Structure of Monomeric Chromium(VI) Oxide Species Supported on

Article pubs.acs.org/JPCC

Structure of Monomeric Chromium(VI) Oxide Species Supported on Silica: Periodic and Cluster DFT Studies Jarosław Handzlik,*,† Robert Grybos,‡ and Frederik Tielens§ †

Faculty of Chemical Engineering and Technology, Cracow University of Technology, ul. Warszawska 24, 31-155 Kraków, Poland Jerzy Haber Institute of Catalysis and Surface Chemistry, Polish Academy of Sciences, ul. Niezapominajek 8, 30-239 Kraków, Poland § UPMC Univ Paris 06, UMR 7574, Laboratoire Chimie de la Matière Condensée de Paris, Collège de France, 11 place Marcelin Berthelot, 75231 Paris Cedex 05, France ‡

S Supporting Information *

ABSTRACT: Silica-supported chromium oxide systems are efficient catalysts for many important chemical processes. Despite many years of investigations, the structure of the surface Cr species is not unambiguously determined. In this work, comprehensive DFT investigations of the monomeric Cr(VI) oxide species on silica under dehydrated conditions are performed. A large number of advanced periodic and cluster models of the SiO2 surface, based on the β-cristobalite structure and different amorphous structures, have been applied. The calculated relative energies of the monooxo and dioxo Cr(VI) species depend on their location on the surface and on the structure of the model. It is concluded that the dioxo Cr(VI) species are thermodynamically preferred, but the presence of the monoxo Cr(VI) species, being in minority, cannot be excluded. According to the vibrational frequency analysis, the asymmetric OCrO stretching mode for the dioxo species and the CrO stretching mode for the monooxo species can overlap.

1. INTRODUCTION Silica-supported chromium oxide systems are well-known as Phillips catalysts for ethene polymerization.1−9 They also exhibit activity in other important catalytic processes, including dehydrogenation and dehydroisomerization of alkanes,9−11 oxidative dehydrogenation in the presence of oxygen12,13 or CO2,14−16 and other selective oxidation reactions.1,17−19 The calcination of the chromia−silica systems results predominantly in formation of highly dispersed surface Cr(VI) oxide species, 1−30 being the active sites or their precursors.1−10,12,13,15−19,30 Reduced Cr(V) and Cr(III) surface species can also be present in small amounts under these conditions, as well as Cr 2 O 3 clusters at higher Cr loadings.1−4,7−17,19−25 The molecular structure of surface Cr(VI) species in calcined Cr/SiO2 catalysts has been discussed in the literature for many years. The data obtained with the UV−vis DR spectroscopy indicated the presence of mono-, di-, and polychromate Cr(VI) species with the monochromate/dichromate ratio depending on the kind of silica support and the chromium loading.1,2,4−6,15,16,21−23,25 According to Raman spectroscopy results, monomeric surface Cr(VI) forms are the dominating or even the only Cr(VI) species for the systems with low Cr loadings.4,5,12,13,17,18,24−29 The isolated Cr(VI) structure is also confirmed by the recent EXAFS-XANES data,3,4,7,29 as well as by studies on a CrOx/SiO2/Si(100) model catalyst using a combination of X-ray photoelectron spectroscopy (XPS), secondary-ion mass spectrometry (SIMS), and Rutherford backscattering spectrometry (RBS) techniques.30 The mono© XXXX American Chemical Society

meric Cr(VI) oxide species supported on silica are usually proposed to be tetrahedral dioxo species (Figure 1a), mainly on

Figure 1. Proposed structures for the monomeric Cr(VI) oxide species on SiO2.4,5,7,13,17,18,24−29.

the basis of Raman, extended X-ray absorption fine structure (EXAFS), and X-ray absorption near-edge structure (XANES) spectroscopy investigations.4,5,7,13,17,18,24−29 However, Lee and Wachs distinguished by Raman spectroscopy two different isolated surface Cr(VI) species in the calcined Cr/SiO2 system under dehydrated conditions.25,26 The first one is the dominant dioxo species, observed at 982 cm−1, whereas the second one, being in minority, is proposed to be monooxo species 4-fold bonded to the silica surface (Figure 1b), characterized by the Raman band at 1011 cm−1. The frequencies in this range (1004−1014 cm1) were also observed by other authors Received: October 17, 2012 Revised: March 26, 2013

A

dx.doi.org/10.1021/jp3103035 | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

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studying the chromia−silica systems.27−29 They were assigned by some authors to the dioxo OCrO asymmetric stretching vibration,27,28 and others had to conclude that a straightforward assignment was impossible because the asymmetric vibrational mode probably overlaps with other vibrational modes.29 Computational chemistry approaches provide complementary information about supported metal oxides, not accessible by experimental techniques.31−38 However, the obtained results may strongly depend on the type and size of the support model,35 hence realistic modeling of heterogeneous catalysts is a challenge. Most reported theoretical studies on Cr/SiO2 systems were based on small cluster models7,27,39−42 or a silsesquioxane model43 representing amorphous silica. Recently, for the first time a realistic periodic model of amorphous silica,44 successfully used in different studies,36,45−48 was applied to investigate relative stabilities of supported Cr(VI) species at different degrees of hydration.38 Several hydrated Cr(VI) structures and two dehydrated species, one with dioxo and one with monooxo functionality, were considered. The silica model corresponded to conditions of a hydroxylated surface, being valid for low and moderate temperatures.38 In this work, the structure and properties of monomeric Cr(VI) oxide species on amorphous silica under dehydrated conditions are theoretically studied with a number of various periodic and advanced cluster models. The results obtained with the periodic and corresponding cluster calculations are compared. Among others, we have used the periodic model of amorphous silica mentioned above,44 but the surface is dehydroxylated to a larger extent, corresponding to high temperatures of the catalyst calcination. Our main aim is to examine which Cr(VI) species, dioxo (Figure 1a) or monooxo (Figure 1b), is most likely present in the calcined Cr/SiO2 system. It is assumed that the distribution of different Cr species between surface silica sites is determined by their thermodynamic stability and not by the kinetics of the preparation method. In a previous study on the molybdena− silica system, it was shown that relative energies of Mo species depend on their localizations on the support.35 Therefore, in the present work many different locations of the Cr(VI) species are considered to determine the relative thermodynamical stabilities of the dioxo and monooxo structures. The vibrational frequency analysis is also performed to compare the theoretical frequencies for the Cr sites with the reported experimental data, and the assignments for the monooxo and dioxo Cr(VI) species on silica are discussed. To the best of our knowledge, such comprehensive theoretical investigations of the chromia−silica system, involving many different models of silica and variously located Cr species, have not been reported so far.

chromium species have been attached to the partially dehydroxylated surfaces with 3.8−3.9 OH nm−2 (unit formula = Si24O57H18) by replacing one or two pairs of silanol groups. Consequently, the surface concentration of the hydroxyl groups after grafting is 2.5−2.6 and 1.3 OH nm−2, for the partially hydrated and dehydrated Cr(VI) species, respectively. The chromium coverage is about 0.6 atoms nm−2 (one Cr atom per unit cell). The bottom four layers are frozen in the geometry of the bulk, whereas the upper five layers, including the chromium site, have been relaxed. In the second series of periodic models, the amorphous silica structure, proposed and verified by Tielens and co-workers44 and further applied in studies on transition metal oxides supported on silica,36,38 is employed. The surface unit cell parameters (a = 12.77 Å, b = 17.64 Å, c = 25.17 Å, including 15 Å of vacuum) were obtained by calculation depending on the final model size supported by an optimal computational power.44 In this work, the original hydroxylated surface with 5.8 OH nm−2 is partially dehydroxylated to simulate the conditions of the catalyst calcination. The final models can be formally viewed as obtained after the grafting of the chromium species on the silica surface with 3.1 OH nm−2 (unit formula = Si27O64H20), resulting in surface concentrations of 2.2 and 1.3 OH nm−2, for the partially hydrated and dehydrated Cr(VI) sites, respectively. The experimentally determined density of the OH groups for the amorphous silica surface decreases from about 2.4 to 1.2 OH nm−2 when the temperature is raised from 673 to 973 K, and it is about 0.7 OH nm−2 at 1073 K.54,55 The calcination of the Cr/SiO2 system is carried out in a wide range of temperatures, from 673 K even up to almost 1273 K,2,4−7 but usually it is about 923 K for the Phillips catalyst.4,5 The chromium coverage in our models is about 0.4 atoms nm−2 (one Cr atom per unit cell), being below the reported monolayer coverage3,17,23,24 and corresponding to the Cr loadings for the typical Phillips catalysts.3,4,28,30 The positions of all atoms in the unit cell have been relaxed. The periodic calculations have been performed with the Vienna Ab Initio Simulation Package (VASP)56−58 using the Perdew and Wang (PW91) generalized gradient approximation exchange-correlation functional.59 For valence electrons, a plane-wave basis set has been employed. Atomic cores are described with the projector-augmented wave method (PAW).60 Standard PAW atomic parameters are used, requiring a cutoff energy of 400 eV (fixed by the oxygen atom). For chromium, the PAW is built with 12 electrons in the valence. The Γ-centered Monkhorst−Pack61 sampling of the Brillouin zone with 2 × 2 × 1 mesh is applied for the models based on the β-cristobalite structure, whereas only the Γ point sampling is used for the amorphous models. Frequency calculations have been carried out by numerical differentiation of the force matrix. All the optimized degrees of freedom are used for the frequency calculations for β-cristobalite-based models. In the case of amorphous models, the chromium atom and its neighbors, including at least the second coordination sphere, are included in the Hessian matrix. The calculations are not spin-polarized. For the graphic presentation of the structures, Materials Studio 5.5 software is used.62 2.2. Cluster Calculations. Three different series of cluster models, derived from the β-cristobalite framework, from the structure of the amorphous silica surface (Materials Studio library62) and from the periodic model of amorphous silica used in this work, have been prepared. The dangling bonds have been saturated with hydrogens replacing the removed Si

2. COMPUTATIONAL MODELS AND METHODS 2.1. Periodic Calculations. Two kinds of periodic models for silica are proposed. In the first case, the models are based on the β-cristobalite structure, 49 often used to represent amorphous silica.35,50−53 The bulk geometry of SiO2 was previously calculated in the tetragonal I42̅ d space group, and the lattice constants were determined.35 Surfaces are modeled by slabs, constructed by cutting the bulk parallel to the (001) and (110) crystallographic planes. The surface unit cell dimensions (Å) are a = 15.21, b = 10.14, c = 28.00 (including 20 Å of vacuum) for the (001) plane and a = 15.44, b = 10.30, c = 28.00 for the (110) plane. Both surfaces of each slab are terminated by oxygen atoms saturated with hydrogens. The B



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atoms. The respective Cr species have been attached to the partially dehydroxylated surface. In the case of the models based on the β-cristobalite structure, the geometries of the Cr species have been optimized together with the upper parts of the SiO2 clusters, analogous to the corresponding periodic models. The bottom four layers and the terminating hydrogens are frozen. All the models obtained from the amorphous silica structure have been fully relaxed. Geometry optimization of the largest systems, containing 63, 72, and 97 Si atoms, has been carried out using the PW91 functional with the split-valence def2-SVP basis set 63 (abbreviated as SVP) for the Cr center and its vicinity, at least the third coordination sphere, and with the SV basis set for other atoms. This basis set combination is denoted here as SVP-SV. Further PW91 single-point energy calculations have employed the triple-ζ valence def2-TZVPP basis set63 (abbreviated as TZVPP) and the SVP basis set, respectively. This basis set combination is denoted here as TZVPP-SVP. The two-layer ONIOM partitioning schemes64 PW91/ SVP:PW91/SV and PW91/SVP:HF/LANL2MB, the latter used in the previous studies on molybdena−silica system,35 have been also applied for the geometry optimization of selected large models (Figure S1, Supporting Information) to compare the results obtained with different approaches. Both the calculated geometries and the relative energies (Table S1, Supporting Information) are very close to each other. In the case of the smaller cluster models, containing 21, 24, 26, and 33 Si atoms, the geometry of the whole system has been optimized at the PW91/SVP level. Vibrational frequencies and Gibbs free energy corrections have been evaluated in the harmonic oscillator and rigid-rotor approximations. The corrections are added to the PW91/TZVPP single-point energies to obtain a better estimate of Gibbs free energies (ΔG). The reported energies (ΔE) are not ZPE-corrected, to enable comparison with the larger cluster models and the periodic models. All systems are considered in closed shell state. The calculations have been done with the Gaussian 09 suite of programs.65 For the graphic presentation of the systems studied, the GaussView 5.0 software66 is used.

Figure 2. Optimized structures of the monooxo (1A, 1B) and dioxo (2A, 3A, 2B, 3B) Cr(VI) oxide species on SiO2. The periodic models represent the (001) surface (1A−3A) and the (110) surface (1B−3B) of β-cristobalite.

structures 2A, 3A, 2B, and 3B are tetrahedrally coordinated, as expected from Figure 1 and earlier theoretical studies.7,27,38,43 Models 2A and 2B represent partially hydrated species with two surface silanols in the neighborhood weakly interacting with one of both oxo ligands (the O···H distances = 2.32−2.65 Å). In the case of the model 2A, a hydrogen bond between the silanols is also formed (the O···H distance = 2.19 Å). After replacement of hydroxyl groups by siloxane bridges, structures 3A and 3B are obtained, corresponding to fully dehydrated conditions. They can be directly transformed to the monooxo species 1A and 1B, respectively. Cluster models of the Cr(VI) oxide species on SiO2, based on the β-cristobalite structure, are presented in Figure 3. The species 1a−3a are attached to the (001) surface and correspond to the periodic models 1A−3A. The species 1b−3b on the (110) surface correspond to the periodic models 1B−3B. The calculated O···H distances for the hydrogen bonds formed in the systems 2a and 2b (1.98−2.04 Å) are shorter than in the case of the corresponding periodic models. The calculated energies for the dehydration reactions of the dioxo Cr species (2A, 2B, 2a, 2b) to the corresponding monooxo species (1A, 1B, 1a, 1b) and the energies of the direct transformation of the dehydrated dioxo species (3A, 3B, 3a, 3b) to the monooxo species are listed in Table 1. It can be seen that the dioxo Cr(VI) species are much more stable than the monooxo species, independently of the model used. In the case of the periodic models, the relative energies for the (001) and (110) surface are close to each other because in both cases the local silica structure in the vicinity of the Cr site is similar (Figure 2). The predicted endothermic effect for the formation of the monooxo Cr(VI) species is about 150 kJ mol−1 larger than in the case of the analogous periodic calculations for the Mo species on β-cristobalite.35 Despite the different calculation methodologies, the corresponding reaction energies for the periodic and cluster models representing the (001) surface are

3. RESULTS AND DISCUSSION The nomenclature of the models discussed in this section is constructed by a number (1−3), a letter (capital or small), and in many cases a superscript roman numeral (I−VI). The numbers 1, 2, and 3 denote the monooxo, partially hydrated dioxo, and dehydrated dioxo Cr(VI) species, respectively. The capital letter specifies a given periodic model, whereas the small letter means a cluster model. If the same capital and small letter is used, the periodic and the cluster model correspond to each other; i.e., they are based on the same silica structure (βcristobalite or amorphous) and represent the same surface. For instance, the periodic model 1A and the cluster model 1a represent the monooxo Cr(VI) species on the (001) βcristobalite surface. The superscripts distinguish between different locations of the Cr(VI) sites on the surface described by the same SiO2 model. 3.1. Surface Cr Species: Models Based on the βCristobalite Structure. Periodic models of isolated Cr(VI) species attached to the partially dehydroxylated (001) surface (series A) and (110) surface (series B) of β-cristobalite are shown in Figure 2. The geometry of the monooxo species 1A and 1B is a distorted square pyramid, whereas the dioxo C



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Figure 4. Optimized structures of the monooxo (1c) and dioxo (2cI− 2cIII, 3cI, 3cII) Cr(VI) oxide species on SiO2. The cluster models are derived from the amorphous silica structure62 (PW91/TZVPP-SVP// PW91/SVP-SV calculations).

Figure 3. Optimized structures of the monooxo (1a, 1b) and dioxo (2a, 3a, 2b, 3b) Cr(VI) oxide species on SiO2. The cluster models are cut off from the (001) surface (1a−3a) and the (110) surface (1b− 3b) of β-cristobalite (PW91/TZVPP-SVP//PW91/SVP-SV calculations).

This silica cluster was previously described and used for preparing the analogous models of the surface Mo species.35 The monooxo species 1c shows distorted square pyramidal geometry, similar to the corresponding monooxo Cr(VI) structures on β-cristobalite. After adsorption of a water molecule on the surface, various dioxo Cr(VI) species (2cI− 2cIII) can be generated from 1c. Hydrogen bonds formed between the oxo ligands and neighboring hydroxyl groups (the O···H distance = 1.76−1.97 Å) are stronger than in the case of the β-cristobalite-based models. Dioxo forms 3cI and 3cII can be directly obtained from 1c or by the dehydration of the species 2cI and 2cII, respectively. Relative energies of the monooxo and dioxo species represented by the c series of the models are shown in Table 2. Dehydration of the most stable dioxo species 2cI to the monooxo structure 1c is a less endothermic process than the analogous reactions on the β-cristobalite surface (Table 1), but there is still a clear energetic preference for the dioxo structure.

Table 1. Energies (ΔE, kJ mol−1) for the Conversion of the Dioxo Cr(VI) Species (2A, 3A, 2B, 3B, 2a, 3a, 2b, 3b) to the Corresponding Monooxo Species (1A, 1B, 1a, 1b) reaction 2A 3A 2B 3B

→ → → →

1A + H2O 1A 1B + H2O 1B

ΔEa

reaction

ΔEb

495 284 478 266

2a → 1a + H2O 3a → 1a 2b → 1b + H2O 3b → 1b

499 280 300 96

a Periodic PW91 calculations. bCluster PW91/TZVPP-SVP//PW91/ SVP-SV calculations.

in perfect agreement. In the case of the (110) surface, the agreement between the results obtained from the periodic and cluster calculations is worse because of the higher flexibility of the cluster model allowing stronger relaxation of the surface and, consequently, better stabilization of the strained monooxo structure. Nevertheless, the general conclusions drawn from the periodic and corresponding cluster calculations employing the β-cristobalite structure of SiO2 are the same, in accordance with the previous theoretical studies on the molybdena−silica system.35 3.2. Surface Cr Species: Models Based on Amorphous Silica Structures. Models of the Cr(VI) species employing a very large silica cluster (97 Si atoms) derived from the structure of the amorphous silica surface62 are presented in Figure 4.

Table 2. Energiesa (ΔE, kJ mol−1) for the Conversion of the Dioxo Cr(VI) Species (2cI−2cIII, 3cI, 3cII) to the Monooxo Species (1c)

a

D

reaction

ΔE

reaction

ΔE

2cI → 1c + H2O 2cII → 1c + H2O 2cIII → 1c + H2O

256 15 0

3cI → 1c 3cII → 1c

146 −146

Cluster PW91/TZVPP-SVP//PW91/SVP-SV calculations. dx.doi.org/10.1021/jp3103035 | J. Phys. Chem. C XXXX, XXX, XXX−XXX


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Figure 5. Optimized structures of the monooxo (1d−1f) and dioxo (2dI−2dIV, 3dI−3dIII, 2eI−2eVI, 3eI−3eV, 2fI−2fIV, 3fI−3fIV) Cr(VI) oxide species on SiO2. The cluster models are derived from the amorphous silica structure62 (PW91/SVP calculations).

Moreover, the surface dehydration reaction 2cI → 3cI + H2O (ΔE = 110 kJ mol−1) is even less endothermic, and consequently, the dehydrated dioxo species 3c is more stable than the monooxo species 1c (Table 2). Other dioxo Cr(VI) species considered here (2cII, 2cIII, 3cII) are energetically

unstable, compared to 2cI and 3cI, and they are also predicted to be less probable than the monooxo structure 1c under dehydrated conditions. To enable efficient calculations of the whole system at higher level of theory, a number of medium-size models of the Cr(VI) E



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strictly dehydrated conditions at high temperatures (Table 4). However, the removal of two hydroxyl groups from the vicinity of the dioxo center 2eII, resulting in water release and the formation of a siloxane bridge (model 3eII), is more preferred than the dehydration of 2eII to 1e. Consequently, both the 3eII and 3eI dioxo species are more stable than the monooxo structure 1e (Table 4 and Table S2, Supporting Information). It can be noted that the predicted thermodynamic preference for the dioxo Cr(VI) species on silica, over the monooxo Cr(VI) species, is stronger than in the case of the Mo/SiO2 system studied previously with similar silica models.35 Periodic models of the Cr(VI) species supported on amorphous silica44 are shown in Figure 6. The monooxo structure 1G has been obtained from the previously reported38 model of the monooxo Cr(VI) species, by removing three water molecules per unit cell. All possible dehydration variants have been considered, and the selected structure 1G represents the lowest energy solution allowing for the desired concentration of the surface silanols, i.e., approximately 1.3 OH nm−2. Additionally, we have checked an alternative location of the monooxo Cr(VI) species on the initial hydroxylated surface, but the first localization38 leads to a more stable structure. The models of the dioxo Cr(VI) species have been obtained from 1G by hydrolysis of two adjacent Cr−O−Si linkages (2GI−2GIV) and by direct rearrangement (3GI−3GIV). In the case of 2GIII, 2GIV, and 3GIII, interactions between oxo ligands and neighboring silanols are observed (the O···H distance = 1.88−2.57 Å). The energies of the partially hydrated dioxo species are close to each other (Table S3, Supporting Information). On the other hand, among the dehydrated dioxo species, 3GI is clearly the most stable system because of easy dehydroxylation of 2GI, involving two adjacent silanols. In the case of 3GII, a strained two-membered Si ring is formed after the dehydration of 2GII. Even more significant surface reconstruction is observed during the dehydration of 2GIII to 3GIII. Here, a new siloxane bridge connects two relatively remote silicon atoms. Finally, after removing two silanols from 2GIV, surface defects, i.e., a three-coordinated silicon and a nonbridging oxygen, are formed instead of a siloxane bridge, resulting in the high-energy system 3GIV. On the basis of the periodic systems, the corresponding cluster models of the monooxo (1g) and dioxo (2gI−2gIV, 3gI− 3gIV) Cr(VI) species have been prepared (Figure 7). For 2gI, 2gII, and 3gI−3gIII, the oxo ligand interacts with a neighboring hydroxyl group (the O···H distance = 1.80−1.99 Å), similar to other dioxo systems. Among the partially hydrated species (2gI−2gIV), 2gII is the most stable one in terms of Gibbs free energy (ΔG873). The energy differences between the species are higher than those for the periodic systems but still not dramatic (Table S3, Supporting Information). As the dehydrated dioxo

oxide species have been prepared (Figure 5). The silica clusters were previously derived from the amorphous silica structure and used for the investigations of the Mo/SiO2 system.35 Different models (series d, e, and f) represent different locations on the surface. For each monooxo Cr species, a number of the dioxo Cr species have been systematically generated, by hydration or direct rearrangement. According to the notation used in this work, 1d−1f are the monooxo Cr(VI) species; 2dI−2dIV, 2eI−2eVI, and 2fI−2fIV are the partially hydrated dioxo species; and finally, 3dI−3dIII, 3eI−3eV, and 3fI−3dIV are the dehydrated dioxo species. The structures 2dI, 2eII, and 2fIII are most stable in terms of Gibbs free energy (ΔG873) among the partially hydrated dioxo Cr species, whereas 3dI, 3eI, and 3fI are the most stable dehydrated dioxo species (Table S2, Supporting Information). Dehydration of the silica surface, accompanied by the formation of strained two-membered Si rings, leads to systems with high relative energies (3dIII, 3eV, 3fIII). The dioxo species with the chromium atom connected via two oxygen bridges with one surface silica atom (2eV, 3eV, 2fIV, 3fIV) are also unstable, which is explained by the formation of a strained ring in each case, consisting of one Cr, one Si, and two O atoms. This is consistent with previously reported results for tetrahedral Mo(VI) alkylidene73 and oxide35 centers on silica. To compare the relative stabilities of the monooxo and the most stable dioxo Cr(VI) species from the series d−f, the energies at T = 0 K and Gibbs free energies at T = 873 K for the respective dehydration and rearrangement reactions are presented in Table 3. Additionally, for the partially hydrated Table 3. Energiesa (ΔE, kJ mol−1) and Gibbs Free Energiesa at T = 873 K (ΔG873, kJ mol−1) for the Conversion of the Dioxo Cr(VI) Species (2dI, 3dI, 2eII, 3eI, 2fIII, 3fI) to the Corresponding Monooxo Species (1d, 1e, 1f)

a

reaction

ΔE

ΔG873

reaction

ΔE

ΔG873

2dI → 1d + H2O 2eII → 1e + H2O 2fIII → 1f + H2O

296 194 254

153 100 145

3dI → 1d 3eI → 1e 3fI → 1f

217 148 226

255 159 218

Cluster PW91/TZVPP//PW91/SVP calculations.

dioxo species, Gibbs free energies for the dehydration reactions leading to the corresponding monooxo species have been calculated as a function of temperature and water vapor pressure (Table 4). Although the energetic parameters depend on the model, i.e., on the specific structure and location of the Cr center on the silica surface, in almost all cases a strong thermodynamic preference for the dioxo species is seen. The only exception is the partially hydrated 2eII species, which can be less stable than the monooxo Cr(VI) species 1e under

Table 4. Gibbs Free Energiesa (kJ mol−1) for the Dehydratation of the Dioxo Cr(VI) Species (2dI, 2eII, 2fIII, 2gI, 2gII) to the Corresponding Monooxo Species (1d, 1e, 1f, 1g) as a Function of Temperature and Water Vapor Pressure 673 K

1073 K

10−2 atm

10−5 atm

10−2 atm

10−5 atm

10−2 atm

10−5 atm

2d → 1d + H2O 2eII → 1e + H2O 2fIII → 1f + H2O 2gI → 1g + H2O 2gII → 1g + H2O

158 93 141 18 53

119 55 102 −21 15

120 67 112 −10 25

70 17 61 −61 −25

82 42 83 −38 −3

21 −20 21 −100 −65

I

a

873 K

reaction

Cluster PW91/TZVPP//PW91/SVP calculations. F



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Figure 7. Optimized structures of the monooxo (1g) and dioxo (2gI− 2gIV, 3gI−3gIV) Cr(VI) oxide species on SiO2. The cluster models are derived from the periodic model of amorphous silica used in this work (PW91/SVP calculations).

Figure 6. Optimized structures of the monooxo (1G) and dioxo (2GI−2GIV, 3GI−3GIV) Cr(VI) oxide species on SiO2. The periodic models represent the surface of amorphous silica44 after partial dehydroxylation.

species are regarded, the energy increases from 3gI to 3gIII, in agreement with the results obtained for the corresponding G



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periodic models. On the other hand, 3gIV is the most stable system, in contrast to the least stable 3GIV. High flexibility of the cluster model prevents formation of surface defects after dehydration of 2gIV, whereas the periodic model, perhaps more realistic, results in a more rigid surface. To compare the relative stabilities of the monooxo and dioxo Cr(VI) species represented by the periodic (series G) and cluster (series g) models, the energies at T = 0 K and Gibbs free energies at T = 873 K for the dehydration and rearrangement reactions of the dioxo structures are presented in Table 5. The dehydration reactions are endoenergetic for

Table 6. Calculated and Experimental Bond Lengths (Å) and Angles (Degrees) for the Reference Gas-Phase Chromium Compounds

ΔEa

reaction

ΔEb

ΔG873b

2GI → 1G + H2O 2GII → 1G + H2O 2GIII → 1G + H2O 2GIV → 1G + H2O 3GI → 1G 3GII → 1G 3GIII → 1G 3GIV → 1G

156 150 154 129 69 −62 −246 −347

2gI → 1g + H2O 2gII → 1g + H2O 2gIII → 1g + H2O 2gIV → 1g + H2O 3gI → 1g 3gII → 1g 3gIII → 1g 3gIV → 1g

127 160 224 204 100 10 −65 193

23 58 46 5 97 −24 −99 114

a

calcdb

exptl67

1.568 1.751 86.2 105.0 calcda

1.536 1.730 86.3 104.7 calcdb

1.547 1.730 86.7 104.0 exptl68

CrOF4

CrO Cr−F F−Cr−F OCr−F

CrO2F2

CrO Cr−F OCrO F−Cr−F OCr−F

1.585 1.727 108.3 110.9 109.4 calcda

1.557 1.702 108.4 110.5 109.5 calcdb

1.575 1.720 107.8 111.9 109.3 exptl69

CrO2Cl2

CrO Cr−Cl OCrO Cl−Cr−Cl OCr−Cl

1.588 2.120 109.2 111.1 109.1

1.556 2.128 108.8 111.4 109.2

1.581 2.126 108.5 113.3 108.7

Table 5. Energies (ΔE, kJ mol−1) and Gibbs Free Energies at T = 873 K (ΔG873, kJ mol−1) for the Conversion of the Dioxo Cr(VI) Species (2GI−2GIV, 3GI−3GIV, 2gI−2gIV, 3gI− 3gIV) to the Corresponding Monooxo Species (1G, 1g) reaction

calcda

Periodic PW91 calculations. bPW91/SVP calculations.

factors have been obtained through a least-squares approach, based on the experimental CrO frequencies.

a Periodic PW91 calculations. bCluster PW91/TZVPP//PW91/SVP calculations.

Table 7. Calculated and Experimental CrO Stretching Frequencies (cm−1) for the Reference Compounds

both the periodic and cluster models; however, at high temperatures and under low water vapor pressure the formation of the monooxo species becomes preferable (Table 4, the results for 1g). On the other hand, alternative dehydration processes resulting in formation of the dioxo species are even more preferred in some cases. Consequently, the most stable dehydrated dioxo species for each silica model (3GI, 3gI, 3gIV) are energetically more favorable than the corresponding monooxo structures (1G and 1g, Table 5), in qualitative agreement with the calculations based on other models (Tables 2 and 3). As the concentration of available surface sites exceeds that of Cr species (see also Section 2.1) and the Cr distribution is most likely controlled by the thermodynamic stability of Cr species, then Cr should occupy the most stable sites. Thus, the dioxo Cr(VI) species appears to be much more probable on the silica surface under dehydrated conditions than the monooxo Cr(VI) forms, although the latter cannot be excluded as the minor species. 3.3. Calibration of the Theoretical Methods. A benchmark study of geometrical parameters and vibrational frequencies with experimentally characterized gas-phase chromium compounds CrOF4, CrO2F2, CrO2Cl2, CrO(OH)2, HCrO(OH), and CrO(OH) has been carried out. The ground state for CrO(OH)2 and HCrO(OH) is triplet, whereas for CrO(OH) it is quartet. The predicted bond lengths and angles are generally consistent with the reported experimental data67−69 (Table 6). Regarding the CrO bonds, the predicted distances are slightly overestimated in the case of the periodic calculations, by approximately 0.01−0.02 Å. The molecular calculations provide a bit underestimated CrO lengths, by about 0.01− 0.025 Å. The scaled theoretical frequencies are satisfactorily close to the experimental data70−72 (Table 7). The scaling

CrOF4 CrO2F2 CrO2Cl2 CrO(OH)2 HCrO(OH) CrO(OH)

calcda

calcdb

exptl

1041 1023 997 1010 980 992 1007 945

1031 1012 995 1003 988 992 1014 961

1027.7c 1016d 1006d 1000d 990d 1002.9e 1012.2e 939.6e

a

Periodic PW91 calculations; the frequencies are scaled by 0.9241. PW91/SVP calculations; the frequencies are scaled by 0.9149. cRef 70. dRef 71. eRef 72. b

3.4. Bond Lengths. The chromium−oxygen bond lengths calculated for the proposed models of the dioxo Cr(VI) species on silica, excluding the least stable structures, are compared in Table 8 with the reported EXAFS data for chromia−silica systems.7,29 Generally, a very good agreement between the theoretical and experimental parameters is achieved. Not surprisingly, taking into account the results obtained for the gas-phase Cr compounds, the predicted CrO bond lengths are slightly higher for the periodic models, compared to the cluster models. On the other hand, both the periodic and cluster calculations give very similar ranges of the single Cr−O bond distances, being a little shorter, on average, than the respective EXAFS values. The theoretical chromium−oxygen bond lengths reported in this work are close to the corresponding values obtained previously for the periodic models of the Cr(VI) dioxo species supported on a more hydrated silica surface.38 3.5. Vibrational Frequencies. In Table 9, the calculated vibrational frequencies for the monooxo and dehydrated dioxo Cr(VI) species are presented together with the Raman spectroscopy data reported for Cr(VI)/SiO2 systems under H



Article

Table 8. Calculated and Experimental Bond Lengths (Å) for the Dioxo Cr(VI) Species on Silica model periodic (β-cristobalite) periodic (amorphous) cluster (β-cristobalite)a cluster (amorphous)b exptl a

2A, 3A, 2B, 3B 2GI−2GIV, 3GI 2a, 3a, 2b, 3b 2cI, 3cI, 2dI, 2dII, 2dIV, 3dI, 3dII, 2eI−2eIV, 2eVI, 3eI−3eIV, 2fI−2fIII, 3fI−3fIII, 2gI−2gIV, 3gI, 3gIV

CrO

Cr−O

1.59−1.61 1.59−1.61 1.56−1.59 1.56−1.59 1.60−1.61c 1.60d

1.76 1.72−1.78 1.74−1.76 1.72−1.79 1.77−1.79c 1.80d

PW91/SVP-SV calculations. bPW91/SVP-SV calculations for 2cI and 3cI; PW91/SVP calculations for other models. cRef 7. dRef 29.

Table 9. Calculateda and Experimental Vibrational Frequencies (cm−1) for the Monooxo and Dioxo Cr(VI) Species on Silica ν(CrO)

dioxo model

νas(OCrO)

νs(OCrO)

νs(Cr−O−Si)

δ(OCrO)

1A 1B 1d 1e 1f

1022 1023 1019, 1034 1006, 1024 1021

1G 1g

1005 1002, 1015

exptl

1011b

3A 3B 3dI 3eI 3fI 3fIII 3GI 3gI 3gIV exptl

1009 1009 1000 979, 992 1015 1010 1007 994, 1001 1004 1004c, 1014d

977 972 942, 956 947 937 979 977 948 975 980−990e

902 900 903 891−914 812 849 919 896 865 905−919f

362 362 355−392 363−435 354 373 366−384 364−379 368−390 394−396g

monooxo model

a

The frequencies are scaled by 0.9241 and 0.9149 for the periodic (PW91) and cluster (PW91/SVP) calculations, respectively. bRefs 25 and 26. cRef 27. dRef 28. eRefs 12, 13, 17, 18, and 24−29. fRefs 25 and 29. gRefs 25, 26, and 28.

dehydrated conditions.12,13,17,18,24−29 The theoretically determined vibrational modes are coupled with the support vibrations, analogous to the previously studied molybdena− silica system.35 The predicted CrO stretching frequencies are above 1000 cm−1 for all the models of the monooxo Cr(VI) species. The calculated numbers are quite close to the experimental value, especially in the case of the amorphous systems 1e, 1G, and 1g which are relatively more stable than other monooxo structures (Tables 1 and 3−5). The experimental frequencies assigned to the asymmetric OCrO stretching mode27,28 are very close to the frequencies assigned by Lee and Wachs to the Cr(VI) monooxo species25,26 (Table 9). On the other hand, the isotopic labeling and polarization studies reported by Stiegman and co-workers29 did not support the straightforward assignment of the band at 1004 cm−1, observed for the chromia−silica system, to the asymmetric stretching mode. The authors suggested that this mode overlaps with other vibrational modes. In most cases, our calculated frequencies for the asymmetric OCrO stretch exceed 1000 cm−1 (Table 9). Although they are lower, on average, than the theoretical CrO frequencies for the monooxo species, the wavenumbers predicted for the modes are quite close to each other, especially for the models 1G and 3GI. Thus, our results indicate that these modes may indeed overlap, which explains why they are not observed as two separate bands. Calculated frequencies for the symmetric OCrO stretching vibrations are lower than the observed fundamentals (Table 9), but for most systems considered (3A, 3B, 3fIII, 3GI, 3gIV) the agreement between the experiment and theory is very good. For other models (3dI, 3eI, 3fI, 3gI), the theoretically evaluated frequencies are significantly diminished because of the interactions between the oxo ligands and the surface hydroxyls. The predicted Cr−O−Si frequencies for the Cr(VI) dioxo species (Si−O−Cr−O−Si symmetric vibrations) are consistent with the experimental results, excluding the

significantly decreased values for the models 3fI, 3fIII, and 3gIV. Finally, the calculated OCrO bending mode frequencies are slightly underestimated, compared to the Raman spectroscopy data. It should be noted, however, that the scaling factors determined on the basis of the stretching CrO frequencies are not accurate for the bending modes because, in general, scaling factors depend on the vibrational wavenumbers.74 Isotopic 18O−16O exchange studies confirmed the dioxo functionality of the dominant Cr(VI) oxide species on silica,26,29 although either the asymmetric stretching mode was not observed in these experiments26 or the respective frequencies could not be unambiguously assigned.29 The calculated isotopic shifts for selected models of the monooxo and dioxo Cr(VI) species are shown in Table 10, in comparison Table 10. Effect of the Isotopic 18O−16O Exchange on the Calculateda and Experimental CrO Stretching Frequencies (cm−1) for the Cr(VI) Oxide Species on Silica ν(Cr16O) ν(Cr18O)

exptl

1f

1g

1021 986, 995 3fIII

1002, 1015 957, 962, 977 3gIV

1011b 967b,c exptl

νas(16OCr16O)

1010

1004

νas(18OCr16O)

989, 1007

νas(18OCr18O) νs(16OCr16O) νs(18OCr16O)

955, 975 979 927, 948, 963 925

993, 996, 1000 966 975 942, 948

954f,g 980b, 986f 942b, 950−951f

935

935b, 943f

νs(18OCr18O)

1004d, 1014e, 1004f,g -

a

Cluster PW91/SVP calculations; the frequencies are scaled by 0.9149. Ref 26. cEstimated value. dRef 27. eRef 28. fRef 29. gNot unambiguously assigned to the asymmetric mode. b

I



Article

with the reported Raman spectroscopy data. The 18O−16O substitution is considered only for the oxo ligands. According to our calculations, the 18O replacement for 16O from the Cr−O− Si linkages hardly influences the CrO stretching mode frequencies, by no more than 1 cm−1. The predicted isotopic shift for the monooxo species depends on the model used. For the more realistic structure 1g, the theoretical Cr18O frequencies are close to the value estimated by Lee and Wachs.26 The calculated asymmetric 18OCrO18 stretching frequencies are in the same range, hence the isotopic exchange probably does not facilitate experimental distinguishing between the monooxo and asymmetric dioxo stretching vibrations. Moreover, these vibrations can be interfered by the more intense symmetric stretching modes of the remaining nonsubstituted or partially substituted dioxo species. In the latter case, the theoretically determined isotopic shift of the asymmetric stretch, which probably has not been experimentally observed so far, is modest (Table 10). In contrast, a larger shift of the symmetric stretching vibration is predicted, in accordance with the experimental results. It should be also noted that for both models 3fIII and 3gIV the calculated 18O CrO16 frequencies depend on the substitution sequence. The further shift of the symmetric mode, corresponding to the dioxo 18OCrO18 species, is not significant.26,29 This effect is very well reproduced by the model 3gIV.

The calculated vibrational frequencies for the Cr(VI) sites on silica are well consistent with the available experimental data.12,13,17,18,24−29 According to our results, the asymmetric OCrO stretching mode for the dioxo species and the CrO stretching mode for the monooxo species can overlap.

■

ASSOCIATED CONTENT

S Supporting Information *

Cluster models of the surface Cr species 1a−3a optimized with the two-layer ONIOM method are presented in Figure S1. Relative energies for the species 1a−3a and relative energies and Gibbs free energies for the dioxo Cr(VI) species (the series d−g and G) are listed in Tables S1−S3. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

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

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported by the Polish National Science Centre, Project No. N N204 131039 (2010-2012), and by PLGrid Infrastructure. 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. F.T. acknowledges the HPC resources from GENCI-[CCRT/CINES/IDRIS] (Grant 2011-[x2012082022]).

4. CONCLUSIONS Extensive theoretical studies on the monomeric Cr(VI) oxide species on silica under dehydrated conditions have been performed using both periodic and cluster DFT approaches. A large number of various advanced models of the SiO2 surface, based on the β-cristobalite structure and different amorphous model structures, have been applied in parallel. Results obtained from the periodic and cluster calculations for the Cr(VI) species supported on the β-cristobalite surface are comparable. In the case of the periodic and corresponding cluster models representing amorphous silica, bigger differences are usually observed, especially in the predicted relative energies of the monooxo and dioxo Cr(VI) species. Nevertheless, all the approaches lead to the same general conclusion that the dioxo species are more stable than the monooxo species under dehydrated conditions. On the other hand, the calculated relative energies significantly depend on the structure of the model. The calculated preference for the dioxo species is stronger in the case of the β-cristobalite-based models than for the models representing the amorphous surface. The latter is more flexible than the β-cristobalite surface, hence the formation of four Cr−O−Si linkages is more facilitated here. This is especially seen for the models derived from the proposed periodic structure of amorphous silica,44 where the predicted thermodynamic preference for the dioxo species under dehydrated conditions is the weakest, that nevertheless found the dominating structure over a large temperature domain. The presence of the monoxo Cr(VI) species on silica, being in minority, cannot be excluded, in accordance with the results of Lee and Wachs.25,26 The relative stabilities of the Cr(VI) species depend on the location of the metal center on the silica surface. This conclusion is consistent with the results obtained recently for the molybdena−silica system.35 It should be noticed, however, that the energetic preference for the dioxo Cr(VI) species over the monooxo Cr(VI) species is stronger than in the case of the analogous models of the Mo(VI) species on silica.

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Structure of Monomeric Chromium(VI) Oxide Species Supported on

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