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Methane Dehydrogenation and Coupling to Ethylene over a Mo/ HZSM-5 Catalyst: A Density Functional Theory Study Danhong Zhou,* Shiying Zuo, and Shuangying Xing Institute of Chemistry for Functionalized Materials, College of Chemistry and Chemical Engineering, Liaoning Normal University, Dalian 116029, People’s Republic China S Supporting Information *

ABSTRACT: In the present paper, we report the density functional theory studies on the structure of the molybdenum active center in Mo/HZSM-5 zeolite catalysts and the reaction mechanisms of methane dehydrogenation and coupling to ethylene (MDHC). Three kinds of active center models, Mo(CH2)2CH3+, Mo2(CH2)42+, and Mo2(CH2)52+, were optimized for the carburized Mo species exchanged on the Brønsted acid sites in HZSM-5 zeolites. The entire catalytic cycle of MDHC was investigated, and the catalytic performances of three different active center models were compared. The catalytic cycle consists of four elementary steps: (1) dissociation of the methane C−H bond; (2) dehydrogenation and C−C coupling; (3) activation of the second methane molecule; (4) elimination of ethylene and molecular hydrogen. It was suggested that methane C−H bond dissociation occurs on the π-orbital of the MoCH2 double bond, and C−C coupling proceeds on d-orbitals of the Mo atom. Dehydrogenation is realized by rupture of two C−H bonds from the adjacent methyl groups on the Mo atom, which is the rate-determining step of whole MDHC reactions.

1. INTRODUCTION Among transition metal carbides, Mo2C presents electronic properties similar to noble metals and exhibits excellent catalytic behavior in numbers of reactions.1,2 A combination of Mo2C with ZSM-5 exhibits unique performance for the aromatization of lower alkanes.3−10 The Mo/HZSM-5 catalyst is a well-known catalyst for methane dehydroaromatization through a bifunctional feature:11−18 the molybdenum performs the dehydrogenation and coupling of methane to ethylene, and the Brønsted acid (B-acid) sites stand for the oligomerization and dehydroaromatization of ethylene.14−16 However, the structure of the active Mo species is still an issue of debate in the literature. It is generally accepted that after preparation of Mo/HZSM-5 catalyst the molybdenum is anchored on the Bacid sites inside zeolite channels as Mo-oxo species; this precursor was reduced and carburized by methane to form molybdenum carbide in the induction period.19−23 Iglesia and co-workers23−27 studied the structure of Mo species using Raman and X-ray absorption spectroscopy (XAS) and proposed that the Mo species was anchored on the frameworks as a (Mo2O5)2+ dimer associating with two adjacent Brønsted acid sites. By using high-field27Al MQ MAS NMR, Ma et al.21,22 inspected the structure of Mo-oxo species and claimed that the exchanged Mo species was monomeric (MoO2)+ with a molybdenum atom anchored to a single framework Al through two oxygen bridges. The results of Tessonnier et al.28 indicated that a monomeric bidentate species of (MoO2)2+ would be formed when the Si/Al ratio was low, and the (Mo2O5)2+ dimer © 2012 American Chemical Society

was formed when the Si/Al ratio was high. Using the density functional theory (DFT) method, we have studied the structures of Mo-oxo species exchanged on the HZSM-5 zeolite and confirmed that the monomeric bidentate (MoO2)2+ species is less stable than the (Mo2O5)2+ dimer.29 It is widely accepted that the working catalysts for methane conversion are the carburized molybdenum species originating from the Mo oxo precursor. However, the real structure of the carburized Mo active center has not been verified unambiguously up to now. The difficulties for experimental determination of the structure of the Mo active center lie in the low loading of Mo (smaller than 8 wt % Mo per unit cell) as well as the coexistence of the external surface Mo species and the inner-channel Mo species. The lack of detailed measurements of the extent and rate of reduction and carburization during this initial carburization process has led to conflicting proposals about the structure and the stoichiometry of carburized Mo species in HZSM-5 zeolite. In some literature, Mo2C was regarded as the working active center.13,14 However, a number of experimental studies revealed that the exchanged molybdenum species may form different types of carbides than the bulk Mo2C.30−36 Wang et al.30,31 examined Mo/HZSM-5 catalysts by X-ray photoelectron spectroscopy (XPS) technique and found that preformation of Mo2C on the HZSM-5 support, Received: September 19, 2011 Revised: January 15, 2012 Published: January 20, 2012 4060

dx.doi.org/10.1021/jp209037c | J. Phys. Chem. C 2012, 116, 4060−4070

The Journal of Physical Chemistry C

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Figure 1. Structures of the ZSM-5 zeolite in view of [100] and the cluster models presenting Al6(2Si)Al6 sites and a single Al6 site.

In the present paper, we address the theoretical study on the structure of the carburized Mo active center on HZSM-5 zeolite and the full catalytic cycle of methane dehydrogenation and coupling to ethylene (MDHC). Three models, Mo2(CH2)52+, Mo2(CH2)42+, and Mo(CH2)2CH3+, were built and optimized to mimic the carburized Mo species exchanged on Brønsted acid sites in HZSM-5 zeolites. The bonding characteristics and electronic properties of the proposed active center models were examined. On the basis of these models, the entire catalytic cycle of MDHC and the reaction mechanisms were investigated. The study may provide valuable insight into the catalytic behavior of the Mo/HZSM-5 catalyst and demonstrates how the methane C−H bond is dissociated and the initial C−C coupling is performed. The remainder of this article is organized as follows. Section 2 gives details of the model selection and calculation method. Section 3 reports the characterization of the active center structures and presents the reaction pathways of MDHC step by step. Section 4 discusses the catalytic mechanisms of Mo/ HZSM-5 catalysts for MDHC.

without coke deposit, could not completely eliminate the induction period. They suggested that the clean surface of MoCx might be too reactive to form higher hydrocarbons, and a coke-modified MoCx surface such as MoCxHy might be the active center in the formation of ethylene. Li et al.27 pointed out that MoCxHy may be the catalytic active center, where the carbon atoms may also be bonded with hydrogen atoms, which would not be detected in the radial structure function. More proposed models like partially reduced Mo2C or MoCxOy species were reported in previous literature.15,32−35 Very recently, Zheng et al.36 have made direct observation of different types of carburized molybdenum species on fresh and working Mo/zeolite catalysts by using ultrahigh field 95Mo NMR spectroscopy. Their results confirmed that the active centers for methane dehydroaromatization are the exchanged Mo species different from the bulk Mo2C. Using the Extended X-ray Absorption Fine Structure (EXAFS) technique, Ding et al.23 reported that the MoCx clusters exchanged on zeolite acid sites include the Mo−Mo unit and Mo−C bond with each Mo atom coordinating by three C atoms. Nevertheless, the present experimental techniques still fail to distinguish the fine feature of this “peculiar” molybdenum carbide. To settle the issue brought from the experimental results, computational calculation would be a helpful approach. However, few theoretical studies on the structure of Mo carbide exchanged on zeolites have been performed. Rocha et al.35 studied the Y zeolite-supported carburized molybdenum species by a DFT method, and the calculated structure of the Mo dimer was compatible with EXAFS results. Zhou et al.37 performed the theoretical investigation of methane dehydrogenation based on the Mo(CH3)3(AlOSi) model of Mo/ZSM5 catalysts. However, these works have not taken into account the real zeolite frameworks. Besides, some theoretical studies regarding methane activation on gas-phase and supported MoOx species37−39 can be found in the literature. In our previous work,40 we have examined the structures of Mox(CH2)y (x = 1∼2, y = 2∼5) models for exchanged Mo carbides on HZSM-5 zeolite and investigated the mechanisms of methane C−H bond dissociation by DFT calculations. However, the entire catalytic cycle from methane to ethylene including the regeneration of active centers has never been reported in the literature up til now.

2. METHODOLOGIES 2.1. Model Selection. Before building the structure of carburized molybdenum species, some factors have been taken into account: (1) each Mo exchanges on one B-acid site and connects with framework aluminum through two oxygen bridges;21 (2) both monomeric and dimeric Mo species are considered for the active center, which may originate from MoO2+/ZSM-5 and Mo2O52+/ZSM-5 precursors, respectively;22,27,29 (3) the Mo−C coordination number is three,27 and (4) the carbons may retain bonded hydrogen atoms to procure the reasonable electronic and geometric structures of Mo carbide species. Although the experimental studies have not confirmed the existence of hydrogen on the working catalysts, one should bear in mind that the fresh carburized Mo species are under methane and molecular hydrogen atmosphere and that the bonded hydrogen would not be detected in the radial structure function. Three models of Mo carbides exchanged on HZSM-5 zeolite acid sites, Mo2(CH2)52+, Mo2(CH2)42+, and Mo(CH2)2CH3+, were constructed, in which the numbers of included hydrogen atoms were determined via optimization. For simplicity, they 4061



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Figure 2. Optimized structures of the active center models of Mo2(CH2)52+, Mo2(CH2)42+, and Mo(CH2)2(CH3)+ exchanged on HZSM-5 zeolite.

Table 1. Geometric Parameters for Optimized Models of Mo2(CH2)52+, Mo2(CH2)42+, and Mo(CH2)2(CH3)+ Exchanged on HZSM-5 Zeolite bond distances (Å) A1 A2 A3 ref23

bond angles (deg)

Mo−C1

Mo−C2

Mo−C3

Mo−Mo

Mo−O1

Mo−O2

C1−Mo−C2

O1−Mo−O2

Mo−C3−Mo

1.914 1.876 1.866 2.13

1.870 2.050 1.864

2.062 2.144 2.191

3.856 2.867 

2.132 2.331 2.287 2.97

2.421 2.138 2.140

85.22 111.65 110.02

90.03 89.25 87.30

138.38 83.91 

existed for optimized parts, except the contaminations related to the fixed atoms. The transition states were validated by only one imaginary frequency mode correlated to the reaction coordination. All reported energies are from the zero-point corrected electronic energies.

are denoted as A1, A2, and A3, respectively. Models A1 and A2 stand for dimeric Mo carbide exchanged on Al6(2Si)Al6 double B-acid sites situated in NNNN (next next nearest-neighboring) position, while model A3 stands for monomeric Mo carbide exchanged on an Al6 single B-acid site. Their geometries refer to the Mo2O52+ and MoO2+ precursors, respectively, for which structures have been reported in our previous computational studies.29,39 The zeolite cluster models were truncated from the ZSM-5 zeolite lattice, and the B-acid sites are on the T6 site. The selection of the B-acid sites has been clarified in our previous papers.29,40 For the Mo dimer, the 6T zeolite cluster model (Si4Al2O19) including Al(2Si)Al double B-acid sites was selected, while for the Mo monomer the 11T cluster model (Si10Al1O10) including a single Al site was selected (Figure 1). The choice of the cluster model in the present work was based on the consideration that the Mo species are connected with the framework oxygen atoms as extra-framework species; the geometry and electronic property of the active center are less affected by the model size according to our previous studies.40 In cluster models, the dangling bond on the second shell framework oxygen or silicon atoms was terminated by the H atom with O−H and Si−H distances fixed at 1.00 and 1.46 Å, respectively, oriented along the bond direction to what would otherwise have been the next framework atoms. During the calculations, the atomic coordinates in the external two layers of the zeolite clusters were fixed in their original crystallographic positions to retain the zeolite structure, while other atoms in the models including the reactants were relaxed. 2.2. Calculation Methodology. All calculations were performed using the Gaussian03 program.41 The nonlocal hybrid B3LYP density functional was used,42,43 and the 631G(d,p) basis set was selected to describe all but the molybdenum atom.44,45 The Hay−Wadt effective core potential46 (LANL2DZ denoted in Gaussian 03) was used for Mo which includes the relativistic effects. Population analysis and the electronic structure analysis were performed by Natural Bond Orbital (NBO) calculations (version 3.2)41 based on the optimized models. The optimization minima were verified by frequency calculations, and no vibrational imaginary frequencies

3. RESULTS 3.1. Structure of Mo Carbide Exchanged on HZSM-5 Zeolite. To obtain the reasonable configuration of exchanged Mo carbide species, we first examined the structures of Mo2C52+ and Mo2C42+ models. The optimized structures and geometric parameters are presented in Figure S1 (Supporting Information). Using NBO analysis, we found that there exist unsaturated nonbonding orbitals on all carbon and molybdenum atoms. The electron occupancy on these long pair orbitals is between 0.73 and 0.93 for the Mo2C42+ model and about 0.90 for the Mo2C52+ model, implying that they might be unstable under experimental conditions. Since the reduction and carburization of MoOx/HZSM-5 were carried out under a CH4/H2 atmosphere, it is essential to examine the thermodynamics of hydrogenation for both models. The reaction free energies at the experimental temperature of 973 K were calculated as follows Mo2C4 2 + + 4H2 → Mo2(CH2)4 2 + ΔG973 = −55.2 kcal/mol Mo2C52 + + 5H2 → Mo2(CH2)52 + ΔG973 = −15.1 kcal/mol

The results indicated that the hydrogenation of both models is exothermic, implying that the Mo carbides containing hydrogen are thermodynamically more stable. After exploring several trial structures, we found that the relevant models containing CH2 species lead to reasonable electronic and geometric structures of exchanged Mo carbide species. The existence of CH2 species in carburized Mo/HZSM-5 catalysts is also supported by some experimental results. Li et al.27 detected the intermediates during methane reactions on carburized Mo/ HZSM-5 catalysts by deuterogenation experiments and found 4062



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starting point in the structural determination, which might lead to uncertainty in the simulation parameters of EXAFS. On the other hand, the Mo−Mo distance in A1 is comparable with that in the Mo2O52+ precursor, which is 3.70 Å by EXAFS measurement.27 In view of these, both A1 and A2 were considered for the active center model of dimeric Mo carbides supported on ZSM-5, and their catalytic activities would be compared. The electronic configurations and natural atomic charges for three models are obtained by NBO analysis and summarized in Table 2. It is found that in all models there exist five d electrons in the valence orbitals of the Mo atom. NAO analysis revealed that the molybdenum atom is in a high-spin state with each d atomic orbital occupied by one electron. For models A1 and A3, all d electrons have participated in bonding with carbons and oxygens. For model A2, there exists a nonbonding d electron on each Mo atom. If both d orbitals stay in an identical phase, a Mo−Mo σ-bond is built, and the model is in the singlet state. Whereas, if both d orbitals stay in reversed phase, no d−d σ-bond is formed, and the model is in triplet state. The singlet state model is energetically more stable than the triplet state by 6.8 kcal/mol. Therefore, in the following calculations we just consider A2 as a singlet state. In next subsections, we will investigate the catalytic cycle of MDHC over the active centers mentioned above. 3.2. Methane Activation on A1. The reaction of methane dehydrocoupling to give ethylene and molecular hydrogen is endoergic.37

that CH2 appears to be the most abundant surface fragment. They suggested that the CHx fragments had stronger interactions with higher coordinative unsaturated Mo centers. Solymosi et al.47 also found CH3 and CH2 species stably adsorbed on Mo2C/Mo(110). On the basis of both experiments and DFT calculations, Wyrwas et al.48 indicated that formation of the MoCH2 bond was energetically favorable in the product of the Mo2Oy− suboxide cluster reacted with methane. Similar structures were found for Mo−methylidene complexes bonded to Al2O3 and HBeta zeolite which were confirmed as the active centers for heterogeneous olefin metathesis by experimental and theoretical studies.49,50 The optimized structures of A1, A2, and A3 are demonstrated in Figure 2, and the selected geometric parameters and natural atomic charges are listed in Table 1. The bonding characteristics are analyzed by NBO calculations and illustrated in Scheme 1. More detailed NBO analyses are Scheme 1. Bonding Characteristics of A1 (Mo2(CH2)52+), A2 (Mo2(CH2)42+), and A3 (Mo(CH2)2(CH3)+) Exchanged on HZSM-5 Zeolite

presented in Table S1 (Supporting Information). In all models, molybdenum is in the symmetric center of trigonal-bipyramid (TBP) anchoring on the framework O−Al−O bridge through Moδ+−Oδ− bonds or Moδ+←Oδ− coordinated interaction. In model A1, each Mo atom holds two MoCH2 bonds, and both Mo atoms are linked through a −CH2− bridge. In model A2, only one MoCH2 bond exists on each Mo, and both Mo atoms are linked through two −CH2− bridges, forming a Mo− C−Mo−C− four-membered ring similar to the framework of bulk Mo2C.35 Model A3 is a monomeric Mo carbide containing two MoCH2 double bonds and a Mo−C single bond, which can be seen as a half part of model A1. Regarding the geometries of these models, it can be seen in Table 1 that for all models the Mo−C distances are 1.87−1.92 Å in MoCH2 double bonds and 2.05−2.19 Å in Mo−CH2− Mo or Mo−CH3 single bonds. These parameters are in good agreement with the experimental values of EXAFS,23 in which the distances of Mo−C are between 2.07 and 2.11 Å. The Mo− Mo distance is 3.86 Å in model A1 and 2.87 Å in model A2. However, the EXAFS data for the Mo−Mo interatomic distance is 2.97 Å.23 With respect to the discrepancy between the calculated values and EXAFS data, one should keep in mind that the EXAFS measurement was the reflection of the average Mo−Mo interatomic distances for various Mo species, and Mo K-EXAFS fine structure was fitted using bulk Mo2C as a

CH 4 → 1/2(C2H 4 + 2H2) ΔE = 30.9 kcal/mol, ΔH 298 = 25.9 kcal/mol

The reaction route of MDHC over A1 consists of four elementary steps as shown in Scheme 2. The energy profiles for all reaction steps are depicted in Figure 3. In this paper, the activation energy of methane C−H bond dissociation is calculated as the difference between the energy of the transition state (TS1 or TS3) and the sum of the energies of the primary active center or intermediate Int2 and the methane molecule since the adsorption energy of methane on the active center is lower by about 0.5 kcal/mol for a smaller zeolite cluster model and about 1 kcal/mol for a larger cluster model including the dispersive effect contributed by the zeolite cavity.40 The optimized structures for the stationary points are displayed in Figure 4, and the geometries of the transition states are demonstrated in Figure 5. First Step: Methane C−H Bond Dissociation. In terms of the natural charges presented in Table 2, the molybdenum and carbon of MoCH2 represent a Lewis acid−base pair able to polarize and break the methane Cδ−−Hδ+ bond. In the transition state TS1, the natural charges on the leaving hydrogen and the carbon in the remaining CH3 fragment of methane are +0.24 and −0.89, respectively. The ruptured

Table 2. NBO Analysis for Optimized Models of Mo2(CH2)52+, Mo2(CH2)42+, and Mo(CH2)2(CH3)+ Exchanged on HZSM-5 Zeolite electronic configuration A1 A2 A3

natural charges

Mo

Mo

C1

C2

C3

O1

O2

[core]5s(0.27)4d(4.78) [core]5s(0.24)4d(4.85) [core]5s(0.28)4d(4.83)

0.98 0.85 0.58

−0.53 −0.47 −0.47

−0.61 −0.85 −0.47

−0.86 −0.73 −0.91

−1.17 −1.23 −1.21

−1.26 −1.19 −1.15

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Scheme 2. Reaction Pathway for the Entire Catalytic Cycle of Methane Dehydrogenation and Coupling to Ethylene over Active Center A1 (Mo2(CH2)52+/ZSM-5)

Figure 3. Reation profiles for methane dehydrogenation and coupling to ethylene over different active centers of Mo 2 (CH 2 ) 5 2+ , Mo2(CH2)42+, and Mo(CH2)2(CH3)+ exchanged on HZSM-5 zeolite.

proton is bonded to the carbon in MoCH2, while the negative methyl fragment CH 3 δ− forms a bond with molybdenum. This step is endoergic (8.9 kcal/mol) with the activation energy of 24.2 kcal/mol, comparable to the energy barriers for methane activation on other metal-supported zeolite catalysts.51,52 Second Step: Dehydrogenation and C−C Coupling. In the second step of this route, the dehydrogenation occurs in Int1 by rupture of two C−H bonds from the adjacent methyl groups on the Mo atom. In the transition state TS2 (Figure 5), a dihydrogen molecule is almost formed (the H−H distance is 0.92 Å) and locates on C′ with the C′−H distances of 1.25 and 1.54 Å, respectively. Simultaneously, C−C coupling tends to take place between the adjacent Mo−methylidene groups. The activation energy of this step is 32.3 kcal/mol with an imaginary frequency of 805i cm−1 corresponding to the stretching mode of C′ → H. After elimination of molecular hydrogen, a quasiethylene is produced and adsorbed on the Mo atom to form intermediate Int2. The reaction of this step is exoergic by 8.2 kcal/mol. In Int2 the quasi-ethylene interacts with Mo through σ-bonding between the p orbital of respective carbon atoms and the dxz and dx2−y2 orbitals of Mo. The molecular orbital plots related to the adsorption complex are illustrated in Figure 6. The calculated result indicated that the dehydrogenation and C−C coupling occur in a synergetic process. The C−C coupling promotes the dehydrogenation reaction and diminishes the activation energy. Third Step: Activation of the Second Methane. In this step, as the methane molecule accesses Int2, the H3C−H bond is

Figure 4. Optimized structures of the stationary states for methane dehydrogenation and coupling to ethylene over active center Mo2(CH2)52+/ZSM-5. The ball-stick mode denotes the atoms concerned with the reactions, and the tube mode denotes the framework atoms of ZSM-5 zeolite.

activated on the adsorption complex of ethylene on Mo species. The split Hδ+ approaches C2 of the adsorbed ethylene, and the residual H3Cδ− binds to Mo (TS3 in Figure 5), resulting in Mo−C2H5 and Mo−CH3 groups in the corresponding intermediate Int3 (Figure 4). The reaction in this step is endoergic (27.5 kcal/mol) with the activation energy of 48.8 kcal/mol. Compared to the first step, methane C−H bond dissociation in this step has to overcome a higher energy barrier, implying that the Mo−C single bond is less active than the MoCH2 double bond. Int3 is less stable than Int2 due to the enhanced steric constraint of the generated Mo(−CH3)(−C2H5) fragment. Fourth Step: Dehydrogenation and Elimination of Ethylene. In Int3, dehydrogenation proceeds through rupture of the β-hydrogen of the Mo−C2H5 group and hydrogen in the Mo− CH3 group. Looking at the geometry TS4 shown in Figure 5, one can notice that in the transition state ethylene is generated and moved away from the Mo atom, leaving the MoCH2 4064



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group reformed, and a H−H pair is situated between them. The imaginary frequency is 1134i cm−1 corresponding to the stretching mode of “C←H···H→C”. The activation energy of this step is 67.4 kcal/mol, which is comparable to the activation energies of the dehydrogenation reaction of hydrocarbons on acidic and metal-supported zeolites.53−55 It is noted that in TS4 the Mo−C1 bond is completely broken, and the geometry of the transition structure is much closer to the final product in which the molecular hydrogen and ethylene molecule are eliminated and the original active center is regenerated. The reaction of this step is endoergic by 21.2 kcal/mol. As the carbon−carbon double bond tends to form, the distance between Mo and C1 is elongated, and rotation of the Mo CH2 group around the Mo−C′ bond axis pushes the H2C CH2 removal from the Mo atom. 3.3. Methane Activation over A2. The reaction route of methane activation over A2 also consists of four elementary steps as shown in Scheme 3; the energy profiles for all reaction steps are depicted in Figure 3. The optimized structures of the relevant stationary points are demonstrated in Figure 7, and the geometries of the transition states are presented in Figure 8. First Step: Methane C−H Bond Dissociation. Similar to the first step over A1, the molybdenum and carbon of MoCH2 represent a Lewis acid−base pair able to polarize and break the methane Cδ‑−Hδ+ bond. In the transition state TS1, charges on the leaving hydrogen and the carbon in the remaining methyl fragment of methane are +0.29 and −0.90, respectively. The methyl fragment CH3δ− attacks the molybdenum, and the ruptured proton attacks the carbon of MoCH2. This step is slightly endoergic (4.8 kcal/mol) and presents the activation energy of 34.0 kcal/mol, which is higher than the energy barrier of methane activation in the first step over A1. An interpretation will be given in Section 4. Second Step: Dehydrogenation and Formation of Ethylene. In the second step of this route, dehydrogenation reaction proceeds between two adjacent methyl groups on the Mo atom within Int1. Two hydrogen atoms ruptured from C−H bonds tend to form a dihydrogen molecule. From Figure 8, it can be seen that in the transition state TS2 the dihydrogen pair with 0.81 Å H−H distance locates on C′, and the imaginary frequency is 880i cm−1 corresponding to the stretching mode of C′→H. The activation energy of 62.1 kcal/mol is much higher than that of TS2 over A1 but equivalent to the energy barrier of TS4 over A1. This is because for A2 the dehydrogenation in the second step proceeds without simultaneous C−C coupling as happened in the case of A1. After the molecular hydrogen is eliminated, both residual methylidene groups on the Mo atom can combine to produce quasi-ethylene adsorbed on Mo. The

Figure 5. Geomeries of the transition states for MDHC over active center Mo2(CH2)52+/ZSM-5. The arrows illustrate the streching mode relevant to the imaginar frequency (presented in parentheses) (bond length in Å; imaginary frequency in cm−1).

Figure 6. NBO and molecular orbital plots showing the interaction between ethylene and the Mo active center in the Int2 for MDHC over Mo2(CH2)52+/ZSM-5.

Scheme 3. Reaction Pathway for the Entire Catalytic Cycle of Methane Dehydrogenation and Coupling to Ethylene over Active Center A2 (Mo2(CH2)42+/ZSM-5)

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corresponding reaction energy from Int1 to Int2 is 11.6 kcal/ mol. It must be noticed that the C−C coupling occurs not simultaneously with the dehydrogenation but after the elimination of the hydrogen molecule. Third Step: Activation of the Second Methane. In this step, a methane molecule approaches Int2; the H3C−H bond breaks down; and the split Hδ+ is transferred to C1 of adsorbed ethylene to form the Mo−C2H5 fragment, while H3Cδ− is connected with Mo to form the Mo−CH3 group. This step is endoergic (16.1 kcal/mol) and displays an activation energy of 24.2 kcal/mol. The barrier of methane activation in this step is lower than that in the third step over A1 by 24.6 kcal/mol because the geometry of TS3 over A2 (Figure 7) bears diminished spatial constraint compared with that of TS3 over A1. Fourth Step: Dehydrogenation and Elimination of Ethylene. In this step, dehydrogenation occurs between the βhydrogen of the Mo−C2H5 group and the hydrogen of the Mo−CH3 group in Int3. In the transition state TS4 (Figure 8), the ethylene is generated and adsorbed on Mo through σbonding. Both ruptured H atoms locate on C″ with a H−H distance of 0.87 Å. The conformation of this transition state is similar to that of TS2 over A1, but its activation energy (57.4 kcal/mol) is much higher than that of TS4 over A1. This result further reveals the fact that without the simultaneous C−C coupling dehydrogenation reaction has to overcome a higher energy barrier. As the final product, both molecular hydrogen and the ethylene molecule are eliminated, and the original active center A2 is regenerated. The reaction energy of this step is 16.8 kcal/mol. 3.4. Methane Activation Over A3. The active center A3 has a similar construction as A1 and can be seen as one-half of A1. The catalytic cycle of MDHC over A3 is also similar to that over A1. The reaction route is shown in Scheme 4; the energy profiles for all reaction steps are depicted in Figure 3; and the optimized structures of the stationary states are demonstrated in Figure 9. The detailed geometries of the transition states are demonstrated in Figure 10. The corresponding activation energies in four elementary steps are 27.3, 38.4, 41.7, and 52.0 kcal/mol (see Figure 3), respectively, which are approximately equivalent to ones over A1. The results imply that the adjacent Mo atom in the dimeric Mo species has a negligible affect on the reaction process of MDHC and plays as a spectator. However, the intermediates over A3 show better stability than over A1 since the monomeric Mo carbide presents larger freedom than the dimeric Mo carbide. By comparison of the above three reaction routes, one can see that methane C−H bond dissociation occurs in the first and third step. However, for A1 and A3, the first step presents a lower energy barrier than the third step, whereas it is inversed for A2. A dehydrogenation reaction occurs in the second and fourth step. For A1 and A3, the activation energies in the second step are nearly half that in the last step, whereas for A2 both the second and last steps present higher activation energies comparable with that in the fourth step on A1 and A3. On the whole, the dehydrogenation processes have to overcome much higher activation energies than that for methane C−H bond activation. The dehydrogenation in the last step of all routes is the rate-determining step for the entire catalytic cycle of MDHC, with the exception that on A2 the dehydrogenation in the second step is more difficult than in the last step.

Figure 7. Optimized structures of the stationary states for methane dehydrogenation and coupling to ethylene over active center Mo2(CH2)42+/ZSM-5. The ball-stick mode denotes the atoms concerned with the reactions, and the tube mode denotes the framework atoms of zeolite.

Figure 8. Geometries of the transition states for MDHC over active center Mo2(CH2)42+/ZSM-5. The arrows illustrate the stretching mode relevant to the imaginary frequency (presented in parentheses) (bond length in Å; imaginary frequency in cm−1). 4066



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Scheme 4. Reaction Pathway for the Entire Catalytic Cycle of Methane Dehydrogenation and Coupling to Ethylene over Active Center A3 (Mo(CH2)2(CH3)+/ZSM-5)

Figure 10. Geometries of the transition states for MDHC over active center Mo(CH2)2(CH3)+/ZSM-5. The arrows illustrate the stretching mode relevant to the imaginary frequency (presented in parentheses) (bond length in Å; imaginary frequency in cm−1).

Broclawik et al.51 calculated the transition state for methane C− H bond cleavage on the GaO/ZSM-5 cluster and obtained the activation energy of 31 kcal/mol. Wang et al.52 studied the first C−H bond activation of methane over the PdO/HZSM-5 system and got the energy barrier of 23 kcal/mol. Our previous results39 for methane activation on MoO2/HZSM-5 led to the activation energy of 38 kcal/mol. In the present work, the activation energies of methane C−H bond dissociation over Mo(CH2)x/HZSM-5 systems (24−48 kcal/mol) are comparable to the results in the literature. For all of these catalysts, methane activations were realized by inserting the methane C− H bond into the metal−oxygen bond with hydrogen pointing toward the oxygen and the methyl group attacking on the molybdenum. In the present study, the activation energies of methane C−H bond dissociation over Mo(CH2)x/HZSM-5 systems (24−48 kcal/mol) are comparable to the results in the literature. It is indicated that the methane C−H bond inserts into the MoCH2 double bond with hydrogen bound to carbon and the residual methyl bound to molybdenum.

Figure 9. Optimized structures of the stationary states for methane dehydrogenation and coupling to ethylene over active center Mo(CH2)2(CH3)+/ZSM-5. The ball-stick mode denotes the atoms concerned with the reactions, and the tube mode denotes the framework atoms of zeolite.

We have calculated the single-point energies for each elementary step involved in MDHC over A1 at a higher level (B3LYP/6-311++G**) and examined the reaction energies and activation energies. It was found that the differences of the values between two methods are lower than 2 kcal/mol. Thus, the sensitivity of the results to the theoretical levels is moderate. In the next section, we will discuss the mechanisms of MDHC and compare the results with previous literature.

4. DISCUSSIONS 4.1. Mechanisms of Methane C−H Bond Dissociation. Many theoretical studies have been performed for methane activation on metal oxide supported zeolite catalysts.38,51,52 4067



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and adsorbed ethylene. By checking the energy gaps, the methane activation can occur between the LUMO of Int1 and the HOMO of CH4. The split Hδ+ approaches C1 of adsorbed ethylene, and the H 3Cδ− binds to Mo, leading to a Mo(−C2H5)(−CH3) fragment. The corresponding activation energy is higher than that in the first step (48 vs 25 kcal/mol), in accordance with the larger energy gap (8.30 eV) between the reactive orbitals in this reaction step. 4.2. Mechanisms of Dehydrogenation. Many theoretical studies have been reported for the dehydrogenation mechanism of light alkanes catalyzed by a zeolite Brønsted acid proton.53,54 Zheng et al.54 studied the ethane dehydrogenation catalyzed by the acidic proton of zeolite and suggested a “carbenium” mechanism. In the transition state, a dihydrogen molecule was almost formed, and the carbon atom attached to the acidic proton became a planar structure. The obtained activation energy was 75.9 kcal/mol. However, the dehydrogenation without the contribution of acidic proton was less studied. Zhou et al. 37 used DFT to investigate the methane dehydrogenation with the Mo(CH3)3(AlOSi) cluster model as the active site in the Mo/HZSM-5 catalyst. The activation of methane was started by adsorbing on the Mo d-orbital; in the transition state a 2e−3c bond was formed, and both of the H atoms were simultaneously activated with an energy barrier of 57.3 kcal/mol. After eliminating the hydrogen molecule, a Mo− methylidene species was formed. Very recently, Pereira et al.55 investigated the dehydrogenation reaction of light alkanes on the (GaH2)+ center exchanged on the MFI zeolite using a T22 cluster and DFT method. In the concerted mechanism, the breaking of the C−H bond and the elimination of both the molecular hydrogen and the ethylene occur simultaneously, and the activation energy obtained is 66.8 kcal/mol. In the transition state, the C−H and Ga−H bonds are to be broken, and the H−H distance is 0.84 Å. On the whole, the activation energies of dehydrogenation in those reports are between 57 and 75 kcal/mol, in the same order of our results for the last step. Regarding the mechanism of methane activation and dehydrogenation, our result is similar to that suggested by Zhou et al.37 As demonstrated in Scheme 5, an active

According to the frontier molecular orbital theory, a reaction prefers to occur between the frontier orbitals having the lowest energy gap. Our calculations indicated that the activation of methane over A1 and A2 proceeds between the LUMO of CH4 (C−H σ*-orbital) and the HOMO of the Mo active centers, while on A3 it was reversed. The frontier molecular orbitals of A1, A2, and A3 are presented in Figure 11. For both A1 and A3,

Figure 11. Frontier molecular orbitals for active centers of Mo2(CH2)52+, Mo2(CH2)42+, and Mo(CH2)2(CH3)+ exchanged on HZSM-5 zeolite.

the HOMO and LUMO are related to π- and π*-orbitals of MoCH2 bonds, respectively. For A2, the HOMO is a d−d σorbital of Mo−Mo, while the π-orbital of the MoCH2 double bond is attributed to the HOMO-1; the energy gap between the HOMO-1 of A2 and LUMO of methane (8.63 eV) is higher by 0.41 eV than that between the HOMO of A1 and LUMO of methane (8.22 eV), which can explain why the activation energy of TS1 over A2 is much higher than that over A1. In the case of A3, the energy gap between the LUMO of A3 and HOMO of CH4 (8.20 eV) is smaller. It is interesting that although the reactive orbitals for these two systems are reversed the energy gaps between the reactive orbitals are similar, and the activation energies of TS1 on A1 and A3 are almost equivalent. With regard to the atomic charges on Mo active centers, one can see in Table 2 that the natural charges of Mo in A1, A2, and A3 are 0.98, 0.85, and 0.58e, respectively, inconsistent with the activities of Mo active centers. Therefore, it is suggested that the methane activation on the MoCH2 bond is controlled by molecular orbitals but not by electrostatic factors. The activation of the second methane follows a similar mechanism. In the case of A1, the HOMO of Int1 is composed mainly of the σ orbitals between Mo and adsorbed ethylene and the π orbital of MoCH2 on the neighboring Mo atom (see Figure 6). The LUMO is mainly the σ* orbital between Mo

Scheme 5. Schematic Mechanism of C−C Coupling and Elimination of Molecular Hydrogen and Ethylene on Zeolite-Supported Mo Carbides

intermediate containing the Mo(−CH3)2 fragment is produced by methane activation, and then dehydrogenation occurs between the adjacent Mo−CH3 groups. In the transition state, the H−H pair situated on C of the Mo−CH2 group, building a 2e−3c unit. In this unit, the carbon is found in the sp3 hybrid state according to the NBO analysis. After elimination of molecular hydrogen, the MoCH2 bond is generated. The geometry of the transition state is closer to the 4068



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via the similar process, the hydrogen molecule and ethylene will be removed, and the original active center is regenerated. The three models of Mo2(CH2)52+, Mo2(CH2)42+, and Mo(CH2)2CH3+ present similar catalytic mechanisms for MDHC. The π-orbitals of the MoCH2 group are responsible for methane C−H bond activation, and the neighboring dorbitals of the Mo atom encourage C−C coupling. Dehydrogenation and C−C coupling occur in a synergetic process, which can reduce the activation energy of the dehydrogenation reaction. It is suggested that dehydrogenation is the ratedetermining step for methane dehydrogenation and C−C coupling to ethylene.

dehydrogenized product. The energy barriers for dehydrogenation are higher than those for methane C−H bond dissociation, comparable to the theoretical results of other dehydrogenation reactions.54,55 However, the energy barriers of the dehydrogenation reaction in the second step over A1 and A3 are obviously lower than that in the last step, implying that the dehydrogenation with simultaneous C−C coupling is much easier to take place. Nevertheless, hydrogenation is the ratedetermining step for MDHC on active center models of A1, A2, and A3, and the corresponding activation energies are 67.4, 62.1, and 52 kcal/mol, respectively. The calculated results account for the experimental fact12−15 that methane conversion on Mo/HZSM-5 occurs at 973 K. One important and challenging question remaining in our proposed mechanisms is the nature of the intermediates involved in the formation of C−C bonds from CHx fragments formed by methane C−H bond activation. Ding et al.23 probed the quenching of CH 4 conversion and examined the deuteriogenation of any present CHx using D2. They found that CH2 appears to be the most abundant surface fragment present during methane reactions, whereas CH3 fragments are less abundant. This experimental result implies that the CH2 and CH3 are possible intermediates over the Mo center, which is in good agreement with our proposed mechanisms. 4.3. Mechanisms of C−C Coupling and Generation of Ethylene. As illustrated in Scheme 5, after elimination of molecular hydrogen, two adjacent Mo−methylidene groups tend to form a C−C σ-bond; the p orbital of each carbon atom overlaps with the dxz and dx2‑y2 orbitals of Mo, respectively, resulting in the chemisorption complex of ethylene on Mo species. The corresponding sorption energy of ethylene on Mo was evaluated as 15.4 kcal/mol. After the second course of methane activation and dehydrogenation, the ethylene molecule is released, and the original active center is regenerated. In all of these processes, the carbon atoms are bonded with d orbitals of Mo. The unsaturated carbons bound with immediately adjacent d orbitals of Mo can combine to form C−C coupling. The MoCH2 π-bonding is stronger than the σ-bonding between Mo and quasi-ethylene; therefore, ethylene can be released when a new MoCH2 bond is formed.

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ASSOCIATED CONTENT

S Supporting Information *

Geometries of the optimized structures of Mo2C42+ and Mo2C52+ species exchanged on HZSM-5 zeolite and NBO analysis of the bonding characteristics for A1 (Mo2(CH2)52+/ ZSM-5), A2 (Mo 2 (CH 2 ) 4 2+ /ZSM-5), and A3 (Mo(CH2)2(CH3)+/ZSM-5). This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: 86-411-82158088. Fax: 86-411-82158088. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We gratefully acknowledge the financial support of the National Natural Science Foundation of China (grants 20773058). The authors thank Prof. Dr. Xinhe Bao from DICP for helpful discussions.

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REFERENCES

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5. CONCLUSION In this Article, we investigate the entire catalytic cycle for methane dehydrogenation and coupling to ethylene over a Mo/ HZSM-5 catalyst by DFT calculations. Three different active center models of Mo2(CH2)52+, Mo2(CH2)42+, and Mo(CH2)2CH3+ exchanged on HZSM-5 zeolite are optimized, and the reaction mechanisms of MDHC on these models are studied and compared. The catalytic cycle of MDHC consists of four elementary steps: (1) dissociation of the methane C−H bond; (2) dehydrogenation and C−C coupling; (3) activation of the second methane molecule; and (4) elimination of ethylene and molecular hydrogen. The methane activation occurs via heterogeneous dissociation of the C−H bond, with Hδ+ and H3Cδ− bonded to C and Mo of the MoCH2 group, respectively. Dehydrogenation proceeds by rupture of two C−H bonds in the neighboring methyl groups on the Mo atom. The residual methylidene groups bonded on the adjacent d orbitals of Mo can combine to form quasi-ethylene adsorbed on the Mo atom. After the second methane molecule is activated 4069



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