Structure of Isolated Molybdenum(VI) and Molybdenum(IV) Oxide

Article pubs.acs.org/JPCC

Structure of Isolated Molybdenum(VI) and Molybdenum(IV) Oxide Species on Silica: Periodic and Cluster DFT Studies Jarosław Handzlik* and Jan Ogonowski Faculty of Chemical Engineering and Technology, Cracow University of Technology, ul. Warszawska 24, 31-155 Kraków, Poland S Supporting Information *

ABSTRACT: The structure of monomeric molybdenum oxide species on silica is still a subject under debate. In this work, a large number of advanced silica models are used to study molybdena−silica system with density functional theory. The calculated relative energies of the monooxo and dioxo Mo(VI) species depend on the location of the Mo center on the surface and on the structure of the model. Periodic and cluster calculations employing comparable models of silica give similar results. It is shown that the monooxo Mo(VI) species can be more stable than the dioxo species under dehydrated conditions, provided that the local structure of silica enables preferable 4-fold bonding to the surface. As most locations are favorable for the 2-fold bonded dioxo Mo(VI) species, they should be dominant in the molybdena−silica system, whereas the monooxo Mo(VI) species are predicted to be in minority. The calculated frequencies of the MoO stretching mode for the monooxo Mo(VI) species are generally higher than the frequencies of the symmetric OMoO stretch for the dioxo species, corresponding to the strongest band observed experimentally. The relative energies of the reduced Mo(IV) species on silica are close to the relative energies of the corresponding Mo(VI) precursors.

1. INTRODUCTION Molybdena−silica systems are of importance in a variety of catalytic processes, among others, selective oxidation reactions1−4 and olefin metathesis.5−7 The active surface Mo forms are dispersed and often proposed to be monomeric species.4−6 Understanding the catalyst structure at the atomic level is extremely important for the investigations of the catalytic reaction mechanisms and necessary in effectively designing new catalysts. The structure of the monomeric molybdenum oxide species on silica is still a subject under debate, despite a number of studies using various spectroscopic techniques for the characterization of the molybdena−silica system.1−5,8−25 Moreover, dehydroxylation of the silica surface, dependent on the temperature, significantly changes its structure,26,27 hence influencing the geometry and properties of the surface molybdenum species.28 The isolated molybdenum(VI) oxide species on silica are often proposed to be tetrahedral dioxo species (Figure 1a), on the basis of Raman, EXAFS, XANES, UV, and photoluminescence studies.8−20 The EXAFS results indicate the presence of two shorter and two longer molybdenum−oxygen bonds, assigned, respectively, to MoO and Mo−O−Si.14−16 On the contrary, other Raman, IR, EXAFS, and XANES investigations1,3,4,21−25 suggested the presence of the isolated monooxo Mo(VI) species under dehydrated conditions. Hence, penta-coordinated molybdenum 4-fold bonded to the silica surface was expected (Figure 1b).3,4,23−25 Lee and Wachs, using combined Raman, IR, and UV−vis spectroscopy augmented with the isotopic 18 O−16O exchange study, concluded that under dehydrated © 2012 American Chemical Society

Figure 1. Proposed structures for the isolated Mo(VI) (a, b) and Mo(IV) (c, d) oxide species on silica.1,3,4,8−20,23−25

conditions the Mo(VI) oxide forms on silica are predominantly present as isolated dioxo species (Figure 1a), whereas the isolated monooxo Mo(VI) species (Figure 1b) are in minority on the surface.18,19 Information concerning the structure of the isolated Mo(IV) oxide species on silica is rather scarce. The geometry of the reduced forms should be related to the geometry of the Mo(VI) precursors.4,17,25 Therefore, the selective reduction of the tetrahedral dioxo Mo(VI) species would result in three-coordinate Received: August 2, 2011 Revised: December 18, 2011 Published: February 1, 2012 5571

dx.doi.org/10.1021/jp207385h | J. Phys. Chem. C 2012, 116, 5571−5584

The Journal of Physical Chemistry C

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theoretical investigations of the molybdena−silica system using many different models of silica have not been reported so far. In the previous paper,34 the relative energies of isolated monooxo and dioxo Mo(VI) species on silica were calculated using several DFT methods and one selected cluster model. For that model, the monoxo form was predicted to be more stable than the dioxo species under dehydrated conditions. In the present work, we show that relative stabilities of both Mo(VI) forms depend on the silica model applied and location of the Mo center. The vibrational frequency analysis is performed to compare the theoretical frequencies for the Mo sites with the reported experimental data, and the assignments for monooxo and dioxo Mo(VI) species on silica are discussed. The structures and relative stabilities of reduced Mo(IV) forms are investigated as well.

monooxo Mo(IV) species (Figure 1c), whereas four-coordinate Mo(IV) species without a terminal oxo ligand (Figure 1d) would be formed from the monooxo Mo(VI) species. Both Mo(IV) forms may probably interchange each other.25 Taking into account some contradictions involved in experimental results, a theoretical approach can be helpful in more detailed interpretation of the spectroscopic data and better understanding the structure of the monomeric Mo(VI) and Mo(IV) oxide species supported on silica. Quantum chemistry methods may also provide some complementary information about supported metal oxide systems, not accessible at this moment by experimental techniques.29 In reported theoretical studies on molybdena−silica systems,16,17,28,30−36 surface Mo species were described using various models of different sizes. On the basis of ab initio calculations applying small silica models with 1−2 silicon atoms, it was concluded that both dioxo and monooxo Mo(VI) structures may be stable.16 Bell and co-workers, using more advanced silica models in their DFT investigations, showed that surface dioxo and monooxo Mo(VI) species can be in equilibrium with each other.17 However, by comparing the experimental XANES, EXAFS, and Raman data for Mo(VI)/SiO2 and Mo(IV)/SiO2 systems with the corresponding theoretical results, the authors concluded that isolated Mo(VI) species on silica exist as dioxo species (Figure 1a), and Mo(IV) forms are present as monooxo species (Figure 1c). Their calculated MoO stretching frequencies for the monooxo Mo(VI) species are higher than the theoretical frequencies for both symmetric and asymmetric OMoO stretching modes for the Mo(VI) dioxo species, giving support for the assignments proposed by Wachs and co-workers.18−20 Those findings were also confirmed by DFT investigations of isolated Mo(IV)28 and Mo(VI)34 oxide species on silica modeled with clusters cut off from the β-cristobalite structure. In contrast, Gregoriades and coworkers in the DFT study on the molybdena−silica system,35 applying polyhedral oligomeric silsesquioxane-based models to describe silica, obtained the theoretical MoO frequency for the Mo(VI) monooxo species lower than the frequency of the symmetric OMoO stretching vibration. Taking into account the experimental data, this result suggests that the monooxo Mo(VI) species may be dominant in the calcinated molybdena− silica system, in opposition to the conclusions of Wachs and coworkers.18−20 In the very recent work of Hermann and coworkers, experimental NEXAFS spectra for the molybdena−SBA15 system were compared with the theoretical spectra for the cluster models of Mo(VI) oxide species on silica.36 On this basis, it was concluded that tetrahedrally coordinated dioxo Mo(VI) species is dominant in the molybdena−SBA-15 catalyst, whereas a pentahedrally coordinated monooxo species exists in minority if at all. It seems that the theoretical results obtained for the molybdena−silica system depend on the type and size of the silica model used in the calculations. Therefore, in the present work, a systematic theoretical study on the structure and properties of monomeric Mo(VI) and Mo(IV) oxide species on silica is undertaken, applying both periodic and advanced cluster models. The results obtained with the periodic and corresponding cluster calculations employing the β-cristobalite structure are compared. Moreover, other cluster models of various sizes, based on the β-cristobalite and amorphous structures of silica, are used as well. In the case of the largest clusters, the hybrid QM/QM ONIOM method is applied37 to enable effective computation. To the best of our knowledge, such comprehensive

2. COMPUTATIONAL METHODS AND MODELS 2.1. Periodic Calculations. The periodic models of silica are based on the β-cristobalite structure.38 Although the high surface area silica is a noncrystalline material, it was reported that its local structure resembles specific faces of β-cristobalite whose bulk density and refractive index are close to those of amorphous silica.26,27 In the previous works28,32−34 and in a number of other computational studies,39−46 the β-cristobalite structure was used to model amorphous silica. The bulk structure of silica has been calculated in the tetragonal I4̅2d space group with Si in 4(a) and O in 8(d) crystallographic positions.38 The cell shape and internal parameters have been relaxed for a set of fixed volumes to determine the equilibrium volume of the lowest energy. Surfaces are modeled by nine-layer slabs, constructed by cutting the bulk parallel to the (001) and (110) crystallographic planes ((100) and (010), respectively, in the notation referring to the Fd3m space group). The surface unit cell dimensions (Å) are a = 15.208 and b = 10.139 for the (001) plane and a = 15.444 and b = 10.296 for the (110) plane. The vacuum between the slabs is set to about 20 Å. Both surfaces of each slab are terminated by oxygen atoms saturated with hydrogens. The bottom four layers are frozen in the geometry of the bulk, whereas the remaining upper layers have been allowed to relax. The models of the surface fully covered with hydroxyl groups (unit formula = Si24O60H24) and partially dehydroxylated (unit formula = Si24O57H18) have been built. The molybdenum species have been attached to the partially dehydroxylated surface by replacing one or two pairs of silanol groups. The periodic calculations have been performed with the Vienna Ab Initio Simulation Package (VASP)47−49 using the Perdew and Wang (PW91) generalized gradient approximation exchange-correlation functional.50 The one-electron wave functions are developed on a basis set of plane waves. Atomic cores are described with the projector-augmented wave method (PAW).51 Standard PAW atomic parameters are used, requiring a cutoff energy of 400 eV (fixed by the oxygen atom). For molybdenum, the PAW is built with 12 electrons in the valence. In the case of the bulk structure optimization, the cutoff energy has been increased to 520 eV. We have used the Γ-centered Monkhorst−Pack52 sampling of the Brillouin zone. On the basis of energy convergence tests, a 444 mesh for the bulk calculations has been chosen. In the case of the surface supercells, being much larger than the bulk unit cell, a 221 mesh has been applied. As an additional test, the geometries and energies for selected models of Mo(VI) surface species have been also calculated with 441 mesh. The total energies obtained with 5572



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221 and 441 mesh differ by less than 1 kJ·mol−1, whereas the differences in relative energies are below 0.1 kJ·mol−1. For selected models, frequency calculations have been carried out by numerical differentiation of the force matrix. All the optimized degrees of freedom were used for the frequency calculations. For the graphic presentation of the structures, Materials Studio 4.4 software is used.53 2.2. Cluster Calculations. Silica cluster models of different sizes have been prepared. A part of them are cut off from the β-cristobalite framework, whereas other models are derived from the structure of the amorphous silica surface (Materials Studio library53). The dangling bonds have been saturated with hydrogens replacing the removed Si atoms. The respective molybdenum species have been attached to the partially or fully dehydroxylated surface. The two-layer ONIOM partitioning scheme has been applied for the geometry optimization of the largest cluster models, containing 63, 72, or 97 Si atoms. In the ONIOM method, the whole system (real system) is divided into the inner layer and the outer layer. This involves cutting off the O−Si bonds in the boundary region, and hence, hydrogen atoms (the link atoms) are added to the inner layer, giving the model system. The total extrapolated energy EONIOM of the whole system is defined as37

employed. In each case, the geometry of the whole system has been fully optimized at the PW91/SVP level, followed by PW91/TZVP single-point energy calculations. It was recently shown that the PW91 functional belongs to the most accurate DFT methods in predicting the relative energies of molybdenum compounds.34 In all cases, the geometry optimization has been carried out employing the Berny algorithm with redundant internal coordinates.58 Harmonic vibrational frequencies and Gibbs free energy corrections have been evaluated for the mediumsize cluster models. The rotational and translational contributions to Gibbs free energy are not included for the models, only for the compounds in the gas phase. The reported energies (ΔE) are not ZPE-corrected, to enable comparison with the larger models. The calculations have been done with the Gaussian 03 suite of programs.59 For the graphic presentation of the systems studied, the GaussView 5.0 software60 is used.

3. RESULTS AND DISCUSSION 3.1. Periodic Models of Silica. The calculated geometrical parameters for the bulk structure of β-cristobalite are in very good agreement with the experimental data38 (Table 1). The

EONIOM = Elow (real) − Elow (model) + Ehigh(model)

Table 1. Cell Parameters (Å), Atomic Distances (Å), and Angles (degrees) for the Bulk Structure of β-Cristobalite (I4̅2d Space Group)

where Elow(real) is the energy of the entire system, calculated at a low level of theory; Elow(model) is the energy of the model system, calculated at the low level method; and Ehigh(model) is the energy of the model system calculated at a high level method. Here, the inner layer includes the Mo species and its vicinity, at least the third coordination sphere of the molybdenum. It was previously shown that such a size of the inner layer is sufficient for the proper description of the molybdenum surface site.33 The scale factor g = 0.5289, determining the O−H bond length in the model system, on the basis of the corresponding O− Si distance in the real system, has been applied. It was verified that the relative energies calculated for the molybdena−silica system are hardly sensitive to the specific value of the scale factor g.33 The geometries of the molybdenum species have been optimized together with the upper parts of the SiO2 clusters based on the β-cristobalite structure, analogous to the periodic models. The positions of other atoms and the terminating hydrogens are frozen. The clusters obtained from the amorphous silica structure have been fully relaxed. The inner layer and the link atoms are described at the DFT level, using the PW91 functional and the split-valence def2-SVP basis set (abbreviated as SVP).54 The 28 innermost electrons of Mo are replaced by the Stuttgart effective core potential (ECP).55 The Hartree−Fock method combined with the LANL2MB basis set (the Hay−Wadt ECP plus minimal basis for Si56 and Mo;57 the STO-3G basis set for O and H) is employed as the low level method. The geometry optimization with the ONIOM scheme has been followed by traditional single-point energy calculations using the PW91 functional for the whole system. The atoms that previously constituted the inner layer are here described with the triple-ζ valence def2-TZVP basis set (abbreviated as TZVP)54 with the Stuttgart ECP for Mo, whereas the SVP basis set is applied for the rest of the system. This basis set combination is denoted here as TZVP-SVP. Medium-size models of the molybdena−silica system, containing 15, 21, 24, or 26 Si atoms and derived from both the β-cristobalite and amorphous SiO2 structures, have been also

a c Si−O Si−O−Si O−Si−O

calcd

exptl38

5.069 7.390 1.624 149.9 108.9 110.7

5.042 7.131 1.611 146.7 107.8 112.8

observed small overestimation of the lattice constants is typical for the GGA DFT methods.40 The obtained values are also close to other theoretical results.39,40,42,44,46,61 As expected,27,39−42,44,46 hydrogen bonds are formed between neighboring silanols on the fully hydroxylated silica surface (Figure S1, Supporting Information). The calculated O···H distances are 1.67 and 1.63 Å, for the (001) and (110) planes, respectively, in accordance with other theoretical studies on β-cristobalite (1.64−1.71 Å).39,42,44 Partially dehydroxylated β-cristobalite surfaces are shown in Figure 2. A water molecule has been eliminated from a hydrogen-bonded silanol pair, and a siloxane bridge is formed. In each case, three water molecules per unit cell have been removed. For the (001) plane, two different dehydroxylation patterns are considered (A and B). Both surfaces hardly differ from each other in energy, by 0.02 eV per supercell. The arrangement of the silanol groups on the partially dehydroxylated (110) surface (C) is analogous to the model B. 3.2. Surface Mo SpeciesPeriodic Models. To model the monomeric Mo(VI) and Mo(IV) species on silica (Figure 1), respective molybdenum oxide structures have been placed on the partially dehydroxylated surfaces A, B, and C. The optimized structures of the Mo(VI) monooxo species (1A) and Mo(VI) dioxo species (2A, 3A) attached to the surface A are presented in Figure 3. The structure 1A has distorted square pyramidal geometry, whereas the molybdenum atom in 2A and 3A is tetrahedrally coordinated, analogous to other theoretical 5573



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Figure 3. Optimized structures of the Mo(VI) (1A, 2A, 3A) and Mo(IV) (1A_r, 2A_r, 3A_r) oxide species on (001) β-cristobalite (periodic models).

3A_r).4,17,25,31 The Mo(IV) species grafted on the surface B (1B_r, 2B_r and 3B_r) have been also optimized (Figure S2, Supporting Information). In all cases, removing one oxo ligand from the Mo(VI) species does not cause other significant structural changes in the system. Consequently, the relative energies of the Mo(IV) species are close to the relative energies of the corresponding Mo(VI) precursors (Table 2), and the

Figure 2. Partially dehydroxylated (001) (A, B) and (110) (C) surfaces of β-cristobalite (periodic models).

results.17,31,34−36 In the case of the model 2A, one of the oxo ligands interacts with two neighboring surface silanols. The calculated O···H distances are 2.28 and 2.34 Å. After the replacement of these hydroxyl groups by a siloxane bridge, the structure 3A is obtained. Hence, the latter, corresponding to fully dehydrated conditions, can be regarded as the product of 2A dehydration and can be directly transformed to the monooxo species 1A. The models of the Mo(VI) sites on the surfaces B (1B, 2B, 3B) and C (1C, 2C, 3C) are fully analogous to the corresponding structures on the surface A (Figure S2, Supporting Information). The calculated energies for the dehydration reactions of the dioxo Mo(VI) species 2A−2C to the corresponding monooxo Mo(VI) species 1A−1C as well as the energies of the direct transformation of the dehydrated dioxo Mo(VI) species 3A− 3C to the monooxo species are presented in Table 2. All these reactions are clearly endothermic. The energies hardly depend on the specific model (A, B, or C) because in all cases the local silica structure in the vicinity of the Mo site is similar (Figure 3 and Figure S2, Supporting Information). Therefore, on the basis of the results obtained with the periodic models proposed, it can be concluded that the dioxo Mo(VI) species on silica are much more stable than the monooxo Mo(VI) species. The reduction of the monooxo Mo(VI) species 1A can result in four-coordinate Mo(IV) species that does not possess a terminal oxo ligand (1A_r, Figure 3), whereas the reduction of the dioxo Mo(VI) species 2A and 3A can lead to monooxo Mo(IV) species with two Mo−O−Si linkages (2A_r,

Table 2. Energiesa (ΔE, kJ·mol−1) for the Conversion of the Dioxo Mo(VI) Species (2A, 2B, 2C, 3A, 3B, 3C) to the Monooxo Mo(VI)Species (1A, 1B, 1C) and for the Conversion of the Monookso Mo(IV) Species (2A_r, 2B_r, 3A_r, 3B_r) to the Mo(IV) Species without the Oxo Ligand (1A_r, 1B_r) ΔE

reaction

a

2A → 1A + H2O

342

2A_r → 1A_r + H2O

2B → 1B + H2O

reaction

ΔE

3A → 1A

134

324

3A_r → 1A_r

136

331

3B → 1B

132

2B_r → 1B_r + H2O

305

3B_r → 1B_r

133

2C → 1C + H2O

327

3C → 1C

113

Periodic calculations.

monooxo Mo(IV) species are predicted to be stable forms. Thus, the relative stabilities of the reduced Mo(IV) species are determined by the relative stabilities of their Mo(VI) precursors. 3.3. Surface Mo SpeciesCluster Models Based on the β-Cristobalite Structure. The models of the Mo species involving large clusters of β-cristobalite and optimized with the hybrid ONIOM method are shown in Figure 4. The Mo(VI) structures 1a−3a and 1b−3b are attached to the partially dehydroxylated (001) surfaces and correspond to the periodic models 1A−3A and 1B−3B, respectively (Figure 3 and Figure S2, 5574



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Figure 4. Optimized structures of the Mo(VI) (1a−3a, 1b−3b, 1b_fd−3b_fd, 1c−3c) and Mo(IV) (1a_r−3a_r, 1b_r−3b_r) oxide species on silica. The cluster models are cut off from the (001) (series a, b) and (110) (series c) β-cristobalite surface (PW91/SVP:HF/LANL2MB calculations). The wireframe parts of the models represent the outer layers.

The Mo(VI) structures obtained with the cluster approach are very similar to the corresponding periodic models. The monooxo species 1a−1c have distorted square pyramidal geometry, whereas the dioxo species 2a−2c and 3a−3c are tetrahedrally coordinated. In the case of 2a−2c, hydrogen bonds are formed between the respective oxo ligands and the neighboring surface silanols. The calculated O···H distances are in the range of 1.90−2.36 Å. Alternative models of partially hydrated dioxo Mo(VI) species have been also considered (2a′−2c′, Figure S3, Supporting Information). These structures

Supporting Information). The 1b_fd−3b_fd species are obtained from the 1b−3b models by full dehydroxylation of the silica surface, excluding two silanols in the vicinity of the Mo site, in the case of 2b_fd. This results in formation of strained two-membered Si rings on the surface and SiO defects on the cluster periphery. Finally, the Mo(VI) species 1c−3c are attached to the partially dehydroxylated (110) β-cristobalite surface and correspond to the periodic models 1C−3C (Figure S2, Supporting Information). 5575



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are more strained than the forms 2a−2c and, consequently, less stable by 50−136 kJ·mol−1. The calculated energies for the dehydration reactions of the dioxo Mo(VI) species 2a−2c to the corresponding monooxo Mo(VI) species 1a−1c and the energies of the direct transformation of the dehydrated dioxo Mo(VI) species 3a− 3c to the monooxo species are listed in Table 3. Similar to the results obtained for the periodic models, all these reactions are endothermic, indicating that the dioxo Mo(VI) species are more stable than the monooxo Mo(VI) species. The full dehydroxylation of the surface (1b_fd−3b_fd) only slightly influences the relative energies, compared to the partially dehydroxylated silica (1b−3b). Interestingly, despite the different calculation methodologies, the corresponding reaction energies for the periodic and cluster models representing the (001) surface are quite close to each other (Tables 2 and 3). Table 3. Energiesa (ΔE, kJ·mol−1) for the Conversion of the Dioxo Mo(VI) Species (2a, 2b, 2b_fd, 2c, 3a, 3b, 3b_fd, 3c) to the Corresponding Monooxo Mo(VI) Species (1a, 1b, 1b_fd, 1c) and for the Conversion of the Monookso Mo(IV) Species (2a_r, 2b_r, 3a_r, 3b_r) to the Corresponding Mo(IV) Species without the Oxo Ligand (1a_r, 1b_r) reaction

a

ΔE

reaction

of the direct transformation of the dehydrated dioxo Mo(VI) species (3d, 3e) to the monooxo species are listed in Table 4. Considering electronic energies at T = 0 K, the dehydration reactions are endothermic, but this effect is much weaker than in the case of the periodic models and large cluster models (Tables 2 and 3). Moreover, reaction Gibbs free energies at T = 873 K are negative, indicating thermodynamic preference for

ΔE

2a → 1a + H2O

343

2a_r → 1a_r + H2O

318

3a_r → 1a_r

2b → 1b + H2O

343

3b → 1b

144

2b_r → 1b_r + H2O

3a → 1a

Figure 5. Optimized structures of the Mo(VI) (1d−3d, 1e−3e) and Mo(IV) (1d_r−3d_r) oxide species on silica. The cluster models are cut off from the (001) β-cristobalite surface and fully relaxed (PW91/ SVP calculations).

82 93

320

3b_r → 1b_r

143

2b_fd → 1b_fd + H2O

321

3b_fd → 1b_fd

121

2c → 1c + H2O

240

3c → 1c

Table 4. Energiesa (ΔE, kJ·mol−1) and Gibbs Free Energiesa at T = 873 K (ΔG873, kJ·mol−1) for the Conversion of the Dioxo Mo(VI) Species (2d, 2e, 3d, 3e) to the Corresponding Monooxo Mo(VI) Species (1d, 1e) and for the Conversion of the Monookso Mo(IV) Species (2d_r, 3d_r) to the Corresponding Mo(IV) Species without the Oxo Ligand (1d_r)

37

PW91/TZVP-SVP//PW91/SVP:HF/LANL2MB calculations.

On the other hand, the energetic preference for the dioxo species on the (110) surface is less strong than in the case of the (001) surface if the cluster models are considered. For the periodic models, this tendency is hardly seen. Nevertheless, the general conclusions drawn from the periodic and corresponding cluster calculations employing the β-cristobalite structure of SiO2 are the same. Similar to the periodic models, reduced Mo(IV) species have been obtained from the respective Mo(VI) structures by removing one oxo ligand (1a_r−3a_r, 1b_r−3b_r, Figure 4). The relative energies of the Mo(IV) species do not differ significantly from the relative energies of the corresponding Mo(VI) precursors (Table 3). To enable calculations of the whole system at higher level of theory, medium-size cluster models of the Mo sites on silica have also been proposed (Figure 5). These systems have been fully optimized, and consequently, the SiO2 part of the model, initially cut off from the β-cristobalite structure, is distorted and more flexible, compared to the large SiO2 clusters with partially frozen geometry. Such an approach is justified by the amorphous structure of silica in real molybdena−silica systems. Models 1d−3d of the monooxo and dioxo Mo(VI) species represent the partially dehydroxylated silica surface. After the replacement of four hydroxyl groups at the edges of each model by two siloxane bridges, the structures 1e−3e are obtained (Figure 5). The calculated energies for the dehydration reactions of the dioxo Mo(VI) species (2d, 2e) to the corresponding monooxo Mo(VI) species (1d, 1e) and the energies

reaction

ΔE

ΔG873

reaction

ΔE

ΔG873

2d → 1d + H2O

53

−48

3d → 1d

−107

−88

2d_r → 1d_r + H2O

43

−44

3d_r → 1d_r

−111

−66

2e → 1e + H2O

57

−48

3e → 1e

−112

−92

a

PW91/TZVP//PW91/SVP calculations.

the monooxo Mo(VI) species at high temperatures. Additionally, Gibbs free energies for the dehydration reaction involving the models 2e and 1e have been calculated as a function of temperature and water vapor pressure (Table 5). It is seen that under dehydrated conditions the monooxo Mo(VI) species is predicted to be more stable than the dioxo species even at T = 473 K. On the other hand, the removal of the two hydroxyl groups from the vicinity of the dioxo Mo(VI) center 2e, i.e., its transformation to 3e, is thermodynamically unfavorable up to strictly dehydrated conditions (Table 5). Thus, the presence of the monooxo Mo(VI) species 1e, not the dioxo species 3e, is predicted under dehydrated conditions. The same conclusion is drawn when the energies and Gibbs free energies for the monooxo species and dehydrated dioxo species are directly compared (Table 4). 5576



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Table 5. Gibbs Free Energiesa (kJ·mol−1) for the Dehydratation of the Dioxo Mo(VI) Species (2e, 2g, 2h, 2i′) to the Corresponding Monooxo (1e, 1g, 1h, 1i) and Dioxo (3e, 3g, 3h, 3i′) Mo(VI) Species As a Function of Temperature and Water Vapor Pressure 473 K reaction

a

10

−2

atm

673 K −5

10

atm

10

−2

atm

2e → 1e + H2O

−22

−49

−52

2e → 3e + H2O

79

52

2g → 1g + H2O

93

66

2g → 3g + H2O

−85

2h → 1h + H2O

9

873 K −5

10

atm

−2

10

atm

10−5 atm

−90

−81

−131

44

6

11

−39

60

21

27

−23

−112

−110

−149

−134

−184

−18

−25

−64

−58

−108

2h → 3h + H2O

−7

−34

−44

−83

−81

−131

2i′ → 1i + H2O

114

87

89

51

65

15

2i′ → 3i′ + H2O

−8

−35

−38

−76

−67

−117


Figure 6. Optimized structures of the Mo(VI) oxide species on silica. The cluster models are cut off from the amorphous silica structure and fully relaxed (PW91/SVP:HF/LANL2MB calculations). The wireframe parts of the models represent the outer layers.

the Mo(IV) species are rather close to the relative energies of the corresponding Mo(VI) precursors (Table 4). 3.4. Surface Mo SpeciesCluster Models Based on the Amorphous Silica Structure. A very large silica cluster (97 Si atoms) representing the partially dehydrated surface with isolated hydroxyl groups has been employed. Geminal silanols are present only on the cluster periphery, as a consequence of the saturation of the dangling bonds by hydrogen atoms. The cluster consists of interconnected (SiO2)n rings of various sizes (n = 3−10), similar to other theoretical structures of amorphous silica.62,63 Whereas the dioxo Mo(VI) species can be placed on our model practically everywhere, it is more difficult to find a location favorable for attaching the monooxo Mo(VI) species being 4-fold bonded to the surface. Some attempts to force the square pyramidal coordination of variously located Mo(VI) centers have been unsuccessful, for instance, for the localization on the four-membered ring, proposed for smaller models.17 Finally, the monooxo Mo(VI) structure 1f (Figure 6) has been considered. It is attached to silicon atoms belonging to a common ten-membered ring or, alternatively described, to fourmembered, five-membered, and six-membered Si rings. The system has been fully optimized using the ONIOM scheme. After adsorption of a water molecule on the surface, various dioxo Mo(VI) species (2f, 2f′, 2f″) can be formed from 1f. In each case, a hydrogen bond is formed between one oxo ligand

The different relative energies of the monooxo and diooxo Mo(VI) species obtained with the large and medium-size cluster models can be explained mainly by higher flexibility of the smaller models. Full geometry optimization of the mediumsize models enables better adaptation of the silica surface to the formation of the four Mo−O−Si linkages for the monooxo Mo(VI) structure. In the case of the partially optimized large silica models maintaining the β-cristobalite structure, the surface is more rigid, and consequently, the Mo(VI) monooxo species are more strained, compared to the medium-size models. The geometry constraints are less important for the dioxo species that are only 2-fold bonded to the surface. Medium-size models of four-coordinate Mo(IV) species not possessing the oxo ligand (1d_r) and three-coordinate monooxo Mo(IV) species (2d_r, 3d_r) are shown in Figure 5. In the cases of 1d_r and 3d_r, the geometries for both triplet and singlet states have been optimized. The triplet state of 3d_r is more stable than the singlet state by 18 kJ·mol−1 (ΔE). On the other hand, the predicted ground state for 1d_r is singlet, lower in energy by 23 kJ·mol−1, compared to the triplet state. This is in agreement with the reported results for smaller models of the Mo(IV) oxide species on silica.17,28 Consequently, all fourcoordinate Mo(IV) species presented in this work are calculated as singlet states, whereas the monooxo Mo(IV) structures are always triplet states. Similar to the results obtained for the periodic and large cluster models (Tables 2 and 3), the relative energies of 5577



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and one or two neighboring hydroxyl groups. Dioxo species 3f and 3f′ can be directly obtained from 1f or by the dehydration of the structures 2f and 2f′, respectively. Relative energies of the monooxo and dioxo Mo(VI) species 1f−3f are compared in Table 6. The dehydration reactions of Table 6. Energiesa (ΔE, kJ·mol−1) for the Conversion of the Dioxo Mo(VI) Species (2f, 2f′, 2f″, 3f, 3f′) to the Corresponding Monooxo Mo(VI) Species (1f) and for the Conversion of the Monookso Mo(IV) Species (2f_r, 2f′_r, 3f′_r) to the Corresponding Mo(IV) Species without the Oxo Ligand (1f_r) reaction

2f → 1f + H2O

101

2f_r → 1f_r + H2O

82

2f′ → 1f + H2O

21

2f′_r → 1f_r + H2O

12

2f″ → 1f + H2O

a

ΔE

4

3f → 1f

−102

3f′ → 1f

−148

3f′_r → 1f_r

−138

PW91/TZVP-SVP//PW91/SVP:HF/LANL2MB calculations.

the dioxo species 2f−2f″ to the monooxo structure 1f are endothermic, but the predicted reaction energy is much lower than in the case of the large models based on the β-cristobalite structure (Table 3). If Gibbs free energies were calculated for the dehydrated conditions, like in the case of the smaller models (Table 5), the monooxo Mo(VI) species 1f would be rather thermodynamically preferred over the dioxo species 2f− 2f″ (compare, for instance, ΔE and ΔG values for the reaction 2e → 1e + H2O, Tables 4 and 5). When the energies of the monooxo species 1f and the dehydrated dioxo species 3f and 3f′ are compared, it is seen that the monooxo structure is more stable (Table 6). Consequently, the surface dehydration reactions 2f → 3f (ΔE = 203 kJ·mol−1) and 2f′ → 3f′ (ΔE = 168 kJ·mol−1) are more endothermic than the corresponding dehydration reactions leading to 1f (Table 6). Thus, the monooxo Mo(VI) species can be present on silica under dehydrated conditions, at least for some locations on the surface. These results differ from those obtained with the large and more rigid models based on the β-cristobalite structure. Similar to the previously discussed models, reduced Mo(IV) species have been obtained from the respective Mo(VI) structures by removing one oxo ligand (1f_r, 2f_r, 2f′_r, 3f′_r, Figure 7). Again, the relative energies of the Mo(IV) species do not differ significantly from the relative energies of the corresponding Mo(VI) precursors (Table 6). To enable efficient calculations of the whole system at higher level of theory, medium-size clusters have been derived from the amorphous silica structure to build the models of the Mo oxide species (Figure 8). Different models (series g, h, and i) represent different locations on the silica surface. The monooxo Mo(VI) species 1g is attached to four-membered, five-membered, and six-membered Si rings. The monooxo structure 1h is attached to Si atoms belonging to coupled five-membered and sevenmembered rings. Finally, the monooxo species 1i is bonded to three-membered and five-membered Si rings.

Figure 7. Optimized structures of the Mo(IV) oxide species on silica. The cluster models are cut off from the amorphous silica structure and fully relaxed (PW91/SVP:HF/LANL2MB calculations). The wireframe parts of the models represent the outer layers.

According to the notation used in this work, 2g−2g″, 2h− 2h″, and 2i−2i″′ are the partially hydrated dioxo Mo(VI) species, whereas 3g, 3g″, 3h, 3h″, and 3i−3i″ are the dehydrated dioxo species. The structures 2g, 2h, and 2i′ are most stable in terms of Gibbs free energy (ΔG873) among the partially hydrated dioxo Mo(VI) species, whereas the models 3g, 3h, and 3i represent the most stable dehydrated dioxo Mo(VI) species (Table S1, Supporting Information). It is noted that the dioxo species with the molybdenum atom connected via two oxygen bridges with one surface silica atom (2h″, 3h″, 2i″′) are the least stable, which can be explained by formation of a strained ring in each case, consisting of one Mo, one Si, and two O atoms. This is in agreement with previously reported results for tetrahedral Mo(VI) alkylidene centers on silica.32 Dehydration of the silica surface, accompanied by the formation of two-membered Si rings, also leads to the systems with high relative energies (3g″, 3h″, and 3i″). 5578



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Figure 8. Optimized structures of the Mo(VI) oxide species on silica. The cluster models are cut off from the amorphous silica structure and fully relaxed (PW91/SVP calculations).

To compare the relative stabilities of the monooxo and dioxo Mo(VI) species shown in Figure 8, the energies at T = 0 K and Gibbs free energies at T = 873 K for the respective dehydration

and rearrangement reactions are listed in Table 7. For the most stable partially hydrated dioxo Mo(VI) species, Gibbs free energies for the dehydration reactions leading to the 5579



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Table 7. Energiesa (ΔE, kJ·mol−1) and Gibbs Free Energiesa at T = 873 K (ΔG873, kJ·mol−1) for the Conversion of the Dioxo Mo(VI) Species (2g, 2h, 2i′, 3g, 3h, 3i) to the Corresponding Monooxo Mo(VI) Species (1g, 1h, 1i) and for the Conversion of the Monookso Mo(IV) Species (2h_r, 2i′_r, 3h_r, 3i_r) to the Corresponding Mo(IV) Species without the Oxo Ligand (1h_r, 1i_r) reaction

ΔE

ΔG873

reaction

ΔE

ΔG873

2g → 1g + H2O

180

61

3g → 1g

197

161

2h → 1h + H2O

98

−25

3h → 1h

9

22

3h_r → 1h_r

92

−34

2i′ → 1i + H2O

183

99

2i′_r → 1i_r + H2O

205

132

2h_r → 1h_r + H2O

a

10

29

3i → 1i

155

158

3i_r → 1i_r

152

184


corresponding monooxo Mo(VI) species and to the corresponding dehydrated dioxo Mo(VI) species have also been calculated as a function of temperature and water vapor pressure (Table 5). It is seen from Tables 5 and 7 that the energy values are different for different models; i.e., they depend on the specific structure and location of the Mo species on the silica surface. The monooxo species 1h is clearly predicted to be thermodynamically preferred over the dioxo 2h species under dehydrated conditions. However, the removal of two hydroxyl groups from the vicinity of the dioxo center 2h, resulting in water release and the formation of the siloxane bridge (model 3h), is even more preferred (Table 5). This is also seen from the direct comparison of 1h and 3h energies (Table 7). On the other hand, the preference for the dioxo Mo(VI) species 3h is not significant (22 kJ·mol−1), hence the presence of the monooxo Mo(VI) species 1h under dehydrated conditions is possible as well. It can be noted that the structure 1h is a bit different from other monooxo Mo(VI) species considered in this work because the coordination of the molybdenum in 1h is rather distorted octahedral than square pyramidal. The monooxo species 1g can be formed from 2g only under strictly dehydrated conditions (Table 5). Moreover, the dehydration of the system 2g to 3g is strongly preferred in these conditions. Consequently, the dioxo Mo(VI) species 3g has much lower energy than the monooxo species 1g (Table 7). On the other hand, another dioxo Mo(VI) species 3g″ is even less stable than 1g, by 30 kJ·mol−1 (ΔG873). Finally, the Mo(VI) dioxo species 2i′ and 3i are predicted to be more stable than the monooxo species 1i even under strictly dehydrated conditions (Tables 5 and 7). Two of the four oxygen linkages between the molybdenum atom and the surface in 1i involve a common silicon atom, which can be the reason for the relatively low energetic stability of this species. For selected Mo(VI) species, the corresponding Mo(IV) structures have been calculated (Figure 9). 2h_r and 2i′_r are the most stable among the partially hydrated monooxo Mo(IV) species, whereas 3h_r and 3i_r represent the most stable dehydrated monooxo Mo(IV) structures (Table S2, Supporting Information). Similar to other results, the relative energies of the four-coordinate and three-coordinate Mo(IV) species are more or less close to the relative energies of the corresponding Mo(VI) precursors (Table 7). It is interesting to compare our predictions for the molybdena−silica system with theoretical results concerning monomeric Mo(VI) species attached to other commonly used

Figure 9. Optimized structures of the Mo(IV) oxide species on silica. The cluster models are cut off from the amorphous silica structure and fully relaxed (PW91/SVP calculations).

supports, like alumina and titania. Only two general types of the Mo(VI) oxide forms have been found on silica, pentacoordinate monooxo species and pseudotetrahedral dioxo species, the 5580



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MoO2(OH)2, and H2MoO2 were carried out to compare the calculated geometrical parameters and/or theoretical vibrational frequencies with the corresponding experimental data. MoOCl4 is a square pyramidal monooxo compound, whereas the others are dioxo structures with the tetrahedral geometry. The calculated (PW91/SVP) bond lengths and angles for MoOCl4 and MoO2Cl2 are close to the reported experimental data66,67 (Table 9). The theoretical bond lengths are slightly

latter being more probable. In the case of the molybdena− alumia system, more Mo species of different geometries were proposed.29 The pentacoordinate square pyramidal monooxo Mo(VI) species was shown to be the most stable on the majority (110) surface of γ-alumina under strictly dehydrated conditions, whereas tetrahedral dioxo Mo(VI) species and fivecoordinate dioxo Mo(VI) species should be dominant on the minority (100) surface. The presence of monooxo Mo(VI) species 3-fold bonded to the alumina surface is also possible. Such distorted-tetrahedral monooxo Mo(VI) species was shown to be most stable on the majority (101) anatase surface under dehydrated conditions.64,65 On the other hand, the dioxo Mo(VI) structure was calculated as the most stable species on the minority (001) anatase surface. Therefore, the geometry of the attached Mo species depends on the support, as a consequence of different structure and properties of the surface of silica, alumina, and titania. 3.5. Reduction Reactions. Mo(VI) oxide species on silica can be reduced to Mo(IV) species in the presence of H214,25 or CO.5,14 In Table 8, the energies at T = 0 K and Gibbs free a

Table 9. Calculateda and Experimental Bond Lengths (Å) and Angles (degrees) for MoOCl4 and MoO2Cl2 MoOCl4 MoO Mo−Cl OMoO OMo−Cl Cl−Mo−Cl a

a

−1

Table 8. Energies (ΔE, kJ·mol ) and Gibbs Free Energies at T = 873 K (ΔG873, kJ·mol−1) for the Reduction Reactions: Mo(VI) + H2 → Mo(IV) + H2O Mo(VI)

Mo(IV)

ΔE

ΔG873

1d 3d 1f 3f′ 1h 3h 1i 3i

1d_r 3d_r 1f_r 3f′_r 1h_r 3h_r 1i_r 3i_r

190 194 188 179 188 187 214 217

184 163 164 158 212 186

MoO2Cl2

calcd

exptl66

calcd

exptl67

1.664 2.310 103.6 86.9

1.658 2.279 102.8 87.2

1.688 2.268 106.5 112.3

1.686 2.258 106.3 113.9

PW91/SVP calculations.

overestimated, which is expected for the GGA DFT methods.68 The predicted MoO distances are longer than the reference values by less than 0.01 Å. In the case of the periodic calculations performed for the same gas phase compounds, this difference is approximately 0.02−0.03 Å.29 Theoretically determined MoO stretching frequencies for all the considered gas phase Mo compounds are compared with the experimental fundamentals69−71 in Table 10. The calculated Table 10. Calculated and Experimental MoO Stretching Frequencies (cm−1) for the Reference Compounds

a

PW91/TZVP-SVP//PW91/SVP:HF/LANL2MB calculations for 1f, 3f′, 1f_r, and 3f′_r; PW91/TZVP//PW91/SVP calculations for other systems.

MoOCl4 MoO2Cl2

energies at T = 873 K for the reduction of monooxo and dioxo Mo(VI) species by H2 are listed. If CO is taken as the reducing agent, the calculated ΔE and ΔG873 values are lower by 88 and 67 kJ·mol−1, respectively. The Gibbs free energies for the reduction of the monooxo Mo(VI) species are always higher than the corresponding quantities obtained for the reduction of the dioxo Mo(VI) species, in agreement with the theoretical results of Bell and co-workers for the MoOx/SiO2 system.17 On the other hand, their reported B3LYP energies (ΔG920) for the reduction of the surface Mo(VI) species by H2 are within 28− 59 kJ·mol−1, hence differing significantly from our numbers. To examine the influence of the DFT method applied on the results, we evaluated ΔG873 for the reduction of 3h, using the single-point energies recalculated at the B3LYP/TZVP level. The obtained value is about 50 kJ·mol−1 lower than that shown in Table 8. The additional reason of the discrepancy in the reaction energies may be the fact that different models of the silica surface were applied in ref 17 and in this study. Indeed, our results show that the energies of the reduction differ from each other up to almost 50 kJ·mol−1 for various models of the monooxo Mo(VI) species and up to 30 kJ·mol−1 for various models of the dioxo Mo(VI) species (Table 8). 3.6. Calibration of the Theoretical Methods. To validate the computational methodology used here, calculations for the gas phase Mo compounds MoOCl4, MoO2Cl2,

MoO2(OH)2 H2MoO2

calcda

calcdb

exptl

1020 992 974 980 969 1010 992

1013 995 976 984 973 1010 992

1015c 997.4d 971.4d 979.3e 985.0e

a

Periodic calculations; the frequencies are scaled by 0.9758. bPW91/ SVP calculations; the frequencies are scaled by 0.9804. cRef 69. dRef 70. eRef 71.

harmonic frequencies are scaled by 0.9758 and 0.9804, for the periodic and PW91/SVP calculations, respectively. The scaling factors have been obtained through a least-squares approach, based on the experimental MoO frequencies. It is seen from Table 10 that the scaled theoretical frequencies are close to the experimental values. 3.7. Bond Lengths. In Table 11, the molybdenum−oxygen bond lengths calculated for the dioxo Mo(VI) species on silica are presented together with the corresponding experimental EXAFS data14−16 available for the molybdena−silica system. The agreement between the theory and experiment is generally very good. As one can expect from the results for the gas phase Mo compounds, the MoO distances obtained from the periodic calculations are slightly higher than the corresponding numbers for the cluster models. The latter values are closer to the experimental bond lengths. In many models, one MoO 5581



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obtained for 1e, 1g, and 1h. The Raman activities calculated for these vibrations are much lower, however, than in the case of the vibrations included in Table 12. Regarding the models of the dehydrated dioxo Mo(VI) species, the frequencies predicted for the symmetric OMo O stretching vibrations are slightly higher, on average, than the experimental values (Table 12). The calculated frequencies for the asymmetric OMoO stretching modes match very well the reported Raman data, with the exception of 3i. In this case the OMoO vibration is very strongly coupled with the Mo−O−Si stretch. For the models of the partially hydrated dioxo Mo(VI) species considered in this work, the theoretically predicted symmetric MoO stretching frequencies are in the range of 966−995 cm−1. The symmetric Mo−O−Si stretching modes for the dioxo Mo(VI) species are mixed with the MoO stretches. The frequencies obtained for the amorphous models are slightly underestimated (Table 12). Finally, the calculated frequencies of the OMoO bending vibration are satisfactorily close to the experimental value, in agreement with Gregoriades and co-workers.35 In most cases, the theoretically predicted frequencies of the MoO stretching mode for the monooxo Mo(VI) species are higher than the frequencies of the symmetric OMoO stretch for the dioxo species. Therefore, our results give rather support for the vibrational assignments proposed by Wachs and co-workers18−20 and are in agreement with the earlier DFT studies,17 in opposition to the proposal of the reversed assignments.35 It can be noted that for molybdena−alumina29 and molybdena−titania64 systems the calculated MoO stretching frequencies for the monooxo Mo(VI) species are also higher than the frequencies for the dioxo species. On the other hand, it is not excluded that the MoO frequencies for the monooxo Mo(VI) forms on silica and the frequencies of the symmetric OMoO stretches for some dioxo Mo(VI) species can overlap (compare the results for 1h, 1i, 3g, and 3h). 3.9. Structure of the Mo(VI) Oxide Species on Silica: A Summary. The calculated relative stabilities of the monooxo and dioxo Mo(VI) species under dehydrated conditions depend on the silica model applied and, in the case of the amorphous models, on the location of the metal center. Periodic calculations employing the β-cristobalite structure indicate strong energetic preference for the dioxo Mo(VI) species (Table 2). Similar results have been obtained from the cluster calculations involving the large silica models of the β-cristobalite structure (Table 3). On the other hand, when fully optimized medium-size silica clusters are applied, initially based on the β-cristobalite geometry, thermodynamic preference for the monooxo Mo(VI) species is shown (Tables 4 and 5). These models are more flexible, compared to the large SiO2 clusters with partially frozen geometry, and therefore, the formation of four Mo−O−Si linkages is more facilitated in this case. It should be

Table 11. Calculated and Experimental Bond Lengths (Å) for the Dioxo Mo(VI) Species on Silica model periodic (β-cristobalite) 2A, 2B, 2C 3A, 3B, 3C cluster (β-cristobalite)a 2a, 2b, 2b_fd, 2c, 2d, 2e, 3d 3a, 3b, 3b_fd, 3c, 3e cluster (amorphous)a 2f, 2g, 2g′, 2h, 2h′, 2i, 2i′ 3f, 3f′ 3g, 3h, 3i, 3i′ exptl

MoO

Mo−O

1.71−1.74 1.71−1.72 1.69−1.72

1.89−1.90 1.90 1.87−1.89

1.69−1.71 1.69−1.73

1.89−1.90 1.85−1.88

1.69−1.71 1.69−1.72 1.70b 1.68c 1.65−1.66d

1.88−1.91 1.85−1.88 1.98b 1.88c 1.86−1.89d

a

PW91/SVP:HF/LANL2MB calculations for the series a−c and f; PW91/SVP calculations for other models. bRef 14. cRef 15. dRef 16.

bond is a bit elongated (1.72−1.73 Å) because of the hydrogen bond formation (Figures 3−6 and 8 and Figure S2, Supporting Information). The MoO bond lengths shown in Table 11 are close to the theoretical MoO distances reported for Mo(VI) dioxo species on alumina29 and titania.64 3.8. Vibrational Frequencies. The scaled theoretical vibrational frequencies for the monooxo and dehydrated dioxo Mo(VI) species are listed in Table 12. These vibrational modes are coupled with the support vibrations, especially for the amorphous cluster models. The calculated frequencies are compared with the Raman spectroscopy data reported for MoO3/SiO2 systems under dehydrated conditions, according to the proposed assignments.18−20 The monooxo MoO stretching frequency determined for the periodic model 1B is slightly higher than the experimental value, whereas the frequency for the more flexible cluster model 1e, also based on the β-cristobalite structure, is a bit underestimated. The MoO stretching modes calculated for the amorphous models 1g and 1h are mixed with the Mo−O−Si stretching vibrations. The theoretical frequencies for 1g are close to the experimental data; however, the existence of this species is rather lowly probable, according to our calculations (Tables 5 and 7). Among the amorphous models, 1h is the most stable monooxo species; however, as was mentioned earlier, its geometry is a bit different from other monooxo Mo(VI) species (Figure 8), and this can explain the relatively low frequency of the MoO vibration, strongly coupled with the Mo−O−Si stretch. The MoO frequency predicted for the 1i structure is even a bit lower, but this species is predicted to be unstable even under strictly dehydrated conditions (Tables 5 and 7). In agreement with the results reported by Bell and co-workers,17 strongly mixed MoO and Mo−O−Si stretching modes with the frequencies in the range of 977−989 cm−1 have been also

Table 12. Calculateda and Experimental Vibrational Frequencies (cm−1) for the Mo(VI) Species on Silica ν(MoO) νs(OMoO) νas(OMoO) ν(Mo−O−Si) δ(OMoO) a

1B

1e

1g

1027 3B

1012 3e

3g

3h

991 969 936 332

991 975 930, 941 341

999 972 907 343

1002 962 901, 930 350

1019, 1030

1h

1i

exptl18,19

1000, 1002 3i

999 3i′

1020 exptl18−20

987 961 896 346

976−988 965−975 932 357−364

988 939 857, 906 328

The frequencies are scaled by 0.9758 and 0.9804 for the periodic and cluster (PW91/SVP) calculations, respectively. 5582



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and cluster models of the surface Mo species 2a′−2c′ are presented in Figures S1−S3. Relative energies and Gibbs free energies of the dioxo Mo(VI) species (the series g−i) and the monooxo Mo(IV) species (the series h and i) are listed in Tables S1 and S2. This material is available free of charge via the Internet at http://pubs.acs.org.

emphasized, however, that these medium-size models refer to one specific location on the surface. Cluster models cut off from the amorphous silica structure enable investigations of various locations of the Mo centers on the support. By examination of the largest amorphous model, it is concluded that most potential locations of the Mo sites on silica are not favorable for the generation of the 4-fold bonded monooxo Mo(VI) species because of geometrical constraints. On the other hand, 2-fold bonded dioxo Mo(VI) species can be easily formed in almost each location. Although the monooxo Mo(VI) species can be more stable than the dioxo species under strictly dehydrated conditions, in most cases it is predicted that the dioxo Mo(VI) species are thermodynamically preferred (Tables 5−7). Thus, we can conclude that the majority of the monomeric Mo(VI) oxide species on silica is present as the dioxo species because geometrical restrictions in most locations on the silica surface make difficult the formation of stable 4-fold bonded monooxo Mo(VI) species. The monooxo species can exist on the silica surface only in favorable locations, just being in minority. These conclusions, additionally confirmed by the vibrational frequencies analysis, are in agreement with the recent experimental18−20 and theoretical17,36 results.

■

Corresponding Author

*Phone: +48 12 6282196. Fax: +48 12 6282037. E-mail address: [email protected].

■

ACKNOWLEDGMENTS This work was supported by the Polish Ministry of Science and Higher Education, Project No. N204 057 32/1465. Computing resources from Academic Computer Centre CYFRONET AGH (grants MNiSW/SGI4700/PK/044/2007 and MNiSW/ IBM_BC_HS21/PK/044/2007) are gratefully acknowledged.

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4. CONCLUSIONS Comprehensive DFT investigations of isolated Mo(VI) and Mo(IV) oxide species on silica have been performed applying both the periodic and cluster approach. For the first time, a large number of different advanced silica models based on the β-cristobalite and amorphous structure have been used in parallel to study the molybdena−silica system. The structures and relative stabilities of the monooxo and dioxo Mo(VI) surface species have been determined. It is shown that periodic and cluster calculations employing comparable models of silica give similar results. On the other hand, the calculated relative energies of the monooxo and dioxo species depend on the location of the Mo center on the surface and on the structure of the model. If the local structure of silica is flexible enough to enable preferable 4-fold bonding to the surface, the monooxo Mo(VI) species can be more stable than the dioxo species under dehydrated conditions. Most locations, however, are favorable for the dioxo Mo(VI) species, which therefore should be dominant in the molybdena−silica system, whereas the monooxo Mo(VI) species is predicted to be in the minority. These conclusions are well consistent with the reported experimental results18−20 and are also supported by the vibrational frequency analysis. In most cases, the calculated frequencies of the MoO stretching mode for the monooxo Mo(VI) species are higher than the frequencies of the symmetric OMoO stretch for the dioxo species, corresponding to the strongest band observed experimentally. The relative energies of the reduced Mo(IV) species on silica are more or less close to the relative energies of the corresponding Mo(VI) precursors. Therefore, it is predicted that the monooxo Mo(IV) species 2-fold bonded to the surface are the dominant Mo(IV) forms, whereas the concentration of the 4-fold bonded Mo(IV) species without the oxo ligand is lower in the reduced molybdena−silica system.

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AUTHOR INFORMATION

ASSOCIATED CONTENT

S Supporting Information *

Periodic models of the fully hydroxylated silica, periodic models of the surface Mo species 1B−3B, 1B_r−3B_r, and 1C−3C, 5583



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Structure of Isolated Molybdenum(VI) and Molybdenum(IV) Oxide

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