structure of monomeric chromium(vi) oxide species supported on silica: periodic and cluster dft...

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

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

*S Supporting Information

ABSTRACT: Silica-supported chromium oxide systems are efficientcatalysts for many important chemical processes. Despite many yearsof investigations, the structure of the surface Cr species is notunambiguously determined. In this work, comprehensive DFTinvestigations of the monomeric Cr(VI) oxide species on silicaunder dehydrated conditions are performed. A large number ofadvanced periodic and cluster models of the SiO2 surface, based on theβ-cristobalite structure and different amorphous structures, have beenapplied. The calculated relative energies of the monooxo and dioxoCr(VI) species depend on their location on the surface and on thestructure of the model. It is concluded that the dioxo Cr(VI) species are thermodynamically preferred, but the presence of themonoxo Cr(VI) species, being in minority, cannot be excluded. According to the vibrational frequency analysis, the asymmetricOCrO stretching mode for the dioxo species and the CrO stretching mode for the monooxo species can overlap.

1. INTRODUCTION

Silica-supported chromium oxide systems are well-known asPhillips catalysts for ethene polymerization.1−9 They alsoexhibit activity in other important catalytic processes, includingdehydrogenation and dehydroisomerization of alkanes,9−11

oxidative dehydrogenation in the presence of oxygen12,13 orCO2,

14−16 and other selective oxidation reactions.1,17−19 Thecalcination of the chromia−silica systems results predominantlyin formation of highly dispersed surface Cr(VI) oxidespecies,1−30 being the active sites or their precur-sors.1−10,12,13,15−19,30 Reduced Cr(V) and Cr(III) surfacespecies can also be present in small amounts under theseconditions, as well as Cr2O3 clusters at higher Crloadings.1−4,7−17,19−25

The molecular structure of surface Cr(VI) species in calcinedCr/SiO2 catalysts has been discussed in the literature for manyyears. The data obtained with the UV−vis DR spectroscopyindicated the presence of mono-, di-, and polychromate Cr(VI)species with the monochromate/dichromate ratio dependingon the kind of silica support and the chromium load-ing.1,2,4−6,15,16,21−23,25 According to Raman spectroscopyresults, monomeric surface Cr(VI) forms are the dominatingor even the only Cr(VI) species for the systems with low Crloadings.4,5,12,13,17,18,24−29 The isolated Cr(VI) structure is alsoconfirmed by the recent EXAFS-XANES data,3,4,7,29 as well asby studies on a CrOx/SiO2/Si(100) model catalyst using acombination of X-ray photoelectron spectroscopy (XPS),secondary-ion mass spectrometry (SIMS), and Rutherfordbackscattering spectrometry (RBS) techniques.30 The mono-

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

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 andWachs distinguished by Raman spectroscopy two differentisolated surface Cr(VI) species in the calcined Cr/SiO2 systemunder dehydrated conditions.25,26 The first one is the dominantdioxo species, observed at 982 cm−1, whereas the second one,being in minority, is proposed to be monooxo species 4-foldbonded to the silica surface (Figure 1b), characterized by theRaman band at 1011 cm−1. The frequencies in this range(1004−1014 cm1) were also observed by other authors

Received: October 17, 2012Revised: March 26, 2013

Figure 1. Proposed structures for the monomeric Cr(VI) oxide specieson SiO2.

4,5,7,13,17,18,24−29.

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studying the chromia−silica systems.27−29 They were assignedby some authors to the dioxo OCrO asymmetricstretching vibration,27,28 and others had to conclude that astraightforward assignment was impossible because theasymmetric vibrational mode probably overlaps with othervibrational modes.29

Computational chemistry approaches provide complemen-tary information about supported metal oxides, not accessibleby experimental techniques.31−38 However, the obtained resultsmay strongly depend on the type and size of the supportmodel,35 hence realistic modeling of heterogeneous catalysts isa challenge. Most reported theoretical studies on Cr/SiO2systems were based on small cluster models7,27,39−42 or asilsesquioxane model43 representing amorphous silica. Recently,for the first time a realistic periodic model of amorphoussilica,44 successfully used in different studies,36,45−48 was appliedto investigate relative stabilities of supported Cr(VI) species atdifferent degrees of hydration.38 Several hydrated Cr(VI)structures and two dehydrated species, one with dioxo and onewith monooxo functionality, were considered. The silica modelcorresponded to conditions of a hydroxylated surface, beingvalid for low and moderate temperatures.38

In this work, the structure and properties of monomericCr(VI) oxide species on amorphous silica under dehydratedconditions are theoretically studied with a number of variousperiodic and advanced cluster models. The results obtainedwith the periodic and corresponding cluster calculations arecompared. Among others, we have used the periodic model ofamorphous silica mentioned above,44 but the surface isdehydroxylated to a larger extent, corresponding to hightemperatures 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 inthe calcined Cr/SiO2 system. It is assumed that the distributionof different Cr species between surface silica sites is determinedby their thermodynamic stability and not by the kinetics of thepreparation method. In a previous study on the molybdena−silica system, it was shown that relative energies of Mo speciesdepend on their localizations on the support.35 Therefore, inthe present work many different locations of the Cr(VI) speciesare considered to determine the relative thermodynamicalstabilities of the dioxo and monooxo structures. The vibrationalfrequency analysis is also performed to compare the theoreticalfrequencies for the Cr sites with the reported experimental data,and the assignments for the monooxo and dioxo Cr(VI) specieson silica are discussed. To the best of our knowledge, suchcomprehensive theoretical investigations of the chromia−silicasystem, involving many different models of silica and variouslylocated Cr species, have not been reported so far.

2. COMPUTATIONAL MODELS AND METHODS2.1. Periodic Calculations. Two kinds of periodic models

for silica are proposed. In the first case, the models are based onthe β-cristobalite structure,49 often used to representamorphous silica.35,50−53 The bulk geometry of SiO2 waspreviously calculated in the tetragonal I4 2d space group, andthe lattice constants were determined.35 Surfaces are modeledby slabs, constructed by cutting the bulk parallel to the (001)and (110) crystallographic planes. The surface unit celldimensions (Å) are a = 15.21, b = 10.14, c = 28.00 (including20 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 areterminated by oxygen atoms saturated with hydrogens. The

chromium species have been attached to the partiallydehydroxylated 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 groupsafter grafting is 2.5−2.6 and 1.3 OH nm−2, for the partiallyhydrated and dehydrated Cr(VI) species, respectively. Thechromium coverage is about 0.6 atoms nm−2 (one Cr atom perunit cell). The bottom four layers are frozen in the geometry ofthe bulk, whereas the upper five layers, including the chromiumsite, 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 oxidessupported on silica,36,38 is employed. The surface unit cellparameters (a = 12.77 Å, b = 17.64 Å, c = 25.17 Å, including 15Å of vacuum) were obtained by calculation depending on thefinal model size supported by an optimal computationalpower.44 In this work, the original hydroxylated surface with5.8 OH nm−2 is partially dehydroxylated to simulate theconditions of the catalyst calcination. The final models can beformally viewed as obtained after the grafting of the chromiumspecies on the silica surface with 3.1 OH nm−2 (unit formula =Si27O64H20), resulting in surface concentrations of 2.2 and 1.3OH nm−2, for the partially hydrated and dehydrated Cr(VI)sites, respectively. The experimentally determined density ofthe OH groups for the amorphous silica surface decreases fromabout 2.4 to 1.2 OH nm−2 when the temperature is raised from673 to 973 K, and it is about 0.7 OH nm−2 at 1073 K.54,55 Thecalcination of the Cr/SiO2 system is carried out in a wide rangeof temperatures, from 673 K even up to almost 1273 K,2,4−7 butusually it is about 923 K for the Phillips catalyst.4,5 Thechromium coverage in our models is about 0.4 atoms nm−2

(one Cr atom per unit cell), being below the reportedmonolayer coverage3,17,23,24 and corresponding to the Crloadings for the typical Phillips catalysts.3,4,28,30 The positionsof 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 thePerdew and Wang (PW91) generalized gradient approximationexchange-correlation functional.59 For valence electrons, aplane-wave basis set has been employed. Atomic cores aredescribed with the projector-augmented wave method(PAW).60 Standard PAW atomic parameters are used, requiringa cutoff energy of 400 eV (fixed by the oxygen atom). Forchromium, the PAW is built with 12 electrons in the valence.The Γ-centered Monkhorst−Pack61 sampling of the Brillouinzone with 2 × 2 × 1 mesh is applied for the models based onthe β-cristobalite structure, whereas only the Γ point samplingis used for the amorphous models. Frequency calculations havebeen carried out by numerical differentiation of the forcematrix. All the optimized degrees of freedom are used for thefrequency calculations for β-cristobalite-based models. In thecase of amorphous models, the chromium atom and itsneighbors, including at least the second coordination sphere,are included in the Hessian matrix. The calculations are notspin-polarized. For the graphic presentation of the structures,Materials Studio 5.5 software is used.62

2.2. Cluster Calculations. Three different series of clustermodels, derived from the β-cristobalite framework, from thestructure of the amorphous silica surface (Materials Studiolibrary62) and from the periodic model of amorphous silicaused in this work, have been prepared. The dangling bondshave been saturated with hydrogens replacing the removed Si

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atoms. The respective Cr species have been attached to thepartially dehydroxylated surface. In the case of the modelsbased on the β-cristobalite structure, the geometries of the Crspecies have been optimized together with the upper parts ofthe SiO2 clusters, analogous to the corresponding periodicmodels. The bottom four layers and the terminating hydrogensare frozen. All the models obtained from the amorphous silicastructure have been fully relaxed.Geometry optimization of the largest systems, containing 63,

72, and 97 Si atoms, has been carried out using the PW91functional with the split-valence def2-SVP basis set63

(abbreviated as SVP) for the Cr center and its vicinity, atleast the third coordination sphere, and with the SV basis setfor other atoms. This basis set combination is denoted here asSVP-SV. Further PW91 single-point energy calculations haveemployed 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 latterused in the previous studies on molybdena−silica system,35

have been also applied for the geometry optimization ofselected large models (Figure S1, Supporting Information) tocompare the results obtained with different approaches. Boththe 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 hasbeen optimized at the PW91/SVP level. Vibrational frequenciesand Gibbs free energy corrections have been evaluated in theharmonic oscillator and rigid-rotor approximations. Thecorrections are added to the PW91/TZVPP single-pointenergies to obtain a better estimate of Gibbs free energies(ΔG). The reported energies (ΔE) are not ZPE-corrected, toenable comparison with the larger cluster models and theperiodic models.All systems are considered in closed shell state. The

calculations have been done with the Gaussian 09 suite ofprograms.65 For the graphic presentation of the systemsstudied, the GaussView 5.0 software66 is used.

3. RESULTS AND DISCUSSIONThe nomenclature of the models discussed in this section isconstructed by a number (1−3), a letter (capital or small), andin many cases a superscript roman numeral (I−VI). Thenumbers 1, 2, and 3 denote the monooxo, partially hydrateddioxo, and dehydrated dioxo Cr(VI) species, respectively. Thecapital letter specifies a given periodic model, whereas the smallletter means a cluster model. If the same capital and small letteris used, the periodic and the cluster model correspond to eachother; i.e., they are based on the same silica structure (β-cristobalite or amorphous) and represent the same surface. Forinstance, the periodic model 1A and the cluster model 1arepresent the monooxo Cr(VI) species on the (001) β-cristobalite surface. The superscripts distinguish betweendifferent locations of the Cr(VI) sites on the surface describedby the same SiO2 model.3.1. Surface Cr Species: Models Based on the β-

Cristobalite 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 areshown in Figure 2. The geometry of the monooxo species 1Aand 1B is a distorted square pyramid, whereas the dioxo

structures 2A, 3A, 2B, and 3B are tetrahedrally coordinated, asexpected from Figure 1 and earlier theoretical studies.7,27,38,43

Models 2A and 2B represent partially hydrated species withtwo surface silanols in the neighborhood weakly interactingwith one of both oxo ligands (the O···H distances = 2.32−2.65Å). In the case of the model 2A, a hydrogen bond between thesilanols is also formed (the O···H distance = 2.19 Å). Afterreplacement of hydroxyl groups by siloxane bridges, structures3A and 3B are obtained, corresponding to fully dehydratedconditions. They can be directly transformed to the monooxospecies 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. Thespecies 1a−3a are attached to the (001) surface and correspondto the periodic models 1A−3A. The species 1b−3b on the(110) surface correspond to the periodic models 1B−3B. Thecalculated O···H distances for the hydrogen bonds formed inthe systems 2a and 2b (1.98−2.04 Å) are shorter than in thecase of the corresponding periodic models.The calculated energies for the dehydration reactions of the

dioxo Cr species (2A, 2B, 2a, 2b) to the correspondingmonooxo species (1A, 1B, 1a, 1b) and the energies of thedirect transformation of the dehydrated dioxo species (3A, 3B,3a, 3b) to the monooxo species are listed in Table 1. It can beseen that the dioxo Cr(VI) species are much more stable thanthe monooxo species, independently of the model used. In thecase of the periodic models, the relative energies for the (001)and (110) surface are close to each other because in both casesthe local silica structure in the vicinity of the Cr site is similar(Figure 2). The predicted endothermic effect for the formationof the monooxo Cr(VI) species is about 150 kJ mol−1 largerthan in the case of the analogous periodic calculations for theMo species on β-cristobalite.35 Despite the different calculationmethodologies, the corresponding reaction energies for theperiodic and cluster models representing the (001) surface are

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


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in perfect agreement. In the case of the (110) surface, theagreement between the results obtained from the periodic andcluster calculations is worse because of the higher flexibility ofthe cluster model allowing stronger relaxation of the surfaceand, consequently, better stabilization of the strained monooxostructure. Nevertheless, the general conclusions drawn from theperiodic and corresponding cluster calculations employing theβ-cristobalite structure of SiO2 are the same, in accordance withthe previous theoretical studies on the molybdena−silicasystem.35

3.2. Surface Cr Species: Models Based on AmorphousSilica Structures. Models of the Cr(VI) species employing avery large silica cluster (97 Si atoms) derived from the structureof the amorphous silica surface62 are presented in Figure 4.

This silica cluster was previously described and used forpreparing the analogous models of the surface Mo species.35

The monooxo species 1c shows distorted square pyramidalgeometry, similar to the corresponding monooxo Cr(VI)structures on β-cristobalite. After adsorption of a watermolecule on the surface, various dioxo Cr(VI) species (2cI−2cIII) can be generated from 1c. Hydrogen bonds formedbetween the oxo ligands and neighboring hydroxyl groups (theO···H distance = 1.76−1.97 Å) are stronger than in the case ofthe β-cristobalite-based models. Dioxo forms 3cI and 3cII canbe directly obtained from 1c or by the dehydration of thespecies 2cI and 2cII, respectively.Relative energies of the monooxo and dioxo species

represented by the c series of the models are shown in Table2. Dehydration of the most stable dioxo species 2cI to themonooxo structure 1c is a less endothermic process than theanalogous reactions on the β-cristobalite surface (Table 1), butthere is still a clear energetic preference for the dioxo structure.

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

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

reaction ΔEa reaction ΔEb

2A → 1A + H2O 495 2a → 1a + H2O 4993A → 1A 284 3a → 1a 2802B → 1B + H2O 478 2b → 1b + H2O 3003B → 1B 266 3b → 1b 96

aPeriodic PW91 calculations. bCluster PW91/TZVPP-SVP//PW91/SVP-SV calculations.

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

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

reaction ΔE reaction ΔE

2cI → 1c + H2O 256 3cI → 1c 1462cII → 1c + H2O 15 3cII → 1c −1462cIII → 1c + H2O 0

aCluster PW91/TZVPP-SVP//PW91/SVP-SV calculations.


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Moreover, the surface dehydration reaction 2cI → 3cI + H2O(ΔE = 110 kJ mol−1) is even less endothermic, andconsequently, the dehydrated dioxo species 3c is more stablethan 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 predictedto be less probable than the monooxo structure 1c underdehydrated conditions.To enable efficient calculations of the whole system at higher

level of theory, a number of medium-size models of the Cr(VI)

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) oxidespecies on SiO2. The cluster models are derived from the amorphous silica structure62 (PW91/SVP calculations).


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oxide species have been prepared (Figure 5). The silica clusterswere previously derived from the amorphous silica structureand used for the investigations of the Mo/SiO2 system.35

Different models (series d, e, and f) represent differentlocations on the surface. For each monooxo Cr species, anumber of the dioxo Cr species have been systematicallygenerated, by hydration or direct rearrangement. According tothe notation used in this work, 1d−1f are the monooxo Cr(VI)species; 2dI−2dIV, 2eI−2eVI, and 2fI−2fIV are the partiallyhydrated dioxo species; and finally, 3dI−3dIII, 3eI−3eV, and3fI−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 dioxoCr species, whereas 3dI, 3eI, and 3fI are the most stabledehydrated dioxo species (Table S2, Supporting Information).Dehydration of the silica surface, accompanied by the formationof strained two-membered Si rings, leads to systems with highrelative energies (3dIII, 3eV, 3fIII). The dioxo species with thechromium atom connected via two oxygen bridges with onesurface silica atom (2eV, 3eV, 2fIV, 3fIV) are also unstable, whichis explained by the formation of a strained ring in each case,consisting of one Cr, one Si, and two O atoms. This isconsistent with previously reported results for tetrahedralMo(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, theenergies at T = 0 K and Gibbs free energies at T = 873 K forthe respective dehydration and rearrangement reactions arepresented in Table 3. Additionally, for the partially hydrated

dioxo species, Gibbs free energies for the dehydration reactionsleading to the corresponding monooxo species have beencalculated as a function of temperature and water vaporpressure (Table 4). Although the energetic parameters dependon the model, i.e., on the specific structure and location of theCr center on the silica surface, in almost all cases a strongthermodynamic preference for the dioxo species is seen. Theonly exception is the partially hydrated 2eII species, which canbe less stable than the monooxo Cr(VI) species 1e under

strictly dehydrated conditions at high temperatures (Table 4).However, the removal of two hydroxyl groups from the vicinityof the dioxo center 2eII, resulting in water release and theformation of a siloxane bridge (model 3eII), is more preferredthan the dehydration of 2eII to 1e. Consequently, both the 3eII

and 3eI dioxo species are more stable than the monooxostructure 1e (Table 4 and Table S2, Supporting Information).It can be noted that the predicted thermodynamic preferencefor the dioxo Cr(VI) species on silica, over the monooxoCr(VI) species, is stronger than in the case of the Mo/SiO2system studied previously with similar silica models.35

Periodic models of the Cr(VI) species supported onamorphous silica44 are shown in Figure 6. The monooxostructure 1G has been obtained from the previously reported38

model of the monooxo Cr(VI) species, by removing threewater molecules per unit cell. All possible dehydration variantshave been considered, and the selected structure 1G representsthe lowest energy solution allowing for the desired concen-tration of the surface silanols, i.e., approximately 1.3 OH nm−2.Additionally, we have checked an alternative location of themonooxo 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 thecase of 2GIII, 2GIV, and 3GIII, interactions between oxo ligandsand neighboring silanols are observed (the O···H distance =1.88−2.57 Å). The energies of the partially hydrated dioxospecies are close to each other (Table S3, SupportingInformation). On the other hand, among the dehydrateddioxo species, 3GI is clearly the most stable system because ofeasy dehydroxylation of 2GI, involving two adjacent silanols. Inthe case of 3GII, a strained two-membered Si ring is formedafter the dehydration of 2GII. Even more significant surfacereconstruction is observed during the dehydration of 2GIII to3GIII. Here, a new siloxane bridge connects two relativelyremote silicon atoms. Finally, after removing two silanols from2GIV, surface defects, i.e., a three-coordinated silicon and anonbridging 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 neighboringhydroxyl group (the O···H distance = 1.80−1.99 Å), similar toother dioxo systems. Among the partially hydrated species(2gI−2gIV), 2gII is the most stable one in terms of Gibbs freeenergy (ΔG873). The energy differences between the species arehigher than those for the periodic systems but still not dramatic(Table S3, Supporting Information). As the dehydrated dioxo

Table 3. Energiesa (ΔE, kJ mol−1) and Gibbs Free Energiesa

at T = 873 K (ΔG873, kJ mol−1) for the Conversion of theDioxo Cr(VI) Species (2dI, 3dI, 2eII, 3eI, 2fIII, 3fI) to theCorresponding Monooxo Species (1d, 1e, 1f)

reaction ΔE ΔG873 reaction ΔE ΔG873

2dI → 1d + H2O 296 153 3dI → 1d 217 2552eII → 1e + H2O 194 100 3eI → 1e 148 1592fIII → 1f + H2O 254 145 3fI → 1f 226 218

aCluster PW91/TZVPP//PW91/SVP calculations.

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

673 K 873 K 1073 K

reaction 10−2 atm 10−5 atm 10−2 atm 10−5 atm 10−2 atm 10−5 atm

2dI → 1d + H2O 158 119 120 70 82 212eII → 1e + H2O 93 55 67 17 42 −202fIII → 1f + H2O 141 102 112 61 83 212gI → 1g + H2O 18 −21 −10 −61 −38 −1002gII → 1g + H2O 53 15 25 −25 −3 −65

aCluster PW91/TZVPP//PW91/SVP calculations.


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

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

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


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periodic models. On the other hand, 3gIV is the most stablesystem, in contrast to the least stable 3GIV. High flexibility ofthe cluster model prevents formation of surface defects afterdehydration of 2gIV, whereas the periodic model, perhaps morerealistic, 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) andcluster (series g) models, the energies at T = 0 K and Gibbsfree energies at T = 873 K for the dehydration andrearrangement reactions of the dioxo structures are presentedin Table 5. The dehydration reactions are endoenergetic for

both the periodic and cluster models; however, at hightemperatures and under low water vapor pressure the formationof the monooxo species becomes preferable (Table 4, theresults for 1g). On the other hand, alternative dehydrationprocesses resulting in formation of the dioxo species are evenmore preferred in some cases. Consequently, the most stabledehydrated dioxo species for each silica model (3GI, 3gI, 3gIV)are energetically more favorable than the correspondingmonooxo structures (1G and 1g, Table 5), in qualitativeagreement with the calculations based on other models (Tables2 and 3). As the concentration of available surface sites exceedsthat of Cr species (see also Section 2.1) and the Cr distributionis most likely controlled by the thermodynamic stability of Crspecies, then Cr should occupy the most stable sites. Thus, thedioxo Cr(VI) species appears to be much more probable on thesilica surface under dehydrated conditions than the monooxoCr(VI) forms, although the latter cannot be excluded as theminor species.3.3. Calibration of the Theoretical Methods. A

benchmark study of geometrical parameters and vibrationalfrequencies with experimentally characterized gas-phasechromium compounds CrOF4, CrO2F2, CrO2Cl2, CrO(OH)2,HCrO(OH), and CrO(OH) has been carried out. The groundstate for CrO(OH)2 and HCrO(OH) is triplet, whereas forCrO(OH) it is quartet.The predicted bond lengths and angles are generally

consistent with the reported experimental data67−69 (Table6). Regarding the CrO bonds, the predicted distances areslightly overestimated in the case of the periodic calculations,by approximately 0.01−0.02 Å. The molecular calculationsprovide a bit underestimated CrO lengths, by about 0.01−0.025 Å. The scaled theoretical frequencies are satisfactorilyclose to the experimental data70−72 (Table 7). The scaling

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

3.4. Bond Lengths. The chromium−oxygen bond lengthscalculated for the proposed models of the dioxo Cr(VI) specieson silica, excluding the least stable structures, are compared inTable 8 with the reported EXAFS data for chromia−silicasystems.7,29 Generally, a very good agreement between thetheoretical and experimental parameters is achieved. Notsurprisingly, taking into account the results obtained for thegas-phase Cr compounds, the predicted CrO bond lengthsare slightly higher for the periodic models, compared to thecluster models. On the other hand, both the periodic andcluster calculations give very similar ranges of the single Cr−Obond distances, being a little shorter, on average, than therespective EXAFS values. The theoretical chromium−oxygenbond lengths reported in this work are close to thecorresponding values obtained previously for the periodicmodels of the Cr(VI) dioxo species supported on a morehydrated silica surface.38

3.5. Vibrational Frequencies. In Table 9, the calculatedvibrational frequencies for the monooxo and dehydrated dioxoCr(VI) species are presented together with the Ramanspectroscopy data reported for Cr(VI)/SiO2 systems under

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

reaction ΔEa reaction ΔEb ΔG873b

2GI → 1G + H2O 156 2gI → 1g + H2O 127 232GII → 1G + H2O 150 2gII → 1g + H2O 160 582GIII → 1G + H2O 154 2gIII → 1g + H2O 224 462GIV → 1G + H2O 129 2gIV → 1g + H2O 204 53GI → 1G 69 3gI → 1g 100 973GII → 1G −62 3gII → 1g 10 −243GIII → 1G −246 3gIII → 1g −65 −993GIV → 1G −347 3gIV → 1g 193 114

aPeriodic PW91 calculations. bCluster PW91/TZVPP//PW91/SVPcalculations.

Table 6. Calculated and Experimental Bond Lengths (Å) andAngles (Degrees) for the Reference Gas-Phase ChromiumCompounds

calcda calcdb exptl67

CrOF4 CrO 1.568 1.536 1.547Cr−F 1.751 1.730 1.730F−Cr−F 86.2 86.3 86.7OCr−F 105.0 104.7 104.0


CrO2F2 CrO 1.585 1.557 1.575Cr−F 1.727 1.702 1.720OCrO 108.3 108.4 107.8F−Cr−F 110.9 110.5 111.9OCr−F 109.4 109.5 109.3


CrO2Cl2 CrO 1.588 1.556 1.581Cr−Cl 2.120 2.128 2.126OCrO 109.2 108.8 108.5Cl−Cr−Cl 111.1 111.4 113.3OCr−Cl 109.1 109.2 108.7

aPeriodic PW91 calculations. bPW91/SVP calculations.

Table 7. Calculated and Experimental CrO StretchingFrequencies (cm−1) for the Reference Compounds

calcda calcdb exptl

CrOF4 1041 1031 1027.7c

CrO2F2 1023 1012 1016d

997 995 1006d

CrO2Cl2 1010 1003 1000d

980 988 990d

CrO(OH)2 992 992 1002.9e

HCrO(OH) 1007 1014 1012.2e

CrO(OH) 945 961 939.6e

aPeriodic PW91 calculations; the frequencies are scaled by 0.9241.bPW91/SVP calculations; the frequencies are scaled by 0.9149. cRef70. dRef 71. eRef 72.


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dehydrated conditions.12,13,17,18,24−29 The theoretically deter-mined vibrational modes are coupled with the supportvibrations, analogous to the previously studied molybdena−silica system.35

The predicted CrO stretching frequencies are above 1000cm−1 for all the models of the monooxo Cr(VI) species. Thecalculated numbers are quite close to the experimental value,especially in the case of the amorphous systems 1e, 1G, and 1gwhich are relatively more stable than other monooxo structures(Tables 1 and 3−5). The experimental frequencies assigned tothe asymmetric OCrO stretching mode27,28 are very closeto the frequencies assigned by Lee and Wachs to the Cr(VI)monooxo species25,26 (Table 9). On the other hand, theisotopic labeling and polarization studies reported by Stiegmanand co-workers29 did not support the straightforward assign-ment of the band at 1004 cm−1, observed for the chromia−silicasystem, to the asymmetric stretching mode. The authorssuggested that this mode overlaps with other vibrational modes.In most cases, our calculated frequencies for the asymmetricOCrO stretch exceed 1000 cm−1 (Table 9). Although theyare lower, on average, than the theoretical CrO frequenciesfor the monooxo species, the wavenumbers predicted for themodes are quite close to each other, especially for the models1G and 3GI. Thus, our results indicate that these modes mayindeed overlap, which explains why they are not observed astwo separate bands.Calculated frequencies for the symmetric OCrO

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 verygood. For other models (3dI, 3eI, 3fI, 3gI), the theoreticallyevaluated frequencies are significantly diminished because ofthe interactions between the oxo ligands and the surfacehydroxyls. The predicted Cr−O−Si frequencies for the Cr(VI)dioxo species (Si−O−Cr−O−Si symmetric vibrations) areconsistent with the experimental results, excluding the

significantly decreased values for the models 3fI, 3fIII, and3gIV. Finally, the calculated OCrO bending modefrequencies are slightly underestimated, compared to theRaman spectroscopy data. It should be noted, however, thatthe scaling factors determined on the basis of the stretchingCrO frequencies are not accurate for the bending modesbecause, in general, scaling factors depend on the vibrationalwavenumbers.74

Isotopic 18O−16O exchange studies confirmed the dioxofunctionality of the dominant Cr(VI) oxide species onsilica,26,29 although either the asymmetric stretching modewas not observed in these experiments26 or the respectivefrequencies could not be unambiguously assigned.29 Thecalculated isotopic shifts for selected models of the monooxoand dioxo Cr(VI) species are shown in Table 10, in comparison

Table 8. Calculated and Experimental Bond Lengths (Å) for the Dioxo Cr(VI) Species on Silica

model CrO Cr−O

periodic (β-cristobalite) 2A, 3A, 2B, 3B 1.59−1.61 1.76periodic (amorphous) 2GI−2GIV, 3GI 1.59−1.61 1.72−1.78cluster (β-cristobalite)a 2a, 3a, 2b, 3b 1.56−1.59 1.74−1.76cluster (amorphous)b 2cI, 3cI, 2dI, 2dII, 2dIV, 3dI, 3dII, 2eI−2eIV, 2eVI, 3eI−3eIV, 2fI−2fIII, 3fI−3fIII, 2gI−2gIV, 3gI, 3gIV 1.56−1.59 1.72−1.79exptl 1.60−1.61c 1.77−1.79c

1.60d 1.80d

aPW91/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

monooxo model ν(CrO) dioxo model νas(OCrO) νs(OCrO) νs(Cr−O−Si) δ(OCrO)

1A 1022 3A 1009 977 902 3621B 1023 3B 1009 972 900 3621d 1019, 1034 3dI 1000 942, 956 903 355−3921e 1006, 1024 3eI 979, 992 947 891−914 363−4351f 1021 3fI 1015 937 812 354

3fIII 1010 979 849 3731G 1005 3GI 1007 977 919 366−3841g 1002, 1015 3gI 994, 1001 948 896 364−379

3gIV 1004 975 865 368−390exptl 1011b exptl 1004c, 1014d 980−990e 905−919f 394−396g

aThe frequencies are scaled by 0.9241 and 0.9149 for the periodic (PW91) and cluster (PW91/SVP) calculations, respectively. bRefs 25 and 26. cRef27. dRef 28. eRefs 12, 13, 17, 18, and 24−29. fRefs 25 and 29. gRefs 25, 26, and 28.

Table 10. Effect of the Isotopic 18O−16O Exchange on theCalculateda and Experimental CrO StretchingFrequencies (cm−1) for the Cr(VI) Oxide Species on Silica

1f 1g exptl

ν(Cr16O) 1021 1002, 1015 1011b

ν(Cr18O) 986, 995 957, 962, 977 967b,c

3fIII 3gIV exptl

νas(16OCr16O) 1010 1004 1004d, 1014e,

1004f,g

νas(18OCr16O) 989, 1007 993, 996,

1000-

νas(18OCr18O) 955, 975 966 954f,g

νs(16OCr16O) 979 975 980b, 986f

νs(18OCr16O) 927, 948,

963942, 948 942b, 950−951f

νs(18OCr18O) 925 935 935b, 943f

aCluster PW91/SVP calculations; the frequencies are scaled by 0.9149.bRef 26. cEstimated value. dRef 27. eRef 28. fRef 29. gNotunambiguously assigned to the asymmetric mode.


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with the reported Raman spectroscopy data. The 18O−16Osubstitution is considered only for the oxo ligands. According toour calculations, the 18O replacement for 16O from the Cr−O−Si linkages hardly influences the CrO stretching modefrequencies, by no more than 1 cm−1. The predicted isotopicshift for the monooxo species depends on the model used. Forthe more realistic structure 1g, the theoretical Cr18Ofrequencies are close to the value estimated by Lee andWachs.26 The calculated asymmetric 18OCrO18 stretchingfrequencies are in the same range, hence the isotopic exchangeprobably does not facilitate experimental distinguishingbetween the monooxo and asymmetric dioxo stretchingvibrations. Moreover, these vibrations can be interfered bythe more intense symmetric stretching modes of the remainingnonsubstituted or partially substituted dioxo species. In thelatter case, the theoretically determined isotopic shift of theasymmetric stretch, which probably has not been experimen-tally observed so far, is modest (Table 10). In contrast, a largershift of the symmetric stretching vibration is predicted, inaccordance with the experimental results. It should be alsonoted that for both models 3fIII and 3gIV the calculated 18OCrO16 frequencies depend on the substitution sequence. Thefurther shift of the symmetric mode, corresponding to thedioxo 18OCrO18 species, is not significant.26,29 This effectis very well reproduced by the model 3gIV.

4. CONCLUSIONSExtensive theoretical studies on the monomeric Cr(VI) oxidespecies on silica under dehydrated conditions have beenperformed using both periodic and cluster DFT approaches. Alarge number of various advanced models of the SiO2 surface,based on the β-cristobalite structure and different amorphousmodel structures, have been applied in parallel.Results obtained from the periodic and cluster calculations

for the Cr(VI) species supported on the β-cristobalite surfaceare comparable. In the case of the periodic and correspondingcluster models representing amorphous silica, bigger differencesare usually observed, especially in the predicted relativeenergies of the monooxo and dioxo Cr(VI) species. Never-theless, all the approaches lead to the same general conclusionthat the dioxo species are more stable than the monooxospecies under dehydrated conditions. On the other hand, thecalculated relative energies significantly depend on the structureof the model. The calculated preference for the dioxo species isstronger in the case of the β-cristobalite-based models than forthe models representing the amorphous surface. The latter ismore flexible than the β-cristobalite surface, hence theformation of four Cr−O−Si linkages is more facilitated here.This is especially seen for the models derived from theproposed periodic structure of amorphous silica,44 where thepredicted thermodynamic preference for the dioxo speciesunder dehydrated conditions is the weakest, that neverthelessfound the dominating structure over a large temperaturedomain. The presence of the monoxo Cr(VI) species on silica,being in minority, cannot be excluded, in accordance with theresults of Lee and Wachs.25,26

The relative stabilities of the Cr(VI) species depend on thelocation of the metal center on the silica surface. Thisconclusion is consistent with the results obtained recently forthe molybdena−silica system.35 It should be noticed, however,that the energetic preference for the dioxo Cr(VI) species overthe monooxo Cr(VI) species is stronger than in the case of theanalogous models of the Mo(VI) species on silica.

The calculated vibrational frequencies for the Cr(VI) sites onsilica are well consistent with the available experimentaldata.12,13,17,18,24−29 According to our results, the asymmetricOCrO stretching mode for the dioxo species and theCrO stretching mode for the monooxo species can overlap.

■ ASSOCIATED CONTENT*S Supporting InformationCluster models of the surface Cr species 1a−3a optimized withthe two-layer ONIOM method are presented in Figure S1.Relative energies for the species 1a−3a and relative energiesand Gibbs free energies for the dioxo Cr(VI) species (the seriesd−g and G) are listed in Tables S1−S3. This material isavailable free of charge via the Internet at http://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Author*Phone: +48 12 6282196. Fax: +48 12 6282037. E-mail:[email protected] authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThis work was supported by the Polish National ScienceCentre, Project No. N N204 131039 (2010-2012), and by PL-Grid Infrastructure. Computing resources from AcademicComputer Centre CYFRONET AGH (grants MNiSW/SGI4700/PK/044/2007 and MNiSW/IBM_BC_HS21/PK/044/2007) are gratefully acknowledged. F.T. acknowledgesthe HPC resources from GENCI-[CCRT/CINES/IDRIS](Grant 2011-[x2012082022]).

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

structure of monomeric chromium(vi) oxide species supported on silica: periodic and cluster dft...

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