Chromium Oxide Species Supported on Silica: A Representative

ARTICLE pubs.acs.org/JPCC

Chromium Oxide Species Supported on Silica: A Representative Periodic DFT Model Hazar Guesmi and Frederik Tielens* UPMC, Univ Paris 06, UMR 7197, Laboratoire de R
eactivit
e de Surface, Site d’Ivry
Le Rafa€el 3, rue Galil
ee, 94200 Ivry-Sur-Seine, France and CNRS, UMR 7197, Laboratoire de R
eactivit
e de Surface, Site d’Ivry
Le Rafa€el, 3 rue Galil
ee, 94200 Ivry-Sur-Seine, France ABSTRACT: The Cr/SiO2 system is investigated using periodic DFT. The model represents the amorphous character of the silica surface and allows the investigation of the effect of hydration on the Cr(VI) monomers. First, the geometry and energetics are discussed and compared with experimental data. The phase diagram plotted from an atomistic thermodynamics model confirms the higher stability of mono-oxo and dioxo chromium, in comparison with species containing Cr
OH groups. In addition, the effect of the siloxane ring size on the spectroscopic signature of chromium is analyzed. A preliminary study is presented on the surface doping effect by Ti on the structure and stability of chromium species. The results reveal that the charge transfer process between Ti and Cr can explain the observed change in the reactivity of chromium species.

1. INTRODUCTION Chromium oxides supported on inorganic oxides, such as SiO2, Al2O3, MCM-41, etc., are typically used as catalysts. Chromium oxide on silica (Cr/SiO2) is the famous Philips catalyst for the polymerization of ethylene at relatively low pressures.1
3 This catalyst is the basis for particle form process in the production of high-density polyethylene (HDPE), one of the most extensively used polymers. Other important catalytic activities are hydrogenation
dehydrogenation, oxidation, isomerization, aromatization, DeNOx reactions, and complete combustion.4
6 The basis for the activity of Cr in such a wide spectrum of reactions lies in the variability of oxidation states, of coordination environments, and of degree of polymerization of Cr oxide species. This variability is especially pronounced on the surface. Thus, knowledge about the surface chemistry of supported chromium oxide species is of key importance in environmental sciences and heterogeneous catalysis. Mainly due to the importance of this system, it has been studied in detail for the last 50 years, experimentally and more recently theoretically. The still growing computational power enables to study models with increasing complexity and reliability. Until now ab initio quantum chemical calculations have been performed on cluster models involving a dozen of atoms.7
9 One of the difficulties to model Cr/SiO2 catalyst, among other points, is the representation of the silica surface, due to its amorphous nature. The objective of this study is to investigate possible atomic models of the silica supported chromium oxide catalysts in hydrated and dehydrated forms, in a similar way to our study on the characterization of vanadium containing silica.10 To this end, density functional theory (DFT) is used to calculate the r 2011 American Chemical Society

structures, vibrational frequencies, and relative stabilities of isolated monomeric chromium species grafted to the surface of amorphous silica. The effect of siloxane ring size was also investigated. The inclusion of small amounts of titanium has a promotional effect on both the polymerization activity and the termination rate of the catalysts.11,12 A further objective of the work is to determine the surface doping effect by Ti on the structure and stability of chromium species. In particular, the effect of Ti content on the charge transfer between Ti and Cr has been investigated together with vibrational frequency analysis. The structures calculated in the present study are compared with experimental literature data obtained by EXAFS and Raman spectra reported for highly dispersed CrOx on silica.7,13
16

2. METHODOLOGY 2.1. Computational Details. All calculations are performed using ab initio plane-wave pseudopotential approach as implemented in VASP.17,18 The Perdew
Burke
Ernzerhof (PBE) functional19,20 has been chosen to perform the periodic DFT calculations with an accuracy on the overall convergence tested elsewhere.21
24 The valence electrons are treated explicitly, and their interactions with the ionic cores are described by the projector augmented-wave method (PAW),25,26 which allows the use of a low energy cut off equal to 400 eV for the plane-wave basis. The Gamma point is used in the Brillouin-zone integration. Received: October 8, 2011 Revised: November 26, 2011 Published: December 06, 2011 994

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Table 1. Reaction Energy Calculated Using eq 1 for the Grafting of the Different Chromium Oxide Models Investigated (Values in eV) modela

a

Figure 1. Top view of the 2  2 unit cell of the amorphous silica surface model on which Cr(VI) oxide is grafted (Cr atom in blue).

ΔEreact

A: Surface + CrO4H2 + 2H2O


0.26

B: Surface + CrO4H2 + H2O


0.89

C: Surface + CrO4H2


2.09

D: Surface + CrO4H2 + H2O

0.13

E: Surface + CrO4H2 F: Surface + CrO4H2
H2O


0.80
1.33

G: Surface + CrO4H2

1.72

H: Surface + CrO4H2
H2O

0.34

I: Surface + CrO4H2
2H2O

0.42

See Figure 1.

The chromium precursor is modeled by a H2CrO4 unit (Cr(VI)). This species is added to the silica unit cell resulting in a chromium coverage of 0.44 atoms nm
2. At this coverage, maximum activity is obtained for the experimental Philips catalyst.29 The H2CrO4 entity is grafted by dehydration of surface silanols, following the reaction H2 CrO4 þ SiO2 ðH2 OÞn ðsurfaceÞ f Ox CrðOHÞy
SiO2 ðH2 OÞn
2x
y ðsurfaceÞ þ ð2x þ yÞH2 O

ð1Þ

With n = initial number of surface silanol groups, x = number of CrdO, and y = number of Cr
OH groups. Theoretically, up to four silanols may be involved in the reaction yielding different modes of grafting: mono, di, tri, and tetra (see Figure 2). Structures involving the different silanol types: isolated (Si
OH), vicinal (HO
Si
O
Si
OH), geminate (HO
Si
OH), and nonvicinal (two Si
OH groups not directly connected) on the surface were considered. Because of the flexibility of the silica surface, these species can be more or less easily accommodated. The reaction energy values (ΔEreact) of reaction 1 for representative sites are compiled in Table 1.

Figure 2. Most stable geometries for the supported chromium oxide grafted on amorphous silica.

3. RESULTS AND DISCUSSION The positions of all the atoms in the super cell are relaxed until the total energy differences decrease below 10
4 eV. Vibrational spectra have been calculated for selected surface species within the harmonic approximation. Only the chromium center and its first and second neighbors (O
Si and OH groups) are considered in the Hessian matrix. This matrix is computed by the finite difference method followed by a diagonalization procedure. The eigenvalues of the resulting matrix lead to the frequency values. The assignment of the vibrational modes is done by inspection of the corresponding eigenvectors. 2.2. Model Description. The hydroxylated silica model structure is described and characterized in our previous work 21 and has been used in the study of vanadium oxide10 and gold27,28 grafted on silica. The model consists of a silica slab (dimensions 12.77  17.64  25.17 Å3 ) made of 120 atoms (Si27O54 3 13H2O), which enables us to model a correct representation of a hydrated silica surface (Figure 1). This model accounts for the experimentally encountered ring size distribution, Si
O
Si and O
Si
O angles, silanols density, and repartition (isolated, associated, and geminals).

3.1. Geometry and Energetics. 3.1.1. Cr(VI)oxide Species Grafted on SiO2 Surface. Figure 2 shows (structure A, B, and C)

mono-, (structure D, E, and F) di-, (structure G and H) tri-, and (structure I) tetra-grafted chromium oxide species on silica support. For mono- and digrafted chromates, the vicinal silanol sites are preferred. Tri- and tetragrafted species need the presence of three and four neighboring silanol sites, respectively. The preference of monografted species to the vicinal HO
Si
O
Si
OH sites may be due to the formation of H-bonds between the chromate Cr
OH groups and surface silanol groups, which stabilize the conformations. Digrafted chromates show a large preference for vicinal silanol sites compared to nonvicinal (geminate) ones (vide ultra). According to the calculated energy values for reaction 1 shown in Table 1, the tri- and tetragrafted chromium species are the highest endothermic configurations followed by the fully hydroxylated di- and monografted chromates. The most stable structures are mono- and dioxo monografted and digrafted species: B, C, E, and F. The geometrically optimized structures have all similar CrdO bond distances of about 1.60 Å (see Table 2), 995

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which are in agreement with the calculated gas phase H2CrO4 molecule CrdO bond distance.30 The chromyl bond as well as the OdCrdO bond angle of dioxo species (109.8°) seem not to be influenced neither by the presence of neighboring Cr
OH groups nor by the chromium grafting mode. In contrast, the bridging Cr
OSi bond distances and the SiO
Cr
OSi bond angles (89
103°) are highly affected by the presence of hydroxyl groups. From EXAFS study, Mosii et al.13 have reported (Cr
O) bond lengths of 1.60 Å and 1.80 Å for terminal and bridging bonds of Cr(VI) species supported on amorphous silica, and no hydroxyl groups were detected. These authors have reported that

dioxo (tSiO)2Cr(dO)2 is the structure that agrees the best with the EXAFS fit. From our calculation, such structure corresponds to configuration F. Using an ab initio cluster approach for calculating Cr(VI)/SiO2 species, Dines and Inglis7 reported an identical OdCrdO angle of 109.8° to the one found in configuration F. However, smaller terminal CrdO bond lengths of 1.579 and 1.581 Å were calculated, probably due to artifacts generated by the small size of the cluster models. 3.1.2. Effect of the Siloxane Ring Size on the Dioxo Chromate Grafting. Siloxane bridges formed upon dehydroxylation can be classified into several groups, depending upon the structure of the immediate surroundings. These structures are characterized by the presence of two-, three-, four-, etc.-membered open siloxane rings (Figure 3). The strain present in these structures decreases with an increasing Si
O
Si bond angle, until an angle of about 150°, being the equilibrium Si
O
Si angle in disiloxane molecule.31 The grafting of chromic acid on suitably spaced silanol groups can originate different species characterized by an increasing bond angle α(SiO
Cr
OSi) and consequently by a decreasing strain in the siloxane ring. In order to analyze the effect of strain in the siloxane rings on the grafted chromic acid, three structures representing chromyl dioxo structures grafted over 2-membered ring (F, see Figure 3), 3-membered ring (F-bis), and 4-membered ring (F-tris) were optimized (see Figure 4). Table 3 presents the calculated bond angles α(SiO
Cr
OSi) in the optimized dioxo species. The bond angle α(SiO
Cr
OSi) increases from 103.7° to 117.8° and the bond lengths d(Cr
OSi) from 1.76 Å to 1.80 Å, with increasing siloxane ring-opening. In contrast, bond distances d(CrdO) and bond angles α(OdCrdO) remain unaltered for all calculated configurations. Nevertheless, the higher stability of structure F, with respect to the computed F-bis and F-tris structures

Table 2. Calculated and XAFS Derived Selected Geometrical Parameters in Chromium/Silica System (Distances in Å
and Angles in Degrees) literature13

this work B d(CrdO)

1.61

C 1.6

E 1.6

1.6 d(Cr
OH)

1.82

1.79

1.81

F 1.6

1.60 ( 0.02

1.6 1.81 1.85

1.8 d(Cr
OSi)

1.83

1.76

1.83 1.81

1.76

d(CrO
Si)

1.64

1.65

1.64

1.65

1.66

1.66

89.69

103.7

α(OdCrdO)a α(SiO
Cr
OSi)b a

109.89

1.80 ( 0.02

109.84

Angles for dioxo chromates. b Angles for digrafted chromates.

Figure 3. Molecular representation of structure F. The dioxo digrafted chromium species is framed. 996

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on the energetic balance of the number of H-bonds broken/ created. Considering the reaction energy ΔEreact (Table 1) calculated according to eq 1, for the best grafting modes as a function of hydration rate, we obtain
0.26,
0.89,
2.09,
1.33, and 0.42 eV for +2, +1, 0,
1, and
2 water molecules, respectively. Negative energy values suggest that the adsorption of the H2CrO4 is favored compared to the initial situation (hydroxylated silica and H2CrO4 in the gas phase) until the abstraction of 2 water molecules. The endothermicity of the reaction leading to the tetragrafted species means that the gain in energy due to the formation of 2 water molecules is not enough to counter-balance the cost of breaking four Si
OH bonds. Indeed, the present calculations report electronic energies only, which are identical to the free energy at 0 K. Under given temperature T and pressure p, the contributions of entropy and chemical potentials have to be taken into account in the free energies. It is interesting to mention here that the synthesis of the grafted Cr(VI)-SiO2 catalyst occurs experimentally through successive steps: after impregnation by the precursor at room temperature, in aqueous or nonaqueous solution, the obtained surface is dried and then calcined to achieve a chemically grafted active site and to burn all reactive species still present at the surface. In the case of the Cr(VI)-SiO2 synthesis, the samples are dried one night at room temperature or at 383 K, then calcined for several hours at 723
773 K, depending on the experimental works5,7,15,32 and references therein. Thus, it is empirically known that a high temperature and dehydration conditions are necessary to obtain the multigrafted Cr-complex. In order to get a more precise picture of the respective stabilities of the mono-, di-, tri-, and tetragrafted Cr(VI) species at the silica surface, we performed calculations using the atomistic thermodynamics approach. To take into account deviations in surface composition and the presence of gas phase, one introduces appropriate chemical potentials to calculate an approximation of the Gibbs free-surface energy. Assuming that the surface is in thermodynamic equilibrium with the gas phases, the chemical potentials are related to a given temperature T and pressure p. This procedure enables us to extend the 0 K and zero pressure DFT results to experimentally relevant environments, thereby bridging the gap between ultrahigh vacuum-like conditions and temperatures and gas phase pressures that are applied in realistic catalytic conditions. We consider that the Cr(VI)/silica system is in contact with a gaseous water reservoir. From the electronic energy, the free energy of the water/Cr(VI)/silica interface under known thermodynamic conditions may be estimated following the approximations used by Digne et al.,33 as originating from Kaxiras et al.34 and Qian et al.35 It consists in the neglect of the variation of the chemical potentials of the surfaces with the adsorption and the consideration of the gas phase as a perfect gas. In the proposed scheme, the free energy of water (including the ZPE correction) in the gas phase is

Figure 4. Different siloxane ring structures used in the calculations for structure F (dioxo digrafted chromium oxide).

Table 3. Reaction Energy Calculated Using eq 1 and Selected Geometrical Parameters for Chromium/Silica System
and Grafted on Different Siloxane Ring Sizes (Distances in Å Angles in Degrees) model ΔEreact

dCrdO

dCr
OSi α(OdCrdO) α(SiO
Cr
OSi)

F


1.33 1.60
1.60 1.76
1.76

109.84

103.70

F-bis


1.14 1.60
1.61 1.79
1.74

108.21

108.13

F-tris
1.04 1.60
1.60 1.80
1.77

108.35

117.84

(0.19 and 0.29 eV, respectively), indicates the preference of Cr for tetrahedral coordination. Interesting to note is that the calculated orbital energies of chromate ions are similar. Miller et al.9 have calculated the orbital energies of the chromate ion establishing that the HOMO level possesses pure oxygen character and that the unoccupied MO levels are mostly chromium character. This means that these species are expected to show similar spectroscopic transitions and cannot be distinguished by UV
vis spectroscopy. Nevertheless, calculations might help to distinguish them. Since from the F structures, structure F is the most stable by (only) 0.2 eV, this structure is expected to dominate. This structure has a chromium atom in a 3-membered ring compared with a 8- and 10-membered ring for structure F-bis and F-tris, respectively. However, because of this small energy difference, the other structures are probably also present as well. 3.2. Thermodymics and Stability of the Chromium Oxide Species. Grafting of chromium oxide species on the silica surface has a relatively small effect on the silica framework and is comparable with what has been found in our previous study on the grafting of V oxide species on silica.10 Depending on their density, surface silanols are generally interacting with their neighbors forming an H-bond network. The grafting reaction perturbs the local H-bond network in two ways: first, surface hydroxyl groups are removed upon grafting, and second, the chromate units might also form hydrogen bonds with the silica support. In the models studied, the Cr
OH groups bind to surface silanols with a stabilization of the structure, in contrast with CrdO groups, which are found to be H-bond free. To summarize, the nature of the silanol group (isolated, vicinal, and geminate) has no influence on the geometry of the grafted precursor with the exception of the monografted species. The overall silica framework is only slightly modified upon Cr oxide grafting. The trigrafted site introduces the largest strain on the silica surface. However, the silanol H-bond connectivity influences the overall reaction energy. The final result depends

ΔGðH2 OÞ ¼ EðH2 OÞ
ððΔHG
TΔSG ðTÞÞ þ RT lnðp=p°ÞÞ

ð2Þ

where E(H2O) is the electronic energy of water calculated at 0 K, ΔHG and ΔSG(T) are the enthalpy and entropy of gaseous water, calculated with the Gaussian03 code36 as a function of the temperature, p is the partial pressure of water vapor and p° is the standard pressure (1 bar). 997

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In summary, the three grafted Cr(VI) species may exist on a silica surface depending on the experimental conditions. They are supposed to reversibly interconvert in the presence of water, and they might coexist on the surface. 3.3. Vibrational Frequency Analysis. Wachs et al.16 found that dehydrated CrO3/SiO2 possesses νs(Cr(dO)2) and νas(Cr(dO)2) at ∼980 and ∼1010
1015 cm
1, respectively. These vibrations correspond well with DFT-calculated values on clusters for a dioxo Cr(dO)2 species, predicted to vibrate at 983/ 1030 cm
1 for the terminal symmetric/asymmetric stretches.7 The asymmetric stretch mode, not detected with Raman in the supported CrO3/SiO2 spectra suggests that the OdCrdO bond angle may be perpendicular or near 90°.14 An isotopic oxygen exchange study with the dehydrated supported CrO3/ SiO2 catalyst shows that the dehydrated dioxo surface (Od)2Cr(
O
Si)2 structure is the main surface chromia species on SiO2.15 In Table 4, we show Cr
OH, Cr
O
Si, and CrdO vibrational frequencies calculated for the different studied models. Next to the calculation of their total energies, spectroscopic data can be used to determine the surface species observed experimentally. Comparing the theoretical frequencies with the experimental ones,15 we can conclude that the model containing the most similarities with the experiment is model F. This was concluded with the use of a scaling factor for the frequencies, independently from the type of bond and normalized on the wellknown silanol vibration. This approach has been used with success in former studies.39
42 Experimental studies are mainly focused on the Cr
O vibrations and less on the Cr
OH hydroxyl vibrations. Nevertheless this information can enable us to confirm that the surface Croxide is present in different degrees of hydration, as a result of reversible interconvertion between them. The scarceness of experimental νCr
OH data is in agreement with the theoretical prediction that the hydrated form of the Cr2O3/SiO2 system becomes unstable already above 200 K; moreover, it would contain only one OH group as shown in model C (Figures 1 and 4). The vibrational frequency for this group is calculated to be 3255 cm
1. Concerning the asymmetric νCrdO (as) vibrations, they are found at 1030, 1016
1020, and 1014 cm
1, for the models C, F, and I, respectively. The symmetric νCrdO (s) are predicted at 983 and 983
986 cm
1, for the models C and F, respectively. Whereas the νCr
OSi vibrations are predicted for the models C, F, and I at 923, 898
939, and 905 cm
1 for the symmetric ones and 808, 780
810, and 19 cm
1 for the asymmetric ones, respectively. Comparing these values with those obtained from experimental Raman spectra, νs(Cr(dO)2 and νas(Cr(dO)2) are observed at ∼980 and ∼1010
1015 cm
1, respectively16), the calculated frequencies for model F are in very good agreement (983
986 cm
1 and 1016
1020 cm
1) with the experiment. This result confirms that the dehydrated Cr2O3/SiO2 system contains no or a negligible amount of Cr
OH groups as predicted from the atomistic thermodynamic model and that the model F used to represent the dehydrated system is a valuable molecular representation of the Cr/SiO2 system. 3.4. Effect of Adding Ti on the Characteristics of Cr-Oxide Grafted on Silica. The inclusion of small amounts of titanium on the Cr/SiO2 catalyst has been found to have a promotional effect both on polymerization activity and on the termination rate of the catalyst.11,43
45 How the chromium ions attach to

Figure 5. Phase diagram (surface energy vs temperature) showing the stability ranges for the different geometries.

By using the above-mentioned formalism, the free energy of the dehydration reaction (eq 1) for the formation of the mono-, di-, tri-, and tetragrafted vanadium complexes at equilibrium conditions are then expressed as ΔG1 ¼ Eðmodel AÞ
2ΔGðH2 OÞ
EððSi
OÞSlabÞ
EðO2 CrðOHÞ2 Þ

ð3Þ ΔG2 ¼ Eðmodel B or DÞ
ΔGðH2 OÞ
EððSi
OÞSlabÞ
EðO2 CrðOHÞ2 Þ

ð4Þ

ΔG3 ¼ Eðmodel G; E; or CÞ
EððSi
OÞSlabÞ
EðO2 CrðOHÞ2 Þ

ð5Þ

ΔG4 ¼ Eðmodel F or HÞ þ ΔGðH2 OÞ
EððSi
OÞSlabÞ
EðO2 CrðOHÞ2 Þ

ð6Þ

ΔG5 ¼ Eðmodel IÞ þ 2ΔGðH2 OÞ
EððSi
OÞSlabÞ
EðO2 CrðOHÞ2 Þ

ð7Þ

In this approach, we consider that the energies of the different types of grafting transitions are independent of the degree of hydration of the silica surface. It is known experimentally that silanols are stable at silica surfaces until 673 K. Above this temperature, silanols begin to condensate into siloxane bridges.37 Thus, our model with 5.8 OH/nm2 corresponding to conditions of a hydroxylated surface, remains valid until the temperature of 673 K. Figure 5 shows the surface free energy Γ, defined as the free energy per surface area, of the mono-, di-, tri-, and tetragrafted Cr(VI)-complexes on the silica surface as a function of temperature (T) for a water partial pressure (p) equivalent to the ambient air water partial pressure (pw = 1500 Pa).38 At these conditions, the monografted model C is the most stable until T = 195 K, followed by the digrafted model F in the large temperature range of 195
425 K, and finally, at T > 425 K, the tetragrafted complex is found as the most stable configuration. These results are fully consistent with the experimental procedure used in the synthesis of Cr(VI)-supported catalysts by grafting methods,15 where samples are heated and annealed at high temperatures to obtain OdCrdO and CrdO surface structures. Note that such species correspond to completely dehydrated conditions. In hydrated conditions (high water pressure or low temperature), the monografted model with one Cr
OH group is stabilized. 998

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Table 4. Calculated Vibrational Frequencies for Selected Vibrations in the Different Models Studied (Frequencies in cm
1; Scaling Factor, 0.943) model A

B

C

D

E

F

frequency

vibration

scaled

model G

3683

νCr
OH

3474

3637 3623

νCr
OH νCr
OH

3430 3417

frequency

vibration

scaled

3670

νCr
OH

3461

3605 2828

νCr
OH νCr
OH

3400 2667

3607

νCr
OH

3402

943

νCr
OSi(s)

889

3281

νCr
OH

3094

934

νCr
OSi (as)

881

949

νCr
OSi

949

3710

νCr
OH

3499

3683

νCr
OH

3473

H

3683

νCr
OH

3473

1077

νCrdO

1016

3666

νCr
OH

3457

910

νCr
OSi(s)

858

1019 952

νCrdO νCr
OSi

961 897

821

νCr
OSi (as)

774

3452

νCr
OH

3255

1076

νCrdO

1014

1092

νCrdO (as)

1030

960

νCr
OSi(s)

905

1042

νCrdO (s)

983

868

νCr
OSi (as)

819

I

978

νCr
OSi

923

3730

νCr
OH

3517

1080

νCrdO (as)

1019

3672

νCr
OH

3463

1045

νCrdO (s)

986

3589 3582

νCr
OH νCr
OH

3385 3379

958 827

νCr
OSi (s) νCr
OSi (as)

904 780

967

νCr
OSi (s)

912

868

νCr
OSi (s)

819

3686

νCr
OH

3476

3673

νCr
OH

3463

F-bis

F-tris

1077

νCrdO (as)

1016

1028

νCrdO (s)

969

1081

νCrdO

1020

996

νCr
OSi (s)

939

938

νCr
OSi(s)

885

859

νCr
OSi (as)

810

865 1082

νCr
OSi (as) νCrdO (as)

815 1020

1042

νCrdO (s)

983

952

νCr
OSi (s)

898

856

νCr
OSi (as)

808


, Table 5. Geometrical Parameters and Bader Charges for Cr(VI) Site Models on Ti-Modified Silica Support (Distances d in Å
1 Angles α in Degrees, Frequencies ν in cm , and Charges q in e) model F

dCrdO

dCr
OSi

1.60

1.76
1.76

F
Ti

1.60

F-2Ti

1.60

1.76

dCr
OTi

α(OdCrdO)

α(O
Cr
O)

109.84

103.70

1.75

109.34

105.36

1.76

109.14

109.2

1.76

the silica surface is not completely clear. By using XPS and optical spectroscopy, Pullukat et al. first have proposed a model representing a monomere chromium oxide site directly linked to the surface titania through two Cr
O
Ti bridges.46,47 McDaniel et al.48 have suggested a similar site model and have reported that the observed promotional effect of titanium probably derives from the creation of Ti
O
Cr links, which change the electronic environment of the chromium active center. Moreover, surface chromate species bridging an isolated surface titanium site and an adjacent surface silica site have also been suggested experimentally.49

νCrdO

νCr
O

q(Cr)

1020 (as)

898 (s)

983 (s)

808 (as)

+2.39

1076 (as) 1038 (s)

929 (s) 758 (as)

+2.41

1070 (as)

872(s)

+2.39

1032(s)

668 (as)

On the basis of these experimental suggestions, three dioxo bridging chromium species 0, 1, and 2 surface titanium sites are modeled to understand the effect of the Ti-modifications environment on the chromium structure and its characteristics. In Table 5 are reported representative geometric parameters as well as atomic Bader charges of the studied structures. The calculated bond distances dCrdO of 1.60 Å as well as the bond angles α(OdCrdO) of 109° remain unchanged depending on the nature of the support. On the basis of equivalent models, Espelid et al.50 and Scott et al.8 have reported similar bond distances dCr
OSi of 1.77 Å and 1.75 Å, respectively. As shown in Table 5, 999

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The Journal of Physical Chemistry C Bader charges on Cr(VI) are 2.39e for both chromium bridging species Cr
O
Si (F) and Cr
O
Ti (F-2Ti) and 2.41e for chromium having a single Cr
O
Ti link (F-1Ti). It is noticeable that the increase in Bader charge with the increase in the Ti content of the models is not monotonous. It is likely that the asymmetric structure (F-1Ti) leads to a much higher charge on the chromium site, which indicates an increase of the electron deficiency on this site configuration. This characteristic may facilitate the reduction of chromate species, thereby resulting in a shorter induction period in the polymerization process. For the sake of completeness, the νCrdO and νCr
O vibrational frequencies were calculated, showing a blue shift when the Cr
O bond is connected to a Ti atom. To our knowledge, the model presented here is the first one representing a realistically and usable ab initio level Cr-oxide silica surface. The next logical step is to use this model catalyst to study its reactivity and analyze/describe the reaction path for the polyethylene formation.

4. CONCLUSIONS Cr/SiO2 catalysts have been calculated using periodic DFT on realistic model systems including Cr(VI) species at different degrees of hydration. The use of an amorphous silica surface slab enabled reproduction of the experimental results and confirmed the monomeric grafted Cr(VI) structure on silica support. From the atomistic thermodynamic approach, one concludes that the most stable species at low temperature is the monografted C model. This configuration corresponds to the fully hydrated Cr(VI) catalyst on the silica support. An increase in temperature or a decrease in hydration stabilizes the digrafted model F as observed experimentally. High temperatures favor the formation of the penta-coordinated CrdO model I. This result confirms that the dehydrated Cr(VI)/SiO2 system contains no or a negligible amount of Cr
OH groups as predicted from the atomistic thermodynamic model and that the model F used to represent the dehydrated system is a valuable molecular representation of the Cr/SiO2 system. Finally, Ti atoms were introduced into the structure, and their effect was discussed through Bader charge analysis and vibrational analysis. The main aim of this study has been reached since it was the construction of a realistic and calculable (using periodic DFT) structure representing Cr(VI) supported on silica. With this model, the investigation of its reactivity (transition states and reaction paths) will be possible for a series of important reactions, as mentioned in the introduction. This step forward will enable us to help shed some light on the question open for some decades now. ’ AUTHOR INFORMATION Corresponding Author

*Tel: +33(1)44276004. Fax: +33(1)44276033. E-mail: frederik. [email protected].

’ ACKNOWLEDGMENT This work was performed using HPC resources from GENCI[CCRT/CINES/IDRIS] (Grant 2011-[x2010082022]) and the CCRE of Universit
e Pierre et Marie Curie; COST action D36. Dr. B. Diawara from LCPS ENS Paris is kindly acknowledged for providing us with ModelView used in the visualization of the structures.

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’ REFERENCES (1) Hogan, J. P.; Banks, R. L. Belg. Patent 530617, 1955. (2) Hogan, J. P. J. Polym. Sci. 1970, 8, 2637. (3) Hogan, J. P.; Norwood, D. D.; Ayres, C. A. J. Appl. Polym. Sci. 1981, 36, 49. (4) Weckhuysen, B. M.; Wachs, I. E.; Schoonheydt, R. A. Chem. Rev. 1996, 96, 3327. (5) Groppo, E.; Lamberti, C.; Bordiga, S.; Spoto, G.; Zecchina, A. Chem. Rev. 2005, 105, 115. (6) Pradier, C. M.; Rodrigues, F.; Marcus, P.; Landaub, M. V.; Kaliya, M. L.; Gutmanb, A.; Herskowitz, H. Appl. Catal. B 2000, 27, 73. (7) Dines, T. J.; Inglis, S. Phys. Chem. Chem. Phys. 2003, 5, 1320. (8) Demmelmaier, C. A.; White, R. E.; van Bokhoven, J. A.; Scott, S. L. J. Catal. 2009, 262, 44. (9) Miller, R. M.; Tinti, S. D.; Case, D. A. Inorg. Chem. 1989, 28, 2738. (10) Islam, M. M.; Costa, D.; Calatayud, M.; Tielens, F. J. Phys. Chem. C 2009, 113, 10740. (11) McDaniel, M.; Welch, M. B.; Dreiling, M. J. J. Catal. 1983, 82, 118. (12) McDaniel, M. P. Adv. Catal. 1985, 33, 47. (13) Moisii, C.; Deguns, E. W.; Lita, A.; Callahan, S. D.; van de Burgt, L. J.; Magana, D.; Stiegman, A. E. Chem. Mater. 2006, 18, 3965. (14) Busca, G.; Lavalley, J. C. Spectrochim. Acta 1986, 42A, 443. (15) Lee, E. L.; Wachs, I. E. J. Phys. Chem. C 2008, 112, 6487. (16) Lee, E. L.; Wachs, I. E. J. Phys. Chem. C 2008, 112, 20418. (17) Kresse, G.; Hafner, J. Phys. Rev. B 1993, 47, 558. (18) Kresse, G.; Hafner, J. Phys. Rev. B 1994, 49, 14251. (19) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865. (20) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1997, 78, 1396. (21) Tielens, F.; Gervais, C.; Lambert, J.-F.; Mauri, F.; Costa, D. Chem. Mater. 2008, 20, 3336. (22) Calatayud, M.; Tielens, F.; De Proft, F. Chem. Phys. Lett. 2008, 456, 59. (23) de Bocarm
e, T. V.; Chau, T.-D.; Tielens, F.; Andr
es, J.; Gaspard, P.; Wang, L. R. C.; Kreuzer, H. J.; Kruse, N. J. Chem. Phys. 2006, 125, 054703. (24) Tielens, F.; Andr
es, J. J. Phys. Chem. C 2007, 111, 10342. (25) Bl€ochl, P. E.; Jepsen, O.; Andersen, O. K. Phys. Rev. B 1994, 49, 16223. (26) Kresse, G.; Joubert, J. Phys. Rev. B 1999, 59, 1758. (27) Wojtaszek, A.; Sobczak, I.; Ziolek, M.; Tielens, F. J. Phys. Chem. C 2009, 113, 13855. (28) Wojtaszek, A.; Sobczak, I.; Ziolek, M.; Tielens, F. J. Phys. Chem. C 2010, 114, 9002. (29) van Kimmenade, E. M. E.; Kuiper, A. E. T.; Tamminga, Y.; Th€une, P. C.; Niemantsverdriet, J. W. J. Catal. 2004, 223, 134. (30) Weckhuysen, B. M.; Wachs, I. E. J. Chem. Soc., Faraday Trans. 1996, 92, 1969. (31) Tielens, F.; De Proft, F.; Geerlings, P. J. Mol. Struct. 2001, 542, 227. (32) Jozwiak, W. K.; Ignaczak, W.; Dominiak, D.; Maniecki, T. P. Appl. Catal. A. 2004, 258, 33. (33) Digne, M.; Sautet, P.; Raybaud, P.; Euzen, P.; Toulhoat, H. J. Catal. 2002, 211, 1. (34) Kaxiras, E.; Bar-Yam, Y.; Joannopoulos, J. D.; Pandey, K. C. Phys. Rev. B 1987, 35, 9625. (35) Qian, G. X.; Martin, R. M.; Chadi, D. J. Phys. Rev. B 1988, 38, 7649. (36) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A., Jr.; Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Salvador, P.; Dannenberg, J. J.; Malick, D. K.; Rabuck, A. D.; Raghavachari, 1000

dx.doi.org/10.1021/jp209680r |J. Phys. Chem. C 2012, 116, 994–1001

The Journal of Physical Chemistry C

ARTICLE

K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Baboul, A. G.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Andres, J. L.; Gonzalez, C.; Head-Gordon, M.; Replogle, E. S.; Pople, J. A. Gaussian 98, revision A.6; Gaussian, Inc.: Pittsburgh, PA, 1998. (37) Bolis, V.; Fubini, B.; Marchese, L.; G., M.; Costa, D. J. Chem. Soc., Faraday Trans. 1991, 87, 497. (38) Guyot, A.; Curtis, G. E.; Libbey, W.Smithsonian Meteorological Tables: Based on Guyot’s Meteorological and Physical Tables; Smithsonian Institution: Washington D.C., 1896. (39) Tielens, F.; Calatayud, M.; Dzwigaj, S.; Che, M. Micropor. Mesopor. Mater. 2009, 119, 137. (40) Tielens, F.; Shishido, T.; Dzwigaj, S. J. Phys. Chem. C 2010, 114, 9923. (41) Tielens, F.; Shishido, T.; Dzwigaj, S. J. Phys. Chem. C 2010, 114, 3140. (42) Tielens, F.; Islam, M. M.; Dzwigaj, D. Micropor. Mesopor. Mater. 2011submitted for publication. (43) Pullukat, T. J.; Hoff, R. E.; Shida, M. J. Polym. Chem. Ed. 1980, 18, 2857. (44) Conway, S. J.; Falconer, J. W.; Rochester, C. H.; Dows, G. W. J. Chem. Soc., Faraday Trans. 1989, 85, 71. (45) Conway, S. J.; Falconer, J. W.; Rochester, C. H.; Dows, G. W. J. Chem. Soc., Faraday Trans. 1989, 85, 1841. (46) Pullukat, T. J.; Shida, M. U.S. Patent 3,780,011, 1973. (47) Hoff, R. E.; Pullukat, T. J.; Shida, M. J. Appl. Polym. Sci. 1981, 26, 2927. (48) McDaniel, M. P. In Handbook of Heterogeneous Catalysis; Ertl, G., Knozinger, H., Sch€uth, F., Weitkamp, J., Eds.; Wiley-VCH, Weinheim, Germany, 2008; p 3733. (49) Jehng, J. M.; Wachs, I. E.; Weckhuysen, B. M.; Schoonheydt, R. A. J. Chem. Soc., Faraday Trans. 1995, 91, 953. (50) Espelid, O.; Borve, K. J. J. Catal. 2000, 195, 125.

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dx.doi.org/10.1021/jp209680r |J. Phys. Chem. C 2012, 116, 994–1001