Periodic Quantum Chemical Studies on Anhydrous and Hydrated

Article pubs.acs.org/JPCA

Periodic Quantum Chemical Studies on Anhydrous and Hydrated Acid Clinoptilolite Karell Valdiviés Cruz,†,‡ Anabel Lam,‡ and Claudio M. Zicovich-Wilson*,† †

Facultad de Ciencias, Universidad Autónoma del Estado de Morelos, Av. Universidad 1001, C. Chamilpa, Cuernavaca (MOR) 62209, Mexico ‡ Laboratorio de Ingenierı ́a de Zeolitas, Instituto de Ciencia y Tecnologı ́a de Materiales (IMRE), Universidad de La Habana, La Habana 10400, Cuba S Supporting Information *

ABSTRACT: Periodic quantum chemistry methods as implemented in the CRYSTAL09 code were considered to study acid clinoptilolite (HEU framework type), both anhydrous and hydrated. The most probable location of acid sites and water molecules together with other structural details has been the object of particular attention. Calculations were performed at hybrid and pristine DFT levels of theory with a VDZP quality basis set in order to compare performances. It arises that PBE0 provides the best agreement with experimental data as concerns structural features and the most stable Al distribution in the framework. The role of the water molecule distribution in the stability of the systems, the most probable structure that they induce in the material, and their eventual influence on further chemical modification processes, such as dealumination, are discussed in detail. Results show that, apart from the usually considered interactions of water molecules with the zeolite framework, that is, a H-bond with Brönsted acid sites and coordination with framework Al as Lewis ones, it is necessary to consider cooperation of other weaker effects so as to fully understand the hydration effect in this kind of materials.

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INTRODUCTION Zeolites are solids with topological periodicity but composition disorder whose most remarkable characteristic is their rich microporous structure. Such a feature allows them to be currently employed as effective adsorbents and molecular sieves.1 Even if there are a growing number of synthetic zeolites designed to display particular properties oriented toward a large variety of industrial roles, the use of natural zeolites is economically competitive as they are easy to extract and are present in huge quantities on earth. However, the relatively small porosity size exhibited by such natural materials does not in general permit incorporation of medium-sized organic molecules of industrial interest like drugs and colorants. Consequently, their potential use as support for medicines or effective molecular sieves for the selective removal of organic contaminants is extremely limited, thus reducing the interest of such materials for technological applications. As a way to exploit the economic advantages of natural zeolites adapting them to industrial requirements, it has been proposed2,3 to develop new materials suitable for processes of interest through chemical modifications of natural ones. These modifications are intended to get molecular sieves of larger pore size so as to ensure better diffusion of relatively large molecules together with a not too expensive way to obtain them. An efficient procedure to reach such a goal is to employ dealumination as a structural modification technique, allowing creation of artificial cavities larger than those exhibited by the © 2014 American Chemical Society

original material. Basically, the technique consists of successive extractions of Al atoms from the framework through acid treatments. Despite its simplicity, the method must be carried out with care as it can provoke structural collapse toward amorphous phases, particularly when the starting zeolites exhibit a low Si/Al ratio.4−6 Clinoptilolite is the most abundant natural zeolite on earth and has a quite low extraction cost. It is, therefore, a good candidate to be used as a starting material for the previously mentioned modification technique. Its crystalline structure was refined by Alberti et al.7 in a monoclinic cell of C2/m space group. The framework is of HEU type; it exhibits a Si/Al ratio between 4.5 and 5.5,1 and 20 water molecules per unit cell can be occluded on average inside of their channels and cavities. Several types of compensation cations like Na+, K+, and Ca2+ may also appear.8 The conventional cell parameters are a = 17.64 Å, b = 17.89 Å, c = 7.39 Å, and β = 116.22°.7 Considering the primitive cell representation, the parameters are a = 12.41 Å, b = 12.57 Å, c = 7.28 Å, α = 69.04°, β = 105.58°, and γ = 88.38°. The Al atoms are in a partially random distribution Special Issue: Energetics and Dynamics of Molecules, Solids, and Surfaces - QUITEL 2012 Received: October 31, 2013 Revised: April 8, 2014 Published: April 14, 2014 5779

dx.doi.org/10.1021/jp410754a | J. Phys. Chem. A 2014, 118, 5779−5789

The Journal of Physical Chemistry A

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Figure 1. Conventional and primitive cells of the HEU framework. The latter is depicted in colors. Yellow and red angles correspond to T and O atoms, respectively. Atoms in the asymmetric unit are labeled according to the usual notation.8 The channels are also shown; 10 MR and 8 MR correspond to the 10-membered and 8-membered ring channels, respectively.

along five topologically distinct sites in the framework, currently labeled as Ti (i = 1−5).7 The average occupation of Al atoms per site is the largest on T2 (up to approximately 40%), followed by T3, with a much lower amount on T5 and T1 and almost null on T4 (see Figure 1).7 Clinoptilolite can be dealuminated up to 46% of the original Al content without perceptible crystallinity loss, yielding a thermally stable material.9 An analysis of the 27Al-NMR spectra allows detection of an increase in the amount of octahedral Al and a simultaneous decrease in tetrahedral Al. This fact could indicate that removal of Al atoms from the framework and formation of extra-framework Al species in the material channels are occurring.9 Recent periodic DFT simulations10 suggested that Al atoms in the T2 position are the easiest ones to be removed during the acid dealumination process of clinoptilolite, followed by those located in T3. It has been shown that such a modified clinoptilolite exhibits an excellent ability for n-paraffin separation.11 Nevertheless, the reaction steps involved in the acid hydrolysis of the Al−O bonds taking place in dealumination still deserve more discussion.12 Use of experimental techniques to understand such processes is a very involved and costly task, while consideration of computational techniques could be an appealing alternative. Reported theoretical studies on clinoptilolite and related materials have been mostly performed with methods based on classical mechanics.13−15 However, to account for processes that involve formation and breaking of chemical bonds, like those occurring in zeolite dealumination, it is mandatory to consider computational methods that explicitly include the description of the electronic structure that is of quantum mechanical nature. The present work is aimed to (a) establish a suitable methodology for studies on different physical and chemical properties of materials derived from natural clinoptilolite, (b) generate acid models of HEU topology with different composition and study their relative stability, so as to define a proper model for further investigations on possible hydrolysis mechanisms of Al−O bonds in acid media that yield dealuminated clinoptilolite, and (c) study the influence of hydration on the local structural features of the material. Periodic quantum chemical methods have been considered at different DFT levels as implemented in the CRYSTAL09

code.16 The program allows computation of the electronic structure of periodic systems and several related properties through the description of the one-electron wave functions as linear combinations of atomic orbitals, which, in turn, are spanned in terms of contracted Gaussian-type orbitals. Such a strategy allows treatment of molecules, 1D polymers, 2D surfaces (slabs), and 3D crystals with the same level of accuracy, thus providing a straightforward extension of the most used methods of the molecular quantum chemistry.

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METHODS Electronic structure calculations were performed using a basis set of valence double-ζ with polarization quality (VDZP). It consists of 6-31G(d,p) sets for H and O and 6-21G(d) and 831G(d) ones for Si and Al atoms, respectively (see the CRYSTAL web page).16 The original sets have been slightly modified by reoptimizing the last sp exponents for O, Si, and Al, resulting in 0.2798, 0.13, and 0.28 bohr−1, respectively. The exponents of the polarized d shells considered for the same atoms were 0.5, 0.5, and 0.47 bohr−1, respectively. This basis set has been employed in previous works on related materials with rather good performances in geometry optimizations and frequency calculations.17−22 Such results evidence a reasonable representation of the potential energy hypersurface (PEH) for the nuclear motion. Hybrid and pristine DFT functionals have been considered for calculations. Concerning the first approach, B3LYP,23,24 B3PW,23,25 and PBE026 schemes have been employed to represent the exchange−correlation contributions. As concerns pristine functionals, PBE27 and BLYP24,28 have been considered. The Hamiltonian matrix was diagonalized in a set of k-points in reciprocal space generated according to the Pack− Monkhorst prescription29 with shrinking factor 2 for sampling in the first Brillouin zone. The resulting number of symmetryirreducible points is 6 and 8 when space groups are C2/m and P1, respectively. The tolerances adopted in the calculation of mono- and bielectronic integrals for the coulomb and exchange series were those recommended in the code manual.16 The exchange−correlation contribution has been integrated numerically on a large pruned grid with 75 points in the radial and a maximum of 434 points in the angular parts around the nuclei 5780



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(see keyword LGRID in the code manual).16 The condition for convergence of the SCF part was that the energy difference between two subsequent cycles must be less than 1 × 10−7 Hartree. Geometry optimizations were carried out employing an analytic gradient technique for both atomic positions and lattice parameters, with a pseudo-Newton algorithm whose Hessian matrix is updated through the BFGS algorithm.16 The coordinate equivalences determined by the space symmetry have been fully kept when possible. Convergence was tested on the root-mean square and the absolute value of the largest component of the gradients and estimated displacements considering the default thresholds documented in the code manual.16 In order to ensure consistency between the final geometry and the approximations considered for the integral evaluation, the FINALRUN option of the code with value 4 has also been employed.16 Basis set superposition error (BSSE) corrections have been performed for the calculation of water adsorption energies, adopting the counterpoise scheme.30 The magnitude of the correction per water molecule has been estimated considering desorption of three water molecules in the most stable model divided by three. Details are given in the next section. Several different models have been generated starting from the primitive cell of the pure silica SiO2-HEU. It exhibits C2/m space symmetry and 18 T sites (54 atoms) in its framework.31 More complex models were obtained from this one by substituting Si with Al atoms in the framework, keeping in all cases the primitive cell representation. Although the conventional cell or even larger supercells would allow a better description of the composition disorder of natural clinoptilolite and derived materials, the relatively ordered structures based on the primitive cell have computational advantages in what concerns their low number of electrons per unit cell and structural degrees of freedom. This favors a clear and detailed description of the processes involved. Eight new structures have been created substituting one Si with Al atoms in either of the T2 or T3 sites and compensating for the resulting charge deficiency with one proton located on one of the four O atoms at the first neighbors of the Al one. Such models are here labeled as HMs[h], where indices s and h refer to the topological labels of the T site where substitution holds and the O-bridging position of the resulting OH groups, respectively. The labeling is according to the prescription provided in ref 7 (see also Figure 1). In the present case, s = 2, 3 (T2 or T3), and h belongs to sets {1, 2, 4, 10} and {2, 3, 7, 9} for each T-site, respectively. The generated cells consist of 55 atoms. To describe structures whose framework composition and cation distribution mimic that of acid9 clinoptilolite, the previously optimized models have been employed to build HEU frameworks with three Al atoms located on sites T2 and T3. The choice of such a cation distribution, here adopted to limit possibilities in the design of the models, is based on previous works, where it was shown that the most stable Al location in the framework is T2 followed by T3, the former having approximately twice the occupancy of the latter.7,9 Accordingly, the experimental low Al occupancy on T1 and T5, mentioned in the Introduction, are disregarded in the present models. The resulting Si/Al ratio in our models is 6, slightly larger than the experimental one of 4.5−5.5.1 Consequently, the construction of the models proceeds through the following steps: (1) one starts from the most stable

HM2[h] model; (2) a Si atom in the T3 position is then substituted by an Al one, creating a OH bridging the h position corresponding to the most stable HM3[h] model and (3) the third Al and the accompanying acidic H atom are set in the positions center-symmetrically equivalent to the acid site in the starting model. Only those distributions that obey Loewenstein’s rule are considered. The obtained models are here labeled as HT[hT2][hT3], where indices hT2 and hT3 refer to the position of the resulting OH bridging in terms of the standard labeling of the O atoms around T2 and T3 sites, respectively (see above).7 In the present work, three HM2[h] and two HM3[h] models were chosen as the most stable ones, generating six HT[hT2][hT3] structures with the above referred procedure. New models exhibit 57 atoms per primitive cell. To represent hydrated acid clinoptilolite, three water molecules, one for each acid site, were disposed into the channels of the most stable HT[hT2][hT3] structures. The position of those water molecules inside of the material channels was first set by means of a Monte Carlo sampling in a NVT ensemble at 300 K with periodic boundary conditions and the Universal Force Field.32 From the 106 configurations generated this way, the 10 most stable ones were chosen and fully optimized at the DFT level considered. The procedure exhibits some lack of rigor as the energy obtained with a classical force field is expected to be in general significantly different than that resulting from more accurate electronic structure calculations as those considered here. Nevertheless, it results in being extremely useful from the practical point of view. This is because the Monte Carlo sampling, even if employing a poor methodology for evaluating energy, allows efficient exploration of a very large number of arrangements and selection of those with chemical sense. After the selection, the lack in the accurate description of the PEH associated with the force field is corrected in a large amount by the optimization performed with much more reliable electronic structure methods. The hydrated models are here labeled as HT[hT2][hT3]-N, where indices hT2 and hT3 have the same meaning as those for the anhydrous models and index N arbitrarily labels each water distribution. The resulting models consist of 66 atoms. The optimized geometry of the corresponding eight structures generated is provided in the Supporting Information (SI) file.

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RESULTS AND DISCUSSION

Performance of Hybrid and Pure DFT Functionals. According to a previous work of some of us,33 in the theoretical treatment of zeolites, the underestimation of long-range van der Waals forces with some DFT approaches is reflected in a bad reproduction of energetic and structural experimental features. Concerning the former, it has been shown that the stability of pure silica zeolites, quantified in terms of the enthalpy of transition to α-quartz, behaves roughly linear with respect to the molar volume.34 Such a result is underestimated by most pristine and hybrid DFT approaches.33 The underestimation also affects the shape of the corresponding PEH as the minima in general exhibit cell volumes larger than those obtained by experimental techniques. The inclusion of an energetic correction to the DFT functional accounting for dispersion in the manner proposed by Grimme35 is actually possible in LCAO periodic calculations,36 but it requires a substantially high basis set level, a fact that would make extremely expensive the computational cost of the present study. Alternatively, we 5781



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here seek a DFT approach that allows minimizing as possible such misestimations. The optimized lattice parameters of pure SiO2-HEU obtained by employing different DFT schemes, the previously reported experimental values for natural7 and calcined acid clinoptilolite,9 and the hypothetical ones for a pure Si framework31 are documented in Table 1. The structure optimized at the PBE0 level of theory is also depicted in Figure 2.

Table 2. Energy Differences of SiO2-HEU with Respect to αQuartz (in kcal·mol−1) and Average Bond Distances and Angles at Different DFT Levels

Table 1. Pure SiO2−HEU Lattice Parameters and Volume (V) in Comparison with Experimental Results for the Natural7 and Calcined Acid9 Materials Together with the Ideal Structure for the Si-HEU Framework31

a

functional

aa

ba

ca

αb

βb

γb

Vc

B3LYP BLYP B3PW PBE0 PBE ref7 ref9 ref31

17.67 17.76 17.61 17.48 17.53 17.64 17.73 17.52

17.80 17.90 17.75 17.69 17.77 17.89 18.09 17.64

7.44 7.49 7.42 7.39 7.42 7.39 7.44 7.40

90.0 90.0 90.0 90.0 90.0 90.0 90.0 90.0

116.2 116.2 116.2 116.2 116.3 116.2 116.0 116.1

90.0 90.0 90.0 90.0 90.0 90.0 90.0 90.0

2101.0 2134.7 2082.0 2048.9 2072.7 2092.2 2144.2 2054.8

a

functional

ΔE

⟨dSi−O⟩a

⟨O−Si−O⟩b

⟨Si−O−Si⟩b

B3LYP BLYP B3PW PBE0 PBE

1.6 1.4 1.0 1.8 1.9

1.627 1.641 1.625 1.623 1.639

109.4 109.5 109.5 109.4 109.5

147.0 145.8 146.3 144.6 142.6

Distances in Å. bAngles in degrees.

mol−1 per SiO2 less stable than α-quartz. The largest values are provided by PBE0 and PBE (1.8 and 1.9 kcal·mol−1, respectively; see Table 2), but they are still lower than the one predicted by the experimental correlation, that is, 2.1 kcal· mol−1.34 The same DFT approaches are those that better reproduce the cell volume, and then, it is expected that they minimize the error derived from the lack in accounting for long-range van der Waals forces in silica-based porous materials. As concerns the HEU structures with a single acid site per unit cell, in Figure S-1 (SI), the different optimized HM structures computed at the PBE0 level of theory are shown. The corresponding energies estimated with the five DFT approaches considered as well as the statistics of the Si−O, Al− O, and O−H distances are documented in Table 3. In all considered cases, Si−O bond distances are overestimated with respect to typical experimental values, which are about 1.605 Å.37 Such an overestimation is a well-documented lack of the DFT methodology in the description of Si−O bonds.22,38 The value of the Si−O distance is the largest one in the case of pure functionals PBE and BLYP, advising against their use for calculations of porous silica-based materials. The remaining bond lengths, that is, Al−O and O−H, are rather well reproduced at every functional level considered (see Table 3). A similar behavior holds concerning bond angles in accordance with the data documented in Tables 1 and S-2 (see the SI). All considered functionals yield average bond angles that are consistent with experimental data on natural clinoptilolite as they are within the range of expected values.7,39 The stability order found for the HM models using all hybrid functionals (i.e., B3LYP, B3PW and PBE0) is HM2[4] > HM3[2] > HM3[9] > HM2[10] > HM2[2] > HM3[7] > HM3[3] > HM2[1], while in the case of the pure functionals PBE and BLYP, the order is different. As concerns the former, HM2[2] moves to the third place, keeping the remaining models in the same order. On the other hand, BLYP provides a drastically different stability order, namely HM3[2] > HM3[9] > HM2[4] > HM3[7] > HM3[3] > HM2[2] > HM2[10] > HM2[1]. Anyway, four DFT schemes agree in the fact that the most stable system is HM2[4], with the Al atom in the T2 framework position. This is in full agreement with XRD experimental reports indicating that Al atoms preferentially occupy T2 sites.7,9 A topological analysis of the HEU framework shows that the sets of six rings that share sites T2 and T3 are of type {4, 52, 8, 10, 12} and {42, 53, 12}, respectively. It is consequently expected that T3 should be in general more stressed than T2 as it shares a larger number of small (four- and five-membered) rings than the latter.22 Rings around each T site are schematized in Figure 3. An additional documentation

Distances in Å. bAngles in degrees. cVolume in Å3.

Figure 2. Pure SiO2−HEU primitive cell. Red and yellow line junctions represent O and Si atoms, respectively.

It turns out that the cell volume of the models here considered for the hypothetical pure silica HEU is in general between experimental data, the lower and upper bounds being the natural and calcined acid materials, respectively. This trend also roughly holds for the cell parameters apart from the case of BLYP in which c slightly exceeds the largest experimental value. The cell parameter that exhibits the largest data dispersion in dependence of the DFT method considered is a, with a standard deviation of 0.11 Å (b and c display 0.08 and 0.04 Å, respectively). While c goes along the channels direction, a and b intersect it, and the largest dispersion of these cell lengths may reflect the differences in efficiency of the methods in describing the strength of the attracting forces between the channel walls, which should be dominated by long-range van der Waals forces.35 As arises from Table 1, among the few DFT approaches explored in this work, PBE0 and PBE provide the smallest cell volumes. In addition, the volume obtained with the former is the closest one to that provided in the literature (2054.84 Å) for an idealized SiO2 framework.31 In Table 2, the energetic stability of pure SiO2-HEU with respect to α-quartz as well as a statistics of the optimized Si−O bond distances and O−Si−O and Si−O−Si bond angles at all considered computational levels are listed. The energetic reference, α-quartz, has been fully optimized in each case. It turns out that all methods gives SiO2-HEU as about 1−2 kcal· 5782



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Table 3. Energy (kcal·mol−1) of HM Models Relative to the Most Stable One and Average Bond Distances (in Å) Obtained Considering Different DFT Functionals functional

model

ΔE

⟨dSi−O⟩

⟨dAl−O⟩

⟨dO−H⟩

B3LYP

HM2[1] HM2[10] HM2[2] HM2[4] HM3[2] HM3[3] HM3[9] HM3[7] HM2[1] HM2[10] HM2[2] HM2[4] HM3[2] HM3[3] HM3[9] HM3[7] HM2[1] HM2[10] HM2[2] HM2[4] HM3[2] HM3[3] HM3[9] HM3[7] HM2[1] HM2[10] HM2[2] HM2[4] HM3[2] HM3[3] HM3[9] HM3[7] HM2[1] HM2[10] HM2[2] HM2[4] HM3[2] HM3[3] HM3[9] HM3[7]

7.3 2.8 2.9 0 1.8 6.2 2.6 5.5 10.1 5.8 5.5 2.8 0 4.4 0.6 3.8 6.4 2.2 2.6 0 1.4 5.8 2.1 4.8 5.8 1.5 2.1 0 1.1 5.0 1.9 3.6 5.3 1.6 1.5 0 0.6 3.7 1.6 2.6

1.629 1.628 1.629 1.628 1.629 1.629 1.628 1.629 1.642 1.642 1.643 1.642 1.642 1.642 1.642 1.643 1.627 1.627 1.627 1.626 1.626 1.627 1.626 1.628 1.625 1.625 1.625 1.624 1.625 1.626 1.625 1.626 1.641 1.641 1.641 1.640 1.641 1.641 1.640 1.642

1.750 1.750 1.751 1.746 1.751 1.755 1.747 1.751 1.762 1.762 1.763 1.757 1.762 1.766 1.759 1.762 1.750 1.750 1.751 1.745 1.750 1.754 1.746 1.750 1.749 1.749 1.748 1.743 1.748 1.752 1.744 1.748 1.763 1.762 1.760 1.754 1.760 1.764 1.757 1.760

0.974 0.970 0.972 0.972 0.971 0.972 0.973 0.979 0.983 0.980 0.981 0.985 0.980 0.983 0.981 0.991 0.972 0.968 0.970 0.971 0.969 0.971 0.970 0.980 0.971 0.967 0.969 0.970 0.968 0.971 0.970 0.981 0.982 0.978 0.980 0.981 0.979 0.983 0.980 0.998

BLYP

B3PW

PBE0

PBE

Anhydrous and Hydrated Models for Acid Clinoptilolite. Figure S-2 (SI) shows the primitive cell of all considered models for anhydrous acid clinoptilolite (HT) optimized at the PBE0 level. According to known experimental data, their composition and cation distribution, that is, three Al atoms and their corresponding protons, somehow mimic the anhydrous material obtained from the natural one upon ammonium cation exchange and calcination.9 The HT structures were generated starting from models HM2[10], HM2[2], HM2[4], HM3[2], and HM3[9] modified according to the prescription detailed in the Methods section and further optimized at the PBE0 level. Taking into account the structural constraints together with Loewenstein and Dempsey rules, just six models result. They are here referred to as HT[10][2], HT[2][2], HT[4][2], HT[10][9], HT[2] [9], and HT[4][9], in accordance with the notation stated in the Methods section. Energy differences between each HT model and the most stable one together with the corresponding average Si−O, Al−O, and O−H distances are documented in Table 4. As it arises from table, the resulting stability order is HT[10] [2] > HT[4][2] > HT[10][9] > HT[2][2] > HT[4][9] > HT[2][9], the two most stable models being practically isoenergetic. On the other hand, comparing the local geometry around T2 and T3 when occupied by Al atoms, it turns out from Table 4 that in these optimized structures, Al atoms in T3 exhibit Al−O bond distances, in general, slightly shorter on average than those appearing when Al is in T2. The local structure around the acid sites does influence their chemical properties; according to Gutmann’s rules,42 it is therefore expected that OH bridging should be slightly more acidic when associated with T3 than that with T2. Indeed, the experimental XRD results that report detailed atomic positions of this kind of materials43−45 show that in natural clinoptilolite, T2−O distances are considerably larger than T3−O ones, at variance with our results. Unlike the anhydrous acid models considered here, the natural material does not exhibit acid sites and, in addition, contains a significant amount of water molecules occluded. As the latter might be a relevant factor in determining the structural particularities of this kind of materials, let us now analyze which is the effect of the presence of water molecules in models for acid clinoptilolite. The different hydrated structures were built starting from the two most stable HT models, that is, HT[10][2] and HT[4][2], and inserting three water molecules in the material cavities according to the Monte Carlo procedure previously described. Figure 4 shows a schematic representation of the 10 generated configurations. Obviously, the considered procedure does not exhaust the possibilities in order to provide a complete enough statistical description of the partially disordered hydrated material. Nonetheless, it at least allows exploring hydration in a systematic way and studying in high detail several configurations that either could appear in the actual samples or exhibit similar chemical features. Lattice parameters and average bond distances of the optimized hydrated models are documented in Tables 5 and 6. Additional structural data are also provided in Tables S-3 and S-4 in the SI. Moreover, their total energy relative to the most stable one, the corresponding hydration energy, and its BSSEcorrected values are presented in Table 7. The BSSE correction term has been estimated to be 8.8 kcal·mol−1 per water molecule. In accordance with the criteria stated in the Methods

concerning those rings is also provided in Tables S-5 and S-7 in the SI. Although hybrid functionals are in general quite good to reproduce structural experimental data, PBE0 appears to be slightly better than the other ones as it performs reasonably well both for short- and long-range interactions present in porous materials with the HEU framework. Other hybrid approaches like B3LYP at a similar basis set level have been considered in previous works to evaluate the energetic properties of related materials with also quite good agreement with experimental data.20,40,41 However, it is worth noting that at variance with PBE0, this functional systematically yields a significant overestimation of the cell volume of SiO2 zeolites together with an underestimation of the stability with respect to α-quartz,33 facts that slightly reduce its comparative quality. Accordingly, PBE0 is the method considered for upcoming results left in this study. 5783



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Figure 3. Small rings to which T2 and T3 sites belong: (a) four-, (b) five-, (c) five-, (d) four-, (e) four-, (f) five-, (g) five-, and (h) five-membered rings. The ring is drawn in red. Balls represent T sites.

Table 4. Energy Difference (in kcal·mol−1) at the PBE0 Level between the Considered HT Models and the Most Stable One and the Corresponding Average Bond Distances (in Å)a

a

model

ΔE

⟨dSi−O⟩

⟨dAl−O⟩

⟨dAl(T2)−O⟩

⟨dAl(T3)−O⟩

⟨dO−H⟩

HT[10][2] HT[2][2] HT[4][2] HT[10][9] HT[2][9] HT[4][9]

0 5.6 0.2 2.9 6.6 6.1

1.628 1.629 1.626 1.628 1.628 1.626

1.751 1.751 1.745 1.748 1.748 1.745

1.751 1.751 1.743 1.751 1.749 1.745

1.749 1.750 1.742 1.742 1.746 1.747

0.966 0.967 0.967 0.966 0.967 0.967

For T = Al, both 2 and framework sites are also considered.

As concerns the hydration energy, it is computed as

section, the chosen water molecules correspond to the most stable model, namely, HT[4][2]-5. Although the choice is somehow arbitrary, the value can be considered a good representative for the whole set of systems as, for instance, in the case of the second most stable model, HT[4][2]-1, the BSSE estimation provides a slightly lower value, that is, 8.3 kcal· mol−1 per water molecule, very close to the one obtained with the most stable model.

ΔE H =

[EZ−w − (EZ + nEw )] n

(1)

where EZ−w, EZ, and Ew are the energies of the hydrated and anhydrous zeolites and a single water molecule, respectively; n is the number of water molecules occluded; here n = 3. 5784



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dispersion of results is consistent with the fact that they describe a variety of possible interactions between water molecules and the solid moiety, and therefore, they somehow sample the most paradigmatic events occurring in the hydrated material. The stability order of the considered hydrated models of acid clinoptilolite appears to be HT[4][2]-5 > HT[4][2]-1 > HT[10][2]-1 > HT[10][2]-4 > HT[10][2]-3 > HT[4][2]-3 ≈ HT[10][2]-5 > HT[10][2]-2 > HT[4][2]-2 > HT[4][2]-4. According to Table 4, the starting HT models are practically isoenergetic; therefore, the differences in stability are to be chiefly attributed to the way that the water molecules interact with inner surfaces of the material. In all considered models, the formation of H-bonds involving the occluded water molecules is observed. These bonds are here classified into three groups, (I) water molecules H-bonded to acid sites, (II) water molecules H-bonded to framework O atoms, and (III) water molecules H-bonded to each other. The first group is expected to display the strongest interactions as the acidic proton, with net electron-acceptor character, interacts with the water oxygen as a donor. In the second group, water H atoms interact with O ones in T−O−Si bridges at the channels walls (T = Si or Al). These O atoms do exhibit moderate electron-donor character, particularly those belonging to Al− O−Si bridges. As concerns the third set, the interactions are presumably the weakest ones because of the low ionic character expected for O and H atoms of the involved water molecules. All of these interactions do contribute to the stabilization of the structures under study. In accordance with the previous classification, Table 8 documents the number of interactions belonging to each of such groups as well as the total number of H-bonds per primitive cell and the average O···H distances (⟨dO···H⟩) in the considered hydrated acid models. The criterion considered for recognizing a H-bond is that the O···H distance should be lower than 2.1 Å. These data together with Mulliken charges on H and O atoms, the detailed O···H distances, among other structural and electronic properties provided in Tables S-7, S-8, and S-9 in the SI file, are here considered so as to rationalize the observed trends in stability of hydrated models, as documented in Table 7. The most stable model, HT[4][2]-5, exhibits several characteristics that seem to chiefly determine its particular stability as its energy, according to Table 7, is substantially lower than that in the other models. In particular, it turns out that adsorbed water molecules establish strong H-bonds, of the type here classified as (I). Each water molecule appears associated with a single acid site, as is shown in Figure 4j, the corresponding H···O distances being lower than 1.45 Ǻ (see Table S-7 in the SI). Additional interactions of type (II) contribute to a further stabilization of the system. A geometric index of the overall strength of such interactions is given by ⟨dO···H⟩, documented in Table 8, which corresponds to a quite small value in this case. The following model in terms of stability is HT[4][2]-1. The total number of H-bonds is larger than the previous one, but just two of them are of the strongest type (I). In average, water molecules are less strongly bonded than in HT[4][2]-5, as revealed by ⟨dO···H⟩ data exhibiting a value of about 0.2 Ǻ larger. This is essentially due to the weaker character of interactions of type (II) and (III) intervening in such a structure. Interestingly, as shown in Figure 4f, this model exhibits an additional type of interaction, which is a coordination between the water O and

Figure 4. Models considered to represent hydrated acid Clinoptilolite: (a) HT[10][2]-1, (b) HT[10][2]-2, (c) HT[10][2]-3, (d) HT[10] [2]-4, (e) HT[10][2]-5, (f) HT[4][2]-1, (g) HT[4][2]-2, (h) HT[4] [2]-3, (i) HT[4][2]-4, and (j) HT[4][2]-5. The dotted lines indicate H-bond interactions.

Equation 1 quantifies the reaction energy (per water molecule) according to the following chemical reaction HM[h T2][h T3] + 3H 2O → HT[h T2][h T3]‐N

(2)

The obtained hydration energy for the present models range from −21 to −14 kcal·mol−1 per water molecule. Such a 5785



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Table 5. Optimized Lattice Parameters at the PBE0 Level and Primitive Cell Volume for Models of Hydrated Acid Clinoptilolite

a

model

aa

ba

ca

αb

βb

γb

Vc

HT[10][2]-1 HT[10][2]-2 HT[10][2]-3 HT[10][2]-4 HT[10][2]-5 HT[4][2]-1 HT[4][2]-2 HT[4][2]-3 HT[4][2]-4 HT[4][2]-5

17.47 17.48 17.48 16.69 17.49 17.42 17.55 16.99 17.48 17.60

17.95 18.05 18.17 16.90 18.02 17.92 17.73 17.26 17.80 18.01

7.38 7.38 7.37 7.41 7.39 7.28 7.35 7.31 7.25 7.30

88.2 88.1 88.2 89.9 91.4 89.3 90.0 91.2 95.4 92.6

116.5 116.4 116.4 116.0 116.0 116.7 116.4 115.5 116.0 115.9

87.4 87.9 88.6 88.4 85.4 93.7 92.9 91.0 91.0 92.0

2064.9 2081.0 2095.0 1876.9 2089.4 2025.1 2046.9 1932.1 2013.8 2076.8

Distances in Å. bAngles in degrees. cVolume in Å3.

Table 6. Average Bond Distances (in Å) for Each Hydrated Modela model

⟨dSi−O⟩

⟨dAl−O⟩

⟨dAl(T2)−O⟩

⟨dAl(T3)−O⟩

⟨dO−Hz⟩

⟨dO−Hw⟩


1.628 1.627 1.628 1.631 1.627 1.629 1.628 1.630 1.628 1.628

1.746 1.748 1.747 1.765 1.748 1.765 1.747 1.749 1.763 1.747

1.745 1.747 1.750 1.779 1.748 1.773 1.748 1.758 1.769 1.748

1.748 1.751 1.741 1.736 1.748 1.749 1.744 1.740 1.740 1.747

1.021 1.007 1.046 1.000 1.019 1.001 1.000 0.994 1.013 1.070

0.980 0.976 0.979 0.991 0.977 0.983 0.984 0.991 0.971 0.976

a For T = Al, the framework type (2 or 3) is also considered. Hz and Hw label those H atoms that belong to the acid site and water molecules, respectively.

Table 7. Energy, ΔE, of the Models for Hydrated HClinoptilolite Relative to the Most Stable One, the Hydration Energy Per Water Molecule, ΔEHa, and the BSSECorrected Hydration Energy Per Water Molecule, ΔEH (corr.)b

a

model

ΔE

ΔEH

ΔEH (corr.)


11.1 16.5 13.6 12.8 14.6 7.1 19.3 14.5 22.1 0

−26.2 −24.4 −25.4 −25.6 −25.0 −27.6 −23.5 −25.2 −22.6 −30.0

−17.4 −15.6 −16.6 −16.8 −16.2 −18.8 −14.7 −16.3 −13.8 −21.2

Table 8. Average Hydrogen Bond Distances, ⟨dO···H⟩ (in Å), Total Number in Each Model and Classification According to the Different Groupsa number per group model

⟨dO···H⟩

total number

(I)

(II)

(III)


1.588 1.770 1.634 1.667 1.583 1.637 1.714 1.707 1.722 1.711

6 7 6 6 5 7 6 5 5 5

3 2 2 2 2 1 3 2 2 3

3 3 2 3 2 4 2 1 1 2

2 2 1 1 2 1 2 2

a

See details in the text. Models are here ordered according to their decreasing stability.

See the definition in the text. bEnergies are given in kcal·mol−1.

that contributes to shorten the ⟨dO···H⟩. At the same time, it does not exhibit any Lewis acid−base interaction between the water O and framework Al atoms, as happens in model HT[4] [2]-1. Accordingly, it is less stable than the latter by about 4 kcal·mol−1, as it turns out from Table 7. A similar analysis may also be applied to model HT[10][2]-4 and the corresponding relative stability. Apart from the number of distinctive characteristics shown in Table 8, a rather relevant difference between both models is the smaller cell volume in the latter, as shown in Table 5. Such a contraction is mainly featured along a and b crystallographic directions, and it is caused by the structural strain generated by a H-bond occurring among one acid proton and an O-bridging. This connects

framework Al atoms, where they play the roles of Lewis base and acid, respectively. In it, the Al acquires a trigonal bipyramidal coordination instead of the tetrahedral one usual in zeolitic frameworks. Even if the former arrangement involves a significant framework strain, it is supposed to bring an additional overall stabilization to the hydrated system that partially compensates for the previously mentioned weaker water framework interactions. Anyway, the energy difference of about 7 kcal·mol−1 indicates that model HT[4][2]-5 seems to be by far the most probable hydrated structure among those considered here. Model HT[10][2]-1 displays features similar to HT[4][2]-1, with a slightly lower number of interactions of type (II), a fact 5786



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the axis containing the acidic OH group but along a perpendicular one containing one of the O-bridging. It is interesting to note that in three of the models, HT[10] [2]-4, HT[4][2]-1, and HT[4][2]-4, the Monte Carlo sampling and further DFT optimization yield structures in which a water molecule appears coordinated with a framework Al atom. Actually, the O atom of one water molecule is coordinated through a Lewis acid−base interaction with one of the Al atoms in position T2 (see Figure 4d, e, and h). The water−O···Al distance for these models is 2.05, 2.10, and 2.22 Å, respectively, in trigonal bipyramidal arrangements around the cation. The fact that in all cases the Al atom directly interacting with water molecule occupies T2 may be interpreted in terms of topological arguments. First of all and in accordance with the ring analysis performed in the previous section and shown in Figure 3, site T2 displays fewer structural constraints than T3 as the latter shares a larger number of small rings than the former. It is then expected that an Al atom in T2 will have also a larger ability for local arrangement so as to coordinate to the water molecule. On the other hand, as T2 is accessible from both the 8- and 10-membered channels, it allows accommodation of such a molecule in an easier way than the Al cation on T3, which is just reachable from the 8-membered channel. Accordingly, one could assume that in an acid attack during a dealumination process, the acid agent might interact with such a five-fold-coordinated Al atom in T2, provoking the breaking of one of the four original O−Al bonds by forming −OH···HO− Al. This bond hydrolysis would be the starting step of the dealumination reaction. This is somehow supported by experimental results that indicate that Al in T2 is the atom most susceptible for elimination from the framework in acid conditions.9 Adsorption of water molecules on T−O−Si (T = Al, Si) bridges, here classified as type (II) H-bonds, can supply additional stabilization to the zeolitic structure if such bridges belong to small structural rings having four or five T atoms. These units are known to exhibit stress owing to the partial rigidity of the TO4 tetrahedra as a result of the slight covalent character of the T−O bonds.22 As it turns out from Table S-9 (see SI), the presence of adsorbed water molecules provides an enlargement of the T−O bonds by 0.01−0.05 Å. Such an enlargement is to be connected to the enhancement of the ionic character of the bond, thus making more flexible the TO4 tetrahedron and allowing some additional relaxation of the ring.22 It arises that models exhibiting the largest number of small rings with at least one T−O−Si bridge interacting with water are the most stable ones or have an intermediate stability, in accordance with the energetic data provided in Table 7. Models HT[4][2]-5, HT[4][2]-1, HT[4][2]-3, and HT[10] [2]-4, display three rings involved in this kind of interaction, and in the three former models, one of such rings is a rather stressed four-membered one (see Table S-9 in the SI). As a matter of fact, at variance with the other models, in HT[4][2]5, the 4-MR that interacts with one of the water molecules includes an Al−O−Si bridge. This may be an additional fact that would explain the exceptional stability of such a model. Apart from the cases of HT[10][2]-1 and HT[10][2]-2 structures, where hydration slightly reverts the average Al−O distance trend between T3 and T2 in the corresponding anhydrous model (see Table 4), Table 6 shows that such a tendency is practically kept or even enhanced after hydration. As a matter of fact, the effect of water molecules in modifying the local geometry around acid sites is supported by some

opposite sides of the 8-MR channel, as shown in Figure 4d. Such an interaction induces a deformation of the channel, giving rise to a slightly strained structure. Another relevant feature of model HT[10][2]-4 is that one of the water molecules is coordinated to an Al atom as it occurs in HT[4] [2]-1 with similar geometrical features. The optimized structure of model HT[10][2]-3 exhibits the smallest ⟨dO···H⟩ among the whole set of considered systems but also a total number of H-bonds lower than that in the previously analyzed ones. Accordingly, the system displays an energy barely 1 kcal·mol−1 higher than that in the previously considered model. In the structure labeled HT[4][2]-3, the total number of Hbonds is similar to that displayed by HT[4][2]-1, and the ⟨dO···H⟩ is even lower. Nonetheless, as in the case of model HT[10][2]-4, the disposition of water molecules within the 8MR channel and their interactions with the O atoms at the walls cause a cell volume contraction, as revealed by Figure 4h and Table 5. As in the previous case, this generates an energetic penalty that makes the model less stable than expected from the local characteristics of the H-bonds. Despite HT[10][2]-4 and HT[4][2]-3 models displaying rather similar hydration features, the absence of a water molecule coordinated to a framework Al in the latter might be the reason for its rather lower stability. In the case of model HT[10][2]-5, even if the exhibited number of H-bonds is large and several are of the strongest type (I), its stability is substantially lower than the roughly equivalent one HT[4][2]-5. The main reason for such a difference is that one of the adsorbed water molecules is simultaneously connected by H-bonds with two acid sites just on opposite sides of the 8-MR channel, a fact that makes difficult an efficient enough interaction between them. This can be observed in the scheme depicted in Figure 4e and is also revealed by the quite large ⟨dO···H⟩ value in Table 8. The three least stable HT models display in all cases a total number of five H-bonds. The stabilizing effect of the presence of water molecules in these cases is not very important, which is reflected in the relatively large ΔE values in Table 7. Although structures HT[10][2]-2 and HT[4][2]-2 exhibit practically the same features in what concerns the H-bond analysis shown in Table 8, both display an overall number of five H-bonds with just one of them of type (II). Other factors should be also considered so as to explain the computed energy difference documented in Table 7 as the former of the couple is comparatively favored by about 2.8 kcal·mol−1 with respect to the other. A more detailed analysis that considers H−O bond distances and Mulliken charges of the involved atoms (see Tables S-7 and S-8 in the SI) indicates that the interaction between one of the water molecules and the O atoms in the cavity wall [type (II)] seems to be stronger in HT[10][2]-2 than that in HT[4][2]-2. This is corroborated by the larger charge on O (0.90 versus 0.72 |e|) and the shorter H−O distance (1.85 versus 2.06 Å). These features together with the slightly larger stability of the corresponding anhydrous model are likely the main reasons for the observed energetic order. As concerns the least stable hydrated model, HT[4][2]-4, it does not display clear features in the way that water molecules interact through H-bonds that could explain its comparative low stability. Interestingly, as arises from Figure 4i, one of the water molecules appears coordinated with a framework Al atom exhibiting a five-fold coordination in the form of a trigonal bipyramid but at variance with other models, like HT[4][2]-1 and HT[10][2]-4; here, the water molecule is not located along 5787



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experimental results on acid clinoptilolite. It has been shown46 that the fully hydrated form of H-clinoptilolite exhibits T2−O distances larger than it holds when the material is partially dehydrated. This reveals an effect that goes in the same direction as our computational results.

atoms coordinated with water molecules in hydrated models. This material is available free of charge via the Internet at http://pubs.acs.org.

■

■

CONCLUSIONS The performance of various functionals within the Kohn−Sham approach, both pure and hybrid, is here studied for zeolitic acid materials with the same topology as natural clinoptilolite. From the methods considered here, it turns out that hybrid functionals reproduce better the known structural features than pristine ones, like PBE or BLYP. Among the hybrids, PBE0 has a slightly better performance than the others. This is because it seems to better account for long-range interactions that determine both the relative stability of porous silica materials with respect to α-quartz and the global structural parameters connected to it, such as the cell volume. Several models have been considered to represent acid clinoptilolite as experimentally obtained through cation exchange from the natural material. The calculated relative stability agrees with previous results in that T2 is the preferential site for Al location, and as concerns the position of the proton, the O-bridging on topological position 4 around the Al atom in T2 is the most favored to allocate it. The acid site on T3 is slightly less stable, and the experimental relationship close to 2:1 between sites T2 and T3 is consistent with this fact. This average situation may be used for models for acid clinoptilolites obtained from cation substitution of natural ones. Hydrated and anhydrous models built up under such an assumption agree very well with known experimental data and provide a good starting point for further studies on structural modifications of these structures. Finally, the detailed consideration and analysis of the considered hydrated models sheds some light on the ways that water molecules may interact with the zeolitic framework and how they can locally and globally influence structural changes with respect to the corresponding anhydrous materials. The stabilization effect induced by the presence of water molecules in the channels and cavities of these materials has been rationalized in terms of the different types of weak interactions occurring between them and with the sites present at the cavity walls. Interestingly, apart from the most evident interactions between water molecules and the framework, such as H-bonds with Brönsted sites or coordination to framework Al atoms, other effects are revealed to be crucial to explain the stability and structural features of the models. This is the case, for instance, with H-bonds of water molecules with O-bridging at the channel walls and/or to each other forming short chains linking opposite sides of small zeolitic cavities. Though the present analysis has been performed by considering the specific case of the HEU framework, most of the present findings can be extrapolated to other zeolites with similar topologic features.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: (52)(777)329-7020. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors acknowledge CONACyT for financial support through Project CB-178853. K.V. also acknowledges CONACyT for a doctoral grant.

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

Optimized geometries of the hydrated models. Optimized lattice parameters and the primitive cell volume together with bond angles and figures for HM and HT models. Type of framework rings where H is located in HM and HT models. Average hydrogen bond distances, Mulliken populations on O and H atoms, and geometrical information on the framework O 5788



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