ZHANG Xiao-Fei LIU Xiu-Juan XU Ruo-Nan WU Ni HUANG Xin WANG Bin

(Department of Chemistry, Fuzhou University, Fuzhou 350116, China)

1 INTRODUCTION

Molybdenum sulfide has intensely caught people's eyes due to their wide applications in the fields of mechanical treatments, catalysts, energy materials and so forth[1-8].In the case of catalysts, it is known that molybdenum sulfide can serve as a promising low-cost alternative to platinum or other noble metals catalyst in hydrogen evolution reaction(HER)[9-14].Additionally, MoS2-based catalysts have been widely used in the process of petroleum refining[15], including the hydrodesulfurization (HDS)and hydrodenitrogenation (HDN) reactions.Meanwhile, considerable attention has been paid to study the active sites in these catalysts[16-25].It is normally accepted that the sulfur vacancies (or coordination unsaturated sites (CUS)) of MoS2are the key active centers[26,27].However, Besenbacher et al.[22]also put forward that the specific brim sites without sulfur vacancies are also responsible for the HDS activity.Furthermore, Vrubel et al.[11]showed that the reduced molybdenum sulfides containing the disulfide ligands appeared to be catalytically active.Several molybdenum complexes which contain various S2ligands have been synthesized recently,which were considered to be able to mimic the MoS2edge sites for the catalytic hydrogen generation[28-31].Despite the progressive work, more detailed studies on the active sites of molybdenum sulfide catalysts are still required.

Previously, many studies have been focused on the synthesis and characterization of a variety of molybdenum polysulfido complexes and their precursors in the condensed phase, and various disulfide species were obtained in these complexes[28-35].Among them, the [Mo2S7]2?anion was found to possess a terminal S22?ligand[32].The [Mo2S8]2?was considered to own two terminal S22?ligands[33].The[Mo2S12]2?was reported to contain four terminal S22?and two bridging S22?ligands[30].The [Mo3S13]2?was predicted to have three bridging S22?and three terminal S22?ligands[29].These molybdenum complexes containing the persulfido (S22?) ligands may lead to the corresponding complexes with supersulfido (S2?) ligands via futher electron transferation,but less is known about their supersulfido complexes[36-40].As is known to all, gas-phase clusters can serve as effective molecular models gaining microcosmic understanding of the sophisticated surface structures and the catalytic processes at the molecular level[41-45].Theoretical calculations have played an indispensable role in describing the accurate structure and properties of gas-phase clusters[46].Over the past few years, considerable efforts have been devoted to studying the mono- and multinuclear molybdenum sulfide gas-phase clusters[47-60].Infrared spectra combined with DFT calculations of neutral mono-nuclear MSn(M = Cr, Mo, W; n = 1～3) clusters have been studied by Andrews's group[59].Joint experimental photoelectron spectra and theoretical investigations on a variety of mono- and multinuclear molybdenum sulfide clusters have also been reported by Gemming et al.[53,57,58].Jiao et al.presented the structure and reactivity of Mo3S9cluster which can be taken as a model for amorphous molybdenum sulfide MoS3[54].An ab initio study on the structural stability of Mo-S clusters and the size specific stoichiometries of magic clusters was reported by Murugan et al.[56], wherein Mo2S5consisting of two bridging S and three terminal S atoms was expected to be the magic cluster.In spite of these efforts, the systematical theoretical investigations on the gas-phase molybdenum sulfide clusters are still required.

In our previous work[61,62], we have reported a theoretical study on the mono-nuclear molybdenum sulfide clusters, MoSn?/0(n = 1～6).To mimic the geometric and electronic properties of molybdenum sulfide surfaces and defects, larger MoxSyclusters in size may be interesting.In the present work, extensive density functional theory (DFT) and coupled cluster theory (CCSD(T)) calculations were performed to elucidate the structural and electronic properties of a range of di-nuclear molybdenum sulfide clusters, Mo2Sn–and Mo2Sn(n = 4～8).The current study represents our continuous research interest in various clusters aiming at providing well-defined molecular models for bulk surfaces and catalysts[61-66].According to our calculations, a behavior of structural evolution was found with the exception of neutral Mo2S8.The neutral Mo2S8can be viewed as replacing two of the terminal S atoms in Mo2S6by the same number of S2units.Interestingly, diverse disulfur ligands, including the supersulfido(S2?) ligands, emerged in sulfur-rich clusters Mo2Sn?/0(n = 7, 8).It was found that the disulfur species may have a key impact on the catalytic activity[67-69].Our calculations showed that the reduced reactions for removing one sulfur atom from the sulfur-rich clusters were spontaneous, whereas the reactions were nonspontaneous if the sulfur atom was removed from the sulfur-deficient clusters.The results suggested that the S2units may play an important role in removing the sulfur atoms from the edge sites of fresh MoS2catalysts.

2 COMPUTATIONAL METHODS

The calculation details for this study are similar to our earlier studies on mono-nuclear molybdenum sulfide clusters, MoSn?/0(n = 1～6)[61,62].Density functional theory (DFT) calculations employing the B3LYP hybrid functional[70-72]were carried out using Gaussian 03 program[73].B3LYP was widely used in quantum chemistry[74].Furthermore, B3LYP had been applied in the other Mo-S systems, which showed good agreement with the experimental data[51,54,59].Additionally, B3LYP also gave reasonably good results which were compared to the available experimental data in our previous work[61-66].As discussed below, we used the results with B3LYP functional for further discussion.A host of initial structures considering different spin states and geometric symmetry were evaluated, and the search for the most stable structures was first performed using the triple-ζ valence plus polarization (def2-TZVP) basis set[75-77]and the corresponding Stuttgart effective core potential for Mo[78](denoted as L-BS hereafter).Then the selected low-lying isomers (?E ＜ 0.50 eV) were further re-optimized at the B3LYP level with the larger basis sets, i.e., the Stuttgart relativistic small core basis set and efficient core potential[78,79]augmented with two f-type and one g-type polarization functions (ζ(f) = 0.338, 1.223; ζ(g) = 0.744) for molybdenum[80]and the aug-cc-pvtz basis set for sulfur and hydrogen[81-83](denoted as H-BS hereafter).Scalar relativistic effects were taken into account via the quasi-relativistic pseudo-potentials.Vibrational frequency was calculated at the same level of theory to confirm that the reported minima have no imaginary frequency.The relative stabilities of several energetically close-lying isomers (?E ＜0.40 eV) were further distinguished with the help of higher-level CCSD(T)[84-88]single point calculations with the H-BS basis sets at the B3LYP optimized geometries.Vertical electron detachment energies(VDEs) were calculated on the basis of the generalized Koopmans’ theorem[89]which had been described detailedly in our previous studies[61-66].All DFT calculations were performed using the Gaussian 03 software package.The CCSD(T) calculations were performed with the MOLPRO 2010.1 package[90].The frontier molecular orbitals were visualized using the VMD software[91].

3 THEORETICAL RESULTS

The optimized geometries for the ground-state and selected energetically low-lying isomers of Mo2Sn–and Mo2Sn(n = 4～8) at the B3LYP/H-BS level of theory are displayed in Figs.1～5.Their relative energies including those isomers within 0.40 eV at the B3LYP/H-BS level together with the results of single-point CCSD(T) calculations are collected in Table 1.Alternative optimized results at the B3LYP/L-BS level for Mo2Sn?/0(n = 4～8) are given in the Supporting Information (Figs.S1～S5).

Fig.1. Optimized structures for Mo2S4 and Mo2S4?.The bond lengths are in angstroms (?)

Fig.2. Optimized structures for Mo2S5 and Mo2S5?.The bond lengths are in angstroms (?)

Fig.3. Optimized structures for Mo2S6 and Mo2S6?.The bond lengths are in angstroms (?)

Fig.4. Optimized structures for Mo2S7 and Mo2S7?.The bond lengths are in angstroms (?)

Fig.5. Optimized structures for Mo2S8 and Mo2S8?.The bond lengths are in angstroms (?)

3.1 Sulfur-deficient clusters:Mo2Sn and Mo2Sn– (n = 4, 5)

Previously, the tribridged structure with three bridging S atoms and the dibridged structure with two bridging S atoms and one terminal S atom were reported to be the possible ground states of the Mo2S3cluster[56,58].To search for the ground states of Mo2S4?/0, a host of initial structures were taken into consideration, including the above mentioned dibridged and tribridged strucutres.Based on the calculations, a nonplanar dibridged structure (Cs,3A'')is shown to be the lowest-energy structure of Mo2S4(Fig.1a).Another triplet state (3A2) with higher symmetry C2vis only 0.04 eV (Fig.1b) higher in energy.The corresponding quintet state (5B1) with C2vsymmetry is located to be 0.15 eV (Fig.1c)higher in energy.The quintet state (5Bg) with C2hsymmetry is 0.21 eV (Fig.1d) higher in energy.The difference between these two quintet states is that two terminal S atoms in the former show a syn relationship, whereas the latter has a anti configuration.In addition, the triplet state (Cs,3A'') with the anti configuration is 0.30 eV (Fig.1e) higher in energy.It seems that the syn configuration is more stable than the anti configuration.The previous studies[47,48,56,58]have also supported the dibridged structure which has the syn configuration to be the ground state of Mo2S4.For the anionic species, the dibridged structure (C2v,4B1) with syn configuration is found to be the lowest-energy structure of Mo2S4?(Fig.1g).Another two dibridged isomers, C2h(4Bg)and C2v(2B1), are located to be 0.18 eV (Fig.1h) and 0.34 eV (Fig.1i) higher in energy, respectively.Other optimized isomers for both the neutral and the anion are much higher in energy and thus not listed in the current paper.More optimized structures at the B3LYP/L-BS level are available in the Supporting Information (Fig.S1).

Starting from the ground states of Mo2S4?/0clusters, extensive structural searches revealed the singlet (Cs,1A') to be the ground state of Mo2S5(Fig.2a).It can be viewed as adding a terminal S atom to the dibridged Mo2S4.The previous studies by Murugan et al.[56]and Gemming et al.[58]also supported our results.The corresponding triplet state (Cs,3A') is 0.17 eV (Fig.2b) higher in energy.For the anionic Mo2S5?, the ground state (Fig.2c) is found to be a doublet state (Cs,2A'), whose geometry is similar to that of the neutral ground state.A quartet (C2v,4A2)is located to be 0.22 eV (Fig.2d) above the ground state.

3.2 Stoichiometric clusters: Mo2S6 and Mo2S6–

The ground state of Mo2S6is identified to have C2v(1A1) symmetry (Fig.3a).It can be deemed as adding a terminal S atom to the Mo2S5ground state.Each Mo atom in Mo2S6is tetra-coordinated with two terminal S atoms and two bridging S atoms.This result is in consistent with the previous study by Gemming et al.[58].It should be mentioned that the isomer with a terminal S2unit was expected to be the most stable structure of Mo2S6by Murugan et al.[56].But this isomer is less stable (＞ 0.50 eV) than the structure in Fig.3a according to our calculation(Fig.S3).For the anionic Mo2S6?, an open-shell (2Ag)structure with D2hsymmetry is found to be the ground state (Fig.3b).

3.3 Sulfur-rich clusters:Mo2Sn and Mo2Sn– (n = 7, 8)

To our knowledge, no other computational studies have been reported for the gas-phase Mo2S7?/0and Mo2S8?/0clusters.On the basis of our calculations on Mo2S6?/0, various initial configurations with different spin multiplicities were studied in search of the ground states of Mo2S7?/0.As shown in Fig.4a, the lowest-energy structure of Mo2S7is predicated to be closed-shell (1A) with C2symmetry wherein a bridging S2unit appears.It can be regarded as replacing one of the bridging S atoms in Mo2S6by a bridging S2unit.The S?S bond length of the S2unit in Mo2S7(Fig.4a) is 2.086 ?.A triplet state (Cs,3A")with a terminal S2unit (Fig.4b) is located 0.26 eV above the ground state.However, this structure becomes the ground state of the Mo2S7?anion (Fig.4d),whereas the structure with a bridging S2unit (Fig.4e)is 0.39 eV higher in energy.The Mo2S7?ground state can be seen as replacing one of the terminal S atoms in Mo2S6?by a terminal S2unit.The terminal S2ligand in Mo2S7?(Fig.4d) is attached in a side-on fashion, and the corresponding S?S bond length is 2.097 ?.

In the case of Mo2S8?/0, we found several closelying isomers of Mo2S8?/0near the lowest-energy structure.As shown in Fig.5a, the ground state of Mo2S8is found to be3B2state with C2vsymmetry,which can be viewed as replacing two terminal S atoms in Mo2S6by two terminal S2units in a syn configuration.The S–S bond lengths in the S2units are calculated to be 1.999 ?, and the Mo–S2bond lengths are 2.468 ?.Another triplet state (C2h,3Bu)which also has two terminal S2ligands but in a anti configuration is 0.20 eV (Fig.5b) above the ground state.In addition, the isomer which can be seen as replacing the remaining bridging S in Mo2S7by a bridging S2unit is much higher in energy (＞ 0.5 eV;Fig.S5).For the anion, the most stable structure of Mo2S8?(Fig.5c) is a doublet state with C2vsymmetry, in which two terminal S2ligands are in a syn relationship as in the case of the neutral.The anti isomer (C2h,2Bg) is shown to be 0.06 eV (Fig.5d)higher in energy.Additionally, the isomer which contains a terminal S3ligand is 0.11 eV (Fig.5e)higher in energy.Similar with the results of Mo2S4?/0,the calculations showed that the syn configuration seems to be more stable than the anti configuration for Mo2S8?/0.

3.4 CCSD(T) single-point calculations for low-lying structures

The low-lying isomers of Mo2Sn(n = 4～8) and their anion species (within 0.40 eV at the B3LYP/HBS level) were further evaluated using higher level single point CCSD(T) calculations at the B3LYP geometries.The relative energies of single point CCSD(T) calculations are summarized in Table 1.As a whole, the results of single point CCSD(T)calculations are in good line with that of DFT/B3LYP calculations, except for the neutral Mo2S4.According to the CCSD(T) calculations(Table 1), the second lowest-energy isomer (C2v,3A2;Fig.1b) of Mo2S4seems more stable than the isomer(Cs,3A'') shown in Fig.1a.Although these two isomers are close in erengy (0.07 eV) at the CCSD(T)level, they are likewise similar in their geometries and electronic structures.Herein, the Mo2S4(C2v,3A2)shown in Fig.1b is tentatively considered to be the ground state.

Table 1. Relative Energies of the Low-lying Isomers of the Mo2Sn?/0 (n = 4～8) Clusters at the B3LYP Level (?E ＜ 0.40 eV), and Comparisons with Those from the CCSD(T) Single-point Calculations at the B3LYP Geometries

4 DISCUSSION

4.1 Interpretation of the simulated spectra and molecular orbital analyses

The experimental PES spectra which can be used as an electronic “fingerprint” of a given cluster could provide valuable electronic information.On the basis of generalized Koopmans’ theorem, the vertical detachment energies (VDEs) for the identified Mo2Sn?(n = 4～8) anionic ground states and the selected low-lying isomers (?E ＜ 0.40 eV) were calculated (Table 2).The introduction to the principles of PES spectra simulation may be found in the early references[92].This simulation method has been extensively used in a number of previous studies[61,66,94-96]and show good agreement with the experi- mental spectra.The simulated PES spectra are presented in Fig.12.The first vertical detachment energy (VDE1st)trend as a function of S content (n) in Mo2Sn?(n =4～8) is displayed in Fig.13.

4.1.1 Mo2S4 and Mo2S4–

The frontier orbitals of Mo2S4and Mo2S4?are illustrated in Fig.6.As mentioned above, the Mo2S4(C2v,3A2) as shown in Fig.1b is considered to be the ground state using the CCSD(T) single-point calculations.Its valence electronic configuration is(18a1)2(10b1)2(6a2)1(19a1)1.Addition of an electron into the empty antibonding orbital 13b2of the neutral (Fig.6a) would lead to the anionic ground state Mo2S4?(C2v,4B1) as shown in Fig.1g.The corresponding valence electronic configuration is(10b1)2(18a1)2(6a2)1(13b2)1(19a1)1.Accordingly, the Mo?Mo distances increase from 2.616 to 2.760 ?,as shown in Fig.1b and 1g.The VDE1stupon photodetachment from the singly occupied bonding orbital (19a1)1, which is mainly characterized by a Mo 4d orbital, is predicted to be 3.39 eV.The fully occupied 10b1MO and below are mainly of S 3p character.Other calculated VDEs from 13b2and below are presented in Table 2.

Table 2. Vertical Detachment Energies (VDEs) of the Lowest-energy Mo2Sn?/0 (n = 4～8)Clusters and Selected Low-lying Isomer (?E ＜ 0.4 eV) at the B3LYP Level

a All energies are in eV.b The labels “α” and “β” denote the majority and minority spins, whereas Sin, Tri and Qui denote the singlet,triplet and quintet Mo2Sn?/0 (n = 4～8) final states upon photodetachment

Fig.6. (a) Frontier molecular orbitals for the neutral Mo2S4 ground state (Fig.1b).(b) Frontier molecular orbitals for the anionic Mo2S4? ground state (Fig.1g)

4.1.2 Mo2S5 and Mo2S5–

The ground state of neutral Mo2S5(Cs,1A') is predicated to be closed-shell species (Fig.2a).The valence electronic configuration of Mo2S5is(36a')2(37a')2.Addition of an electron into the empty bonding orbital 38a' of the neutral (Fig.7a) would lead to the anionic ground state Mo2S5?(Cs,2A'; Fig.2c)with a valence electronic configuration of(36a')2(37a')2(38a')1.As shown in Fig.7b, the singly occupied molecular orbital (SOMO) 38a' and the fully occupied orbital 36a' primarily correspond to the Mo 4d orbitals, and the orbital 37a' is characterized by S 3p feature.The first detachment channel for Mo2S5?is derived from the removal of the SOMO 38a', for which the calculated VDE is 3.76 eV.

Fig.7. (a) Frontier molecular orbitals for the neutral Mo2S5 ground state (Fig.2a).(b) Frontier molecular orbitals for the anionic Mo2S5? ground state (Fig.2c)

4.1.3 Mo2S6 and Mo2S6–

The neutral Mo2S6(Fig.3a) is stoichiometric in which each Mo achieves its highest oxidation state Mo6+.In other words, all of six valence electrons of Mo [4d55s1] are used to form bonds with the S atoms.The valence electronic configuration of the neutral Mo2S6(C2v,1A1) cluster is (24a1)2(12b1)2(19b2)2.The highest occupied molecular orbital (HOMO) 19b2and lowest unoccupied molecular orbital (LUMO)25a1are depicted in Fig.8a.All MOs from HOMO and below are S 3p-based orbitals, and the LUMO is primarily featured by the Mo 4d orbital.When one extra electron is added to the neutral Mo2S6, the ground state of Mo2S6?(Fig.3b) would still maintain the skeleton of neutral (Fig.3a) but the rhombus Mo2S2unit in the neutral is distorted relative to the anion.The valence electronic configuration of Mo2S6?(D2h,2Ag) is (4b3g)2(10b2u)2(15ag)1.In this D2hstructure, the extra electron delocalized on the two Mo atoms, as is evidenced from its SOMO 15ag(Fig.8b).The photodetachment from SOMO 15agyields the VDE1stwith a calculated value of 4.51 eV.The remaining calculated VDEs from 10b2uand below are presented in Table 2.

4.1.4 Mo2S7 and Mo2S7–

For the sulfur-rich species Mo2S7, the structure with a S2unit in the bridging fashion is predicated to be the neutral ground state (Fig.4a), for which the valence electronic configuration is(35a)2(33b)2(36a)2(34b)2.All the MOs are featured by 3p orbital of S atom (Fig.9a).The ground state of anion Mo2S7–(C1,2A) is predicted to be open-shell with a terminal S2group (Fig.4d).The valence electronic configuration of this anion is(65a)2(66a)2(67a)2(68a)1(69a)2(70a)2(71a)2. The calculated S?S bond length in this S2group is 2.097 ?, which is similar with the free S22?(1Σg+) dianion(2.180 ? calculated at the same level).The two fully occupied orbitals 71a and 65a correspond to the π*orbitals of S2group (Fig.9b).Hence, the Mo2S7–C1(1A) can be considered as the addition of a S22?unit to the cationic Mo2S5+.Photodetachment from the fully occupied orbital 71a yields the first PES band with the calculated VDEs of 4.32 eV (α) and 4.26 eV(β).The detachment origining from the singly occupied orbital 68a1requires a higher energy (5.00 eV).

Fig.8. (a) Frontier molecular orbitals for the neutral Mo2S6 ground state (Fig.3a).(b) Frontier molecular orbitals for the anionic Mo2S6? ground state (Fig.3b)

Fig.9. (a) Frontier molecular orbitals for the neutral Mo2S7 ground state (Fig.4a).(b) Selected frontier molecular orbitals for the anionic Mo2S7? ground state (Fig.4d)

4.1.5 Mo2S8 and Mo2S8–

The frontier MOs of Mo2S8and Mo2S8?are illustrated in Fig.10.The ground state of Mo2S8is found to be3B2state with C2vsymmetry (Fig.5a).The valence electronic configuration for the neutral species is (16b1)2(26a1)2(17b1)1(13a2)1(18b1)2(27a1)2.The corresponding frontier MO pictures are shown in Fig.10a, in which two singly occupied orbitals 13a2, 17b1and two doubly occupied orbitals 16b1and 18b1correspond to the π* orbitals of two bound S2units in Mo2S8(C2v,3B2).Furthermore, the S?S bond length of the S2moiety (1.999 ? in Fig.5a) is very close to that of free S2?(2Πg) anion (2.029 ? calculated at the same level).The spin density analyses further certify that two unpaired electrons are separately located on two S2units (Fig.11a).Therefore, the Mo2S8(C2v,3B2) may be viewed as two S2?units adhered to the cationic Mo2S42+.For the anionic species, the valence electronic configuration is (16b1)2(26a1)2(17b1)2(27a1)2(13a2)2(18b1)1.As shown in Fig.10b, the singly occupied MO 18b1and three doubly occupied MOs 13a2, 17b1and 16b1correspond to the π* orbitals of the S?S moieties.The bond length of S2unit (2.055 ?) is between that of the bound S2–and S22–anions (1.999 ? in Fig.5a and 2.097 ? in Fig.4d, respectively).The spin density analyses show that an unpaired electron is equiprobably shared by two terminal S2groups(Fig.11b).Therefore, the Mo2S8?(C2v,2B1; Fig.5c)cluster can be described as a resonance hybrid of two equivalent Csstructures with both S2?and S22?units. As shown in Table 2 and Fig.12e, photodetachment from the fully occupied 13a2orbital(Fig.10b) of Mo2S8?yields the first PES band with the calculated VDE1stof 3.58 eV (β).

Fig.10. (a) Selected frontier molecular orbitals for the neutral Mo2S8 ground state (Fig.5a).(b) Selected frontier molecular orbitals for the anionic Mo2S8? ground state (Fig.5c)

Fig.11. Valence bond descriptions and numerical electron spin density (in |e|) for the ground state of Mo2S8–/0 clusters.The numerical spin density was shown in parentheses

Fig.12.Simulated photoelectron spectra from the ground states for Mo2Sn? (n = 4～8) clusters at the B3LYP/H-BS level.The simulations are done by fitting the distribution of calculated VDEs with unit-area Gaussian functions of 0.1 eV width

Fig.13. Calculated first vertical detachment energies (VDE1st)of Mo2Sn? (n = 4～8) as a function of S content (n)

4.2 Structural evolution of Mo2Sn?/0 (n = 4～8) clusters

As noted above, a series of thiomolybdate dianion Mo2Sn2?(n = 6～9) have been prepared and characterized in condensed phase[33].It was pointed out that six homologues [Mo2Sn]2?(n = 6～12) dianions may be obtained from any other by either adding sulfur or removing sulfur by triphenylphosphine(Ph3P)[32].In our paper, similar structural evolutions are found for the gas-phase Mo2Sn?/0(n = 4～8)clusters.

It is worth to mention that Mo2S6showed the highest stability among a series of Mo2Syclusters by Gemming et al.[58].They indicated that the structure of Mo2S6may be used as a motif of larger MoxSyclusters or the bulk MoS3phase.In our calculations,the ground state of Mo2S6(C2v,1A1; Fig.3a)possesses four Mo=S double bonds and four Mo?S single bonds, in which each Mo atom has reached its highest oxidation state of +6.

For the neutrals, with the increasing sulfur content,the formal oxidation state of molybdenum increases until reaching its highest oxidation state of +6.Meanwhile, the sulfur atoms occupy the terminal sites in Mo2Snclusters (n = 4～6) successively.After both Mo atoms get the highest oxidation state, the disulfur units (i.e., S2) begin to emerge.Namely, one of the bridging S atoms in Mo2S6is replaced by a bridging S2unit for the Mo2S7cluster.Then for the Mo2S8cluster, two of the terminal S atoms in Mo2S6are replaced by the same number of terminal S2ligands.

Similar evolutionary regularities are also found for the anionic Mo2Sn?(n = 4～6) clusters.They preserve the structural skeleton of their neutral counterpart.In Mo2S7?cluster, one of the terminal S atoms in Mo2S6?is replaced by a terminal S2ligand.Subsequently in the Mo2S8?cluster, two terminal S atoms in Mo2S6?are replaced by the same number of terminal S2ligands.Furthermore, based on the relative stability of Mo2S4?/0and Mo2S8?/0(Figs.1 and 5), it seems that the syn configuration is more stable than the anti one.

4.3 Trend of VDE1st as the function of S content in Mo2Sn? (n = 4～8)

Fig.13 depicts the trend of calculated VDE1stas a function of S content in the Mo2Sn?clusters.The trend of VDE1stcan be qualitatively understood from the frontier MO analysis (Figs.6～10).The VDE1stincreases nearly linearly as a function of sulfur content (n = 4～6), clearly showing a behavior of sequential sulfidation of Mo2dimer.The valence electrons of molybdenum (4d55s1) are sequentially transferred to the added S atoms, along with the number of Mo 4d-based orbitals decrease (Figs.6～8).Interestingly, the VDE1stsuddenly begins to reduce after that.The reason why the VDE1ststarts to decrease can also be comprehended from the frontier MO analysis as shown in Figs.9 and 10.When n reaches 7 (i.e., Mo2S7?), the detachment is origining from the fully occupied π* orbitals (71a)of a S2unit, leading to the decrease of VDE1st(from 4.51 to 4.26 eV).When n is equal to eight (i.e.,Mo2S8?), we found the VDEs1stcorresponds to the detachment from the singly occupied π* orbitals(18b1) of two S2moieties.The further decreasement of VDE1stfrom 4.26 to 3.58 eV may be a consequence of distribution of an unpaired electron over the π* orbitals of two S2groups.

4.4 Reduction reaction of H2 on the Mo2Sn?/0 (n = 4～8) clusters

Afanasiev et al.[67,68]showed that the S22?species located at the edges of fresh MoS2catalysts play a key part for the catalytic activity.Recently, Karunadasa and co-workers[28]have reported the synthesis of a side-on bound MoIV-disulfide complex, which could mimic the MoS2edge sites for the catalytic hydrogen generation.It is interesting to note that diverse S2units are found in the sulfur-rich clusters Mo2Sn?/0(n = 7, 8) in our work.

The MoS2catalysts are usually used in the gaseous environment of H2/H2S at raised temperature.The experiment pointed out that the kinetics of S2group interaction with hydrogen could be promoted by the reactant H2and hindered by the product H2S[67].Thus, we proposed the reaction (Eq.1)removing a sulfur atom from Mo2Sn?/0(n = 4～8)clusters.The driving force can be estimated by the negative values of Gibbs free energy differences(ΔG) of this reaction, which are obtained by the following equation (eq.2) and summarized in Table 3.

Table 3. Calculated Free Energy Differences (ΔG) for the Proposed Reaction (Eq.1) at the B3LYP/H-BS Level of Theory

In light of the values of ?G, the driving forces of the proposed reactions increase as a function of n.For the proposed reaction (Eq.1; n = 5, 6), the sulfur is removed from the terminal S of Mo2S5?/0and Mo2S6?/0.The corresponding values of ?G (Table 3)are positive (Reactant-favored).After both of the Mo atoms reach their maximum oxidation state of+6, the S2units begin to emerge.The energy costs(?G) of sulfur atom losing from various S2units start to be negative (Product-favored).So, for the sulfur-rich clusters Mo2Sn?/0(n = 7, 8), regardless of the kinetic factor, the proposed reactions (Eq.2)may be energetically (thermodynamically) favored.In the neutral Mo2S7, the bridging disulfide (S22?)ligand appears.The Gibbs free energy difference(?G) is predicted to be ?0.94 kcal·mol-1, which should correspond to the removal of S atom from the bridging disulfide S22?moiety in Mo2S7.As regards its anion and Mo2S8?, the S atoms from terminal S22?and terminal S2?units are removed in the reaction(Eq.1; n = 7, 8), respectively.The corresponding?G is estimated to be ?12.51 kcal·mol-1(S22?for Mo2S7?) and ?14.74 kcal·mol-1(S2?for Mo2S8?),respectively.Generally, the driving forces (??G)that remove a sulfur atom from various S ligands in Mo2Sn?/0(n = 4～8) clusters can be sorted in the order: t?S2?＜ b?S22?＜ t?S22?＜ t?S2?, which in turn stand for the terminal S atom, bridging (μ2-η1:η1)S22?, terminal (η2) S22?and terminal (η2) S2?unit,respectively.It seems that the S2?units are more reactive with H2which would take a S atom away in the form of releasing H2S molecule.Coordination unsaturated sites (CUS) can be obtained by removing sulfur atoms from the edges of MoS2catalyst under the H2atmosphere[67].The order may provide insight into the the pretreatment of fresh MoS2catalysts under hydrogen conditions.

5 CONCLUSION

We report a systematical theoretical study on a range of dinuclear metal sulfide clusters: Mo2Sn–and Mo2Sn(n = 4～8).DFT and CCSD(T) calculations were carried out to elucidate the chemical bonding and geometric and electronic properties of Mo2Sn–/0clusters.The calculations showed that the sulfur atoms tended to occupy the terminal sites of the clusters continuously in the process of sequential sulfidation.After the oxidation state of Mo atoms gets the maximum of +6, diverse disulfur ligands emerged in the sulfur-rich Mo2Sn–/0(n = 7, 8)clusters.Additionally, by means of calculating the free energy differences (?G) of the reaction (eq.1),we found that the values of ?G were positive for the sulfur-deficient and stoichiometric clusters (eq.2; n= 5, 6), but negative for the sulfur-rich species (Eq.2;n = 7, 8).The driving forces (?ΔG) for the reactions eliminating sulfur from diverse S ligands in Mo2Sn?/0(n = 4～8) clusters followed the general order t?S2?＜ b?S22?＜ t?S22?＜ t?S2?.This order may provide insight into the pretreatment of fresh MoS2catalysts under H2atmosphere.

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