Theoretical Study of the Adsorption of Alkylamines in H-Mordenite

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Theoretical Study of the Adsorption of Alkylamines in H‑Mordenite: The Role of Noncovalent Interactions Lenin Díaz Soto,*,†,‡ Aníbal Sierraalta,† Rafael Añez,† and Marco Antonio Chaer Nascimento‡ †

Laboratorio de Química-Física y Catálisis Computacional, Centro de Química, Instituto Venezolano de Investigaciones Científicas, Apartado 21827, Caracas 1020 A, Venezuela ‡ Instituto de Química, Universidade Federal do Rio de Janeiro, Cidade Universitária, CT Bloco A sala 412, Rio de Janeiro, RJ 21949-900, Brazil S Supporting Information *

ABSTRACT: The adsorption of NH3 and alkylamines (MeNH2, Me2NH, and Me3N) on H-mordenite was studied using density functional theory (DFT) and the ONIOM method. The adsorption of the probe molecules was investigated with a set of functionals (B3LYP, B3LYP-D3, CAM-B3LYP, LC-ωPBE, and ωB97X-D) properly chosen to verify the importance of noncovalent interaction on the adsorption process. The adsorption energy increases with the size of the amine and with the type of functional used, according to the trend B3LYP-D3, ωB97X-D > CAM-B3LYP, LC-ωPBE > B3LYP. The noncovalent contribution to the adsorption energy is higher for Me3N, reaching 92 kJ/mol when B3LYP-D3 is used and 70 kJ/mol for ωB97X-D. Although the adsorption energies for each amine span a wide range of values depending on the functional used, the geometries of equilibrium are quite similar. The adsorption energies obtained by full geometry optimization of the complexes do not differ appreciably from those of single-point calculations using the geometries optimized at the B3LYP:UFF level of calculation, suggesting that for these systems the single-point strategy may be a reasonable alternative to reduce the computational cost of including noncovalent corrections in DFT results. A comparison was also made with the experimental differential heats of adsorption. At low coverage the computed Eads at the T4 site corrected for the basis set superposition (BSSE) and zero-point vibration energy errors exhibit the same trend of the experimental ΔHads with the degree of methylation observed by Lee et al. (J. Am. Chem. Soc. 1996, 118, 3262−3268) as opposed to the one by Chen et al. (J. Catal. 1994, 146, 257−267). Also, the results obtained at the B3LYPD3:UFF level of calculation including BSSE corrections strongly suggest that the falloff observed on the ΔHads x coverage diagram, normally attributed to site heterogeneity, may be due to a combination of two factors: the number of molecules adsorbed on a given site and the acid site local configuration.

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INTRODUCTION One of the main uses of alkylamines is as additives for the synthesis of colloidal semiconductor nanocrystals.1 Furthermore, it has been reported that nitrogen hybrid zeolites with MeNH2, Me2NH, Me3N, EtNH2, n-PrNH2, and n-ButylNH2 increase the basicity of MFI-type zeolites by the incorporation of N atoms into the framework.2 As the first step of this process involves the adsorption of the amine on the zeolite framework, it is necessary to determine how this process is affected by the structure of the alkylamines. Mordenite (MOR) is one of the most abundant zeolites in nature,3 and its protonic form (H-MOR) has been used in chemical processes such as hydrocarbon isomerization,4 nparaffin cracking,5 and alkylation reactions6 and in the selective catalytic reduction (SCR) of NO.7 The quantitative adsorption of alkylamines in H-MOR has been investigated using the microcalorimetry technique.8,9 In these experiments the zeolite is kept at constant temperature in the cell where the probe molecules are then introduced. The differential heat of adsorption is measured as a function of the probe molecules © XXXX American Chemical Society

introduced in the cell (coverage), and the curve representing its variation with the coverage is normally analyzed in terms of three different regions, which are interpreted as resulting from the interaction of the probe molecules with different sites of the zeolite.10 The highest adsorption enthalpy (ΔHads) values observed at low coverage are attributed to the probe molecules’ adsorption at the Lewis acid sites, followed by a region of midrange values of coverage and of ΔHads which is associated with the adsorption at the Brønsted acid sites. Finally, the region of high coverage and lower ΔHads is associated with the physisorption process. Additionally, in the Brønsted zone, the observed decrease of ΔHads with increasing coverage is attributed to the heterogeneity of the sites,11 i.e., to the existence of strong and weak Brønsted sites. The two experimental results8,9 for the alkylamine adsorption on HMOR differ substantially. The disagreement could be related to Received: December 8, 2014 Revised: March 23, 2015

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DOI: 10.1021/jp5122189 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

order Møller−Pleset perturbation theory (MP2) naturally provides a description of the vdW interactions and is the most economical computational method beyond the HF approximation, the MP2 energy exhibits deficiencies.19,20 To correct the MP2 shortcoming, several works have been developed to correctly account for the noncovalent interaction.20−25 On the other hand, coupled-cluster with single and double excitations plus perturbative triple excitations (CCSD(T)) furnishes a more rigorous description;26 however, because of its high computational cost, it is presently restricted to small systems. Among the methodologies used in computational chemistry, density functional theory (DFT) is widely employed in several fields because it drastically reduces the computational costs. Despite its broad application, a major drawback of DFT is its deficiency in describing noncovalent interactions such as vdW and hydrogen bonds. Several works involving isomerization reactions,27,28 potential energy surfaces for dimers,29 energy of alkane molecules,30 and conformation of biomolecules,31,32 among others, have been dedicated to evaluating the relevance of including noncovalent contributions in DFT calculations. To overcome this limitation, several correction schemes have been proposed, and a new generation of DFT functionals has been developed. A partial list is provided below. (a) Semiempirical corrections added a posteriori which incorporate a dispersion term Edispersion, EDFT‑dispersion = EDFT + E dispersion . There are several approaches to compute Edispersion,29,33,34 which is proportional to ΣNAB,A Me3N > MeNH2 > NH3] agrees with the experimental ΔHads of Lee et al.,9 the absolute values differ from the experiments. The authors attributed this discrepancy to the absence of terms to describe noncovalent interactions in the B3LYP functional. Because of the technological importance of these systems and the uncertainties in the experimental ΔHads values, further theoretical and experimental studies are needed. However, care must be exercised when performing theoretical calculations because noncovalent interactions should play a significant role in the adsorption process;17 both the model and the level of calculation should be properly chosen to consider such effects. Noncovalent interactions, such as van der Waals (vdW) and hydrogen bonds, are well-known to play an important role in the stability and reactivity of many different species. Because the noncovalent interactions are much weaker than the covalent interactions, their theoretical description requires a much larger computational effort. The vdW interactions result from electronic density fluctuations on two neutral atoms, molecules, or molecular fragments, and their magnitude depends on the features of the interacting species.18 Post-Hartree−Fock (HF) techniques are needed to take into account vdW dispersion interactions. Even though secondB


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valence of the most external Si atoms was saturated with H atoms. This model contains 60 tetrahedron centers (60T) in the high-level and 204 tetrahedron centers (204T) in the lowlevel regions. High-level implies that the atoms therein are being treated at a high quantum-mechanical level of theory as opposed to the low-level ones, treated by classical mechanics or at a lower quantum mechanical level. The low-level atoms were treated by the universal force field approach (UFF) and also at the HF level with the minimal basis STO-3G (HF/STO-3G) set. During the optimization procedure, the atoms belonging to the low-level regions were fixed to maintain the MOR structure. For the high-level region, five distinct DFT treatments were considered: (a) a standard calculation using the B3LYP functional; (b) the a posteri correction to the B3LYP results as introduced by Grimme et al.,33 B3LYP-D3; (c) a calculation using the hybrid exchange−correlation functional CAM-B3LYP which considers long-range correction to B3LYP;58 (d) the long-range correction LC-ωPBE functional59 to the short-range exchange functional ωPBE; and (e) the empirical dispersion correction proposed by Chai and Gordon, ωB97X-D,60 to the ωB97X long-range functional. The Hay and Wadt pseudopotential61 with its corresponding basis sets was used for H, Si, Al, and O atoms belonging to the MOR. The full-electron 6-31++G(d,p) basis set was used for the NH3, MeNH2, Me2NH, and Me3N molecules as well as for the H atom of the acid Brønsted sites. Frequency calculations at 1 atm and 298.15 K were performed to obtain the zero-point vibrational energies (ZPVE). The Brønsted sites in the acidic MOR structure (H-MOR) are created by replacing a Si atom by an Al atom at the four different T sites and adding a proton to the crystallographically distinct O atoms to compensate the negative charge. According to our previous results,43 the proton binds preferentially to oxygen atoms O7a (T1) (Figure 2a), O3b (T2) (Figure 2a), O1b (T3) (Figure 2b), and O2b (T4) (Figure 2b). However, the acid site at T3 is energetically highly unfavorable in comparison with the other sites and for this reason will not be further considered.

they involve high computational costs. Alternatively, hybrid methods, which combine quantum and classical mechanics, can be used to model large systems at moderate computational costs. ONIOM47,48 is a type of hybrid method that has been successfully used in studies of NH3 and H2O adsorption on acid chabazite49 and amines adsorption on Li-MOR and Na-MOR.50 According to the two-layer ONIOM methodology, the system to be treated is divided in two parts (or layers), one of them (high-level) described by quantum mechanical methods while the other (low-level) is treated either by classical mechanics or at a less rigorous quantum mechanical level. Although the ONIOM methodology reduces the computational costs, the size of the region of the zeolite which can be treated by methods that account for dispersion effects42,51,52 is still small compared to the cluster size. Generally, the way to include dispersion in ONIOM calculations is through MP2 in the highlevel region, either by performing a full optimization42,51 or a single-point calculation on the geometry obtained at a lower level of calculation.53−55 Alternatively, other researchers have employed parametrized functionals such M06L51 or M06-2X.56 Recently, Van der Mynsbrugge et al.52 included dispersion in their results obtained with a two-layer ONIOM calculation using B3LYP at the high-level and a posteriori correction and the ELC−DF scheme. xc In this work, we employ the ONIOM method (QM/MM) and (QM/QM′), as implemented in the Gaussian-03/09 program (G03, version RevD.02; and G09, version RevC.01)57 to study the adsorption of alkylamines on HMOR and the influence of noncovalent interactions in the adsorption process. In light of our results, a reinterpretation of the falloff on the differential heat of adsorption (x) coverage diagram is attempted.

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COMPUTATIONAL DETAILS AND MODELS

The MOR unit cell contains four different tetrahedron (T) sites, namely, T1, T2, T3, and T4. A model of MOR which contains the four tetrahedron sites with 1011 atoms (Figure 1) was employed to perform two-layer ONIOM calculations. The

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RESULTS AND DISCUSSION H-MOR Structure. Table 1 shows the average relative errors for the distances and angles of the H-MOR structure. The calculation results was compared with the experimental values from the X-ray spectrum of a synthetic MOR with a Si/ Al ratio of 7.62 The average relative error in the distances, Δε (d), and angles, Δε(a), around the four nearest T−O distances and T−O−Si angles for each T center were calculated as follows: Δε(X ) =

1 4

∑ |%Δε(X )| =

1 4

∑

⎡X − X ⎤ cal ⎢ exp ⎥ × 100% Xexp ⎥⎦ ⎢⎣ (1)

where X indicates distances or angles. The values are quite insensitive to the choice of the (high/ low) levels of treatment for all the sites, varying in the range 8.0% ≤ Δε(d) ≤ 9.0%. On the other hand, the Δε(a) values show a more pronounced dependence not only on the level of treatment but also on the site, varying in the range 4.7% ≤ Δε (a) ≤ 8.4%, according to the following trends: ωB97X-D > LC-ωPBE > B3LYP:HF ∼ CAM-B3LYP at T1, ωB97X-D > LC-ωPBE > CAM-B3LYP > B3LYP:HF at T2, and B3LYP:HF

Figure 1. Model of MOR. High-level, balls and sticks; low-level, wireframes. C


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bond lengths are shown in Table 3. All the results were obtained at the B3LYP:UFF level of treatment inasmuch as this level furnishes the lowest Δε(a) and Δε (d) values comparable to all the other levels of treatment considered. From Table 2 it is clear that, independent of the site, the N− H(1) and N−H(2) (except for Me3N) bonds are considerably enlarged relative to their values in the free molecules (N−H = 1.016 Å), while N−H(3) and N−H(4) are less affected on adsorption. This is due to the fact that the N−H(1) bonds are the ones resulting from the interaction of the amine N atom with the Brønsted site while the N−H(2) bonds are involved in a hydrogen bond with a framework O atom, as shown in Figure 3a−l. Moreover, these figures illustrate how the position of the amines inside the zeolite depends on the type of site and the structure of the amine. Excluding NH3, whose interaction with the zeolite involves the formation of two hydrogen bonds independent of the site, for the methylamines the number of these bonds depends on the location of the Brønsted site. For instance, only one hydrogen bond is formed (the one involving the Brønsted site) for MeNH2 adsorbed on site T2 as well as for Me2NH adsorbed on sites T1 and T2 and for Me3N adsorbed on all the sites. As shown in Table 3, the O−H bond lengths depicted in Figure 3 are typical of a hydrogen bond. The N−C bond distances in the methylamines are also enlarged relative to their respective values in the free amines, but the increase in the bond length, for each amine, is almost independent of the adsorption site. Next we considered the effect of the different schemes of calculation to take into account the noncovalent interactions on the amine−H-MOR structures. The changes in the geometrical parameters of all the amine−H-MOR complexes caused by the inclusion of noncovalent interactions can be expressed in terms of two statistical parameters: the range (R)

Figure 2. Location of the different oxygen atoms attached to Al atom at (a) T1, T2 and (b) T3, T4.

R = dmax − dmin

> LC-ωPBE > CAM-B3LYP ∼ ωB97X-D at T4. In general, the B3LYP:UFF combination gives higher Δε(d) and lower Δε(a) values. Considering all the sites, the ωB97X-D:HF/STO-3G combination produces the largest deformation in the H-MOR structure. Adsorption of Alkylamines. The NR3 molecules interact with the Brønsted sites of H-MOR to form [HNR3]+ species which may be stabilized by hydrogen bonds and vdW interactions with the framework atoms. The strength of the interaction will depend on the amine and the local structure of the sites. Therefore, we considered the adsorption of each amine [H3C-NH2, (H3C)2-NH and (H3C)3-N] on sites T1, T2, and T4 compared to that of NH3 of a previous study.43 Table 2 shows the N−H bond lengths of the amines adsorbed on sites T1, T2, and T4 and Figure 3a−l the respective optimized geometries. Selected H−O and N−C

(2)

and the standard deviation (S) ⎡ ∑N (d − d ̅ )2 ⎤1/2 i ⎥ S=⎢ i ⎢⎣ ⎥⎦ N−1

(3)

where dmax and dmin are the maximum and minimum distances, respectively, for a given bond considering all the schemes employed; d̅ is its average value, and N is the number of the methodologies employed. The results of this analysis are shown in Table 4. In general, the geometrical parameters of all complexes, independent of the adsorption site, differ very little from the respective B3LYP:UFF values (Tables 2 and 3), meaning that the structure of the complexes is quite insensitive to the different

Table 1. Average Relative Error (%), for Distances Δε(d) and Angles Δε(a) for Parameters Selected of H-MOR at T1, T2, and T4 Sites T1

a

T2

T4

method

Δε(d)

Δε(a)

Δε(d)

Δε(a)

Δε(d)

Δε(a)

B3LYP:UFFa B3LYP:HF/STO-3G CAM-B3LYP:HF/STO-3G LC-ωPBE:HF/STO-3G ωB97X-D:HF/STO-3G

9.0 8.2 8.1 8.1 8.0

4.7 5.8 5.7 6.2 6.5

9.3 9.3 9.1 9.5 9.4

5.0 5.5 5.9 7.8 8.2

9.4 9.0 8.8 8.8 8.6

6.5 8.4 7.8 8.1 7.8

Ref 43. D


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Table 2. N−H Bond Length (Angstroms) for the Amines in the Amines−MOR Systems at T1, T2, and T4 Sites Calculated with B3LYP:UFFa NH3b T1 T2 T4 a

MeNH2

Me2NH

Me3N

N−H(1)

N−H(2)

N−H(3)

N−H(4)

N−H(1)

N−H(2)

N−H(3)

N−H(1)

N−H(2)

N−H(1)

1.078 1.086 1.086

1.038 1.035 1.045

1.026 1.020 1.021

1.018 1.020 1.020

1.066 1.071 1.071

1.033 1.032 1.041

1.026 1.021 1.021

1.065 1.063 1.063

1.024 1.027 1.037

1.057 1.062 1.062

N−H (calculated, free) in NH3, MeNH2, and Me2NH: 1.016 Å. bRef 43.

role in the process of adsorption. On the other hand, no general trend is observed for the Eads as a function of the degree of methylation or the site of adsorption, except for site T2 in which case, independent of the level of calculation, Eads increases with the degree of methylation. Nevertheless, the adsorption energy average values, Eads (Table 5), clearly show a tendency of increasing Eads with the degree of methylation at all levels of calculation except for B3LYP:UFF and B3LYP:HF/ STO-3G. At this point it is important to mention that no unique trend is observed in the experimental values of ΔHads as a function of the degree of methylation. While for Chen et al.8 the order is MeNH2 > Me2NH > NH3 > Me3N, for Lee et al.9 the ΔHads values follow the order Me2NH > Me3N > MeNH2 > NH3. The relative contribution of the noncovalent interactions (dispersion and hydrogen bonds) to Eads can be established by comparison of the adsorption energies obtained at the B3LYPD3 and ωB97X-D levels with the B3LYP and ωB97X values, respectively, using HF/STO-3G as a low-level. The results for sites T1, T2, and T4, shown in Table 6, indicate that Eads(B3LYP) < Eads(ωB97X) while the dispersion contribution is larger for B3LYP. This is understandable because ωB97X is a long-range corrected hybrid functional, whereas B3LYP is not. The importance of the corrections for the noncovalent interactions is more pronounced for the results obtained at the B3LYP level than for the ωB97X results. For example, from the total adsorption energy Eads of Me3N at site T1, 56% is due to the D3 correction while only 38% is due to the D correction to the ωB97X value. In general, the noncovalent interactions contribution to Eads increases with the degree of methylation as the interaction of the amine with the MOR framework also increases. This relation between the adsorbate size and the degree of correction due to noncovalent interactions was observed by Van der Mynsbrugge et al.52 when studying the adsorption of benzene and small alkanes on H-ZSM-5 and Hbeta zeolites. The only theoretical result reported is the one by Jiang et al.16 who, employing a two layer ONIOM (B3LYP/6-31G(d, p):HF/3-21G) methodology with a cluster containing 6T centers in the high-level and 20T in the low-level, calculated Eads for NH3, MeNH2, Me2NH, and MeNH3 on H-MOR when the acidic proton is attached to the O10 atom in the T4 site. Using this configuration in our model we obtained Eads values that differ from the Eads(Jiang et al.) values by 44, 48, 28, and 18 kJ/mol for NH3, MeNH2, Me2NH and Me3N, respectively, at the B3LYP:HF/STO-3G level of calculation. This large discrepancy is certainly due to the size of the cluster used by Jiang et al.16 We have also considered the possibility of using single-point calculations to obtain the Eads. The single-point strategy consists of performing a full geometry optimization with a low-cost methodology and using this geometry to perform a

DFT approximations. Amid the N−H distances, the N−H(1) presents the largest variations in R and S, for all amines. This is understandable because this bond results from the interaction of the amine N atom with the Brønsted site. The N−H−O hydrogen bonds are the most sensitive to changes in the DFT treatment exhibiting the largest S values. Figure 4 shows the results for the amines adsorption energy (Eads) at sites T1, T2, and T4 for different (high/low) levels of calculation. As expected, the Eads of the amines depends on the site of adsorption and the level of calculation employed. Some general trends for the adsorption energy Eads are evident from Figure 4. (a) The highest values of Eads are always the ones obtained at the B3LYP-D3:UFF, HF/STO-3G level while the lowest are the ones obtained at the B3LYP:UFF level of calculation. (b) The Eads results obtained using B3LYP and B3LYP-D3 are quite insensitive to the choice of the low-level, UFF or HF/STO-3G, for all the amines and sites of adsorption. (c) Independent of the amine and the site of the adsorption, the Eads results obtained with the a posteriori Grimme correction (B3LYP-D3) and ωB97X-D as high level and HF/STO-3G as low level are very similar, parallel each other, and increase with the degree of methylation. (d) For all the amines and sites of adsorption, the Eads results obtained at the CAM-B3LYP and LC-ωPBE as high level and HF/STO-3G as low level are practically the same and parallel each other. Even though our model does not contemplate all the atoms belonging to the MOR main channel in the high-level, the small variation of the adsorption energies computed with B3LYP as the high-level and UFF or HF/STO-3G as a low-level demonstrates that the interaction between the amine and the channel is well represented by the high-level region. In fact, we have used this same model in a previous work43 where the Eads(NH3) obtained with the ONIOM methodology was compared to the results using a pseudospectral method. The model employed in the pseudospectral calculations takes into account the entire MOR cavity represented with 247 atoms (72T). The results obtained showed that the NH3 adsorption energies for the two models at T1, T2 and T4 differ at most by 3.3 kJ/mol, depending on the adsorption site (T1, T2, or T4). Besides, using B3LYP:UFF the distances between any O atom from the main channel belonging to low level and the H atom from the amine that points to that direction of the zeolite vary from 4.2 Å for Me3N to 6.1 Å for NH3. Therefore, the interaction between the amines and that part of the channel may be considered negligible. Overall, the Eads values follow the trend B3LYP < CAMB3LYP, LC-ωPBE < B3LYP-D3, ωB97X-D, which is consistent with the fact that noncovalent interactions play an important E


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Figure 3. Interaction of the amines with H-MOR: (a) NH3 (T1), ref 43; (b) NH3 (T2), ref 43; (c) NH3 (T4), ref 43; (d) MeNH2 (T1); (e) MeNH2 (T2); (f) MeNH2 (T4); (g) Me2NH (T1); (h) Me2NH (T2); (i) Me2NH (T4); (j) Me3N (T1); (k) Me3N (T2); and (l) Me3N (T4) calculated with B3LYP:UFF.

the geometries optimized at the B3LYP:UFF level of calculation (Table 7). The results show that except for the values obtained with ωB97X-D at sites T1 and T2, there is practically no difference between the Eads calculated with the two strategies. Consequently, the single-point strategy for these systems could be a reasonable alternative to reduce the

single-point calculation at a higher level of theory. Even though this strategy is widely employed in theoretical studies, its accuracy depends on the methodologies used for the full optimization and single-point calculations, and on the system under study. We have compared the Eads generated by full optimization with the results of single-point calculations using F


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Table 3. H−O and N−C Bond Length (Angstroms) for the Amines in the Amines−MOR Systems at T1, T2, and T4 Sites Calculated with B3LYP:UFFa NH3b T1 T2 T4 a

MeNH2

Me2NH

H(1)−O

H(2)−O

H(1)−O

H(2)−O

N−C

H(1)−O

1.564 7a 1.541 3b 1.519 2b

1.848 7b 1.903 7c 1.794 2d

1.611 7a 1.599 3b 1.571 2a

1.936 7b

1.488

1.635 7a 1.649 3b 1.617 2b

1.492 1.749 2b

1.490

H(2)−O

1.787 2d

Me3N

N−C(1)

N−C(2)

H(1)−O

N−C(1)

N−C(2)

N−C(3)

1.492

1.491

1.497

1.495

1.491

1.493

1.494

1.500

1.493

1.494

1.489

1.489

1.714 7a 1.644 3b 1.657 2b

1.496

1.497

1.498

N−C (calculated, free) in MeNH2, 1.466 Å; Me2NH, 1.459 Å; and Me3N, 1.457. bRef 43.

Table 4. Statistical Parameters for the Evaluation of N−H, N−C, and H−O Bond Spread among the DFT Methodologies for the Amines−MOR Systems at T1, T2, and T4 Sitesa T1 NH3

MeNH2

Me2NH

Me3N

a

N−H(1) N−H(2) N−H(3) N−H(4) H(1)-O H(2)-O N−H(1) N−H(2) N−H(3) H(1)-O H(2)-O N−C N−H(1) N−H(2) H(1)-O H(2)-O N−C(1) N−C(2) N−H(1) H(1)-O N−C(1) N−C(2) N−C(3)

T2

T4

1.065 1.035 1.033 1.017 1.611 1.925 1.057 1.032 1.030 1.642 1.958 1.482 1.066 1.023 1.591

0.021 0.006 0.010 0.002 0.080 0.122 0.014 0.004 0.008 0.060 0.181 0.015 0.007 0.003 0.068

8.0 2.2 3.9 1.0 29.3 51.5 5.3 1.6 3.8 23.8 66.6 6.4 2.9 1.3 26.8

1.086 1.031 1.020 1.020 1.529 1.977 1.067 1.030 1.020 1.598

0.008 0.004 0.002 0.002 0.035 0.134 0.009 0.004 0.002 0.023

5.0 2.2 1.1 1.0 15.6 56.6 3.3 1.5 1.1 9.4

1.491 1.063 1.025 1.618

0.015 0.008 0.003 0.054

6.3 3.4 1.1 22.8

1.484 1.488 1.057 1.694 1.487 1.488 1.484

0.016 0.015 0.006 0.070 0.018 0.016 0.016

6.9 5.6 2.3 7.8 0.6 0.4 0.4

1.488 1.488 1.055 1.704 1.492 1.487 1.487

0.015 0.016 0.013 0.080 0.016 0.015 0.015

6.1 6.8 4.6 10.6 0.4 0.4 0.4

1.085 1.041 1.019 1.021 1.526 1.803 1.070 1.037 1.021 1.579 1.836 1.480 1.062 1.035 1.600 1.814 1.478 1.478 1.065 1.611 1.488 1.489 1.491

0.009 0.007 0.004 0.003 0.030 0.050 0.007 0.007 0.003 0.036 0.089 0.014 0.007 0.003 0.026 0.059 0.015 0.014 0.005 0.071 0.018 0.017 0.017

3.6 2.7 1.8 1.3 17.3 25.6 3.0 2.7 1.2 19.3 15.1 3.4 2.9 1.3 11.4 5.6 3.6 3.0 2.4 7.4 0.6 0.5 0.5

Bond average (d̅, angstroms) is in roman text, range (R, angstroms) in italics, and standard deviation (S × 103) in bold.

Figure 4. Eads(amines) dependence over the DFT methodology and the site studied.

computational cost of including noncovalent corrections to DFT results. Comparison with the Microcalorimetry Results. In the Introduction, we presented possible reasons for the discrepancy in the two experimental determinations8,9 of ΔHads for alkylamines in H-MOR. Because in the work by Chen et al.8

the authors themselves recognized that the measurements being conducted sequentially on the same sample for all the amines could have blocked some of the sites for subsequent experiments, we will focus on the comparison with the results by Lee et al.9 G


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Table 7. Difference in the Eads (Kilojoules per Mole) from Full Optimization and Single-Point Methodologies for CAM-B3LYP:HF/STO-3G, ωB97X-D:HF/STO-3G, and LC-ωPBE:HF/STO-3G at T1, T2, and T4 Sites

Table 5. Eads (Kilojoules per Mole) for Each Amine at T1, T2, and T4 Sites

a

method

NH3

MeNH2

Me2NH

Me3N

B3LYP:UFF B3LYP:HF/STO-3G B3LYP-D3:UFF B3LYP-D3:HF/STO-3G CAM-B3LYP:HF/STO-3G ωB97X-D:HF/STO-3G LC-ωPBE:HF/STO-3G

146.9a 146.2 185.4 185.6 156.3 177.4 155.5

174.4 176.2 226.9 229.4 187.3 221.3 186.4

182.3 182.8 258.5 247.7 196.4 242.1 194.0

180.0 180.2 262.4 269.4 199.3 265.9 198.2

T

amine

CAM-B3LYP: HF/STO-3G

ωB97X-D: HF/STO-3G

LC-ωPBE: HF/STO-3G

T1

NH3 MeNH2 Me2NH Me3N NH3 MeNH2 Me2NH Me3N NH3 MeNH2 Me2NH Me3N

0.4 0.1 2.2 1.2 −7.6 0.4 −0.1 0.6 0.5 0.6 0.6 1.8

0.7 1.9 6.5 5.0 −9.5 −9.7 −7.0 −3.5 0.8 3.6 3.2 4.6

0.9 1.8 3.2 3.1 −3.2 −2.4 −2.4 −1.3 0.2 0.1 0.2 1.4

T2

Ref 43.

Only for the T4 center do our reported Eads values follow the same trend of the ΔHads with the degree of methylation observed by Lee et al.,9 except for the results obtained at the B3LYP-D3 and the ωB97X-D level of calculation which, according the previous studies,28 may exhibit overbinding mainly when used with DZ-type basis sets. With the purpose of determining the influence of the basis set superposition error (BSSE) and the zero-point vibration energy (ZPVE) on the calculated Eads values and on their trend with the degree of methylation, we considered these corrections on values obtained with all the functionals previously used. The results obtained after the BSSE correction show the same trend as before, independent of the functional used (Figure 5a). Comparison of the BSSE corrected and uncorrected values show that BSSE reduces the Eads for all the cases, with a maximum reduction of 28% for the Me3N adsorption energy obtained at the B3LYP:HF/STO-3G level of calculation. It is worth mentioning that the BSSE error using a DZ or a TZ basis set for the amines is practically the same and that the corresponding Eads exhibit the same trend as before (see Supporting Information). The same correction was applied to the Eads values for adsorption on centers T1 and T2 (Figure 5b). It is clear from Figure 5b that only for adsorption at T4 do the calculated Eads follow the trend observed experimentally. Inclusion of the ZPVE correction on the Eads (T4) values obtained at the B3LYP-D3:UFF with BSSE correction does not affect the Eads trend but reduces Eads (T4) by 6−9% (Figure 5c). Furthermore, the calculated Eads(BSSE), Eads(BSSE, ZPVE), and ΔHads(BSSE, ZPVE) present the same behavior as the experimental ΔHads (Figure 5c). The aforementioned results are corroborated by the experimental work of Lukyanov et al.15 and our previous results,43 which showed that the T4 site is the position most probable to sit the Al atom and that the O2 atom is the most favorable one to attach the proton. Therefore, it is quite reasonable to assume that the amines will adsorb preferentially at T4.

T4

Because of the predominant importance of dispersion and BSSE to the description of the adsorption process, these effects must be taken into account in any attempts at interpreting the microcalorimetry experiments. For this purpose we shall use hereafter the B3LYP-D3:UFF(BSSE) level of calculation which is the less time-consuming level of calculation which properly takes into account all the mentioned effects. A possible way to make the comparison with the experimental results is to use the relative percentage of occupied sites, as determined by Lukyanov et al.55 and the adsorption energies for NH3, to obtain a weight-average. When this strategy is employed, it is possible to determine whether the microcalorimetry behavior is dominated by adsorption at the isolated sites. Table 8 shows the Eads(NH3) associated with each T-O ordered according to the site relative stability. Assuming that all sites are involved at any coverage and using the data from Table 8, the weight-average ⟨Eads(NH3)⟩ is 165.0 kJ/mol, which is practically equal to the Eads(NH3) at T4 (O2). Therefore, the assumption that all sites are involved at any stage of the process does not explain the falloff of the differential heat of adsorption (x) coverage. The acid site T4 (O2) is the more stable and, according to Lukyanov et al.,55 the one which has the larger number of H attached to it, that is, most of the Brønsted acid sites are formed by attaching a proton to T4 (O2) sites. Consequently, at a low coverage of NH3 it is reasonable to assume that the adsorption will take place preferentially at this site and that the observed Eads shall be due mainly to this site. As the coverage increases, all the T4 sites will be occupied and the molecules will adsorb at sites T1, T2, and T3. Assuming that the adsorption will take place according to the site relative stability [T2 (O3); T1 (O7);

Table 6. Dispersion Contribution to the Eads (Kilojoules per Mole) for B3LYP-D3:HF/STO-3G and ωB7X-D:HF/STO-3G for the Amines−MOR Systems at T1, T2, and T4a NH3 T1 T2 T4

a

B3LYP-D3 ωB7X-D B3LYP-D3 ωB7X-D B3LYP-D3 ωB7X-D

143.4 154.3 137.6 142.9 157.7 163.1

MeNH2

41.9 26.7 40.5 20.4 35.7 24.7

174.1 184.8 171.0 176.6 183.5 189.8

54.7 39.8 54.4 32.8 50.4 40.1

Me2NH 167.7 182.9 183.4 189.1 197.4 206.8

66.8 52.3 65.1 45.4 62.8 49.8

Me3N 165.1 186.8 193.3 209.6 182.3 198.3

91.8 70.4 91.5 66.8 84.3 65.8

In italics: Eads(B3LYP-D3) − Eads(B3LYP) and Eads(ωB97X-D) − Eads(ωB97X). H


Article


Figure 5. Corrected Eads(amines): (a) BSSE correction for the different DFT methodologies at T4; (b) BSSE correction over the B3LYP-D3:UFF methodology at T1, T2, and T4; and (c) Eads, Eads(ZPVE), and ΔHads(ZPVE) calculated at B3LYP-D3:UFF(BSSE) methodology at T4 and the experimental ΔHads reported by Lee et al.9

Table 8. Eads (Kilojoules per Mole) for NH3 over Different T (O) Configurations T

O

%a

Eads(NH3)

%b

T4 T2 T1 T2 T3 T3 ⟨Eads⟩

2 3 7 5 1 9

39.1 11.7 11.5 12.8 13.4 11.5

162.4 158.2 158.1 186.6 160.9 168.1 165.0

19.2 18.9 21.0 22.0 18.9 166.6

Table 9. Eads (Kilojoules per Mole) for NH3 on T4 in T4(H)T(H) and on T1 or T4′ in T4(NH4)T(H) Obtained at the B3LYP-D3:UFF(BSSE) Level of Calculation 1NH3

2NH3

3NH3

T4(NH4) 162.4 T4(NH4)T1(H) 159.6 T4(NH4)T4′(H) 140.0

T4(NH4)(NH3) 101.0 T4(NH4)T1(NH4) 156.7 T4(NH4)T4′(NH4) 167.8

T4(NH4)(NH3)(NH3) 74.4 T4(NH4)T1(NH4)(NH3) 127.9 T4(NH4)T4′(NH4)(NH3) 92.7

a

Acid sites experimental distribution, ref 55. bAcid sites distribution after excluding T4.

discounting for the Lewis sites. To verify the influence of a second site, close to the preferential T4 site, as the coverage increases, we performed a series of calculations of Eads for NH3 involving the T4 site and a second T1 or T4 neighbor site, as depicted in Figure 6. We considered two types of structures with two acid sites, one of them being the preferential T4 site, T4(H)T1(H) and T4(H)T4′(H), and two types of structures with NH3 adsorbed at T4, T4(NH4)T1(H) and T4(NH4)T4′(H). From the results in Table 9, it is clear that Eads [T4(NH4)] < Eads [T4(NH4)T(H)], implying that the presence of another T4 acid site near T4 decreases the amine Eads at this site. The Eads(NH3) of the second NH3 adsorbed at T4(NH4)T(H) is similar to those obtained at T4(H); in addition, Eads [T4(NH4)] > Eads [T4(NH4)T(NH4)(NH3)]. These results show that the falloff of the differential heat of adsorption (x) coverage may be better understood in terms of multiple adsorption on a given site and the interaction among species adsorbed in neighbor sites of the zeolite cell rather than being due to site heterogeneity.

T2 (O5); T3 (O1); and T5 (O9)] it is clear from Table 8 that the microcalorimetry trend cannot be explained. Finally, excluding T4 the distribution of acid sites changes as shown in Table 8. Using this new distribution, the weight-average ⟨Eads(NH3)⟩ is equal to 166.6 kJ/mol, which is similar to the Eads(NH3) at low coverage. The results of this analysis indicate that an alternative explanation is needed for the falloff of the differential heat of adsorption (x) coverage. When a second molecule of NH3 is considered in the T4(NH4) site, the Eads for this second NH3 is 101.0 kJ/mol which represents a drop of 61.4 kJ/mol (38%) relative to the adsorption energy of a single NH3 molecule, Eads(NH3), adsorbed at T4; when a third molecule is adsorbed, the Eads drops even further, to 54% of the adsorption energy of a single molecule at T4 (Table 9). This behavior is consistent with what is observed experimentally by Lee at al.9 Furthermore, the H-MOR employed by Lee et al.9 has SAR = 15 which, according to the authors, implies that the zeolite may formally have two Brønsted sites per unit cell, after I


Article


Considering the different sites of H-MOR, the Eads follows the trend T4 > T1 ∼ T2 (NH3); T1 > T4 > T2 (MeNH2); T4 > T2 > T1 (Me2NH); and T2 > T4 > T1 (M3N). The presence of a second site close to the preferential T4 site decreases the adsorption energy of NH3 as the coverage is increased, and a considerable drop in Eads of NH3 is observed when more than one molecule is adsorbed on a T4 site. These results show that the falloff of the differential heat of adsorption (x) coverage may be better understood in terms of multiple adsorption on a given site and the interaction among species adsorbed in neighboring sites of the zeolite cell rather than being due to site heterogeneity.

■

ASSOCIATED CONTENT

S Supporting Information *

Adsorption energies uncorrected for the methodologies used and adsorption energies using basis set superposition error correction for different calculation methodologies. This material is available free of charge via the Internet at http://pubs. acs.org.

Figure 6. Location of the neighbor T1(H) and T4′(H) sites relative to T4(H).

■

■

CONCLUSIONS The adsorption of NH3, MeNH2, Me2NH, and Me3N at different positions of H-MOR was investigated by density functional methodologies that include noncovalent interaction such as vdW and hydrogen bonds. The optimal structures and adsorption energies were obtained by full optimization using a two-layer ONIOM method. The H-MOR structure is more susceptible to deformations for the combination ωB97X-D:HF/STO-3G when compared to the experimental results. On the other hand, the optimal structures for the amine−zeolite complexes are very similar for all the (high/low) levels of treatment considered. Depending on the site of adsorption and on the degree of methylation, these complexes are stabilized by one or two hydrogen bonds with the framework oxygen atoms. The adsorption energies computed with B3LYP as the high level are quite insensitive to the choice of the low level, UFF or HF/STO-3G, for amines and sites providing that the high-level region is large enough (60T). Overall, the Eads values follow the trend B3LYP < CAM-B3LYP, LC-ωPBE < B3LYP-D3, ωB97XD, which is consistent with the fact that noncovalent interactions play an important role in the process of adsorption. The adsorption energies obtained by full geometry optimization of the complexes do not differ appreciably from the ones of single-point calculations using the geometries optimized at the B3LYP:UFF level of calculation. The results show that except for the values obtained with ωB97X-D at sites T1 and T2, there is practically no difference between the Eads calculated with the two approaches, which is an indication that the single-point strategy for these systems could be a reasonable alternative to reduce the computational cost of including noncovalent corrections in DFT results. The behavior of the experimental differential heat of adsorption (x) coverage was also examined. At low coverage, when the adsorption takes place mainly at the isolated sites where the Al is preferential located, our Eads values for adsorption at site T4 follow the same trend of the ΔHads with the degree of methylation observed by Lee et al.9 The functionals that contain dispersion, B3LYP-D3 and ωB97X-D, reproduce the experimental trend when the BSSE correction is consider, while the ZPVE correction on the results obtained at the B3LYP-D3 + BSSE level does not alter the tendency.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS M.A.C.N. acknowledges financial support from CNPq, FAPERJ, and INOMAT. The rest of the authors acknowledge the financial support given by the Misión Ciencia project.

■

REFERENCES

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Theoretical Study of the Adsorption of Alkylamines in H-Mordenite

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