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# Stability and Acidity of Sites at the External Surface and at Point Defects of Faujasite

Thomas Jarrin, Theodorus de Bruin, Céline Chizallet

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Thomas Jarrin, Theodorus de Bruin, Céline Chizallet. Stability and Acidity of Sites at the External Surface and at Point Defects of Faujasite. ChemCatChem, 2023, 15 (3), pp.e202201302. 10.1002/cctc.202201302. hal-04180001

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# Stability and Acidity of Sites at the External Surface and at Point Defects of Faujasite

Thomas Jarrin,[a] Theodorus de Bruin,[b] and Céline Chizallet*[a]

Faujasite is one of the most industrially employed zeolite for its catalytic properties. The strong Brønsted bulk bridging Al–OH–Si sites are often thought to be the main origin of the Brønsted acidity of faujasite. However, many reactions also take place at the surface of the material and of its mesopores, where other types of acid sites exist. This study aims at unraveling the nature and strength of faujasite bulk and surface acid sites. Using Density Functional Theory (DFT), we rank the faujasite

acid sites based on their stability, investigate their dehydration properties, and study their Brønsted and Lewis acidity via the adsorption of pyridine. Calculations are performed on cells with high (47 for bulk cells and about 300 for surface slabs) and low Si/Al ratio (about 3) and on cells containing defects under the form of silanol nests. These environments generate Brønsted acid sites of various strengths, and strong Lewis acid sites, even in the absence of extra-framework species.

## Introduction

Zeolites are nanoporous aluminosilicate materials with a well-defined crystalline structure. They are composed of an arrangement of $TO_4$ tetrahedra (T being Si or Al) linked together at their corner by oxygen atoms and forming a rigid 3D network exhibiting pores having diameters in the range of the nm. Atoms occupying the T sites forming 4 bonds with oxygen atoms, $Si^{4+}$ are the default ions, but $Al^{3+}$ cations can also occupy the sites. In this case, off-framework cations acting as charge compensators are present. They are commonly $Na^+$, $Li^+$ or $H^+$. In the present article, we consider structures with protons ($H^+$) as compensating cations. The $Al^{3+}$ and $H^+$ cations present in the structure provide a vast array of properties to the zeolites, useful for applications such as ion exchange, gas separation and catalysis.[1,2] Among the more than 230 different existing zeolite structures catalogued by the International Zeolite Association (IZA),[3] this study deals with the FAU one, which constitutes the basic framework of the faujasite material.[4] The Y zeolite corresponds to Si/Al ratio higher than 2.[5] Zeolite Y has been historically widely employed for the

catalysis of hydrocracking reactions, inter alia,[6] and is now thought to be an excellent candidate for biomass conversion[7] and plastic recycling,[8] due to its large pores. The FAU framework is made of an arrangement of sodalite cages connected by double six-membered rings (D6R). Each sodalite cage is connected to 4 other sodalite cages. The network is composed of two types of pores: small cavities inside the sodalite cages and supercages resulting from the arrangement of sodalite cages. The network of cages and pores is presented in Figure 1.

<figure><img src="image_13.png" /><figcaption>**Figure 1.** The FAU framework and proton position (black dots) labelling are displayed in the top figure. T sites are located at the vertices and oxygen atoms at the center of the edges. The structure of the top figure is not complete (sodalite cages not connected to 4 other cages) in order to highlight the presence of a supercage. The bottom figure is a representation of the real proton positions.</figcaption></figure>

<figure><img src="image_14.png" /></figure>

Supporting information for this article is available on the WWW under
https://doi.org/10.1002/cctc.202201302

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© 2022 The Authors. ChemCatChem published by Wiley-VCH GmbH. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

<footnote>[a] Dr. T. Jarrin, Dr. C. Chizallet
IFP Energies nouvelles,
Rond-Point de l'échangeur de Solaize, BP3,
69360, Solaize, France
E-mail: celine.chizallet@ifpen.fr
Homepage: https://www.ifpenergiesnouvelles.com/page/celine-chizallet</footnote>

<footnote>[b] Dr. T. de Bruin
IFP Energies nouvelles,
1 et 4 Avenue de Bois Préau,
92852, Rueil-Malmaison, France</footnote>
<figure><img src="image_16.png" /></figure>

The faujasite structure can also be envisioned as a diamond lattice, where the lattice sites are occupied by sodalite cages (the sites correspond to the centers of the sodalite cages). Consequently, the conventional unit cell of faujasite is a cubic cell, containing 8 sodalite cages. A smaller triclinic primitive cell can be constructed for the diamond lattice, with, in the case of faujasite, two sodalite cages occupying the two sites of the cell. The detailed characteristics of the faujasite primitive triclinic cell are detailed in the Model construction section.

The bridging Si–OH–Al sites within the bulk of zeolite materials have been known for a long time to be responsible for the Brønsted acidity of zeolites, and faujasite in particular.[9–11] In the case of faujasite, much effort has been devoted to the understanding of the structure, stability and reactivity of extra-framework species obtained after dealumina- tion treatments.[12–15] But for a long time, the properties of the external surface of zeolite crystallites have not been considered worth studying. However, recent applications of faujasite require reduced mass transfer limitations, which can be achieved thanks to materials with high (external surface)/ (internal surface) and/or high (mesoporous surface)/(micro- porous surface). Among the adequate zeolites are the nano- crystals zeolites,[16–19] hierarchical zeolites[20,21] and zeolites nanosheets.[22] Most importantly, steaming is often applied to adjust the Si/Al ratio of faujasite samples,[21,23] and to generate mesopores, which surface is likely to resemble that of the border of the crystallites. Also, “pore-mouth catalysis”, i.e. surface catalysis, is expected to occur for zeolites which pores are smaller than the molecules to be converted.[24,25] Therefore, not only the bulk, but also the surface properties of faujasite become of tremendous significance. As it was shown in several theoretical works for the MFI, BEA and MOR frameworks,[26–29] the surface properties can be very different from those of the bulk and need to be properly investigated. In this regard, some theoretical works were also dedicated to study faujasite surface properties.[30–32] However, none tackled the question of stability and acidity of the surface sites, which is the main focus of this article. Indeed, using DFT, we study the stability of the external surface sites of faujasite, the acidity of the sites as well as their hydration and dehydration properties, when relevant. In order to provide results to be compared to experimental and industrial cases, we investigate the mentioned aspects of cells with different Si/Al ratio as well as on cells with silanol nests defects. The atomic structure files of all the systems discussed in this article are available online on an online Open Science Framework repository.[33] We encourage the readers to refer to it throughout the article.

Methodology

Computational Details

Periodic DFT calculations are carried out using the Vienna Ab Initio Simulation Package (VASP) code.[34–36] The Perdew, Burke and Ernzerhof (PBE)[37] exchange and correlation functional is employed, and the Projected Augmented Wave (PAW)[38] method is used to describe core-electron interactions. Corrections on the van der

Waal's interactions are integrated via the D2 method of Grimme.[39]
This level of theory was validated against higher level methods in
Ref. [40]. Unless specified otherwise, all calculations are performed
at the gamma-point with an energy cutoff of 400 eV. The
convergence criterion for the self consistent cycle is always chosen
equal or inferior to 10<sup>-6</sup> eV. All atomic positions relaxation
calculations are considered converged when the force on each
atom is less than 0.02 eV/Å. The built-in VASP conjugate-gradient
algorithm is employed for atomic positions relaxation. For non-
symmetric surface slabs, even if negligible, a dipolar correction is
added to remove unphysical interactions between vertical periodic
images of the surface slabs. The calculation of some quantities
employed in the next sections requires the computation of the
atomic vibration frequencies. To perform such calculations we use
the central finite difference method implemented in VASP to
compute the Hessian matrix, with a displacement width of ±0.01 Å
for each ion. For bulk cells, all atoms are allowed to vibrate, while
for surface slabs, the 100 atoms closest to the surface are allowed
to vibrate. Vibration calculations have been performed on slabs in
which the Al atoms of interest were located close enough to the
surface so that the chosen rule is well suited.

Model Construction

The triclinic primitive cell of the FAU framework is employed in the calculations. Starting from the conventional cubic purely silicic cell available on the IZA website,[3] the primitive cell is constructed and optimized (cell and atoms are allowed to move), with a cutoff of 800 eV, in order to avoid optimization errors attributed to the change of the cell volume with respect to the constant number of plane waves. Then, the cell parameters are fixed and the atomic positions are relaxed with a cutoff of 400 eV. After this 2 step optimization process, the purely silicic primitive cell parameters are the following: a=b=c=17.314 Å and α=β=γ=60°. From this optimized bulk cell, surface slabs are constructed with the Materials Studio surface cleavage tool. The experimental literature points towards the large dominance of the (111) orientation. Alfredsson et al.[41] used High-Resolution Transmission Electron Microscopy (HR-TEM) to identify the (111) facets at the surface of faujasite samples. The same facets orientations were observed using Atomic Force Microscopy (AFM) by Anderson et al.[42] and Wakihara et al.[43] Faujasite crystals tend to adopt an octahedral shape, for which all the facets are of the (111) type. Different orientations exist only at the edges of the crystals. The same conclusion was reached for mesopores internal surface, with the (111) orientation being identified with HR-TEM as the preferred one.[44] Therefore, we consider only the (111) surface orientation of faujasite in the construction of our surface models. HR-TEM and AFM experiments also revealed the existence of steps at the surface of the faujasite samples.[41,43] Those steps could not be integrated into our surface slabs, as it would require to work with cells of deterrent sizes for DFT calculations. The surface slabs are constructed with a vacuum layer of 25 Å, to avoid interactions between vertical periodic images. As it will be shown in the next section, three different surface terminations are considered: D6R complete, sodalite complete and sodalite incomplete. Names adopted in this article for the surface terminations are the same as in the previously cited experimental papers which first identified those terminations.[41,42] The cell parameters of the silicic surface slabs for those three terminations respectively are:

• a = b = 17.314 Å, c = 61.054 Å, α = β = 90°, γ = 120°

• a = b = 17.314 Å, c = 56.031 Å, α = β = 90°, γ = 120°

• a = b = 17.314 Å, c = 50.023 Å, α = β = 90°, γ = 120°

Side views of those terminations are displayed in Figure 2. The
results regarding the convergence of the surface energies with the
<figure><img src="image_17.png" /></figure>

<figure><img src="image_18.png" /><figcaption>**Figure 2.** (111) cleavage planes from the silicic bulk cell as it is looked from the [101] direction (top left), surface T sites nomenclature for the considered surface terminations (top right) and side and top views of the silicic surfaces (bottom). The different colors of the surface models of the top right corner correspond to the non-equivalent surface T sites.</figcaption></figure>

size of the slabs are given in Figure S1 of the SI. The narrowest slabs displayed already show satisfactory convergence. Thus, for the D6R complete, sodalite complete and sodalite incomplete surface slabs, we choose a number of SiO₂ species respectively equal to 108, 96 and 84.

Bulk cells and surface slabs with only one Al atom (high Si/Al ratio) are constructed by replacing one Si atom by an Al atom in the silicic cell, and adding one compensating proton on a first neighboring oxygen atom to the Al atom. Four possible proton positions exist per T site, shown in Figure 1, which are named in this article in agreement with the nomenclature adopted in the literature.[45–47] As displayed in Figure 1, the O1H and O4H protons lie in the supercage, the O2H proton is at the intersection between the sodalite cage and the supercage, and the O3H proton at the intersection between the D6R and the sodalite cage.

In cases of cells constructed with more than one Al atom, the rules derived by Dempsey et al.[5,48] (i.e. one by one substitution of Al by Si starting from a Si/Al = 1 cell conserving centrosymmetry and zero net dipole moment) were followed for defining the Al atoms locations in the bulk. The Dempsey rules were found as valid by

ab initio calculations on 12 MR clusters.[49] The constructed Si/Al = 3 cell is the same as the one identified by Klinowski et al.[50] as the most plausible one, despite the methodology employed by Dempsey et al. and Klinowski et al. being different. The Loewenstein rule is followed for all our cells,[51] i.e. next-nearest-neighbor Al substitution patterns are avoided. We also staid true to the experimental observations of Czjzek et al.[46] in terms of number of protons in O1H, O2H, O3H and O4H positions. For bulk cells having a Si/Al ratio of 3 (12 Al atoms per primitive cell), 6 protons are placed in O1H positions, 4 in O3H positions and 2 in O2H positions. Different arrangements of proton positions were tested, and the one giving the lowest energy for the desired distribution was chosen. For this low Si/Al ratio bulk cell, cell parameters are re-optimized with a 800 eV cutoff, and the obtained values are the following: a = 17.614 Å, b = 17.650 Å, c = 17.576 Å, α = 59.92°, β = 60.06°, γ = 59.79°. The surface slabs with a low Si/Al ratio (about 3) are constructed starting from the optimized bulk Si/Al = 3 cell. The low Si/Al ratio surface slabs also incorporate a vacuum layer of 25 Å.

In the bulk, all T sites of the FAU framework are equivalent. However, the presence of a surface breaks the symmetry, and the
equivalence between all T sites is lost. The surface sites can be classified based on their distance to the outermost surface layer. We choose to name T1 the sites located at the outermost surface layer, T2 the ones first neighbor to the outermost surface layer and T3 the ones second neighbor to the outermost surface layer. Figure 2 displays the surface T sites nomenclature.

Si–O– dangling bonds created during the construction of the surface are capped with H atoms, and OH groups are added to undercoordinated Si. Thus, surfaces are saturated with OH groups.

## Calculated Quantities

The alumination energy $Δ_U_{Al}$ which characterizes the stability of the aluminated sites, is calculated with the following equation:

$$Δ_U_{Al} = U_{Al}^{slab} + U_{Si(OH)_4} - U_{Si}^{slab} - U_{Al(OH)_3H_2O} \quad (1)$$

where $U_{Al}^{slab}$ is the calculated electronic energy of the aluminated slab (or bulk cell), $U_{Si}^{slab}$ is the calculated electronic energy of the silicic slab (or bulk cell) and $U_{Si(OH)_4}$ and $U_{Al(OH)_3H_2O}$ are the calculated electronic energies of the isolated Si(OH)$_4$ and Al(OH)$_3$(H$_2$O) species which ensure the stoichiometry conservation of our reaction. The choice of the reference is made to be able to compare with previous reports.[26,27]

To rank the thermodynamic stability of the surfaces, we calculate the temperature- and pressure-dependent surface free energies $γ_{surf}(T, P_{H_2O})$ following the theoretical derivation of Reuter et al.[52] The formula we use to calculate $γ_{surf}(T, P_{H_2O})$ for symmetric silicic surface slabs is the following:

$$γ_{surf}(T, P_{H_2O}) = 1/2A[G_{surf}(T, P_{H_2O}) - N_{H_2O}G_{H_2O}(T, P_{H_2O}) - N_{SiO_2}G_{Si}^{zeo-bulk}] \quad (2)$$

where A is the area of the considered surface, $G_{surf}$ is the Gibbs free energy of the surface, $G_{H_2O}$ is the Gibbs free energy of gaseous water, $G_{Si}^{zeo-bulk}$ is the Gibbs free energy of bulk zeolite, $N_{H_2O}$ is the number of water molecule adsorbed on the surface (including silanols) and $N_{SiO_2}$ is the number of SiO$_2$ units within the zeolite surface slab. The electronic and vibrational contributions to the Gibbs free energy of the surface slabs ($G_{surf}$) and the bulk cell ($G_{Si}^{zeo-bulk}$) are included. For the water terms ($G_{H_2O}$) of Eq. 2, electronic, vibrational, translational and rotational contributions are taken into account. We have employed an improved method[53] for the extraction of the bulk Gibbs free energy $G_{Si}^{zeo-bulk}$ to ensure good convergence of our surface free energies with the slab thickness. Eq. 2 can be adapted to calculate surface free energies of non-silicic (with one Al atom or more) surfaces.[26]

The acidity of bulk and surface sites is investigated by adsorbing pyridine, a well-known strong basic probe molecule. The strength of its adsorption quantifies the strength of the Lewis or Brønsted acidity of the sites. The adsorption energy of pyridine $Δ_{ads}U_{py}$ is computed as follows:

$$Δ_{ads}U_{py} = U_{ads-py}^{zeo} - U_{no-py}^{zeo} - U_{py}^{molecule} \quad (3)$$

where $U_{ads-py}^{zeo}$ and $U_{no-py}^{zeo}$, respectively are the electronic energy of the slab (or bulk cell) after and before pyridine adsorption and $U_{py}^{molecule}$ the electronic energy of a single pyridine molecule. The temperature- and pressure-dependent desorption temperature of pyridine $T_{des}^{py}$ is also computed from Eq. (3) and additional vibration calculations. Formulas for thermodynamic quantities calculations

can be found in Ref. [54]. The desorption temperature is defined as the temperature at which $ΔG = 0$ kJ/mol.

All frequencies obtained in our vibration calculations, even very low ones, are considered for the computation of thermodynamic quantities. However, in our calculations, due to the large size of our systems, from 0 to 4 low spurious imaginary frequencies (below $40 \text{ cm}^{-1}$) remain. To be able to compute vibrational thermodynamic quantities from those imaginary frequencies, we converted them to real frequencies. The choice of the method to deal with imaginary frequencies is somewhat arbitrary, and other choices could have been made. When relevant, the influence of the choice of the method will be discussed.

The dehydration properties are simulated and quantified in an equivalent manner as presented for pyridine.

## Results and Discussions

### Surface Terminations Stability

The different surface models mentioned in the Model construction section were constructed following the minimal cut hypothesis.[55] It states that the most stable surface models are those that are cleaved from a bulk structure for which a minimal number of bonds are cut.

In the case of the (111) surface of faujasite, it leads to three different terminations having an equal and minimum number of dangling Si–OH bonds at the surface (see Figure 2). The water coverage of the three terminations is $1.2 \text{ H}_2\text{O/nm}^2$. The minimal cut hypothesis is validated for faujasite by HR-TEM[41] and AFM[42,43] observations, which identified those three terminations as the dominant ones at the surface of faujasite crystals. Therefore, in this article, we only consider the following three terminations (see Figure 2):

* D6R complete termination: the sodalite cage bonds right above the D6R are cut, leaving a complete D6R exposed at the surface. For sake of conciseness, the termination is sometimes called D6R comp. in the following.

* Sodalite complete termination: the surface plane cuts the bonds in the middle of the D6R, leaving an exposed complete sodalite cages exposed. This termination is sometimes called soda complete or soda comp. in the following.

* Sodalite incomplete termination: sodalite cage bonds right below the D6R are cut, leaving an opened incomplete sodalite cage exposed at the surface. This termination is sometimes called soda incomplete or soda inc. in the following.

Important aspects of the structure of the surface terminations are the types and orientations of the silanols. As can be seen on Figure 2, for the three terminations, all silanols are terminal ones. For all the surface terminations, all the silanols are divided in pairs, one silanol being the H-bond donor, and the other the H-bond acceptor. All pairs are independent as no H-bond are formed between pairs.

While HR-TEM and AFM studies identified the D6R complete, sodalite complete and sodalite incomplete terminations as the only plausible ones, it is not clear which is the preferred one. The original HR-TEM study of Alfredsson et al.[41] identifies the
<figure><img src="image_19.png" /></figure>

D6R complete termination at the surface of the FAU inter-growth part of an EMT sample, and the sodalite incomplete termination at the surface of a FAU sample. Also, Wakihara et al.[43] clearly stated that the three terminations can coexist. To help clarifying those observations on the surface terminations, we calculated the surface energy $\gamma_{surf}$ for each of the terminations, using Eq. (2). The results are given in Table 1, for a partial pressure of water of 1 bar and a temperature of 400 K (corresponding to a typical zeolite synthesis temperature).[56,57] The electronic and vibrational contributions of the surface slabs, the bulk cell and the water molecules are taken into account. The translational and rotational contributions to the Gibbs free energy of the water molecules are also considered.

According to our calculations, even if the sodalite complete termination seems to be slightly thermodynamically favored, the differences between the calculated surface energies are so small that no surface model can be eliminated. It seems to corroborate the experimental observation that the three terminations can be found, without one being strongly favored compared to the others. In the next sections, the three terminations will thus be considered.

<table><caption>**Table 1.** Surface energies of the D6R complete, sodalite complete and sodalite incomplete terminations for a water pressure of 1 bar and a temperature of 400 K.</caption><thead><tr><th></th><th>D6R comp.</th><th>Soda comp.</th><th>Soda incomp.</th></tr></thead><tbody><tr><td>γ<sub>surf</sub> (mJ/m<sup>2</sup>)</td><td>120.6</td><td>115.9</td><td>124.2</td></tr></tbody></table>

Stability of the Aluminated Sites

The motivation behind the calculation of the alumination energy (with Eq. (1)), which is nothing else but a quantification of the stability of the aluminated sites, is to characterize the nature and structure of the acid sites in the bulk and at the surface. In the present section, all model slabs and cells integrate one Al atom only. Cells with Si/Al = 3 will be employed in the next sections.

Regarding the bulk, to gain a deeper understanding than the classical picture of bridging bulk Al–OH–Si Brønsted acid sites (BAS), we introduced a silanol nest in some bulk cells, and studied the influence of those silanol nests on the environment and stability of the bridging acid sites. Silanol nests correspond to defects arising during the synthesis or after dealumination/ desilication treatments. We considered Al³⁺ cations first or second neighbors with respect to the silanol nest. The presence of an Al³⁺ cation first neighbor to a silanol nest means Al–OH groups can be found in the bulk. Thus, Al–H₂O bulk sites can arise, following a proton transfer from a nearby bridging proton to the Al–OH group, or simply because the synthesis process led to the compensating proton being located on the Al–OH.

For the surface sites, we investigated the stability of the outermost sites (T1), but also the T2, T3 and pore-mouth sites (defined here as a site belonging to the bottom of the first complete supercage below the external surface). When considering the outermost surface site, as Al–OH species are present, Al–H₂O groups can be formed, as it was observed for ZSM-5[26] and zeolite Beta.[27]

Figure 3 depicts the alumination energy of all the investigated sites. They are classified based on the proton position

<figure><img src="image_20.png" /><figcaption>**Figure 3.** Alumination energy calculated for all the Al sites investigated, on cells with only one Al atom.</figcaption></figure>
<figure><img src="image_21.png" /></figure>

(O1H, O2H, O3H and O4H), their nature (bridging or Al–H₂O, surface or bulk), the distance of the Al atom to the outermost surface layers for surfaces (T1, T2, T3 or pore-mouth), and the presence of defects or not for bulk cells. In some cases, the lowest energy structures are depicted. The detailed data depicted in Figure 3 is available under the form of tables (Tables S1 to S7) in the SI.

The first striking feature of Figure 3 is the increased stability of bulk and surface Al–H₂O sites compared to bridging bulk and surface sites. For the surfaces, this observation has been made already in the cases of ZSM-5 and Beta.[26,27] However, the possibility to have Al–H₂O sites within the bulk had never been studied before. The enhanced stability of those sites compared to bridging ones reveals they are very likely to be found in real materials, and should therefore be taken into account in future studies on faujasite, and probably other zeolites. The TO1H, TO3H and TO4H Al–H₂O bulk sites are even more stable than the surface Al–H₂O sites, by 5 to 15 kJ/mol. This is due to the possibility for the two hydrogens of the Al–H₂O groups within the bulk to form hydrogen bonds with nearby silanols, whereas the investigated surface-terminated Al–H₂O groups can only form one hydrogen bond. Also, we report a dispersive energy contribution of the alumination energy ranging from –9 kJ/mol to –19 kJ/mol for bulk Al–H₂O systems, as compared to –5 kJ/mol, –3 kJ/mol and –10 kJ/mol for D6R complete, sodalite complete and sodalite incomplete terminations, respectively. The water molecules within the bulk thus benefit from a stabilizing confinement effect.

It can also be observed from Figure 3 that the stability ranking based on the proton position is unchanged for most of the bridging proton cases (surface and bulk). The O3H protons almost always lead to the most stable sites (15 cases out of 17), followed in the great majority of cases (12 cases out of 15) by O1H protons, themselves followed by O2H protons and finally O4H protons (10 cases out of 12). This observation corroborates the experimental work of Czjzek et al.[46] who identified in a Y faujasite sample the O1H and O3H protons as the most frequent ones, O2H as existing though rarer protons and O4H as completely absent. When the protons are not perturbed by nearby silanols, like it can be the case for protons neighbor to defects and outermost surface protons, the proton positions are the ones presented in Figure 1: the O1H and O4H protons lie in the supercage, the O2H proton is located inside the six membered ring (6MR) which connects the sodalite cage and the supercage and the O3H proton lies in the 6MR which belongs to a D6R, thus connecting a D6R and a sodalite cage. The unperturbed protons do not form any hydrogen bond with framework oxygens.

Regarding the bridging surface protons, it can be seen that there are no clear discrepancies on the alumination energies based on the nature of the surface termination (D6R complete, soda complete or soda incomplete). The surface bridging proton sites show important variations in the alumination energies compared to ideal bulk bridging sites, the lowest being of –54 kJ/mol and the highest of –7 kJ/mol for the T1 bridging sites, compared to –28 kJ/mol and –18 kJ/mol for ideal bulk bridging sites. It is interesting to note that the most

stable outermost surface sites are more stable than the bulk ideal ones, and that the less stable outermost surface sites are less stable than ideal bulk bridging ones. A plausible reason for this large variation in the alumination energies is probably the increased framework flexibility and the presence of silanols. Indeed, the enhanced framework flexibility makes it possible for some protons to form hydrogen bonds with framework oxygens, which stabilizes the structure. This is for example the case for the T1O3H protons of the D6R complete termination, i.e. the most stable one of the bridging T1 sites. This example is displayed in Figure 3. On the contrary, the presence of silanols can destabilize the structure compared to ideal bulk cases as it might happen that protons find themselves in a situation where they are subjected to steric and Coulomb repulsions. To support the above arguments, one can note that variations in the alumination energies similar to the ones of the surface T1 sites are observed in the bulk in the presence of silanol nests. The presence of silanols inside the bulk increases the framework flexibility locally, and leads to steric and electrostatic effects that are not present in a defect-free bulk situation. Still considering surfaces, it can be observed that the variations in the alumination energies decrease with the T2, T3 and pore-mouth sites. As the sites are further and further away from the outermost surface layer, the flexibility and surface-related steric effects caused by the presence of the surface decrease. The ideal bulk situation is even nearly reached for pore-mouth sites.

Focusing on the bulk bridging sites in the vicinity of defects, an important destabilization of the aluminated sites can be observed for some sites first neighbor with defects, but not for the ones second neighbor. This is due to the increased vicinity of silanols with protons first neighbor to defects, which leads to unfavorable steric and electrostatic effects. The most stable sites (–53 kJ/mol and –55 kJ/mol) are found to be the ones located in a second neighbor position to defects. We find that this position of aluminated sites as second neighbor to defects favors, compared to sites first neighbor to defects, the creation of hydrogen bonds between the proton and silanols, thus explaining the lower alumination energies. This situation is depicted in Figure 3.

A great diversity of FAU aluminum sites being covered, it is interesting to compare what we obtained with previous theoretical studies on MFI[26] and BEA.[27] The most stable surface Al–H₂O site was found to have an alumination energy of about –150 kJ/mol in MFI,[26] and about –80 kJ/mol[27] in BEA. In FAU we calculated it to be equal to –73 kJ/mol. This value is directly comparable to the one obtained in BEA, but twice smaller than the one of MFI. However, the very low value in MFI was obtained on a surface model not respecting the minimal cut hypothesis. Consequently, the number of dangling bonds and thus the density of surface silanols is very high on this specific model. It results that a dense network of H-bonds stabilizes the Al–H₂O species at the surface. Restricting the comparison to surface models respecting to the minimal cut hypothesis, the minimum values are of about –80 kJ/mol for MFI, directly comparable to FAU and BEA. Concerning the bridging protons, in the bulk the lowest values were found to be about –45 kJ/mol both for BEA and MFI. In FAU, we calculated it to be
<figure><img src="image_22.png" /></figure>

−28 kJ/mol. This discrepancy can be explained by the bigger pores of the FAU framework, which prevents the groups to benefit from the stronger confinement effects observed in BEA and MFI. At the surface of FAU, we found a minimum alumination energy for bridging groups of −54 kJ/mol, as compared to about −60 kJ/mol and −90 kJ/mol for BEA and MFI respectively. Similarly to the case of surface Al–H₂O groups,

restricting ourselves to MFI surface models built following the minimal cut hypothesis, the values are about −60 kJ/mol for MFI as well.

## Dehydration Properties of the Al–H₂O Sites

In MFI, it was observed that the dehydration of Al–H₂O surface groups can conduct either to the formation of Alill species or Aliv, in the latter case by rearrangement of the structure and bonding of Alill with a framework oxygen to form Aliv.[26]

For the studied surface terminations of faujasite having a high Si/Al ratio, only Alill species were found. While, on surface slabs having a low Si/Al ratio of 3, the desorption of a water molecule can either lead to Alill or Aliv depending on the local structure around the Al atom. Figure 4 displays examples of Alill and Aliv surface sites.

In the previous section, it was shown that the presence of silanol nests in the bulk of faujasite conducts to the formation of bulk Al–H₂O groups of very high stability. Water desorption on those bulk Al–H₂O groups lead, regardless of the Si/Al ratio, to the formation of Alill species. The thereby formed Alill bulk sites make part of a network of three silanols arranged in the same plane and forming a triangle where all the OH groups are both donor and acceptor. The Alill sits opposite to this silanol nest.

Table 2 shows the calculated (with Eq. (3)) desorption energy of H₂O (ΔdesUH₂O = −ΔadsUH₂O), as well as the corresponding desorption temperature (Tdes) for a water pressure of 10⁻⁴ bar, for bulk (surface) Si/Al = 3 and Si/Al = 47 (Si/Al = 300) cells (slabs).

The calculated desorption temperatures for the surfaces range from 390 K (soda incomp. with low Si/Al) to 692 K (soda comp. with low Si/Al). The Si/Al ratio plays an important role as it favors the formation of Aliv. According to our calculations, the formation of such species is associated with an easier desorption. Indeed, in Table 2 it can be seen that for the D6R complete and soda incomplete terminations, for which the low

<figure><img src="image_23.png" /><figcaption>**Figure 4.** Low Si/Al D6R complete, sodalite complete and sodalite incomplete surfaces before and after dehydration. The distance between the Al atom at stake and the closest oxygen atom candidate for the creation of an extra 4th bond after dehydration is indicated for each case.</figcaption></figure>

<table><caption>**Table 2.** Desorption energy (ΔdesUH₂O), desorption temperature (Tdes) for a water pressure of 10⁻⁴ bar, and nature (Alill or Aliv) of the dehydrated sites investigated.</caption><thead><tr><th></th><th></th><th>ΔdesUH₂O (kJ/mol)</th><th>Tdes (K)</th><th>Nature</th></tr></thead><tbody><tr><td rowspan="2">D6R complete</td><td>High Si/Al</td><td>152</td><td>535</td><td>Alill</td></tr><tr><td>Low Si/Al</td><td>126</td><td>485</td><td>Aliv</td></tr><tr><td rowspan="2">Soda comp.</td><td>High Si/Al</td><td>159</td><td>667</td><td>Alill</td></tr><tr><td>Low Si/Al</td><td>183</td><td>692</td><td>Alill</td></tr><tr><td rowspan="2">Soda incomp.</td><td>High Si/Al</td><td>150</td><td>579</td><td>Alill</td></tr><tr><td>Low Si/Al</td><td>104</td><td>390</td><td>Aliv</td></tr><tr><td rowspan="4">Bulk</td><td>O1H</td><td>High Si/Al</td><td>155</td><td>655</td><td>Alill</td></tr><tr><td>O2H</td><td>High Si/Al</td><td>166</td><td>641</td><td>Alill</td></tr><tr><td>O3H</td><td>High Si/Al</td><td>165</td><td>581</td><td>Alill</td></tr><tr><td>O4H</td><td>High Si/Al</td><td>187</td><td>723</td><td>Alill</td></tr><tr><td></td><td>Low Si/Al</td><td>221</td><td>861</td><td>Alill</td></tr></tbody></table>
<figure><img src="image_24.png" /></figure>

Si/Al case leads to the formation of an Al<sub>IV</sub> site, T<sub>des</sub> is lower than for the Al<sub>III</sub> high Si/Al case (485 K vs 535 K for the D6R complete case and 390 K vs 579 K for the soda incomplete case). This is because the creation of an extra Al–O bond to form an Al<sub>IV</sub> species stabilizes the dehydrated states, which thus becomes easier to form. The formation of stabler Al<sub>IV</sub> dehydrated states in cells with low Si/Al is certainly allowed by the combined effects of an enhanced flexibility of the network as well as an increase of the ionicity of the framework oxygens, both caused by the increase of the number of Al atoms. However, this observation does not hold for the soda complete termination for which at low Si/Al, the Al<sub>III</sub> structure is conserved at dehydration, and for which the desorption temperature is even slightly higher than for the high Si/Al case. For this specific case, the local structure in the vicinity of the considered site certainly did not allow for a sufficient increase of the network flexibility to form an Al<sub>IV</sub> site and to reach a significantly stabler dehydrated state. Actually, it can be noticed that, before water desorption, the distances between the Al atom and nearby framework O atoms which could be at stake for the creation of an Al–O bond following water desorption (reported in Figure 4) are always greater in the cases for which desorption led to Al<sub>III</sub> compared to the ones for which it led to Al<sub>IV</sub>. This is surely not the only argument, but the initial distance seems to play an important role.

For the sake of comparison, in MFI, the desorption temper-
atures calculated at the surface ranged from 492 K to 691 K.[26]
Our calculated desorption temperatures for faujasite are overall
of the same order of magnitude, except for the specific case of
the sodalite incomplete low Si/Al surface for which we find a
low value of 390 K. Nonetheless, the point we made in the
previous paragraph regarding the lower desorption temper-
ature associated to Al<sub>IV</sub> sites is not always true for MFI. The
differences in the local structure of the two zeolites probably
explain this discrepancy. Indeed, in the case of MFI, differences
in silanol coverage from one surface to another was also found
to influence the desorption temperature, the higher the cover-
age, the stronger the hydrogen-bond network, the higher the
water desorption temperature.[26] For the present faujasite (111)
surfaces, the coverage is constant from one cleavage to
another, so this parameter is not influential.

Also, it is interesting to note that in agreement with a
previous theoretical study on MFI,[58] we were able to force the
relaxation of the Si/Al = 47 dehydrated states (it was not tested
on other cells) to structures displaying double membered rings
(2MR) at the surface: the oxygen of a nearby silanol connects to
the dehydrated AlIII, forming an AlIV and a 2MR. The situation is
depicted in the article of Treps et al.[58] The stability of those
2MR surface sites is similar to the one of the classical AlIII surface
sites. They are not considered further for the investigation of
the acidity of the sites as the 2MR structure tends to break
whenever pyridine is adsorbed on the Al (see the Lewis acidity
section).

Considering the bulk Al–H₂O sites, for the high Si/Al cases,
the desorption temperatures obtained range from 581 K to
723 K. They are therefore of the same order as the high Si/Al
surface desorption temperatures (535 K to 667 K). However, the
effect of the Si/Al ratio is more drastic in the bulk. If, for the two

examples investigated, it does not lead to the formation of Al<sub>IV</sub> species, the desorption temperatures are dramatically increased at low Si/Al. For a bulk site with a H<sub>2</sub>O proton in O2H position, the desorption temperature increases from 641 K to 910 K when moving from high to low Si/Al ratio. For the O4H case, it becomes 861 K (instead of 723 K initially). There are certainly multiple explanations for this observation. An enhanced confinement effect with the increased number of Al and protons might complicate the desorption of water and conduct to higher desorption temperatures. The nature of the hydrogen bonding of the water molecules in low Si/Al cells might also be of some significance: in cells with only one Al atom (high Si/Al ratio), the H<sub>2</sub>O molecule sitting on the Al is a hydrogen bond donor to nearby silanols, whereas when more Al atoms are present (low Si/Al ratio), the H<sub>2</sub>O molecule forms hydrogen bonds with silanols but also with Al–OH species, which strength certainly is different.

Focusing now on the absolute values of the desorption
temperatures, it appears that at the surface, reasonable temper-
ature encountered during industrial processes (typically
> 500 K) can lead to water desorption and formation of Al<sub>III</sub>
species. In the bulk, with a high Si/Al ratio, the calculated
desorption temperatures are also reasonable enough to state
that bulk Al<sub>III</sub> sites can form for T > 600 K. For low Si/Al ratios,
the desorption temperatures are greater.

In conclusion, while water desorption can occur for both
high and low Si/Al ratios at the surface, desorption at bulk sides
is only feasible for high Si/Al ratios. Such ratios can still be
encountered, since depending on the synthesis route and post-
treatment, Al can get unevenly distributed[59] creating local
pockets with a high Si/Al ratio, for which the formation of Al<sub>III</sub> is
easier.

Probing the Acidity of the Sites

A vast diversity of structures has been investigated; bulk with
and without defects, three different surface terminations,
various Si/Al ratios. Resulting from this diversity, a large number
of acid sites with different local topologies and chemistries has
been modeled. The purpose of this section is to measure the
Brønsted and/or Lewis acidity of those sites. To achieve this, we
quantify both the adsorption energy Δ<sub>ads</sub>U<sub>py</sub> and the desorption
temperature T<sub>des</sub> of pyridine, a well-known probe molecule,<sup>[60]</sup>
on Brønsted and Lewis acid sites.

On a strong BAS, pyridine is adsorbed on the proton and
leads to the creation of a pyridinium ion, whereas on a LAS
pyridine is adsorbed directly on the Al atom with the formation
of a Al–N bond. Weak BAS on which pyridine adsorption did
not lead to proton transfers and creation of a pyridinium ion
were also simulated, but are not presented here. All of those
sites were silanols.

It has been experimentally demonstrated many times[61–64]
that the Infrared (IR) proton signals in faujasite can be divided
in three main categories: surface silanols, High Frequency (HF)
protons located in the supercage and Low Frequency (LF)
located in the sodalite cage. By using ammonia as a probe
molecule instead of pyridine,[47,65] or in rare cases with pyridine,[63] it is even possible to distinguish between the two proton positions of the LF band (O2H and O3H). Computations on the subject, including ours presented in Table 3, also display this splitting in three main categories.[66]

It is observed by IR spectroscopy that upon pyridine adsorption, in samples with a high Si/Al, both HF and LF bands disappear, or at least lose intensity, whereas in samples with a low Si/Al, only the HF band intensity decreases.[62,63] However, it is important to note that pyridine is a relatively bulky molecule, and is thus unable to enter the sodalite cage. Therefore, the BAS located inside the sodalite cage in principle cannot be attained by pyridine. This raises the question of the disappearance of the LF IR band at high Si/Al, which originates from O2H and O3H protons. There are two main interpretations presented in the literature. The most natural one is the hypothesis of the proton jumping from the sodalite cage to the supercage, and thus becoming accessible to pyridine.[62]

The second one invokes LAS adsorption of pyridine on Al atoms in anti position to the protons, thus perturbing indirectly the absorption band of the bridging OH[63] (see Figure 5). The first hypothesis has already been investigated and quantified through different mechanisms, taking advantage of existing silanol nests defects in the structure[67] or not.[68] It was proven that proton jumps are plausible mechanisms in FAU, even if more activated without the contribution of silanols:[68] the energy barrier for a proton jump from the O3 to the O2 position is 67.0 kJ/mol, and 108.0 kJ/mol from O3 to O4. In this section will be quantified the LAS pyridine adsorption energy for the “anti position” mechanism, thus enriching the discussion regarding the mechanisms leading to sodalite proton and pyridine interactions.

It is important to note that most of the IR spectroscopy studies dealing with pyridine in faujasite consider that pyridine

cannot adsorb on the O2H proton, because it is a “sodalite cage” proton. However, the O2H proton is located in the 6MR at the frontier between the sodalite cage and the supercage (see Figure 1). Therefore, we see no steric-related reason which would justify not to try to adsorb pyridine on the O2H proton. On the contrary, despite being supercage protons, the O4H protons are not probed. Indeed, according to the work of Czjzek et al.[46] and our alumination energy results (see Stability of the aluminated sites) the presence of O4H protons in faujasite samples is very unlikely. We therefore consider the O2H proton as a possible candidate for pyridine adsorption in the following, but not the O4H one.

Figure 6 gives a schematic representation of the investigated acid sites, as well as of the Brønsted and Lewis pyridine adsorption mechanisms which are presented in the following.

<table><caption>**Table 3.** Vibration frequencies of bulk faujasite OH groups. Our harmonic frequency calculations are performed on a model with Si/Al=47. The experimental data was obtained on a defect-free HY sample with Si/Al=2.7. There is no experimental data for the T1O4H protons because no protons were found in O4H position in the employed sample.</caption><thead><tr><th rowspan="2">Proton position</th><th colspan="2">Frequency (cm<sup>-1</sup>)</th></tr><tr><th>This work</th><th>Expt.[47]</th></tr></thead><tbody><tr><td>T1O1H (HF)</td><td>3717</td><td>3637</td></tr><tr><td>T1O2H (LF)</td><td>3604</td><td>3550</td></tr><tr><td>T1O3H (LF)</td><td>3622</td><td>3501</td></tr><tr><td>T1O4H (HF)</td><td>3692</td><td></td></tr><tr><td>Surface silanols</td><td>3720-3800</td><td></td></tr></tbody></table>

<figure><img src="image_25.png" /><figcaption>**Figure 5.** Pyridine adsorption on Al in anti position to the bridging proton.</figcaption></figure>

<figure><img src="image_26.png" /><figcaption>**Figure 6.** Schematic views of the Al sites investigated, as well as their Brønsted and Lewis expression regarding pyridine adsorption.</figcaption></figure>
<figure><img src="image_27.png" /></figure>

Figure 7 and Figure 8 display the adsorption energies $\Delta_{ads}U_{py}$ divided into their dispersive (D2 component of the adsorption energy) and non-dispersive parts, and the desorption temperatures $T_{des}$ of pyridine (for $P_{py}=10^{-4}$ bar) on various bulk and surface BAS (Figure 7) and LAS (Figure 8) of faujasite. In the same figures are also displayed the structures of pyridine adsorbed on some characteristic acid sites. The data used to construct Figure 7 and Figure 8 is detailed in Table S8 and Table S9 of the SI. Brønsted acidity focuses on BAS adsorption of pyridine, while Lewis acidity deals with LAS adsorption. In the figures of the following sections, for sake of conciseness,

when nothing is specified regarding the Si/Al ratio of a cell or surface slab, it has a high Si/Al (47 for bulk, 46 for bulk without defects and about 300 for surface slabs). However, when the cell or slab is said to be of the Y type, it means it has a low Si/Al ratio of about 3.

<figure><img src="image_28.png" /><figcaption>**Figure 7.** Adsorption energies $-\Delta_{ads}U_{py}$ and desorption temperatures $T_{des}$ (for $P_{py}=10^{-4}$ bar) of pyridine on BAS of the bulk and of the surface of faujasite. $-\Delta_{ads}U_{py}$ is divided into its non-dispersive and its dispersive contributions. Atomic structures for some adsorption sites are also depicted. The Y specification designates cells with a low Si/Al of about 3.</figcaption></figure>

<figure><img src="image_29.png" /><figcaption>**Figure 8.** Adsorption energies $-\Delta_{ads}U_{py}$ and desorption temperatures $T_{des}$ (for $P_{py}=10^{-4}$ bar) of pyridine on LAS of the bulk and of the surface of faujasite. $-\Delta_{ads}U_{py}$ is divided into its non-dispersive and its dispersive contributions. Atomic structures for some adsorption sites are also depicted. The Y specification designates cells with a low Si/Al of about 3.</figcaption></figure>
<figure><img src="image_30.png" /></figure>

## Brønsted Acidity

### Ideal Bulk Bridging Groups

In bulk Si/Al=47 cells, pyridine is strongly adsorbed both on the Brønsted O1H ($-\Delta_{ads}U_{py}=200$ kJ/mol) and O2H sites ($-\Delta_{ads}U_{py}=173$ kJ/mol). The value we report for the O1H site is equal to the one calculated for faujasite by Liu et al.[69] on a similar cell, and is quite close to the bulk site sampled in MFI by Treps et al.[26] for which $-\Delta_{ads}U_{py}=213$ kJ/mol was obtained. Our results clearly indicate that pyridine can strongly adsorb (and form pyridinium ion) on the O2H proton, contrary to the belief commonly spread in the literature. However, it is true that $-\Delta_{ads}U_{py}$ is lower on the O2H than on the O1H site, meaning that whenever possible, pyridine would tend to adsorb first on the O1H proton.

According to the bulk Y (low Si/Al) case, the strength of the BAS in terms of adsorption energies is not perturbed by the Si/Al ratio. Indeed, we report the very close values of $-\Delta_{ads}U_{py} = 182$ kJ/mol for the Y case and $-\Delta_{ads}U_{py} = 200$ kJ/mol for the high Si/Al case. The slightly lower value for the low Si/Al case could be explained by the presence of protons in the vicinity of the pyridinium ion, responsible for steric and electrostatic repulsion. However, surprisingly, when looking at the $T_{des}$ we calculated, there is a significant discrepancy between the high Si/Al and low Si/Al case. For the high Si/Al case, $T_{des}=775$ K, whereas for the low Si/Al case, $T_{des}=616$ K. The origin of this discrepancy is actually to be looked at in the vibrational entropy term of the Gibbs free energy. Indeed, we find that the vibrational entropy difference between the adsorbed and desorbed states is significantly greater in the high Si/Al case than in the low Si/Al one, thus explaining the discrepancies in the calculated $\Delta G$ and thus in $T_{des}$. Data related to the entropy of the just discussed systems are displayed in Figure S2 of the SI, together with a more detailed description of the reasoning. Nonetheless, the $T_{des}$ are high in both cases, and bridging O1H sites can be considered strong BAS in low Si/Al and in high Si/Al materials. However, please note that with low Si/Al cells, the variety of local environments is nearly infinite. Thus, the reported values are calculated on individual cases, and do not account for the wide variety of possible cases. Still, other local environments for pyridine adsorption have been tested, and all gave results similar to the reported values.

Low vibration frequencies having a significant impact on the entropy, we tried another method (the default method is to convert imaginary frequencies to real ones) to deal with low frequencies on the bulk bridging O1H high and low Si/Al cases: all imaginary frequencies are converted to real frequencies of $50 \text{ cm}^{-1}$, and real frequencies below $50 \text{ cm}^{-1}$ are set to $50 \text{ cm}^{-1}$. The purpose of this method is to get rid of the influence of the low frequencies. It has been used in the literature before,[13,70] and proved to be globally unaffected by the choice of the cutoff value. We did not see any noticeable difference on the calculated $T_{des}$, and on the $\Delta S$ curves. $T_{des}$ obtained with this method are presented in Table S10 the SI.

## Bulk with Defects

We focus in this paragraph on pyridine adsorption in, never considered before, bulk cells with silanol nests. The adsorption of pyridine on Al–O1H–Si BAS in the vicinity of silanol nests, in cells with high and low Si/Al, leads to $-\Delta_{ads}U_{py}$ of –197 kJ/mol and –191 kJ/mol respectively. Those values are very close to the defectless cells, both with high and low Si/Al ratio. The $T_{des}$ are also in the range of what is obtained for defectless cells. In defectless bulk cells we found $T_{des}$ of 775 K for the high Si/Al case, 616 K for the low Si/Al case, to be compared to the $T_{des}$ of 685 K and 789 K obtained for the high Si/Al and low Si/Al defective cells, respectively. Overall, the presence of defects does not seem to modify drastically the acidity of the bulk O1H BAS. However, once again we observe a discrepancy in the $T_{des}$ between the bulk with defects high Si/Al and low Si/Al cases, whereas the adsorption energies are very similar. Just like for the bulk cells without defects, the origin of this discrepancy is to be found in the vibrational entropy contributions to $\Delta G$. With defects, however, the situation is reversed compared to the bulk cells without defects, as the higher $T_{des}$ is found for the low Si/Al case. The vibrational entropy variations for the bulk with defects Al–O1H–Si bridging high and low Si/Al cases are displayed in Figure S3 of the SI.

In the case of bulk bridging sites in the vicinity of defects, we also compared the data presented in Figure 7 with data obtained with the $50 \text{ cm}^{-1}$ cutoff method. This time, discrepancies significant enough to be reported are noticed. The high Si/Al $T_{des}$ increases, whereas the low Si/Al $T_{des}$ decreases. In the end, both $T_{des}$ are very close. The effect of the entropy is thus negligible. It reveals the choice of the method to deal with low frequencies can have an influence on the results. However, the conclusion we draw from the results still are the same, i.e. $T_{des}$ values are nearly as high as in the absence of defects, and testify of strong BAS. Quantitative data regarding those aspects are reported in Table S10 in the SI.

The presence of Al–H₂O sites within the bulk in defective cells allows to study pyridine adsorption on one of the protons BAS of the water molecule. The calculated $-\Delta_{ads}U_{py}$ for pyridine adsorption on Brønsted Al–H₂O sites in the bulk is equal to 154 kJ/mol. The dispersive energy part is of 45 kJ/mol. It seems that bulk Al–H₂O sites, despite not being as strong as bulk bridging sites, can act as strong BAS.

## Surfaces

The analysis of pyridine adsorption results of the three surface terminations reveals that strong BAS can also be found at the surface. Indeed, the adsorption of pyridine on high Si/Al surface bridging Al–O1H–Si groups displays $-\Delta_{ads}U_{py}$ of 171 kJ/mol, 169 kJ/mol and 160 kJ/mol for the D6R complete, soda complete and soda incomplete terminations, respectively. The reported values are lower but still comparable to the O1H bulk one, following the same global trend as what was obtained for MFI.[26] The dispersion energy part for bridging O1H in the bulk at high Si/Al is greater than for the D6R complete and soda
<figure><img src="image_31.png" /></figure>

complete terminations, indicating a partial loss of confinement effect at the external surface. However, in the case of the sodalite incomplete termination, the dispersion energy part is significant, and even greater than in the bulk (50 kJ/mol vs 44 kJ/mol). This increase can be explained by the accessibility of the sodalite cage to pyridine in the case of the sodalite incomplete termination. Indeed, the sodalite cage is opened. Therefore, pyridine can benefit from a very important stabilizing confinement effect, similar to what is depicted for the soda incomplete Al–H₂O case of Figure 7.

To assess the significance of the Si/Al ratio on the acidic character of the Brønsted surface sites, we simulated the adsorption of pyridine on D6R complete, sodalite complete and sodalite incomplete slabs with Si/Al ≈ 3 (low Si/Al). For adsorption on a BAS Al–O1H–Si, we report the following values for –Δ<sub>ads</sub>U<sub>py</sub>: 172 kJ/mol, 157 kJ/mol and 155 kJ/mol, respectively for the D6R complete, soda complete and soda incomplete terminations. And for T<sub>des</sub>: 673 K, 675 K and 590 K. The –Δ<sub>ads</sub>U<sub>py</sub> are very similar to the surfaces high Si/Al cases for which we have 171 kJ/mol, 169 kJ/mol and 160 kJ/mol respectively. However, the calculated T<sub>des</sub> are greater with a low Si/Al (especially for the sodalite complete termination), as we have for the high Si/Al cases 602 K, 531 K and 502 K. Just like for the previous cases for which such a discrepancy was observed between the –Δ<sub>ads</sub>U<sub>py</sub> values and the T<sub>des</sub> values, the explanation lies in the vibrational entropy contributions of the ΔG quantities. The variations of the vibrational entropy ΔS for the sodalite complete cases are displayed in Figure S4 of the SI.

By comparing the bridging sodalite complete data of Figure 7 with T<sub>des</sub> calculated with the 50 cm<sup>-1</sup> cutoff method, we observe once again that the chosen method can have a significant influence. The discrepancy between low and high Si/ Al T<sub>des</sub> is reducing (discrepancy of about 140 K with the default method compared to about 60 K with the 50 cm<sup>-1</sup> cutoff method). This is not surprising considering that the 50 cm<sup>-1</sup> method somehow cancels the influence of the low frequencies. Nonetheless, the conclusions remain unchanged: strong BAS can be found at the surface. Quantitative data related to those aspects are presented in Table S10 in the SI.

Overall, just like in the bulk, the effect of the Si/Al ratio has a small effect on the adsorption energies, and an important effect on the desorption temperatures. However, qualitatively, the strength ranking of the BAS is not altered by the Si/Al ratio. Once again, please note that with cells and slabs of low Si/Al ratio, i.e. lots of Al atoms, there is a huge variety of environments for the acid sites. Consequently, not all sites can be tested and what we report in Figure 7 can only be a part of the complete picture.

On the three considered surface terminations, we also simulated pyridine adsorption on Brønsted Al–H₂O sites, which are the most stable surface sites according to our stability investigation of the Stability of the aluminated sites section. Pyridine adsorption on BAS Al–H₂O sites of the D6R complete and soda complete terminations is quite weak compared to adsorption on bridging protons. Indeed, we report –Δ<sub>ads</sub>U<sub>py</sub> values of 107 kJ/mol and 115 kJ/mol, and T<sub>des</sub> of 397 K and 420 K respectively. Interestingly, pyridine strongly adsorbs on

the Al–H₂O BAS of the sodalite incomplete termination: –Δ<sub>ads</sub>U<sub>py</sub> = 159 kJ/mol and T<sub>des</sub> = 549 K. The very high dispersive energy part (82 kJ/mol) of the specific case of the sodalite incomplete termination reveals pyridine is greatly stabilized by confinement effects due to its interactions with nearby atoms of the sodalite cage (opened and thus accessible in the case of the sodalite incomplete termination). This situation is depicted in Figure 7.

## Lewis Acidity

### Ideal Bulk Bridging Groups

Results regarding pyridine adsorption on LAS are reported in Figure 8. For the case of bulk Si/Al = 47 cells, the calculated energy for adsorption in anti (see Figure 5) on the Al connected to the O2H proton is really low compared to the BAS adsorption directly on the O2H proton (–76 kJ/mol vs –173 kJ/mol) indicating that the adsorption of pyridine on the Al is very unlikely. Moreover, the T<sub>des</sub> of 298 K reported shows that in experimental conditions, the pyridine would certainly desorb from this site. In addition, we tried to adsorb simultaneously two pyridine molecules on the Al–O2H–Si site, one on the BAS O2H, and the other one on the Al LAS. We have observed that the simultaneous adsorption is not possible, and that the LAS pyridine desorbed, leaving in place the pyridine adsorbed on the BAS. Consequently, it is very improbable that pyridine adsorption on the bulk Al–(O2H–Si) LAS can occur in experiments. The simulation of pyridine adsorption on the Al–(O3H–Si) site gives –Δ<sub>ads</sub>U<sub>py</sub> = 116 kJ/mol and T<sub>des</sub> = 444 K. Those values are significantly greater than for the LAS Al–(O2H–Si), but drastically lower than what is reported for average BAS bulk sites (about 200 kJ/mol). For comparison, –Δ<sub>ads</sub>U<sub>py</sub> = 141 kJ/mol for LAS adsorption in the bulk of MFI.[26] This value is greater than the one we have calculated in FAU, but shows about the same discrepancy with bulk BAS adsorption than what we found for faujasite. Our results on FAU, and previous results obtained on MFI[26] indicate that the mechanism proposed by Phung et al.[63] of pyridine adsorption on LAS in anti position to the proton is energetically not favored compared to adsorption on BAS. On the Al–O2H–Si species, we showed the LAS adsorption is very unlikely to occur, as the site favors its BAS character. However, the O3H proton being located at the intersection between the D6R and the sodalite cage (see Figure 1), it cannot be attained by pyridine, and BAS adsorption is not possible. Consequently, LAS adsorption of pyridine on the Al connected to the O3H proton becomes plausible, as there is no other competitive adsorption mechanism.

When decreasing the Si/Al ratio, the desorption energy –Δ<sub>ads</sub>U<sub>py</sub> on the LAS Al–O3H–Si site remains nearly unchanged (114 kJ/mol). The T<sub>des</sub> is slightly decreased, going from 444 K in the high Si/Al case to 393 K for the low Si/Al case. Overall, the Si/Al ratio does not seem to play a major role, even though it is impossible to be exhaustive on the local adsorption sites environments with cells with low Si/Al.
<figure><img src="image_32.png" /></figure>

Bulk with Defects

It was demonstrated in the Dehydration properties of the Al–H2O sites section that bulk Al–H2O species present in the vicinity of silanol nests can dehydrate to form Alill species at temperatures highly dependent on the Si/Al ratio. For bulk high Si/Al cells with defects, those temperatures are somewhat reasonable and can be attained in industrial processes. It is thus worth studying the Lewis acidity of those sites. The strength of pyridine bonding on those bulk high Si/Al sites is significant, as attests the very high $-\Delta_{ads}U_{py}$ and $T_{des}$: 206 kJ/mol and 804 K respectively. It is an important observation which could prove the existence of a strong bulk Lewis acidity in materials undergoing harsh thermal treatments, coming from the framework itself and not only from Extra Framework Aluminum (EFAL) as it is usually considered. To our knowledge, this has never been reported before, and could probably shed light on existing and yet to come experimental results.

For defective cells with a low Si/Al, the calculated water desorption temperatures in the Dehydration properties of the Al–H2O sites section are significantly higher. It is thus unlikely that Alill would appear, but for the sake of comparison we simulated the adsorption of pyridine on those sites as well. Similarly to the high Si/Al case, pyridine bonds strongly to those sites, i. e. $-\Delta_{ads}U_{py}$ = 228 kJ/mol and $T_{des}$ = 799 K. If they were to exist in real materials, those sites would also act as strong framework LAS.

Surfaces

Contrary to the bulk situation for which it was impossible to adsorb a pyridine molecule on an Al–(O1H–Si) LAS in anti (the pyridine would be inside the sodalite cage, which is impossible), the specific geometry of the D6R complete and sodalite incomplete surface terminations made it possible. We report $-\Delta_{ads}U_{py}$ values of 100 kJ/mol and 121 kJ/mol for the adsorption of pyridine on D6R complete and sodalite incomplete high Si/Al Al–(O1H–Si) LAS. The difference between those two values can be explained by the important dispersive contribution to the energy for the sodalite incomplete surface. The pyridine is able to access the interior of the sodalite cage in this specific termination, and is thus stabilized by confinement effects. Those values are lower than the ones obtained for adsorption on BAS. Knowing that two pyridine molecules cannot be adsorbed on the same Al–OH–Si site, one on the BAS and the other on the LAS, the site can thus only express its Brønsted character.

The water desorption temperatures discussed in the Dehydration properties of the Al–H2O sites section for the surface high Si/Al slabs revealed that Alill sites can be formed at temperatures reachable in experiments and industrial processes. As expected, those sites act as strong LAS, on the three studied surface terminations studied. The $-\Delta_{ads}U_{py}$ and $T_{des}$ are similar between those Alill surface sites, Alill bulk sites and strong bulk and surface BAS (about 200 kJ/mol). The desorption energy values we have obtained for high Si/Al surfaces range from

187 kJ/mol to 196 kJ/mol depending on the terminations. For MFI, Treps et al.[26] found desorption energies ranging from 194 kJ/mol to 256 kJ/mol. These are higher values, but of the same order of magnitude as what we have for FAU, and thus in agreement with the global trend that surface Alill sites act as strong LAS.

On the low Si/Al surface models constructed, the data of the Dehydration properties of the Al–H2O sites section showed that Alill and Aliv sites could form quite easily following thermal treatment. The adsorption of pyridine on the Aliv sites led to the breaking of the 4th Al–O bond induced by water desorption (see Figure 4). Thus all sites can be considered Alill regarding pyridine adsorption. For the D6R complete, soda complete and soda incomplete surfaces with low Si/Al, we report the following values for $-\Delta_{ads}U_{py}$ and $T_{des}$ for pyridine adsorption on LAS: 196 kJ/mol and 738 K, 213 kJ/mol and 788 K, 179 kJ/mol and 643 K, respectively. Those values show that those sites act as strong LAS, and are similar to the ones obtained with slabs with high Si/Al. It can still be noted that a small but noticeable discrepancy in $T_{des}$ between the D6R complete high and low Si/Al cases exist, even if the adsorption energies are nearly equal. Just like for the BAS for which this behavior was observed, the vibrational entropy is responsible for it. The application of the 50 cm⁻¹ cutoff method on those D6R complete systems only marginally modified the calculated $T_{des}$ compared to data obtained with our default method (imaginary frequencies conversion into real ones). Entropy variations (with the default imaginary frequencies conversion method) upon pyridine adsorption for those systems are plotted in Figure S5 of the SI. Data comparing the methods employed to deal with imaginary and low frequencies are also presented in Table S10 in the SI. Overall, the Si/Al ratio effect does not seem to be significant either regarding pyridine adsorption on LAS. Our pyridine adsorption simulations on Alill surface sites confirms the conclusion drawn from pyridine adsorption on bulk Alill sites i.e. EFAL are not always necessary to explain the strong Lewis acidity observed in faujasite.

Our results regarding the Lewis acidity of framework Alill sites corroborate the recent findings of Yakimov et al.[71] The authors showed by a combination of ¹H, ¹⁵N, ²⁷Al MAS NMR and DFT modelling in mordenite, that Lewis acidity in fully dehydrated and EFAL-free MOR samples can originate from framework-associated Alill sites, i.e. (Si-O)₃Al interacting with an adjacent siloxane bridge. Those pseudo-Alill observed after dehydration originate from Alvi sites of the fully hydrated material.[72] In our case, the situation is not exactly the same as we did not study the influence of the hydration of the Al sites on the Lewis acidity, and only considered truly tricoordinated sites. However, Yakimov et al.[71] also admit that the presence of truly tricoordinated (Alill) would hardly be detected by MAS NMR due to the large Cq (nuclear quadrupolar coupling constant) of those species. Overall, our results on FAU and the ones of Ravi et al.[72] and Yakimov et al.[71] on MOR point towards the existence of strong framework LAS, originating from framework Alill species.
<figure><img src="image_33.png" /></figure>

## BAS and LAS Signatures in the Vibration Frequencies of Pyridine

In IR experiments, Bronsted and Lewis acidity can be distinguished by analyzing the shift in the 19b vibration mode of pyridine.[73] It has been observed experimentally, and reproduced by theoretical calculations in 3- and 12-ring clusters and in H-SSZ-13, that the 19b vibration is blue-shifted by 5–20 cm⁻¹ for adsorption at a LAS and 90–110 cm⁻¹ at a BAS (114–125 cm⁻¹ in calculations).[74,75] According to our calculations, pyridine in the gas phase was found to have a 19b mode of 1423 cm⁻¹, thus in perfect agreement with previous theoretical calculations.[74,75] In a Si/Al = 47 bulk cell incorporating a O1H site, the 19b mode of a pyridinium ion (pyridine adsorbed on a TO1H BAS) is shifted to 1540 cm⁻¹. At a bridging O1H surface (D6R complete) site, it is shifted to 1543 cm⁻¹. The surface does not seem to have a significant effect on the vibration frequency. When pyridine is adsorbed on a Alᵢᵣ⁻O3H LAS in a Si/Al = 47 bulk cell, the 19b mode of pyridine is shifted to 1439 cm⁻¹. On a LAS bulk dehydrated Alᵢᵣ site, the 19b mode of pyridine is shifted to 1443 cm⁻¹. It is thus impossible to differentiate the type of LAS from the 19b vibration frequencies. At the D6R complete surface, pyridine adsorbed on a dehydrated Alᵢᵣ LAS gives a frequency of 1441 cm⁻¹ for the 19b mode, very close to the other LAS-related values reported. To sum up, we find that adsorption on a LAS induces a blue-shift by 15–20 cm⁻¹, and adsorption on a BAS a blue-shift by about 120 cm⁻¹. BAS and LAS lead to 19b frequencies differing by about 100 cm⁻¹. Those values are in very good agreement with the published experimental and theoretical literature.[73,75]

## Conclusions

In the present work, we propose models of the external surface of faujasite zeolite, as well as models for point defects, that shed light on the diversity of Brønsted and Lewis acid sites likely to exist in such areas.

From a thermodynamic standpoint, the (111) D6R complete, (111) sodalite complete and (111) sodalite incomplete surface terminations are of similar stabilities and are thus plausible descriptions of the surface of faujasite. In agreement with previous theoretical works on other zeolites, at the surface of faujasite, Al–H₂O groups are found to be more stable than classical bridging groups. In addition, our calculations on defective bulk cells incorporating silanol nests allowing for the modelling of Al–H₂O bulk sites revealed those species are also more stable than bulk bridging groups close to defects. Upon heating, dehydration of the Al–H₂O groups leads to Alᵢᵣ species regardless of the Si/Al ratio within the bulk and at the surface for high Si/Al ratio slabs. In surface slabs of low Si/Al ratio, it can lead to both Alᵢᵣ and Alᵣ species depending on the local environment in the vicinity of the Al–H₂O sites. Calculated temperatures of water desorption from those sites are highly dependent on the ability of the network to rearrange into an Alᵣ species, and to the Si/Al ratio. At the surface, regardless of the Si/Al ratio, the water desorption temperatures range from

390 K to 670 K. It is thus highly plausible that water desorbs from the surface during industrial processes, in which temperature can be superior to 500 K. In the bulk, with a high Si/Al ratio, the temperatures obtained range from 580 K to 720 K, and are of about 900 K with a low Si/Al ratio. Consequently, it is harder to desorb water in the bulk, especially when high Si/Al ratio are involved.

The acidity investigation performed revealed that not only the well-known bulk bridging OH groups but also surface bridging OH groups can act as strong BAS. Al–H₂O surface sites are weak BAS except for the specific case of the sodalite incomplete termination for which pyridine benefits from a stabilizing confinement effect, which makes the adsorption stronger. In the bulk, those sites can be envisioned as mild BAS. LAS as strong as the bulk BAS are found in the bulk and at the surface when pyridine adsorbs directly on the dehydrated Alᵢᵣ and Alᵣ species. This needs water desorption prior to attack of the site by a base but could reveal it is not always necessary to resort to the presence of EFAL to explain the strong Lewis acidic character sometimes observed in faujasite. The adsorption of pyridine on Al in anti position to the bridging proton always led to weak adsorption. Moreover, the simultaneous adsorption of pyridine on a same Al–OH–Si site, one molecule occupying the BAS and the other the LAS always led to the removal of the LAS adsorbed pyridine and the strong bonding of the proton with the BAS adsorbed pyridine. Adsorption following a BAS mechanism must thus be favored, except in cases for which the proton is located in the sodalite cage (O3H protons), for which the only possible mechanism is the Lewis one. Our comparison of pyridine adsorption characteristics on cells and slabs of different Si/Al ratio reveals it has very little effect on the adsorption energies, but sometimes have a strong one on the calculated pyridine desorption temperatures. Our thermodynamic investigation reveals this surprising effect must take its origin in the vibrational entropy of the studied systems.

## Acknowledgements

Calculations were performed using HPC resources from IFP Energies Nouvelles (ENER440) and from GENCI-CINES (Grant A0020806134). This work has been supported by the Common Research laboratory CARMEN (ENS de Lyon, CNRS, IFPEN, Claude Bernard Lyon 1 University, Sorbonne University and University of Strasbourg). We thank the partners of the project for fruitful discussions that have helped in the elaboration of the models.

## Conflict of Interest

The authors declare no conflicts of interest.

## Data Availability Statement

The atomic structure files and calculations input and output files that support the findings of this study are available online
<figure><img src="image_34.png" /></figure>

on a public Open Science Framework (OSF) repository.[33] for
which the following DOI has been issued: 10.17605/OSF.IO/
HXF5D.

Keywords: Zeolites • External surface • Catalysis • Acidity • Density Functional Theory

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Manuscript received: October 27, 2022

Revised manuscript received: December 9, 2022

Accepted manuscript online: December 9, 2022

Version of record online: January 19, 2023