ground electronic states whereas M2 S5 − and M2 S6 − clusters have doublet ground states. This is in accordance with expectations that lower spin states will be more stable as the clusters get close to valence saturation. Optimized lowest energy structures for Mo2 Sn − and W2 Sn − clusters are given in Figures 1 and 2, respectively. The relative energies of other isomers and excited states (within 1 eV of the ground state) are listed in Tables I and II. The naming of the systems has been done following a previously used notation.6(e),12(a),25 It is based on the number of sulfur atoms attached to the two metal atoms. It is denoted by three integers ijk where i represents the number of terminal S atoms on the “left” metal, j represents the number of S atoms bridging the two metal atoms, and k represents the number of terminal S atoms on the “right” metal atom. For

TABLE I. Relative energies and electronic states of low-energy isomers of Mo2 Sn − (n = 4, 5, and 6). Systems

Structure

Symmetry

Term symbol

Relative energy (eV)

Mo2 S4 −

121 121 121 121 220 121 121 220 121 121

C2V C2h C2V C2V C2V C2V C2V C2V C2h C2h

4B

1

4B

g

0.00 0.17 0.32 0.34 0.48 0.49 0.57 0.86 0.98 1.02

221 221 212 212

CS C1 CS C2

Mo2 S5 −

Mo2 S6

−

222 222

D2h C2V

2A 1 2B 1 4B 1 2A 2 2B 2 4A 1 2B u 6A u 2 A

4B

0.00 0.21 0.82 1.38

2A g 4B 1

0.00 1.71

4A 2 A

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TABLE II. Relative energies and electronic states of low-energy isomers of W2 Sn − (n = 4, 5, and 6). Systems

Structure

Symmetry

Term symbol

Relative energy (eV)

W2 S4 −

121 121 121 121 121 121 211 220 121

C2V C2V C2h C2V C2V C2V C1 C2V C2h

4B

1

2B

1

0.00 0.08 0.15 0.17 0.18 0.27 0.62 0.63 0.74

221 221 212 212

CS C2V C2V C2

4A 2 2A 1 4B

0.00 0.34 0.54 1.43

222 222

D2h C2

2A g 4B

0.00 2.09

W2 S5 −

W2 S6 −

4B g 2A 1 2B 2 2A 2 4A 4B

1

4B

u

2 A

example, in Mo2 S4 , “211” denotes the isomer where two terminal S atoms are bonded to the left Mo atom, one is a bridging S atom between the two metals, and one terminal S atom is bonded to the right Mo atom. Similarly in the “121” isomer, one terminal S atom is attached to the each metal center and two S atoms are acting as bridging S atoms. Table I shows that the lowest energy structure of M2 S4 − (for both Mo and W) has two bridging sulfurs with C2V symmetry. The electronic state in both cases is 4 B1 . The corresponding geometries for Mo and W are shown in Figures 1(a)

FIG. 1. Optimized lowest energy structures for (a) Mo2 S4 − (quartet), (b) Mo2 S5 − (doublet), (c) Mo2 S6 − (doublet), (d) Mo2 S4 − (doublet), and (e) Mo2 S5 − (quartet). Black, red, and blue numbers are showing bond lengths, atomic charges, and spin density values, respectively.

FIG. 2. Optimized lowest energy structures for (a) W2 S4 − (quartet), (b) W2 S5 − (doublet), (c) W2 S6 − (doublet), (d) W2 S4 − (doublet), and (e) W2 S5 − (quartet). Black, red, and blue numbers are showing bond lengths, atomic charges, and spin density values, respectively.

and 2(a). We denote this as a cis-structure since the terminal S-atoms on both metal atoms are pointed in the same direction. We also have a low-lying trans isomer with C2h symmetry (4 Bg electronic state) lying 0.17 eV above the cis-structure for Mo2 S4 − (0.15 eV for W2 S4 − ). A doublet spin state (121) lies 0.32 eV and 0.08 eV above the ground state for Mo2 S4 − and W2 S4 − clusters, respectively.20 One can easily notice some significant structural differences between the lowest quartet and doublet electronic geometries for M2 S4 − clusters. The metal-metal bond distance is substantially reduced on going from high spin state to low spin state (Figs. 1(a) vs 1(d) for Mo2 S4 − , and Figs. 2(a) vs 2(d) for W2 S4 − cluster). Merely looking into the geometry of the most stable doublet 121 structures in Figures 1(d) and 2(d), we can conclude that there is significant amount of metal-metal bonding as revealed by the very short bond distance between metal atoms. However, Figs. 1(d) and 2(d) show that the structure is significantly strained due to the projection of two bridge bonds downwards distorting the planarity of the four-membered ring whereas in the quartet state (Figs. 1(a) and 2(a)) the bridging sulfide bonds are quite open and nearly hold the planarity of the four-membered ring. This rationalizes the greater stability of high spin state for M2 S4 − clusters. The spin density values also show interesting differences between the quartet and doublet states. For M2 S4 − cluster in its high spin state, the spin density values (Figs. 1(a) and 2(a)) over the metal centres are very high, indicating almost all the three unpaired spins are located on the metal centres. But the scenario is different in the case of doublet electronic state (Fig. 1(d)) where the unpaired spin density is almost equally distributed over the two metal centres along with the terminal sulphur atoms. It is important to point out that similar systems have been studied previously14(f) and the trends observed in the

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structural parameters are similar. As in the case of previous work,14(f) our current investigation shows that the M=S bond lengths in terminal S atoms do not change with the number of S atoms in the cluster (M=S bond lengths in M2 S4 − and M2 S5 − occur in the narrow range between 2.16 Å and 2.17 Å). However, the M−M bond length increases with the number of S atoms in the cluster (as also pointed out in Ref. 14(f)). The metal-metal bonding in Mo2 S4 − clusters depends on the electronic states. For example within the “121” family, M–M bond distances strongly depend on the electronic state and range from 2.2 Å to 2.7 Å for Mo (e.g., 2.2 Å for the 2 A1 state, 2.3 Å for the 2 B1 state and 2.7 Å for the 4 B1 ground state). For comparison, the Mo–Mo distances can occur over a fairly wide range: 1.96 Å in sextuply bonded21 diatomic Mo2 , ∼2.2 Å in triply bonded22 complexes, 2.73 Å in metallic Mo, and 3.16 Å in layered MoS2 .23 This suggests that there is significant contribution of M–M direct bonding in M2 S4 − , but more prominently in the excited states. On moving to higher stoichiometry clusters (M2 S5 − and M2 S6 − ), there is very little direct M–M bonding and the M–M interaction is mostly dominated by M−S−M bridging sulfur bonds. For example, the M−M bond length increases from 2.7 Å to 3.0 Å on going from Mo2 S4 − to Mo2 S5 − (and 2.8 Å to 3.1 Å on going from W2 S4 − to W2 S5 − ). We have also compared the structural features of our calculated sulfide cluster anions with the corresponding Mo and W oxide cluster anions having the same stoichiometry. Wang et al.24 and Yoder et al.25 have investigated the geometries and electronic structures of W2 On − and Mo2 On − clusters, respectively. On comparison between M2 S4 − and M2 O4 − clusters, the major difference is in the relative position of the 121 and 211 isomers. For the sulfides considered in this study, we find that the doublet states of the 211 isomers are not stable and convert spontaneously to the 121 isomers. The migration of a terminal sulfur atom to a bridging position occurs without an activation barrier. For the corresponding quartet states of the sulfides, we see some slight differences between the two metals. No 211 minimum was found on the quartet surface for Mo2 O4 − , again converting without a barrier to the 121 isomer. However, the 211 isomer is a shallow minimum for W2 O4 − , though quite high in energy (>0.5 eV relative to the ground state). As expected, the activation barrier for conversion to the 121 isomer is very small ( Mode 1 > Mode 3 >> Mode 4 for Mo, and Mode 1 > Mode 2 > Mode 4 ≈ Mode 3 for W, respectively. While the differences in the barriers are small, this indicates that while bridging sulfur atom is preferred over the terminal one for Mo2 S4 − , opposite trend is observed for W2 S4 − . The trends parallel the stabilities of the corresponding interaction complexes: Complex B is more stable for Mo while Complex A is more stable for W. This is understandable for Mo since bridging S atoms for Mo2 S4 − bear higher negative charges than the terminal ones (Fig. 1). While the charges are similar for W, the relative barriers for W2 S4 − suggest a higher reactivity for the terminal W−S bond. This is interesting since it differs from our previous observation12(b) in tungsten oxides where the bridging atom was more reactive. The results suggest that subtle changes can make significant differences when the energy differences are small. It is also interesting to notice the energetic barrier associated with Mode 4 (Fig. 7) reaction pathways for Mo and W, leading to the formation of the metal hydride bond. The barrier for W is significantly smaller and the resulting intermediate more stable. The rationalization for this observation is that W, being a third row transition metal, is more electropositive than Mo and hence shows greater tendency for oxidation. As a result, the metal hydride bond between W−H will be more ionic (hence stronger) than Mo−H. In other words, we can say that H will be more hydridic in W−H bond than in Mo−H bond. The M−H bond strengths occur in the following ranges: Mo−H (65–75 kcal/mol) < W−H (70–80 kcal/mol).26

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TABLE III. Barrier heights and corresponding intermediate energies (kcal/mol) for various modes of water reaction to M2 S4 − (M = Mo and W) cluster in terms of energy at 0 K. Cluster

Modes

Complex

TS1

Intermediate-1

TS2

Intermediate-2

TS3

Product

Mo2 S4 −

I II III IV

−8.8 (A) −10.0 (B) −3.8 (C) −1.6 (D)

3.2 1.7 5.1 12.3

− 23.3 − 15.6 − 29.1 − 52.9

− 2.3 − 3.1 − 10.1 ...

− 27.4 − 52.9 − 52.9 ...

2.9 − 14.1 − 14.1 − 14.1

− 34.8 − 34.8 − 34.8 − 34.8

W2 S4 −

I II III IV

−7.3 (A) −6.3 (B) −5.6 (C) −3.1 (D)

1.2 3.6 5.3 5.2

− 28.7 − 22.3 − 24.9 − 67.7

− 14.4 − 10.9 − 23.6 ...

− 45.7 − 67.7 − 67.7 ...

− 13.5 − 28.8 − 28.8 − 28.8

− 50.7 − 50.7 − 50.7 − 50.7

Step 3: H atom migration Initial water addition in most cases leads to an intermediate containing a hydroxyl group as well as a thiol group. To proceed with the aim of eliminating hydrogen from this structure, two factors are important: the distance between the H-atoms and the atomic charge on each of them. Ideally, the H-atoms must possess atomic charge density of opposite signs making their interaction favorable. The intermediate from Step 2 does not qualify for either of these. To make the two hydrogen atoms interact, we propose migration of the Hatom of the thiol group to the nearest metal center to make a metal hydride bond. This will basically meet both the requirements prior to successful hydrogen elimination. Table III shows the barriers for hydrogen migration (TS2, kcal/mol), the energy of the intermediates (Int-1) from Step 2 leading to the transition state, and the energy of the hydride intermediates (Int-2) formed in this step. Again, Wclusters show lower energetic barriers than Mo-clusters due to the formation of stronger hydride bonds. The smooth mobility of H-atom inside the cluster is not unusual and very easily accomplished. Since we assume a gas phase environment under collision-free conditions, the energy gained during an exothermic step is not lost; rather it is available for the subsequent steps. For example, the initial addition of water in Mode 1 injects the cluster with 23.3 kcal/mol (Mo2 S4 − ) and 28.7 kcal/mol (W2 S4 − ) of energy. Since the hydrogen migration barriers are smaller than this energy gained, the H-atom can easily roam around inside the cluster to find a chemically suitable place. It is interesting to note that the H-atom migration is easiest in Mode 3 since it occurs at a less coordinated metal center. Finally, as seen from the reaction profiles Step 3 is highly exothermic in all cases. At this stage of the reaction, we again refer to the spin crossover. For Mo2 S4 − in Mode 1 and Mode 2 reaction path-

ways, spin crossover happens only after the Int-1 is formed (i.e., at step 3). Step 4: Elimination of molecular hydrogen and formation of product Elimination of molecular hydrogen largely depends on the interaction of the two H-atoms. As mentioned earlier, the separation between two H-atoms and the charge density on them are the guiding factors for the desired occurrence. In this report, we propose two different unique ways of hydrogen elimination. The first (Type 1) involves the pair of hydrogen atoms where one of them comes from either a hydroxyl group or a thiol group and the other one is a metal hydride. This has been seen previously in the case of the reactions of the corresponding oxides,12(b),12(e) and is seen in most of the reactions in this study as well. Table III shows the barriers (kcal/mol) and corresponding products for this step. This shows that energetic barriers for H2 elimination are much lower than the barriers for the previous reaction steps for all clusters. A second, more unusual, type of hydrogen elimination is also seen in some cases. In type 2, one of the H-atoms is from a hydroxyl while the other is from a thiol group. Type 2 hydrogen elimination is illustrated in Mode 1 channel (shown as Mode 1A) (Fig. 5(b)). It important to point out here is that even with the lack of structural prerequisites elimination of H2 is possible in Mode 1A, perhaps due to the fact that the positive charge density on H-atom of the thiol group is quite low. However, Type 2 barriers are still larger than those in Type 1. 2. M2 S5 −

The reactivity order for M2 S5 − (Table IV) is slightly different from the trend seen in M2 S4 − . In this case, the bridged

TABLE IV. Barrier heights and corresponding intermediate energies (kcal/mol) for various modes of water reaction to M2 S5 − (M = Mo and W) cluster in terms of energy at 0 K. Cluster

Modes

Complex

TS1

Intermediate-1

TS2

Mo2 S5 −

I II III

− 12.7 − 12.5 − 12.5

0.7 − 1.4 0.2

− 28.3 − 18.7 − 28.9

− 7.4 − 7.2 12.7

W2 S5 −

I II III

− 11.9 − 11.1 − 11.1

0.8 − 0.5 1.9

− 24.3 − 19.6 − 28.2

− 13.2 − 6.6 7.0

Intermediate-2

TS3

Product

− 13.4 − 13.4 − 14.3

8.1 8.1 11.6

− 30.1 − 30.1 − 30.1

− 27.5 − 27.5 − 25.2

− 6.6 − 6.6 − 2.1

− 43.7 − 43.7 − 43.7

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S atom is the more reactive center for both metals due to its higher charge accumulation (Fig. 1(b)) and is similar to the behavior in the corresponding oxides.12(b) Figs. 8 and 9 show Mode 1 (terminal S attack) and Mode 2 (bridged S attack) reaction pathways, respectively, for M2 S5 − . Green and black solid lines refer to the mechanism where the hydride transfers from the terminal thiol group at Step 3 for Mo and W, respectively. To explore additional possibilities for H-migration, we have also attempted another route involving migration of the hydride from terminal or bridged hydroxide to the metal atom at Step 3. This is also shown in Fig. 8 and Fig. 9 (Blue and red solid lines refer to this mechanism for Mo and W, respectively). This obviously increases the energetic barrier for Step 3 (compared to the route where hydride migrates from thiol to the metal center) since hydroxyl has a higher detachment energy. Table IV show the barriers and corresponding intermediates for the different steps. The low reaction barrier for initial water attachment suggests that the reaction will go through the Mode 2 pathway. In the case of W2 S5 − , low energy pathways are available for the elimination of hydrogen via the modes discussed here, leading to W2 S5 O− . However, for Mo2 S5 − cluster, there appears to be no low energy pathway for either hydrogen migration or H2 elimination involving the hydroxide. Thus, the reaction may lead to a trapped Step 2 intermediate or may be unreactive if the reverse reaction occurs. Mode 3 reaction pathways for M2 S5 − are shown in Fig. S1 and involve significantly higher barriers. Though the ground state structures of W2 S5 − and W2 O5 − cluster12(b) are different, we compare the water reactivity between these two types of clusters to give a broad overview of the similarities and differences. Mayhall et al.12(b) observed that for the W2 O5 − cluster, most of the reaction proceeds through the bridging oxygen center and subsequently trapped as a W2 O6 H2 − intermediate due to the large reaction barrier associated with the H2 elimination step. This is different from the reaction energy profiles for W2 S5 − . Our study shows that lower reaction barriers are available in the case of W2 S5 − for H2 elimination. If we compare all the common water attachment modes, we notice that the initial water attachment is barrierless for M2 S5 − , whereas modest barriers are observed for M2 S4 − . This is somewhat surprising initially since the less saturated cluster may be expected to undergo reaction more readily as indicated from the decrease (Table V) in free energy. However, we can understand this on the basis of the charges on

the target metal center. When the water molecule approaches the clusters, the equal charge distribution on both metal centers in M2 S4 − makes it less reactive than for M2 S5 − cluster where only the lower coordinated metal atom is exclusively available to make a metal bound hydroxide bond. It is clear that difference in metal coordination numbers can effectively alter the water reactivity in such small clusters. 3. M2 S6 −

In this cluster, both metal centers are highly coordinated. Hence it is difficult for water to have an orientation near this cluster to form an appropriate complex that can lead to a metal-bound hydroxide with a low energy barrier. Table VII also shows that reaction with M2 S6 − cluster is highly endothermic and hence very unlikely to occur. It is important to point out here is that neutral M2 O6 cluster can generate OH groups in the form of a M2 O6 H4 as pointed out in Ref. 12(e). 4. Free energies at 298 K

Our discussions so far have been in terms of the energies (including zero point corrections) at 0 K. It is known that there is a significant entropic penalty in such bimolecular reactions at higher temperatures. To consider this, we have computed the free energies (298 K) for all the species within the standard harmonic oscillator-rigid rotor approximations (Tables V and VI). As expected, the free energies are higher by 7–10 kcal/mol for most of the reaction steps. The free energy barrier for the rate-determining step appears to be around 7 kcal/mol, fairly significant at 298 K. For comparison, the barriers for W2 S4 − are higher by about 5 kcal/mol than the corresponding barriers for W2 O4 − seen in our previous study,12(b) suggesting that the reactions for the sulfides may be slower. Many of the initial complexes discussed in the paper (Tables V and VI) are not bound on the free energy scale at 298 K. This is due to the entropic penalty of 7–8 kcal/mol (at 298 K) as the cluster and the water molecule interact and form a complex. In such cases, the reaction directly proceeds via the transition state. However, this entropic penalty is temperature dependent, and the complexes are bound on the free energy scale at 0 K (i.e., on the enthalpy scale). Thus, the initial complexes will play a role at lower temperatures. Since two infinitely separated reactant molecules come together to form

TABLE V. Barrier heights and corresponding intermediate energies (kcal/mol) for various modes of water reaction to M2 S4 − (M = Mo and W) cluster in terms of free energy at 298 K. Cluster

Modes

Complex

TS1

Intermediate-1

TS2

Intermediate-2

TS3

Product

Mo2 S4 −

I II III IV

1.7 1.1 6.8 8.8

10.6 7.3 14.1 20.8

− 15.3 − 6.6 − 21.0 − 44.1

5.2 4.5 2.3 ...

− 16.7 − 44.1 − 44.1 ...

10.8 − 6.9 − 7.0 − 7.0

− 36.7 − 36.7 − 36.7 − 36.7

W2 S4 −

I II III IV

3.4 0.5 7.6 9.3

7.7 11.3 13.7 13.8

− 20.5 − 12.8 − 16.9 − 60.2

−6.4 −2.3 −16.7 ...

− 34.9 − 60.2 − 60.2 ...

− 5.5 − 21.8 − 21.8 − 21.8

− 52.5 − 52.5 − 52.5 − 52.5

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TABLE VI. Barrier heights and corresponding intermediate energies (kcal/mol) for various modes of water reaction to M2 S5 − (M = Mo and W) cluster in terms of free energy at 298 K. Cluster

Modes

Complex

TS1

Intermediate-1

Mo2 S5 −

I II

1.2 − 1.0

8.6 7.1

− 19.3 − 9.3

0.3 0.9

W2 S5 −

I II

− 0.1 − 0.0

9.1 7.0

− 15.4 − 10.1

− 5.3 2.1

the complex, the structure of the complex contains important information on the direction of approach related to the long range interactions between the species. Moreover, since the molecular complex prepares the system to reach the activation barrier of the corresponding transition state, the complex often has significant amount of structural similarity with the transition state.12(b) Thus, while the population of such initial complexes will be very low at 298 K, they have significance at lower temperatures in “preparing” the reactant molecules to go over the transition state to reach the products. At higher temperatures, the role of the initial complex is minimal. Overall, for most of the reaction modes for M2 S4 − cluster, the rate determining step is the first barrier corresponding to TS1, i.e., the initial proton transfer step. The reaction is then governed by this barrier since the succeeding reactions can occur without any additional energy as long as the energy is not dissipated into vibrational modes or by collisions. However, for Mode 1 channel, TS3 is nearly isoenergetic with TS1 on the free energy scale at 0 K (2.9 kcal/mol vs 3.1 kcal/mol) or at 298 K (10.8 kcal/mol vs 10.6 kcal/mol). Thus, unlike the other reactions, TS3 will also govern this Mode 1 reaction along with TS1.

TS2

Intermediate-2

TS3

Product

− 4.3 − 4.3

13.9 13.9

− 32.2 − 32.2

− 18.0 − 18.0

0.5 0.5

− 45.7 − 45.7

1. Intermediate-1 (involving hydroxyl (OH) and thiol (SH) groups). 2. Intermediate-2 (involving metal hydride and hydroxyl groups). Since we are considering different modes of water attachment based on the position of the water molecule around the substrate, we can analyze various bonding patterns of these intermediates in terms of oxidation states on the metal centers. We will discuss intermediate-2 first. Two unique structures for intermediate-2 have been proposed which can be categorized in the following types. Type A: Both the metal hydride and metal hydroxide group involves the same metal (Mode 1 reaction for M2 S4 − clusters). Type B: Metal hydride and metal hydroxide groups involve two different metal centers (Mode 2, 3, and 4 reactions for M2 S4 − clusters). Both type A and type B intermediates are shown in Fig. 10 along with the formal oxidation states on the metal centers. In type A intermediate-2, one metal is bonded to three different sulfur atoms (two bridging S atoms are bonded to the metal with single bond character and one terminal S atom

C. Oxidation states on the metal centers

Since we are exploring the chemistry of binary transition metal sulfide clusters, it is useful to focus on the formal oxidation states on the metal centers. Formal oxidation states on both metal centers along various points on the PES are shown in Figures 10 and 11. It is interesting to note that the metal centers in the M2 S4 − clusters undergo changes in formal oxidation states throughout the PES. In Sec. III C, we discuss this aspect in detail explaining how it can be used to understand the stability factors of different reaction intermediates. We can classify the intermediates in all the reaction profiles into two different categories. TABLE VII. Free energies of the reactions between M2 Sx − (M = Mo and W, X = 4, 5, and 6) cluster and H2 O. Reaction Mo2 S4 − + H2 O = Mo2 S4 O− + H2 Mo2 S5 − + H2 O = Mo2 S5 O− + H2 Mo2 S6 − + H2 O = Mo2 S6 O− + H2 W2 S4 − + H2 O = W2 S4 O− + H2 W2 S5 − + H2 O = W2 S5 O− + H2 W2 S6 − + H2 O = W2 S6 O− + H2

G (kcal/mol) − 37.7 − 32.2 30.4 − 53.7 − 45.2 22.0

FIG. 10. Oxidation states on the metal centers for the different species along the potential energy surface for the reaction of water with the M2 S4 − cluster.

204301-11

A. Saha and K. Raghavachari

J. Chem. Phys. 139, 204301 (2013)

IV. CONCLUSIONS

In this report, we have carried out a computational investigation to find the low lying structures of Mo and W sulfides (M2 Sx − , x = 4–6). The factors that determine the stability of the clusters with different spin multiplicities have been analyzed. Subsequently, a detailed mechanistic study has been performed to explore the water reactivity of these metal sulfides. We observe that all the metal sulfides have the doublet ground electronic state except for M2 S4 − clusters, which have quartet ground electronic states. All the lowest energy isomers for Mo and W sulfides have two bridging sulfide bonds, notably different from the corresponding metal oxides19, 20 in some cases. This is partly due to the fact that the M–O–M angle in the metal oxides is much more strained than the M– S–M angle in the metal sulfides. Mo–S bond lengths are significantly larger than the Mo–O bond lengths, allowing the metal sulfides to have more strain free bridging sulfur bonds with less repulsion. Since the ground state structures for the oxides and sulfides are different in many cases, we do not indulge in direct comparison of different modes of water reactivity associated with each type of clusters. Based on our computational mechanistic study, the following conclusions can be highlighted:

r In all the reaction schemes, both the metal atoms (Mo FIG. 11. Oxidation states on the metal centers for the different species along the potential energy surface for the reaction of water with the M2 S5 − cluster.

with double bond character), resulting in a +4 oxidation state, and the other metal atom has a +6 oxidation state hosting both the hydride and hydroxide groups. However, in type B, both metal centers are in the same oxidation state (+5). One can easily observe that type B intermediate-2 (Mode 2, 3 and 4) is significantly more stable than type A intermediate-2 (Mode 1). This confirms our previous observation13(h) that the most competitive structures of transition metal oxo-species often involve both metal centers in the same oxidation states. We can also classify intermediate-1 into two different unique categories. Type A: Both thiol (SH) group and hydroxyl group are bonded to the same metal atom (Mode 1). Type B: The thiol (SH) group and hydroxyl group are bonded to two different metal centers (Mode 3) or it is a bridging thiol (SH) group (Mode 2). Both types are shown in Fig. 10. In type A intermediate-1, both metals are in same oxidation state whereas in type B, metals are present in different oxidation states. Again, type A intermediate-1 (Mode 1) is relatively more stable than type B intermediate-1 (Mode 2 and 3) in their respective electronic states. In the case of M2 S5 − clusters (Fig. 11), both Mode 1 and Mode 2 intermediates show similar oxidation states on the metal centers at similar points of PES except for intermediate1. Mode 1 involves type A internediate-1 whereas Mode 2 shows type B intermediate-1. Both Mode 1 and Mode 2 involve type A intermediate-2.

r

r

r

r

and W) follow the same trend of reaction energy profiles. But irrespective of the proposed modes of reaction channels, W always found to bear the lower energy barriers and larger exothermicities, attributed to the stronger bonds involving W due to its position in the periodic table. While both metals show the same trends in the reaction profiles, they can differ in the rate determining steps. Our study indicates that for M2 S4 − (M = Mo and W) clusters and W2 S5 − clusters the rate determining step is the initial water addition, while elimination of molecular H2 determines the rate of the reaction for Mo2 S5 − cluster. Our study shows that, for W2 S4 − , terminal sulfur attack is more favored than the bridge sulfur atom, whereas for Mo2 S4 − and M2 S5 − (M = Mo and W) cluster, bridging sulfur atom is found to be the most potential reaction center for initial water attack. M2 S6 − does not undergo any reactions with water. There are significant differences in the reactivity of Mo2 S5 − and W2 S5 − . While W2 S5 − can lead to W2 S5 O− with low barriers, Mo2 S5 − may be trapped as Mo2 S5 OH2 − since it has significantly higher barriers. While the reaction energy barriers are low at 0 K, the free energy barriers at 298 K for the dissociative addition of water are about 7 kcal/mol or larger, suggesting that the reactions may be slow.

ACKNOWLEDGMENTS

This work was supported in its entirety by the Department of Energy Grant No. DE-FG02-07ER15889.

204301-12

A. Saha and K. Raghavachari

APPENDIX: GEOMETRIES AND ENERGIES

Cartesian coordinates of all the calculated structures and transition states are provided in the associated file.27

1 J.

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