Computational Study of Brønsted Acidity of Mordenite. Effect of the

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Computational Study of Brønsted Acidity of Mordenite. Effect of the Electric Field on the Infrared OH Stretching Frequencies German Sastre,*,† Naonobu Katada,‡ and Miki Niwa‡ Instituto de Tecnologia Quimica U.P.V.-C.S.I.C., UniVersidad Politecnica de Valencia, AVenida Los Naranjos s/n, 46022 Valencia, Spain, and Department of Chemistry and Biotechnology, Graduate School of Engineering, Tottori UniVersity, 4-101 Koyama-cho Minami, Tottori 680-8552 Japan ReceiVed: May 12, 2010; ReVised Manuscript ReceiVed: August 4, 2010

Electric fields have been claimed to influence intrinsic acidity on zeolites, and in this work, we try to establish a relation between the electric field and Brønsted acidity. In this study, we use experimental data from commercial samples of mordenite (Si/Al ≈ 4-8) and we make periodic first-principles calculations of the infrared OH stretching bands with periodic density functional methods on several reliable models of a mordenite unit cell with a composition of Si40Al8O96H8 (Si/Al ) 5). Experiments show a high-frequency band at 3610 cm-1 and a low-frequency band at 3585 cm-1, and the computational results give frequencies in the range of 3600-3510 cm-1, slightly lower due to the PAW-GGA methodology employed. A rationalization of the IR frequencies found has been attempted on the basis of physicochemical properties of the microporous material. No correlation has been found with geometrical parameters, such as SiO(H)Al angles, or chemical parameters, such as the number of Al neighbors. No clear relation was found between the cage size where the Brønsted site vibrates and the OH frequency, in disagreement with some common interpretations, this suggesting that a complex mixture of short- and long-range factors is at play. We, however, found that a parameter related to the electric field at the proton site correlates with the OH frequencies over a large sample of centers of different O types, SiO(H)Al angles, and number of Al neighbors. 1. Introduction Zeolites were first introduced as acid catalysts in the late sixties when they became industrially employed in fluid catalytic cracking,1 and since then, they continue to be reference materials.2,3 Today, zeolite applications cover a broad range of processes related to the upgrading of crude oil and natural gas, such as fluid catalytic cracking (FCC), hydrocracking, dewaxing, aliphate alkylation, isomerization, oligomerization, transformation of aromatics, transalkylation, hydrodecyclization, and conversion of methanol to hydrocarbons, just to name a few of them.4-6 In the words of Jule A. Rabo, “The uniform intracrystalline microporosity, providing access to very large and welldefined surface, the molecular sieve effect, and the strong electrostatic field centered at zeolite cations, promise unique opportunities from the start for important efficiency and economic improvements in gas and liquid sorption and separation technologies. Indeed, in a short few years the practical use of these phenomena resulted in the development of a variety of new, diverse industrial sorption and separation processes throughout the chemical and fuel industries, worldwide”.7 These porous materials allow tailoring the acidity through the control of the number and strength of the acid centers in a structural environment where a wide and growing variety of topologies, currently 194, are available.8 Brønsted acid sites consist of SiO(H)Al units, whose acidity depends on a large variety of factors, such as topology of the zeolite, crystallographic type of O-site, local geometry, chemical composition (Si/Al ratio), electronic distribution, and Al distribution. * To whom correspondence should be addressed. E-mail: gsastre@ itq.upv.es. † Universidad Politecnica de Valencia. ‡ Tottori University.

Mordenite is known by its pronounced acidity, which has led to its use in cracking of alkanes and olefins, isomerization of hydrocarbons, dewaxing of heavy petroleum fractions,9 and high selective catalyst in disproportionation and transalkylation of xylenes.10,11 Its specific pore system contains large 12-ring main channels with an elliptical shape of ca. 6.7 × 7.0 Å along the [001] crystallographic axis, to which side pockets are connected in the [010] direction formed by 8-rings with a ca. 3.4 × 4.8 Å aperture.8 This strongly interconnected large + small microporous system generates important confinement effects, as was shown by ammonia and acetonitrile adsorption.12-15 Acidity measurements by NH3 TPD (temperature-programmed desorption) showed a higher effective acid strength for hydroxyls in the side pockets.16 In H-mordenite, the vOH band for acidic OH groups is usually rather broad and has an unusual low frequency component that is perturbed by adsorption of NH3 but not of pyridine, suggesting that the corresponding OH groups are located in the side pockets of the structure. It was suggested17 that such a low OH frequency was due to H bonding of the acidic proton with the oxygen neighbors in the small 8-rings, and this aspect will be studied in our computational study. In acidic mordenite with Si/Al ) 5, Alberti found18 that (a) the Brønsted acid sites are, at least, of two types; (b) there are protons vibrating in 8-rings and 12-rings; (c) the relative population of OH sites in the 12-ring is certainly not less, and is indeed probably larger than that in the 8-ring or in the side pocket; and (d) for the four tetrahedral sites, T1-T4, the two sites T3 and T4, which constitute the 4-rings, are the richest in Al.18,19 According to this and to some Al population analysis, Alberti18 suggested proton locations on the following oxygens: O2 (12-ring), O7 (12-ring), and O9 (8-ring), and later, a study by Marie et al.20 also pointed at O2, O7, and O9 as the location of the acid sites. Later, this aspect will be treated in more detail.

10.1021/jp104316e  2010 American Chemical Society Published on Web 08/23/2010

Brønsted Acidity of Mordenite Datka et al.21 identified, however, that the stronger acid sites were located in the 12-rings. In our group,22 two types of hydroxyls were found and ammonia interacted with both, whereas pyridine adsorption diminished the adsorption of the high-frequency OH band only. In a sample with Si/Al ) 7.5 and with sodium cations totally exchanged by ammonium cations, two bands at 3616 and 3585 cm-1 on which ammonium cations are absorbed were measured, with the band at low frequency being more populated. The latter is in contradiction with the above results by Alberti.18 IRMS-TPD (infrared mass spectroscopy/temperature-programmed desorption) determinations of ammonia adsorption give values of 147 and 155 kJ/mol for the OH centers, corresponding to the highfrequency and low-frequency bands, respectively. Other studies have tried to elucidate the Brønsted acidity of mordenite through the enthalpies of ammonia adsorption.23-25 Recently,26 we made a study in high silica zeolites where we correlated the acid strength (ammonia adsorption of centers excluding polidentate H bonding) with the Al-O bond length. Here, we move to the study of a zeolite with a large Al content (low Si/Al) where the role of neighbor centers cannot be neglected. We are interested in extracting general trends on acidity that help to understand Brønsted acidity in zeolites. 2. Methodology and Models 2.1. Structure and Location of the Acid Sites in Mordenite. Topologically, mordenite contains four T-sites (T ) Si, Al) and 10 O-sites, with 14 possible arrangements of Brønsted sites, as indicated in Table 1, where also the accessibility of 10 O-sites (Figure 1) is indicated. We have defined four different microporous environments in the acid sites of mordenite (Figures 1 and 2): (a) pockets made by two 8-rings, (b) 12-ring channels, (c) small cavities where the proton vibrates inside 5-rings, and (d) elliptical 8-ring channels. The pockets (parallel to b), formed by two 8-rings (called 8-ring-p1 and 8-ring-p2), are perpendicular and interconnected to the 12-ring channel (parallel to c). The “8-ring-p1” intersects the 12-ring channel, whereas the “8-ring-p2” intersects the 8-ring elliptical channel (Figure 2). The O-sites and T-sites are labeled through the notation introduced by Gramlich et al.,27 which was then adopted by most groups working on mordenite.28 Other groups29 followed a different notation, which, for the sake of comparison, is included as the Supporting Information. 2.2. Models. Mordenite is a natural and synthetic zeolite with an idealized composition of Na8Al8Si40O96 × nH2O and with varying Si/Al contents: 4.3-6.0 (natural) and 5.0-12.0 (synthetic).30,31 We have considered a unit cell with the idealized composition above, and we have created a distribution of Na and Al compatible with the experimental observations. We have then replaced sodium cations by protons that we have located in positions according to the following criteria: (i) From the four tetrahedral sites, T1-T4, sites T3 and T4 are the richest in Al. The distribution of Al in T1-T4 sites should be similar to the experimentally found 18/10/43/29.18 (ii) There are protons accessible to pyridine (ca. 67%) and protons inaccessible to pyridine (ca. 33%), but accessible to NH3.16,20,21,32,33 Table 1 indicates the accessibility to the centers. (iii) Among the possible distributions, those with highest energy should be discarded. (iv) The protons produce two OH signals in the IR spectra at 3610 and 3585 cm-1.34-36 We have used a high throughput computational technique to generate random configurations of Al and protons in a H8Al8Si40O96 mordenite unit cell with the following two

J. Phys. Chem. C, Vol. 114, No. 36, 2010 15425 TABLE 1: Structural Data of Pure Silica Mordenite and Topological Data of Mordenited fourteen different combinations of Brønsted sites in mordenite Si1-O1(H)-Al3 Al1-O1(H)-Si3 Si2-O2(H)-Al4 Al2-O2(H)-Si4 Si1-O3(H)-Al2 Al1-O3(H)-Si2 Si3-O4(H)-Al4 Al3-O4(H)-Si4 Si2-O5(H)-Al2 Si1-O6(H)-Al1 Si1-O7(H)-Al1 Si2-O8(H)-Al2 Si3-O9(H)-Al3 Si4-O10(H)-Al4 T-O-T labels T-O-Ta Si1 O1 Si3 Si2 O2 Si4 Si1 O3 Si2 Si3 O4 Si4 Si2 O5 Si2 Si1 O6 Si1 Si1 O7 Si1 Si2 O8 Si2 Si3 O9 Si3 Si4 O10 Si4

145 144 159 166 144 150 136 180 147 148

ring indexa

number

locationb,c

5 3 · 82 53 · 8 · 12 53 · 12 4 · 52 52 · 8 52 · 8 52 · 8 · 12 54 4 · 84 4 · 82 · 122

16 16 16 8 8 8 8 8 4 4

pocket-8-2 + elliptic-8 12-ring + pocket-8-1 12-ring small cavity pocket-8-1 pocket-8-2 12-ring small cavity elliptic-8 12-ring

a All the analyses of the final geometries obtained (bonds and angles) in the unit cells were performed with the zeoTsites software88 and the calculation of the ring index.89 TOT angles correspond to the SiOSi angles of the pure silica mordenite as found in the Atlas of Zeolite Framework Types.8 b Five different environments are present in mordenite: two 8-ring pockets (pocket-8-1 and pocket-8-2), 12-ring channel, small cavities where the proton vibrates inside 5-rings, and elliptical 8-ring. c Accessibility to pyridine and ammonia is as follows: (i) accessible to pyridine, O2, O5(?), O7, O10; (ii) accessible to ammonia, O1, O2, O3, O5, O6, O7, O9, O10; (iii) unaccessible to ammonia, O4, O8. d Bond angles in degrees.

constraints: The Lowenstein rule, generally followed in zeolites, should be obeyed, and thus, no Al-O-Al linkages should be present. The protons should be attached to oxygens belonging to SiOAl units. From the hundreds configurations generated, we have selected only those following the above criteria i-iii. To assess criterion iii, the energy corresponding to hundreds of configurations could not be done at a quantum chemistry level and, rather, an atomistic forcefield approach was selected (see section 2.3). Filtering the results through criteria i-iii gives four distributions, which we will call “configurations 1-4”. Periodic quantum chemistry calculations will then be used to test whether the configurations 1-4 follow the criterion iv above. Further, from these calculations, we will try to rationalize the factors determining the OH frequencies found. On a second stage, a larger (1 × 1 × 2) unit cell, H15Al15Si81O192, with a similar Si/Al ratio, will be used to generate further configurations, called “configurations 5-10”, following the same criteria in order to complete the periodic quantum chemistry calculations. Altogether, 122 Brønsted sites will be studied, this giving a sufficiently large statistically representative set of results. 2.3. Atomistic Forcefield Calculations. Atomistic forcefield calculations will be only a minor part of this study that is mostly based on a periodic quantum chemistry approach (see section

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Figure 1. Top: mordenite structure across [001] showing the 10 different possible locations of the Brønsted sites. Bottom: view across [010]. Table 1 gives details of the centers.

2.4). For the sake of efficiency, when random Al, H configurations of the H8Al8Si40O96 mordenite unit cell are created, the energetic criteria iii above can only be successfully applied to many configurations by using an atomistic approach. A specific software, called “zeoTAl”, was developed to generate several hundreds of unrepeated configurations within a given number of Al and H atoms, satisfying, as said above, the Lowenstein rule and that the protons belong to oxygens contained into SiOAl linkages. From all the configurations generated, the energy was calculated with the atomistic forcefield and computational techniques used in previous work.37-39 The four configurations found following criteria i-iii are included as the Supporting Information. 2.4. Periodic Quantum Chemistry Calculations. All the calculations were performed with full optimization of the atomic Cartesian coordinates of the system as well as the unit cell parameters. The orthorhombic u.c. of mordenite was selected, and the u.c. parameters were optimized while keeping the R ) β ) γ ) 90° orthorhombic cell requirements. Successive cell sizes were created in steps of changing (2% of the initial volume and taking the minimum energy value of the corre-

Sastre et al. sponding curve “energy versus cell size”. Density functional energy calculations were performed using the Vienna Ab-initio Simulation Package (VASP).40 The Kohn-Sham equations were solved variationally in a plane-wave basis set using the projector augmented wave (PAW) method of Blochl41 as adapted by Kresse and Joubert.42 The exchange-correlation energy was described by the PW91 generalized gradient approximation (GGA) functional.43 Brillouin zone sampling was restricted to the Γ-point. During the geometry optimizations, the plane-wave cutoff was set to 400 eV. By monitoring the convergence of energy differences with respect to plane-wave cutoff and Brillouin zone sampling, we estimate the errors due to these to be less than 0.075 eV. The same choice of plane-wave cutoff and Brillouin zone sampling was made in a study of a similar material by Bucˇko et al.44 The convergence criterion for the electronic self-consistency measured by the change in the total energy between successive iterations was set to 10-5 eV/u.c. Atomic positions were relaxed within a conjugate-gradient algorithm until all the forces acting on the atoms were lower than 0.03 eV/Å. For the calculation of the OH vibrational frequencies, the consideration of the full dynamical matrix is a computationally grand challenge. However, it is well known that the OH stretching modes are almost pure eigenmodes and hence separated from the other vibrational modes of the framework atoms. We have then calculated the OH frequencies through two different approaches. First, in continuation with our previous work, we use a finite difference method,45,46 by obtaining the energy of the system within the same methodology at small OH displacements (up to (0.12 Å, in intervals of (0.03 Å) of the equilibrium positions. Instead of using a quadratic fit of energy against displacements, which gives the approximated harmonic frequency, the corrected anharmonic frequencies have been obtained modeling the potential through a third-order polynomial. All the frequencies reported are anharmonic frequencies. More details can be found in the Supporting Information of our previous work.46 Second, we use the previously generated plot of energy versus OH displacements (up to (0.12 Å, in intervals of (0.03 Å) of the equilibrium positions. The energy values were best fitted with a sixth-order polynomial. The resulting monodimensional nuclear Schro¨dinger equation was solved by following a numerical algorithm,47 by means of the program ANHARM.48 We present here the latter, more accurate, results based on the wave function approach, whereas the results obtained through the first method (polynomial approach) will be included in the Supporting Information. All the VASP jobs were run on Altix-XE250-Infiniband (E5472) and Itanium2 (3.0 GHz CPU, 12 MB L2 Cache, and 1.6 MHz FSB speed) machines exploiting the parallel processing in different degrees going from 8 to 32 processors. 3. Results and Discussion 3.1. OH Frequencies of the Acid Sites in the H8Al8Si40O96 Mordenite Unit Cell. Four configurations with a unit cell with a composition of H8Al8Si40O96 were generated satisfying the experimental considerations in criteria i-iii (see section 2.2). They have the following distribution of Al-sites: Al1/Al2/Al3/ Al4 ) 2/1/3/2 = 25/13/37/25%, similar to the experimental18 18/10/43/29%. The ratio of centers accessible to pyridine and accessible to ammonia49 is 5/3 (proton locations are 3 O2, 2 O7, and 3 O9), close to the experimental20,21,32,33 result, =2. Details of the configurations can be found in Table S1, in the Supporting Information, where the full unit cells in CIF format are also given. The calculated anharmonically corrected OH

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Figure 2. Schematic representation of the channels of mordenite. The 12-ring and 8-ring channels go through [001] and are connected through the so-called “mordenite pockets”. Pockets are made of two different parallel 8-rings, one of them (highlighted lighter) is close to the 12-ring and is called “pocket-8-1” (see Table 1), whereas the other 8-ring type (highlighted darker) is close to the elliptical 8-ring and is called “pocket-8-2” (seeTable 1).

TABLE 2: Characterizationa of the Four Al Configurations in the Mordenite Unit Cell (Si40Al8O96H8) and VASP Calculated Anharmonic OH Frequencies (cm-1) νOH (cm-1) site

num

conf1

conf2

Al4-O2 Al4-O2 Al2-O2 Al4-O2 Al4-O2 Al1-O7 Al1-O7 Al3-O9 Al3-O9 Al3-O9

1 2 3 4 5 6 7 8 9 10

3580

3549

3572 3583

3558

3588 3033 3510 3569 3542

3555 3567 2987 3517 3551 3548

conf3

conf4

3531 3565 3552

3623 3563

2898 3033 3517 3559 3532

3584 3555 3097 3497 3557 3530

a Each SiO(H)Al acid site belongs to one of the fourteen types described in Table 1, which can be univocally named by the code AlxOy as it appears here in the “site” column. Each configuration is labeled as conf1-conf4. Ten different acid site locations are considered, of which only eight are “occupied” in each configuration, as specified in column “num”. The Supporting Information contains cif files corresponding to the configurations.

frequencies are shown in Table 2 (configurations labeled as “1-4”). A few considerations can be extracted from these results. Some Brønsted sites located on Al1-O7, present anomalous too small νOH values between 2898 and 3097 cm-1. This is due to the fact that the OH is vibrating in a 5-ring (more details are presented in the Supporting Information). As a consequence, a strong H bond with an opposite oxygen appears, which weakens the OH bond, and hence, the frequency decreases drastically.

This has been observed elsewhere50-52 and does not resemble the experimental system; hence, we will not take these frequencies into consideration for the infrared analysis as they do not correspond to any signals observed. Because of the H-bond interaction, the OH mode will no longer be detached from the others, but rather mixed to the oxygen atom causing the H bond. This suggests that the corresponding calculated OH frequencies of anomalous centers will be less accurate. More details are given in the Supporting Information. Two groups of OH frequencies can be observed (Table 2): protons vibrating in O2-sites and O7-sites (anomalous O7-sites excluded) within the range of 3555-3623 cm-1 and protons vibrating in O9-sites within the range of 3497-3569 cm-1 (but mostly, 66% of them, within 3497 and 3555 cm-1). Therefore, the calculated bands (3555-3623 and 3497-3555 cm-1) are in reasonable agreement with the bands observed in most of the literature,17,18,21,22,35,36 centered at 3616 and 3585 cm-1. The calculated values are below the experimental due to the PAWGGA methodology employed, as has been noted elsewhere.53 A comparison with previous computational work is not possible because other groups29,54 have only studied the OH frequencies of mordenite at high Si/Al ratios, without considering the influence of Al neighbors, previously shown to be crucial.46 Seventeen centers vibrate in the range of 3555-3623 cm-1, and nine centers vibrate within 3497-3555 cm-1 (Table 2), giving a ratio of 17/9 between centers in the high-frequency (HF) and low-frequency (LF) bands. This is in reasonable agreement with some infrared experiments that show an HF/LF ratio close to 2: Alberti, 1.98;18 Zholobenko et al., 2.0;34 and Makarova et al., 2.2.55 Other studies, however, give different values: Martucci

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Figure 3. VASP calculated anharmonic OH frequencies corresponding to the configurations of H8Si40Al8O96 (configurations 1-4) and H15Si81Al15O192 (configurations 5-10) unit cells. The protons vibrating at lower frequencies are included in the Supporting Information. Protons are classified according to the O type they are attached to. (O2 + O7) sites vibrate into 12-rings, whereas sites attached to O9 vibrate into 8-rings.

et al., 0.76;56 Niwa et al., 0.42/0.77;22 Datka et al.,21 3.0/3.5; and Wakabayashi et al., 32/25.36 3.2. OH Frequencies of the Acid Sites in the H15Al15Si81O192 Mordenite Unit Cell. To have a wider set of centers that make the statistics more conclusive, we have generated six new different Al distributions on a larger (1 × 1 × 2) unit cell following, again, criteria i-iii in section 2.2. The six distributions generated, called “configurations 5-10”, contain six protons on O2, four protons on O7, and five protons on O9. The unit cells were fully optimized following the same procedure than that in the previous case. Figure 3 shows the results obtained, including the previous four configurations for the sake of comparison. Our differentiation into HF (3555-3623 cm-1) and LF (3497-3555 cm-1) is somewhat arbitrary because the two bands are not clearly separated, but throughout the 10 configurations, this gives a ratio of HF/LF ) 83/26 ) 3.2. This is not close to the previously mentioned value of 2 but shows, qualitatively, the larger abundance of centers vibrating at HF with respect to LF. 3.3. Correlation of OH Frequencies with Structural and Chemical Parameters. It is a topic of discussion whether OH frequencies of Brønsted sites in zeolites can be correlated to structural and chemical, short- and long-range, parameters. It is the main aim of this study to contribute to clarify which factors affect OH frequencies. The OH stretching frequency is somewhat related to the strength of the OH bond and hence with the intrinsic capability to release the proton, hence, a measure of “intrinsic acidity” of a Brønsted site.57 Certainly, protons are always transferred to a reactant (base) molecule and then “acidity” becomes the capability to protonate a base,58,59 this scale of acidity depending on the basic molecule chosen. The “intrinsic acidity”, without external dependency of the interacting molecule, remains a valid approximation to the acidity of the solid material.60 3.3.1. OH Frequencies and SiO(H)Al Angles. Some previous studies indicate a linear correlation between acidity-related zeolitic properties and SiO(H)Al angle,53,61 based on the fact that the p-character of the O-H bond should increase (scharacter should decrease) with increasing the Si-O-Al angle, and an increase in p-character is related with the weakness of

Sastre et al.

Figure 4. Plot showing that no correlation could be found between νOH and SiO(H)Al angle of all the Brønsted sites (10 configurations) considered in this study. Protons are classified according to the O type they are attached to. (O2 + O7) sites vibrate into 12-rings, whereas sites attached to O9 vibrate into 8-rings. A certain trend of decreasing νOH with increasing SiO(H)Al angle is, however, found.

the O-H bond.62 Most results correlating acidity and SiO(H)Al angle were obtained in particular cases and with low-quality methods and/or models. Brand et al.63 concluded that “proton affinities were found to depend on the shapes of the clusters chosen, suggesting that structural differences beyond the SiO(H)Al bridge may play a significant role in determining proton affinities”. In agreement with that, other studies46,64-67 indicate that SiO(H)Al angles alone do not determine the OH frequencies. A different conclusion was obtained by Grajciar et al.,68 who found that centers in ferrierite showed a correlation between OH frequencies and SiO(H)Al angle for different types of centers and two different Si/Al ratios. Our results in Figure 4 show that OH frequencies are not determined by the SiO(H)Al angle of the Brønsted site. Nevertheless, a weak trend can be guessed in the direction pointed by previous studies, which expect that an increase of the Si-O-Al angle weakens the O-H bond, and hence, OH frequencies decrease. 3.3.2. OH Frequencies and Al Neighbors. This topic was explored in a previous study46 finding no relation between the number of Al neighbors (or Si/Al ratio) and OH frequencies. Barthomeuf,69 Jacobs and Mortier,17 and Kazansky70 found that the Al content affects the νOH, which increased as the Al content decreased up to Si/Al ) 6 and remains constant at lower Al contents (Si/Al > 6). Pelmenschikov et al.71 found that the chemical factor (Si/Al) does not influence strongly the νOH when fixing the geometry of the central Brønsted site, and it is the geometry that mainly affects OH frequencies. A study by Datka et al.72 employed clusters to simulate Brønsted sites corresponding to Si(nAl) (n ) 1-4). To better isolate the chemical (Si/ Al) effect on OH frequencies, the SiO(H)Al angle was fixed in all the clusters and the results showed variations of only within 7 cm-1 in the νOH. Sierka et al.73 simulated faujasite with different Al contents, and the νOH values did not show a strong relation with Si(nAl) environments. In a related study, Eichler et al.74 concluded that OH frequencies are influenced by longrange interactions and cannot be explained by local effects. Our main conclusion regarding this point46 was that the Si/ Al ratio clearly influences the OH frequency and this occurs through two mechanisms: (i) a short-range effect by which the Si/Al ratio influences the geometry of the local Brønsted site,

Brønsted Acidity of Mordenite and (ii) a long-range effect by which the Si/Al ratio influences the electronic density and hence the electrostatic environment of the Brønsted site. Within a Si/Al ≈ 5, we have studied whether different Al distributions may influence the OH frequencies. The Al neighbors of the SiO(H)Al site were considered through (i) number of Al neighbors of the Si atom (a number between 0 and 4) and (ii) number of Al second neighbors of the Al atom (a number between 0 and 9-12 depending on the Al topology). Our results (see Figures S1 and S2 in theSupporting Information) show no correlation between the Al environment and OH frequencies. 3.3.3. OH Frequencies and CaWity Size. It has been traditionally claimed that protons vibrating in large cages show νOH larger than those vibrating in small cavities,17 rationalized as follows. Large cavities provide a “less perturbed” environment because protons are farther from other atoms. Acid sites vibrating in small cavities can be considered to be “perturbed” as a consequence of the more restricted environment, where all other interacting atoms are closer to each other. In such cases, a 1/r2 relationship between the bathochromic shift observed and near neighbor oxygen distances in the same ring as the acid site was proposed.17 The latter observation has been taken by many authors as suggesting that the shift is proportional to the size of the cavity in which the proton vibrates and have assigned IR bands based on this assumption alone, without any consideration of the local environment not part of the immediate cavity. In fact, environments outside the cavity can easily be more influential based on a 1/r2 relationship, and this suggests to use parameters based on the electrostatic potential in order to try to tackle variations of OH frequencies. Our results (Figure 3) can be easily analyzed in terms of cavity size just by taking into account that centers on (O2 + O7) vibrate in large cavities and O9 protons vibrate in small cavities (see Table 1 and Figure 1 for location of centers). Although many centers at the small cavities (O9) vibrate at low OH frequencies and many centers at the large cavities (O2 + O7) vibrate at large frequencies, the correlation is not sufficiently general because many centers not following such a rule can also be found (Figure 3). The wide range of νOH found for a given cavity size indicates that factors other than the cavity size are playing a fundamental role in determining the νOH. Our results are in agreement with previous work75,76 where no consistent correlation between νOH and cavity size was found. A number of cases where almost identical OH frequencies for protons vibrating within different sized cavities confirmed such a lack of correlation. In fact, the “cavity size argument” does not take into account the interactions between the proton and nearby atoms that are “behind” the proton and outside the cavity. Neighbor atoms not directly in the same ring may be closer, and thus more influential, than those in the ring, particularly for larger cavities. 3.3.4. OH Frequencies and Electric Field. Since the early studies relating electrostatic potential and zeolite properties by Dempsey77 and Goursot,78 a number of studies have succeeded in relating the electric field created by the zeolite framework with the frequency shifts of N2O or CO adsorbed in zeolite cations,79-82 and similar concepts have been proposed for water83 and ionic surfaces.84 In our previous work,75 we applied atomistic lattice energy minimization and Mott-Littleton methodologies to determine equilibrium geometries and vibrational properties of acid sites in a variety of structures and compositions of both aluminosilicates and silicoaluminophosphates. The model extensively

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Figure 5. Plot showing the correlation between νOH and EFH (electric field at the proton site measured from OH elongation). Configurations 1-4 refer to Brønsted sites in the H8Si40Al8O96 unit cell, and configurations 5-10 refer to Brønsted sites in the H15Si81Al15O192 unit cell. More details are given in the Supporting Information.

demonstrated to reproduce experimental structures and gave good agreement with experimental vibrational properties. For example, in mordenite, we observed75 two bands at 3600 and 3572 cm-1, compared with 3612 and 3585 cm-1 from experiment; and similarly, we calculated shifts to lower wavenumbers with decreasing Si/Al in faujasite. In the quest of structural properties that correlate with the resulting OH vibrations, we found that short-range interactions are not adequate to identify variations in OH vibrational properties. Instead, we considered that the long-range Coulombic interactions are dominant and observed a remarkable correlation between νOH and the gradient norm of the electrostatic potential at the proton when considering the acidity of a small set of zeolites and SAPOs,85 which was later confirmed on a wider set of structures.66,75 Different physicochemical parameters related to the electric field can be invoked, such as electric field or electric field gradients at the proton site,86,87 to relate their properties with those of the OH frequencies. In this study, we have used the gradient of the electrostatic potential at the proton site as the OH elongates (which has dimensions of electric field), and we will refer to as EFH. This is equivalent to the component of the electric field at the proton site in the direction of the OH bond. The results (Figure 5) show a much clearer correlation than any of the previously tested parameters and indicate larger OH frequencies (lower acidity) as EFH. increases. The correlation is followed by all the Brønsted sites considered regardless of O type (O2, O7, and O9), environment (small and large cavities), configuration (10 aluminum configurations sampled), SiO(H)Al angle, AlO distance, etc. A fundamental question arising is why this descriptor, EFH, shows a good correlation with νOH. Theoretical arguments were presented elsewhere.86,87 The electric field on a positive test charge exerts a force parallel to such a field. Therefore, increasing values of the slope of the electrostatic potential as the proton is displaced along the OH bond relate to Brønsted sites more strongly attached (less acidic) and hence with larger νOH. Electric fields are influenced by all the other parameters previously discussed (Si/Al content, Al distribution, cavity size, SiO(H)Al angle, and AlO distance), and so, the correlation found does not dismiss the importance of all the other factors but rather takes them all into account properly with an inverse distance relationship dependence, which means that centers more distant contribute less importantly. Structural and

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chemical distortions will affect more importantly neighbor than distant centers, but distant centers will also be taken into account. 4. Conclusions The understanding of the properties of zeolites at a fundamental level is a priority task. We have used a first-principles methodology in order to help to clarify the nature of the intrinsic acidity of the Brønsted acid sites. Periodic models of mordenite with a Si/Al = 5 ratio were fully optimized by using a planewave approach. We have calculated anharmonicity-corrected OH stretching frequencies. Our results show that the νOH of a given center cannot be correlated with parameters depending on short- or medium-range properties, such as SiO(H)Al angle, AlO distance, oxygen type, cavity size, or aluminum distribution. Instead, a property related to the electric field at the proton site is demonstrated to correlate with intrinsic acidity. The correlation has been tested for a wide variation of factors, including 122 acid sites. Our parameter is the gradient of the electrostatic potential at the proton site as the OH elongates (which has dimensions of electric field). This is equivalent to the component of the electric field at the proton site in the direction of the OH bond. Calculation of electric fields at proton sites in other zeolites can be useful to obtaining valuable information about the acidity of each center, and this can be related to the catalytic properties with implications on reactivity. Acknowledgment. G.S. thanks the following centers for making available their supercomputational resources: “Barcelona Supercomputing Centre” (BSC), “Centro de Supercomputacio´n y Visualizacio´n de Madrid” (CeSViMa), “Centro Te´cnico de Informa´tica” (CTI-CSIC), Red Espan˜ola de Supercomputacio´n (RES), and the Distributed European Infrastructure for Supercomputing Applications (DEISA) Consortium for the provision of the ACIDFAU project. G.S. thanks Dr. Doris Vogtenhuber for many insightful suggestions regarding the VASP code. Prof. Piero Ugliengo is acknowledged for kindly making available the ANHARM software and for useful discussions. Supporting Information Available: Details on the calculation of anharmonically corrected OH frequencies, electric fields, plots of νOH with respect to Al neighbors and AlO distance, and cif files corresponding to the configurations studied in the mordenite unit cells, Si40Al8O96H8 (four configurations) and Si81Al15O192H15 (six configurations). This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) (a) Wadlinger, R. L.; Kerr, G. T.; Rosinski, E. J. U.S. Patent 3,308,069, 1967. (b) Plank, C. J.; Rosinski, E. J.; Rubin, M. K. U.S. Patent 4,046,859, 1977. (2) Corma, A. Chem. ReV. 1997, 97, 2373. (3) Perez-Ramirez, J.; Christensen, C. H.; Egeblad, K.; Christensen, C. H.; Groen, J. C. Chem. Soc. ReV. 2008, 37, 2530. (4) Sto¨cker, M. Microporous Mesoporous Mater. 2005, 82, 257. (5) Flanigen, E. M. Pure Appl. Chem. 1980, 52, 2191. (6) Rabo, J. A.; Schoonover, M. W. Appl. Catal., A 2001, 222, 261. (7) Rabo, J. A. Appl. Catal., A 2002, 229, 7. (8) Baerlocher, Ch., McCusker, L. B., Olson, D. H., Eds. Atlas of Zeolite Framework Types, 7th ed.; Elsevier: Amsterdam, The Netherlands, 2007; http://www.iza-structure.org. (9) Dyer, A.; Singh, A. P. Zeolites 1988, 8, 242. (10) Bankos, I.; Klyachko, A. L.; Brueva, T. R.; Kapustin, G. I. React. Kinet. Catal. Lett. 1986, 30, 297. (11) Marie, O.; Thibault-Starzyk, F.; Massiani, P.; Lavalley, J. C. Stud. Surf. Sci. Catal. 2001, 135, 220. (12) Zecchina, A.; Marchese, L.; Bordiga, S.; Paze, C.; Gianotti, E. J. Phys. Chem. B 1997, 101, 10128.

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