A Periodic Structure Density Functional Theory Study of Propylene

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J. Phys. Chem. B 2002, 106, 3248-3254

A Periodic Structure Density Functional Theory Study of Propylene Chemisorption in Acidic Chabazite: Effect of Zeolite Structure Relaxation X. Rozanska,*,† Th. Demuth,§ F. Hutschka,# J. Hafner,§ and R. A. van Santen† Schuit Institute of Catalysis, Laboratory of Inorganic Chemistry and Catalysis, EindhoVen UniVersity of Technology, P.O. Box 513, NL-5600 MB EindhoVen, The Netherlands, Institut fu¨ r Materialphysik, UniVersita¨ t Wien, Sensengasse 8, A-1090 Wien, Austria, and TotalFinaElf, De´ partement Chimie des Proce´ de´ s, Centre Europe´ en de Recherche et Technique, B.P. 27, F-76700 Harfleur, France ReceiVed: April 26, 2001; In Final Form: September 6, 2001

Density functional theory (DFT) periodic structure calculations have been employed to investigate the interaction of propylene within the acidic chabazite zeolite (Si/Al ) 11). In agreement with previous studies, it is found that secondary alkoxy formation is preferred over primary alkoxy formation. Steric constraints appear not to affect the course of the reaction. Analysis of the radial distribution of the zeolitic atoms with respect to the Brønsted site aluminum atom allows further insight into the reaction. Changes in the zeolite oxygen atom position are more significant than those of the zeolite silicon atoms. Relaxation of unit cell size and shape has a dramatic influence on energetic parameters of the reaction path.

1. Introduction Zeolites are important molecular sieves or heterogeneous catalysts.1 They have been first introduced on a large scale in the 1950s for petrochemical processes. They present the advantages, in comparison with previously used alumina-based catalysts, of having a better long-term stability, and yielding a higher product selectivity. The higher selectivity of this class of catalysts originates from the well-defined micropore structures of the zeolite crystals, which lead to size- and shape-dependent adsorption, reaction, or diffusion of the reactants or products.1 Zeolites become acidic catalysts when a Si atom tetrahedrally coordinated by oxygen atoms is substituted by Al. The excess charge on the framework has to be neutralized by a cation.2 The zeolite crystal shows acidic catalyst features when the cation is a proton. The proton binds to an oxygen atom forming a bond between an Al atom and a Si atom. Many studies have focused on the analysis of acidic zeolite catalysts.2-10 Besides being ionic crystals, zeolites are characterized by a small dielectric constant3 ( around 5) and by a substantial charge screening.4 As a consequence, whereas acidic zeolites induce products similar as those known from superacid-catalyzed reactions, they show an intrinsic reactivity that can be better compared to gas-phase reactions.5 Zeolite micropores have been shown to have a stabilizing effect on the carbocationic transition states with respect to gas-phase results, which can be on the order of 10%30% of the activation energies.6,7 This stabilization has been demonstrated to be of a short-range electrostatic nature7a and to involve polarization of zeolite oxygen atoms.7b-c It is well-known from previous studies that the zeolitic Brønsted acid site can be described as a local defect in the zeolite crystal.8 Therefore, small molecular fragments that model a zeolitic Brønsted acid site can mimic zeolitic reactivity.2 However, we have shown in a previous study,9 in agreement * To whom correspondence should be addressed. Fax: +31 40 245 5054. E-mail: [email protected]. † Eindhoven University of Technology. § Universita ¨ t Wien. # Centre Europe ´ en de Recherche et Technique.

Figure 1. Reaction mechanisms involved in the chemisorption of propylene catalyzed by an acidic zeolite.

with Ramachandran et al.,7b that a more complex relationship exists between reactant and zeolite catalyst. Especially, electron delocalization from Brønsted site atoms to other zeolite framework atoms has been shown to be important in reaction.2,7b-9 This implies that not only the Brønsted acid site but also a significant zeolite area surrounding the transition state participates in the catalytic event. Then, the overall description of the zeolite elasticity becomes important.2,8 Hammond et al.10 proposed a method to investigate zeolite framework elasticity. They have shown that the flexibility of zeolites is very different from one structure to another. They have shown as well that within a zeolite some frame parts are more flexible than others. On the basis of this, they predicted that specific parts of a zeolitic catalyst could be better suited for the location of the catalytic site because a much larger elasticity of the zeolite could allow a more important lowering of the activation energy barrier. In this study, we will focus on the question of how the zeolite structure changes during a reaction and will quantify the energetic consequence of the zeolite elasticity on a reaction. We will study the chemisorption of propylene in an acidic zeolite (see Figure 1). This reaction has been the subject of several experimental11,12 and theoretical13,14 studies and is a wellunderstood prototype example of a reaction with the acidic site

10.1021/jp011587m CCC: $22.00 © 2002 American Chemical Society Published on Web 03/06/2002

A Periodic Structure DFT Study

Figure 2. Structure of the chabazite zeolite (CHA). Four unit cells are shown, among which one has been displayed using a ball-andstick representation.

in a zeolite. The reaction, which starts from propylene physisorbed to the acidic proton, leads to the formation of a more stable chemisorbed propylene, or alkoxy, species. Such a reaction has been shown to occur experimentally at room temperature within an acidic zeolite.12 In principle, this reaction can produce two different alkoxy species (a primary and a secondary alkoxy species), but experiments show that only the secondary alkoxy species is formed.11-12,15 This is explained by the fact that the formation of a transient primary carbenium ion is energetically more demanding than the formation of a secondary carbenium ion.15 Alkoxy species are important intermediates in, for instance, the alkylation reaction of aromatics with olefins catalyzed by acidic zeolites.11 We will computationally analyze both reaction pathways. The Vienna Ab Initio Simulation Package (VASP) will be employed for this purpose.16 We will use chabazite (see Figure 2).17 Large supercages that are connected to each other through six windows formed by eight-member rings characterize this zeolite. It has been used in several other theoretical studies (using quantum mechanicalmolecular mechanic code (QM/MM)14,18 or density functional theory (DFT) periodic structure codes19). The unit cell of this zeolite is composed of 12 Si atoms (in the case of a fully dealuminated zeolite) and 24 oxygen atoms. It is a relatively small unit cell compared to other zeolites, which facilitates the calculations. 2. Method As already mentioned, VASP has been used to perform all calculations.16 The total energy is obtained by solving the Kohn-Sham equations of the local density approximation (LDA) with the Perdew-Zunger exchange-correlation functional.20 The results are corrected for nonlocality within the generalized gradient approximation (GGA) with the PerdewWang 91 functional.21 However, LDA optimizations without GGA correction have also been performed to assess the influence of the gradient corrections. VASP uses the planewaves basis set and pseudopotentials.22 A cutoff energy of 400 eV has been used. Brillouin zone sampling is restricted to the Γ-point. A quasi-Newton forces-minimization algorithm has been employed for all calculations. Convergence was assumed to be achieved when forces were below 0.05 eV/Å.

J. Phys. Chem. B, Vol. 106, No. 12, 2002 3249 For the systems that are labeled “f”, the size and shape of the unit cell have been fully relaxed. Calculations with a fixed volume and shape of the unit cell have been done for comparison to evaluate the importance of this relaxation. For these systems, we used the shape and volume of the unit cell optimized for chabazite with a single Brønsted acidic site. These systems have been labeled “c”. Within all unit cells, all atoms have been allowed to fully relax. No symmetry constraints have been used. Others constrained systems have been used in this study. They will be described later. The relaxation phenomena during the reaction have been analyzed using atomic radial distribution constructed with periodic boundary conditions.23 The transition state (TS) search method in VASP is the nudged elastic band (NEB) method.24 Several images of the system are defined along the investigated reaction pathway. These images are optimized by allowing a relaxation in the subspace perpendicular to the reaction coordinate. When all forces in the intermediate states fall below 0.08 eV/Å, the transition state is optimized separately. 3. Results 3.1. Chabazite Unit Cell. The fully dealuminated unit cell of chabazite has been optimized within the GGA (UC_si_gga) and LDA (UC_si_lda). The geometries of these unit cells are reported in Tables 1 and 2. With the GGA, the size and shape of the unit cell (UC_si_gga) are in good agreement with those that have been measured from X-ray spectroscopy.25 However, as already mentioned by Jeanvoine et al.19 or Bra¨ndle et al.,28 GGA calculations induce an overestimation of the bond lengths, which results in slightly bigger unit cells than experimental ones. On the other hand, LDA calculations give a significant underestimate of the unit cell (UC_si_lda) volume with respect to experimental data. The differences in volume are +5.7 Å3 and -28.4 Å3, respectively. A silicon atom is substituted with an aluminum atom and a proton is introduced, connected to an oxygen atom. The resulting Si/Al ratio is 11 for the unit cell (see Figure 3). For the GGA calculation, further optimization of the system leads to a unit cell (UC_f_gga) around 8 Å3 bigger than UC_si_gga. Experimental data report also an increase of the volume when a Brønsted acidic site is introduced. This effect on the volume with an increase of the Al/Si ratio has first been demonstrated by Kramer et al.2d,8a Ugliengo et al.26 also noticed such an effect in a periodic semiclassical//DFT study of chabazite zeolite. They found a linear variation of the volume with respect to Al/Si with a divergence at high Al concentration. However, they could not confirm this conjecture by comparison with experimental data because no systematic study of this property is available. In the LDA, the introduction of the aluminum atom does not lead to any significant change in the volume of the unit cell (UC_f_lda), in contradiction with what is experimentally observed (see Table 2). Only one location of aluminum and proton has been considered in our study. We selected the Brønsted acidic site in a configuration that has been shown to be the most stable (see Figure 3).19,28 Moreover, the proton displays a relative high mobility around the aluminum atom and can jump from one oxygen atom to another.6,29 We will not extend deeper the discussion on the chabazite unit cell calculations because Jeanvoine et al.19 performed a full study of this zeolite using the same method. Similar results were obtained in both their and our study.

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TABLE 1: The Most Important Parameters of the Geometries of the Brønsted Sites (UC) and of Adsorbed to the Brønsted Sites Propylene (Ads) within the Acidic Chabazite Zeolite Unit Cells as Obtained from the Periodic Structure Calculationsa UC_f_lda

Ads_f_gga

AlO1 AlO2 AlO3 AlO4 O1Ha O1Si1 O2Si2 O3Si3 O4Si4 HaC1 HaC2

UC_f_gga 1.91 1.69 1.67 1.70 0.98 1.70 1.58 1.57 1.59

1.87 1.68 1.65 1.68 0.98 1.68 1.57 1.55 1.57

1.90 1.69 1.67 1.71 1.01 1.69 1.57 1.57 1.58 2.03 2.41

Ads_c_gga 1.89 1.69 1.67 1.71 1.01 1.69 1.57 1.56 1.58 2.01 2.41

Ads_fc_gga 1.89 1.69 1.68 1.71 1.01 1.69 1.57 1.57 1.59 2.00 2.42

Ads_f_lda 1.86 1.68 1.67 1.70 1.03 1.67 1.56 1.55 1.57 1.88 2.26

AlO1Si1 AlO2Si2 AlO3Si3 AlO4Si4 AlO1Ha AlO1Si1Ha

129.2 141.6 161.1 153.4 112.7 -177.8

126.5 134.4 167.2 157.1 112.6 169.8

127.3 142.3 162.1 152.5 115.1 157.7

127.5 141.7 162.8 153.6 114.4 -169.5

128.3 142.0 161.9 153.4 114.5 -157.1

123.4 135.5 168.6 157.8 118.1 -161.2

a Distances are in Å and angles in deg; gga stands for generalized gradient approximation; lda stands for local density approximation; f means that, for this calculation, the shape and size of the periodical unit cell has been fully optimized; c means that the shape and size of the unit cell are the same as those of UC; fc means that the shape and size of the unit cell are the same as those of UC and that all atoms except H, C, Al, and the four O atoms connected to Al have the same positions as in UC.

TABLE 2: Geometries of the Chabazite Unit Cells for the Different Systems Considered in the Studya a

b

c

R

β

γ

volume

UC_si_gga UC_si_lda ref 25b ref 26

9.26 9.15 9.23 9.37

9.25 9.10 9.23 9.37

9.22 9.10 9.23 9.37

93.6 94.3 94.3 94.8

93.9 94.4 94.3 94.8

93.7 94.1 94.3 94.8

785.0 750.9 779.3 814.5

UC_f_gga UC_f_lda ref 27c ref 26 ref 28

9.25 9.11 9.28 9.44 9.45

9.28 9.08 9.28 9.44 9.34

9.31 9.14 9.28 9.39 9.40

94.3 94.8 94.3 94.2 93.8

93.9 94.5 94.3 95.1 95.4

93.5 93.8 94.3 95.6 94.6

793.4 749.0 792.3 827.5 820.6

Ads_f_gga Ts_i_f_gga Ts_n_f_gga i-Alk_f_gga n-Alk_f_gga Ads_f_lda Ts_i_f_lda i-Alk_f_lda

9.24 9.27 9.31 9.24 9.25 9.09 9.16 9.13

9.28 9.24 9.18 9.21 9.21 9.11 9.10 9.02

9.31 9.30 9.29 9.31 9.29 9.14 9.14 9.09

94.1 94.3 95.0 94.2 94.3 93.8 95.2 94.2

93.9 94.1 94.7 94.1 94.2 93.3 94.7 94.6

93.6 94.0 94.2 94.0 94.0 93.2 94.7 94.3

793.2 790.1 785.9 785.9 783.8 752.7 752.7 741.4

label or source

a The vector lengths are in Å, the angles in deg and the volume in Å3. b Experimental data. c Experimental data for a Si/Al ratio of 16. The other systems have a Si/Al ratio of 23.

3.2. Physisorbed Propylene. In the case of the systems for which propylene is physisorbed to the acidic proton, the volume of the unit cell does not change much for LDA (Ads_f_lda) as well as for GGA (Ads_f_gga) (see Tables 1 and 2). As also observed in comparative studies of LDA versus GGA geometries, all bond lengths are shorter for LDA than for GGA geometries (see Table 1).30 The adsorption energy of propylene in the acidic chabazite unit cell (Ads_f_gga) is -21 kJ/mol for the GGA. This adsorption energy is low and does not match with the expected experimental adsorption energy, which should be on the order of -60 kJ/mol.14 However, this is predictable because DFT methods are not able to describe the van der Waals dispersion contribution.2n,9,31,32 The adsorption of propylene within the nonrelaxed acidic chabazite unit cell has also been studied (see Ads_c_gga in Table 1). Slight geometrical differences can be perceived when a comparison with Ads_f_gga calculations is made (see Table 1). The adsorption energy of propylene in the acidic chabazite for Ads_c_gga is -20 kJ/mol. On the other hand, the computed

Figure 3. Location of the Brønsted acidic site within the chabazite framework and labels used to designate zeolitic and propylene atoms.

adsorption energy obtained in the LDA is a crude overestimation (Ads_f_lda). The adsorption energy is -96 kJ/mol in this case. Because this result is quite unrealistic, we did not consider further LDA calculations for a fixed size and shape of the unit cell. 3.3. Chemisorption Transition States. All geometrical data of the transition states considered for the chemisorption reaction computed in this study are gathered in Table 3. For all transition states, one observes that the distances between the acidic proton and the carbon atom to which the proton will be attached are close to the distances that will be eventually obtained when the C-H bond will be formed (HaC1 or HaC2 between 1.2 and 1.3 Å). The O1Ha bonds have already been dissociated. They changed from around 1.0 Å to around 1.5-1.7 Å. Besides this, the carbocationic nature of the hydrocarbon molecule is still very strong. The distances between the carbon atom (C2 or C1) and the oxygen atom O2 that will be involved in the alkoxy bond are relatively large; they range from 2.45 to 2.61 Å for

A Periodic Structure DFT Study

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TABLE 3: The Most Important Parameters of the Geometries of the Transition States that Lead to the Chemisorption of Propylene within the Acidic Chabazite Zeolite Unit Cells as Obtained from the Periodic Structure Calculationsa Ts_i_f_gga Ts_i_c_gga Ts_i_fc_gga Ts_n_f_gga Ts_i_f_lda AlO1 AlO2 AlO3 AlO4 O1Ha HaCxb O2Cyb O1Si1 O2Si2 O3Si3 O4Si4 AlO1Si1 AlO2Si2 AlO3Si3 AlO4Si4 AlO1Ha O1HaCxb AlO2Cyb

1.75 1.73 1.72 1.72 1.70 1.17 2.62 1.60 1.58 1.57 1.58 146.0 136.8 139.1 144.2 103.9 173.5 114.4

1.76 1.73 1.72 1.72 1.70 1.17 2.61 1.60 1.59 1.58 1.58 145.7 136.8 139.8 145.3 103.7 173.5 114.1

1.77 1.76 1.74 1.71 1.83 1.16 2.61 1.60 1.59 1.62 1.59 150.4 138.4 132.7 149.6 103.9 169.4 114.5

1.78 1.72 1.71 1.72 1.52 1.26 2.45 1.62 1.59 1.57 1.59 134.0 138.5 146.6 143.9 106.5 176.6 113.5

1.74 1.71 1.69 1.69 1.49 1.22 2.41 1.59 1.57 1.56 1.57 142.1 134.2 143.2 145.2 105.2 173.0 116.1

a Distances are in Å and angles in deg; gga stands for generalized gradient approximation; lda stands for local density approximation; f means that, for this calculation, the shape and size of the periodical unit cell has been reoptimized; c means that the shape and size of the unit cell are the same as those of UC; fc means that the shape and size of the unit cell are the same as those of UC and that all atoms except H, C, Al, and the four O atoms connected to Al have the same positions as in UC; i refers to i-propoxy (or secondary alkoxy species) and n to n-propoxy (or primary alkoxy species). b The value of x and y is 1 and 2, respectively, for the i-isomer and 2 and 1, respectively, for the n-isomer of propyl alkoxy species.

the GGA calculations. The energies of the transition states that lead to the formation of the isopropoxy species are +56 and +60 kJ/mol with respect to the physisorbed state for the fully optimized unit cell Ts_i_f_gga, and for the fixed shape and size unit cell Ts_i_c_gga, respectively. In the case of the LDA calculation (Ts_i_f_lda), the activation energy of the isoproproxy formation is +54 kJ/mol with respect to Ads_f_lda. This is another illustration of the fact that, although adsorption energies are strongly influenced by the choice of the functional, the energy differences between different adsorbed configurations (including transition states) are almost the same in the LDA and the GGA. The transition state that gives as a product the

n-alkoxy species has been computed only using the GGA and for a fully optimized unit cell (see Ts_n_f_gga in Table 3). The activation energy of this reaction is high, more than a factor of 2 higher than the activation energy for Ts_i_f_gga, with Eact ) 128 kJ/mol. This high activation energy value for primary alkoxy species formation supports the theoretical study of Rigby et al.15 Comparison of the geometries of Ts_i_f_gga and Ts_n_f_gga agrees with the observation of Sinclair et al.;14 they found that the distance between the carbon atom and the oxygen atom involved in the alkoxy bond is shorter for the primary alkoxy because the primary carbocationic transition state is a less stable carbocation than the one involved in the formation of a secondary alkoxy species. With respect to the volume of Ads_f_gga, one notes a small decrease of the volume of Ts_i_f_gga and Ts_n_f_gga (∆V is -3.1 and -7.3 Å3, respectively) (see Table 2). The volume of the unit cell does not change for the LDA transition-state system with respect to Ads_f_lda volume. 3.4. Chemisorbed Propylene. When the alkoxy species is formed, the volume of the unit cell decreases slightly (see Table 2). For the isopropoxy or secondary alkoxy species, labeled as i-Alk_(f or c)_(gga or lda), the volume of the unit cell decreases by -7.3 Å3 with respect to Ads_f_gga and -11.3 Å3 with respect to Ads_f_lda for i-Alk_f_gga and i-Alk_f_lda, respectively. Also, in the formation of the n-propoxy species (nAlk_f_gga), the volume of the unit cell decreases; the difference in volume between Ads_f_gga and n-Alk_f_gga is 9.4 Å3. The geometries of the alkoxy species are reported in Table 4. The energy level of i-Alk_f_gga is -27 kJ/mol with respect to Ads_f_gga. For the system with a fixed geometry of the unit cell (i-Alk_c_gga), the change in energy of the chemisorbed propylene with respect to the physisorbed propylene is similar. The energy difference is -23 kJ/mol. Indeed, it appears that the further relaxation and optimization of the size and shape of the unit cells for the physisorbed, transition state, and chemisorbed systems has a similar effect on the different states. For Ads_gga, Ts_i_gga and i-Alk_gga systems, the energy differences between the fully relaxed and constrained systems are 1, 5, and 5 kJ/mol, respectively. Therefore, the trends shown in the reaction energy diagrams of the reaction with fixed or nonfixed unit cell parameters are similar (see parts a and b in Figure 4). In the case of the LDA calculations, the energy level of the zeolitic isopropoxy system (i-Alk_f_lda) with respect to

TABLE 4: The Most Important Parameters of the Geometries of the Chemisorbed Propylene or Alkoxy Species within the Acidic Chabazite Zeolite Unit Cells as Obtained from the Periodic Structure Calculationsa AlO1 AlO2 AlO3 AlO4 O2Cyb O1Si1 O2Si2 O3Si3 O4Si4 AlO1Si1 AlO2Si2 AlO3Si3 AlO4Si4 AlO2Si2Cyb

i-Alk_f_gga

i-Alk_c_gga

i-Alk_fc_gga

n-Alk_f_gga

i-Alk_f_lda

1.69 1.87 1.69 1.70 1.55 1.57 1.69 1.58 1.59 133.0 125.6 159.7 143.7 178.5

1.72 1.89 1.72 1.71 1.56 1.57 1.69 1.59 1.59 131.1 125.9 159.5 150.1 175.8

1.70 1.90 1.69 1.72 1.59 1.57 1.67 1.59 1.63 128.9 129.8 152.0 151.5 176.4

1.71 1.87 1.69 1.70 1.51 1.58 1.69 1.57 1.59 133.7 125.7 157.8 141.8 -178.9

1.69 1.84 1.67 1.69 1.50 1.57 1.67 1.55 1.57 130.7 122.0 162.0 139.4 175.2

a Distances are in Å and angles in deg; gga stands for generalized gradient approximation; lda stands for local density approximation; f means that for this calculation, the shape and size of the periodical unit cell has been reoptimized; c means that the shape and size of the unit cell are the same as those of UC; fc means that the shape and size of the unit cell are the same as those of UC and that all atoms except H, C, Al, and the four O atoms connected to Al have the same positions as in UC; i refers to i-propoxy (or secondary alkoxy species) and n to n-propoxy (or primary alkoxy species). b The value of x and y is 1 and 2, respectively, for the i-isomer and 2 and 1, respectively, for the n-isomer of propyl alkoxy species.

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Figure 4. Reaction energy diagrams of the chemisorption reaction of propylene catalyzed by an acidic chabazite (Si/Al ) 11) as obtained from the periodic calculations: (a) secondary alkoxy formation in GGA for unit cells fully optimized; (b) secondary alkoxy formation in GGA for unit cells constrained to the volume and shape of the UC_f_gga unit cell (see Tables 1 and 2); (c) primary alkoxy formation in GGA for a fully optimized unit cells; (d) secondary alkoxy formation in LDA for a fully optimized unit cells.

the LDA calculation physisorbed propylene (Ads_f_lda) is -40 kJ/mol (see part d in Figure 4). 4. Discussion 4.1. Primary Versus Secondary Alkoxy Species Formation. As also observed in the study of Rigby et al.,15 the energetic difference between the primary (n-Alk_f_gga) and secondary alkoxy species (i-Alk_f_gga) is too small to explain the observed absence of primary alkoxy species. Differences in the activation energy have to be considered to explain this (see parts a and c in Figure 4). In the case of small cluster calculations, the activation energy for the formation of isopropoxy species from propylene is reported to be around 90 kJ/mol.14,15 In our periodic study, we observed that the transition states are stabilized. This is in agreement with the findings of Zygmunt et al.,7a who used zeolitic clusters composed of up to 193 atoms. The stabilizing effect of the chabazite structure (Si/Al ) 11) on this transition state can be estimated to be on the order of 30 kJ/mol with an activation energy of Eact ) 56 kJ/mol. Such an activation energy barrier agrees with the experimental observations that report that the proton-induced reaction of propylene in acidic zeolite occurs readily at room temperature and low propylene loading.12 According to the experimental observations, one expects an apparent activation energy close to zero, which induces an activation energy on the order of 60 kJ/mol (i.e., on the order of the adsorption energy of propylene) and an exothermic reaction because no physisorbed propylene is observed. Since the pioneering studies of Haag et al.,33 it is well-known that the apparent activation energy in a zeolite is directly related to the activation energy and the adsorption energy.9,32a In this study, the propylene alkoxy species are situated at similar energies to that obtained for fully optimized zeolitic cluster DFT calculations.7,14 4.2. Relaxation of Zeolite Atoms. When one analyzes the changes in the radial distribution of the silicon atoms or oxygen atoms with respect to the aluminum atom during the reaction in the GGA calculations, one notes that the chabazite structure is affected not only locally during the reaction (see Figure 5 and Tables 1, 3, and 4). No large modifications of the radial distribution of Si with respect to Al are noted among the physisorbed, transition, and chemisorbed states. This remains

valid for the fully relaxed and constrained systems. On the other hand, the situation is completely different when the radial distribution of the zeolitic oxygen atoms with respect to the aluminum atom is analyzed. As observed in other theoretical studies,2 the first oxygen shell around the Al atom is strongly affected during the reaction because in the TS the oxygen atom to which the proton is bonded is not equivalent to the others (see Tables 1, 3, and 4). For this first shell of atoms, the fully relaxed and constrained unit cells calculations lead to similar results. This picture is different for the second shell of zeolitic oxygen atoms with respect to the Al atom. There, as a general trend, one observes that the Al-O distances are slightly longer in the case of a constrained size and shape of the unit cell compared to those in the fully optimized calculations. The sum of all these slight differences leads to energy differences of around 5 kJ/mol between the fully optimized and constrained calculations. Moreover, it can be seen in Figure 5 that the second oxygen shell with respect to Al is very different in the physisorbed and chemisorbed states. The shortest distance between the Al atom and a second shell oxygen atom is 3.5 Å in Ads, whereas it becomes 3.3 Å in i-Alk. Similarly, the oxygen atoms of the second shell retract themselves toward the aluminum atom in the transition and chemisorbed states with respect to the physisorbed state; the maximum Al-O distance is around 4.3 Å for Ads and Ts_i and 4.5 Å for Ads. It is well-known from dynamic simulations or Monte Carlo diffusivity studies that full relaxation of the zeolite lattice, especially atomic relaxation, can have a significant influence on adsorption and diffusion of hydrocarbon species.34,35 This becomes of great importance when the guest molecule has a size similar to the zeolite host micropore. We will now consider in detail the effect of zeolite atom relaxation in reaction. The calculations are achieved at the GGA level. The extreme situation is when all zeolite atoms, except Al and the four oxygen atoms around it, are fixed. The fixed zeolite atoms have the same positions as in UC_f_gga. In all of the cases, H and C atom positions have been fully optimized. The volume and shape of the unit cell are not optimized. The geometry of the system is very similar as in the case of the physisorbed propylene system (see Ads_fc_gga in Table 1). The adsorption energy of propylene is almost not affected (Eads ) -17 kJ/

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J. Phys. Chem. B, Vol. 106, No. 12, 2002 3253

Figure 5. Radial distributions of zeolitic oxygen atoms (left) and zeolitic silicon atoms (right) for the physisorbed propylene (top), chemisorption transition state (middle), and secondary chemisorbed propylene or isopropyl alkoxy species (bottom) as obtained from the GGA periodic calculations.

TABLE 5: Effect of the Absence of the Zeolite Framework Relaxation in the Propylene Chemisorption in Chabazite as Observed from the Periodic DFT Calculations (in kJ/mol) Eads Eact ∆Eσ-π

1a

2b

3c

4d

5e

-21 +56 -27

-20 +60 -23

-19 +62 -14

-17 +70 +10

-16 +91 +23

a The unit cell and all atomic positions are fully optimized (see part a in Figure 4). b All atomic positions are optimized in the constant volume and size chabazite unit cell (see part b in Figure 4). c Si atoms except the first four ones around the Al atom are fixed in the constant volume and size chabazite unit cell. d The positions of H, C, Al, and four O and four Si around the Al atom are optimized in the constant volume and size chabazite unit cell. e The positions of H, C, Al, and four O around the Al atom are optimized in the constant volume and size chabazite unit cell.

mol) (see 5 in Table 5). This changes completely in the case of the transition state that leads to the formation of isopropyl alkoxy species (TS_i_fc_gga). The constraints on the zeolite atoms result in a large increase of the activation energy, which jumps from Eact ) 57 kJ/mol to Eact ) 91 kJ/mol. This large augmentation in the activation energy does not seem to be related to severe modifications of the transition state geometry, as can be seen in Table 3. The large increase in activation energy has also repercussions on the isopropyl alkoxy species energy level. The reaction becomes endothermic with an energy difference between the

π-system and the alkoxy species of ∆Eσ-π ) +23 kJ/mol, whereas it is ∆Eσ-π ) -27 kJ/mol for the fully relaxed system (see Table 5). Once more, the comparison of the geometries between the constrained situation (i-Alk_fc_gga) and the nonconstrained situation (i-Alk_f_gga) must be carefully monitored to find the source of such a large increase in energy (see Table 4). It is only by taking into consideration all of the slight differences in bond lengths and angles that the large energy difference can be explained. By decreasing the constraints on the zeolite atomic positions, the energies of the transition state and alkoxy species systems slightly move toward the energies of the fully relaxed system (see Table 5). When the four silicon atoms connected to the oxygen atoms around Al are also allowed to relax, the reaction remains endothermic (∆Eσ-π ) +10 kJ/mol), whereas the activation energy decreases by 21 kJ/mol (see 4 in Table 5). Interestingly, when all oxygen atoms are allowed to move their positions, whereas only the four Si(x)1,2,3,4) are free, the activation energy is very close to that of the free system (see 3 in Table 5). The difference in activation energy is only 2 kJ/mol. The activation energy is reasonably predicted with this level of constraint on the model. However, the reaction energy, besides being exothermic, is still relatively high compared with the fully optimized systems (∆∆Eσ-π ) +9 kJ/mol). The radial distributions presented in Figure 5 illustrate clearly how important the relaxation of the zeolite framework during the course of a reaction is. All zeolite atoms get involved in

3254 J. Phys. Chem. B, Vol. 106, No. 12, 2002 the relaxation. They only change slightly their individual atomic positions, but the overall changes lead to dramatic energy differences. A good estimation of the activation energy can be obtained when zeolite atoms neighboring the active site and all zeolite oxygen atoms in the immediate surrounding of the TS are allowed to relax. However, the alkoxy species energy level is still overestimated with this model, and only the full zeolite atoms relaxation allows a correct estimation of its energetics. 5. Conclusions A periodic DFT study of the chemisorption of propylene within acidic chabazite has been performed. It is found, in agreement with small zeolite cluster studies,14,15 that secondary alkoxy formation is preferred over primary alkoxy formation because of a large difference in activation energies. It is found that steric constraints do not play a crucial role in the reaction. Moreover, a decrease of the activation energy of around 30 kJ/ mol is obtained with respect to data reported in the cluster studies. With respect to the GGA, the LDA leads to similar relative reaction energies but overestimates the adsorption energy of propylene within the acidic chabazite. On the other hand, the GGA calculations underestimate the adsorption energy because of the absence of the van der Waals contribution. The analysis of the radial distribution of the zeolitic atoms with respect to the Brønsted site aluminum atom gives further insight into reactions catalyzed by zeolites. The radial distribution of the silicon atoms with respect to the aluminum shows very little changes for different reaction paths. This is different for the zeolitic oxygen atoms. They appear to be strongly affected in the first as well as in the second shells of atoms around the aluminum atom. In the transition and chemisorbed states, the second shell oxygen atoms with respect to the aluminum atom show a tendency to contract themselves toward the Brønsted site. This affects the volume of the unit cell. When the size and shape of the unit cell are fixed, the changes on the oxygen atoms distribution still exist but are slightly less important. Full relaxation of the unit cells has a limited influence on the energies. Reaction pathways investigations with a fixed volume and shape unit cell can therefore be considered as a good approximation. Finally, systems with fixed zeolite atomic positions have shown in the last part of the study to give large overestimations of the energies. Only physisorbed propylene is not affected. To obtain a good estimate of activation energy, it appears important to optimize the positions of a large number of zeolitic oxygen atoms in the immediate surrounding of the transition state. A fully optimized system is crucial in the estimation of the alkoxy species energy. Acknowledgment. Computational resources have been granted by the Dutch National Computer Facilities (NCF). This work has been performed within the European Research Group “Ab Initio Molecular Dynamics Applied to Catalysis”, supported by the Centre National de la Recherche Scientifique (CNRS), the Institut Franc¸ ais du Pe´ trole (IFP), and TotalFinaElf. X.R. thanks TotalFina for the financial support. References and Notes (1) Venuto, P. B. Microporous Mater. 1997, 2, 297. (2) (a) Sauer, J. Chem. ReV. 1989, 89, 199. (b) Schro¨der, K. P.; Sauer, J.; Leslie, M.; Catlow, C. R. A.; Thomas, J. M. Chem. Phys. Lett. 1992, 188, 320. (c) Sauer, J.; Ugliengo, P.; Garrone, E.; Saunders, V. R. Chem. ReV. 1994, 94, 2095. (d) Van Santen, R. A.; Kramer, G. J. Chem. ReV.

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