A DFT Study on Single Brønsted Acid Sites in Zeolite Beta and Their Interaction with Probe Molecules

: Zeolites are subjects of intensive research, as they have vast industrial applications. However, exact nature of catalytic active sites remains elusive. With this research, we attempt to shed light on the Brønsted acid sites in zeolite beta modiﬁcation A and correlate the widely used TPD methods of their identiﬁcation with the theoretically determined strongest and weakest acid sites. A diverse set of probe molecules with a wide range of acid strength of their conjugated acids is applied to determine the heats of their adsorption over protonated zeolite beta samples. The molecules studied were acetonitrile, dimethyl sulﬁde, dimethyl sulfoxide, isothiazole, pyridine, tetrahydrofuran, and ammonia. It was found that the heat of adsorption of the probe molecules correlated with the acid strength of acid sites only partially. Only some of the strong acid sites were able to be identiﬁed, while the weakest acid site was often identiﬁed correctly. To conclude, the widely used method of zeolites acid sites studies delivers only partially correct results, and the conclusions from such TPD studies should be treated with caution.


Introduction
Zeolites have attracted tremendous attention due to their vast industrial catalytic applications [1], employment in organic synthesis processes, separation of chemical compounds [2], usage in environment remediation processes [3], applications in agriculture [4], and diverse biological and biomedical uses [5].Recent applications of zeolite catalysts involve upgrading biomass to produce fuels and other valuable raw materials [6] and trapping and burning of exhaust hydrocarbons during cold engines start-ups [7].
For obtaining the highest yield of reactions, desirable selectivity, and stability of zeolite catalysts, it is necessary to prepare catalysts with optimized porous structure [1,11], number, strength, and locations of acid sites [12].Brønsted acid sites are usually the active centers for acid-catalyzed reactions.
With the development of quantum chemical computations, density functional theory (DFT) calculations became an important additional method for zeolites characterization [44].For obtaining information regarding the strength of acid sites, a quantity such as the energy of deprotonation (DPE) in a vacuum is conveniently computed.Additionally, information regarding various compounds adsorbed over the acid sites is calculated [45].NMR shifts for 29 Si are computed for drawing conclusions regarding the exact environment of Si according to the experimentally observed signals [46].Sites preferentially occupied with Al tetrahedral positions (T sites) are deduced from DFT computations [47].The relative stability of various Al-substituted T sites in zeolite beta have been studied previously in a number of works [48].Hydrogen bonding was found to exert a large influence on the properties of Brønsted acid sites [49].However, the results are strongly method-dependent.Correlation of acid strength and interaction energy with adsorbed probe molecules was studied by Boronat and Corma [50].It was found that specific interactions of adsorbed probe molecules strongly affected the adsorption energy.
In the present work, we additionally investigate the relative stability of completely deprotonated Al-substituted zeolite beta samples with different locations of Al atoms and study the relative stability and acid strength of different protonated forms.Then, the adsorption of several probe molecules over the protonated samples was studied.The test molecules used have a wide range of acid strength of their protonated forms.These molecules were selected in such a way that their largest dimension is smaller than the diameter of pores of zeolite beta.It was found that energy of adsorption of different probe molecules did not correlate with the acid strength of Brønsted acid sites in zeolite beta.

Results and Discussion
First, we studied the stability of single Al-substituted zeolite beta with Al atoms located in all different T sites.Optimization of such structures resulted in some distortions of the lattice that were not large, and the entire zeolite framework retained its main characteristics.Figure 1 demonstrates the energy of the Al-substituted zeolite beta for all substituted T sites computed by the two employed methods.
With the development of quantum chemical computations, density functional theory (DFT) calculations became an important additional method for zeolites characterization [44].For obtaining information regarding the strength of acid sites, a quantity such as the energy of deprotonation (DPE) in a vacuum is conveniently computed.Additionally, information regarding various compounds adsorbed over the acid sites is calculated [45].NMR shifts for 29 Si are computed for drawing conclusions regarding the exact environment of Si according to the experimentally observed signals [46].Sites preferentially occupied with Al tetrahedral positions (T sites) are deduced from DFT computations [47].The relative stability of various Al-substituted T sites in zeolite beta have been studied previously in a number of works [48].Hydrogen bonding was found to exert a large influence on the properties of Brønsted acid sites [49].However, the results are strongly method-dependent.Correlation of acid strength and interaction energy with adsorbed probe molecules was studied by Boronat and Corma [50].It was found that specific interactions of adsorbed probe molecules strongly affected the adsorption energy.
In the present work, we additionally investigate the relative stability of completely deprotonated Al-substituted zeolite beta samples with different locations of Al atoms and study the relative stability and acid strength of different protonated forms.Then, the adsorption of several probe molecules over the protonated samples was studied.The test molecules used have a wide range of acid strength of their protonated forms.These molecules were selected in such a way that their largest dimension is smaller than the diameter of pores of zeolite beta.It was found that energy of adsorption of different probe molecules did not correlate with the acid strength of Brønsted acid sites in zeolite beta.

Results and Discussion
First, we studied the stability of single Al-substituted zeolite beta with Al atoms located in all different T sites.Optimization of such structures resulted in some distortions of the lattice that were not large, and the entire zeolite framework retained its main characteristics.Figure 1 demonstrates the energy of the Al-substituted zeolite beta for all substituted T sites computed by the two employed methods.As we can see in Figure 1, substitution of different T sites resulted in considerably different energy of the Albea221c -structures, with the difference span of nearly 14mHa for the first computational method and nearly 7 mHa (18 kJ/mol) for the second method.As we can see in Figure 1, substitution of different T sites resulted in considerably different energy of the Albea221c -structures, with the difference span of nearly 14mHa for the first computational method and nearly 7 mHa (18 kJ/mol) for the second method.In agreement with our previous study, locating Al in sites T5 and T6 produced the most stable structures.Relative stability of other Al-substituted T sites depends markedly on the computational method used.In general, the sites T7, T8, and T9 were the next less stable sites.However, the stability of sites T1 to T4 depended strongly on the method of computation, and from these results, we cannot say what are the least stable Al locations in zeolite beta structure.The energy difference of up to 14 mHa equaled 37 kJ/mol.This significantly exceeded the thermal energy fluctuation 3RT typically used for the hydrothermal synthesis of zeolites, which equals 7 kJ/mol at room temperature and 13 kJ/mol at temperature 250 • C.However, according to the second computational method, the energy difference between different structures was 18 kJ/mol, which approaches the thermal fluctuations range of 13 kJ/mol for the hydrothermal synthesis.Therefore, it is possible that substitution of any T sites is possible during the hydrothermal synthesis from the thermodynamic point of view.Higher quality offset was used for the second method of computation, and this adds confidence to the conclusion that substitution of Al to different T sites is not governed by thermodynamics but rather by some kinetics features, influence of template molecules, and reaction synthesis media.

Energy, Hartrees
Next, we considered protonated models of HAlbea221c with proton attached to all possible adjacent oxygen atoms exposed in the external walls of the zeolite framework.Figure 2 demonstrates data on energy of all variants of protonated Brønsted acid sites computed by the two methods of computation.As we can observe, the protonated sites T5 and T6 were again the most stable structures.Protonated sites T1 and T2 were the least stable structures according to the first computational method, while T1 was the least stable according to the second computational method.The rest of the structures possessed intermediate stability.The entire range of stability spanned the range of 14 mHa for the first computational method as well as for the second computational method.According to the results presented, one can determine the most profitable location of protonation for each of the T sites.Since the range of energy for different protonated oxygen atoms covered a wide range of energy, only selected protonated sites were stable enough to be present in the zeolite beta structure.
Catalysts 2023, 13, 833 3 of 15 In agreement with our previous study, locating Al in sites T5 and T6 produced the most stable structures.Relative stability of other Al-substituted T sites depends markedly on the computational method used.In general, the sites T7, T8, and T9 were the next less stable sites.However, the stability of sites T1 to T4 depended strongly on the method of computation, and from these results, we cannot say what are the least stable Al locations in zeolite beta structure.The energy difference of up to 14 mHa equaled 37 kJ/mol.This significantly exceeded the thermal energy fluctuation 3RT typically used for the hydrothermal synthesis of zeolites, which equals 7 kJ/mol at room temperature and 13 kJ/mol at temperature 250 °C.However, according to the second computational method, the energy difference between different structures was 18 kJ/mol, which approaches the thermal fluctuations range of 13 kJ/mol for the hydrothermal synthesis.Therefore, it is possible that substitution of any T sites is possible during the hydrothermal synthesis from the thermodynamic point of view.Higher quality offset was used for the second method of computation, and this adds confidence to the conclusion that substitution of Al to different T sites is not governed by thermodynamics but rather by some kinetics features, influence of template molecules, and reaction synthesis media.
Next, we considered protonated models of HAlbea221c with proton attached to all possible adjacent oxygen atoms exposed in the external walls of the zeolite framework.Figure 2 demonstrates data on energy of all variants of protonated Brønsted acid sites computed by the two methods of computation.As we can observe, the protonated sites T5 and T6 were again the most stable structures.Protonated sites T1 and T2 were the least stable structures according to the first computational method, while T1 was the least stable according to the second computational method.The rest of the structures possessed intermediate stability.The entire range of stability spanned the range of 14 mHa for the first computational method as well as for the second computational method.According to the results presented, one can determine the most profitable location of protonation for each of the T sites.Since the range of energy for different protonated oxygen atoms covered a wide range of energy, only selected protonated sites were stable enough to be present in the zeolite beta structure.Thereafter, we considered the acid strength of different protonated Brønsted acid sites.Figure 3 demonstrates the deprotonation energy for all the constructed acid sites shown in Figure 2. The lower deprotonation energy indicates larger acid strength of the corresponding acid sites.In Figure 3A, one can observe that there were several acid sites with prominently low DPE and high acid strength.They were T1 HO94 and T2 HO95, Thereafter, we considered the acid strength of different protonated Brønsted acid sites.Figure 3 demonstrates the deprotonation energy for all the constructed acid sites shown in Figure 2. The lower deprotonation energy indicates larger acid strength of the corresponding acid sites.In Figure 3A, one can observe that there were several acid sites with prominently low DPE and high acid strength.They were T1 HO94 and T2 HO95, followed by less acidic T6 HO495 for the first computational model and T1 HO94 and T2 HO95, followed by less acidic T9 HO426, T3 HO241, T7 HO363, and T7 HO490 for the second computational method.The site with the prominently large DPE and, consequently low acid strength, was T4 HO338 for the first method of computation and T4 HO338 for the second method of computation.Therefore, both computational methods provided concurrent information regarding the strongest and weakest acidic Brønsted sites.

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Catalysts 2023, 13, 833 4 of 15 followed by less acidic T6 HO495 for the first computational model and T1 HO94 and T2 HO95, followed by less acidic T9 HO426, T3 HO241, T7 HO363, and T7 HO490 for the second computational method.The site with the prominently large DPE and, consequently low acid strength, was T4 HO338 for the first method of computation and T4 HO338 for the second method of computation.Therefore, both computational methods provided concurrent information regarding the strongest and weakest acidic Brønsted sites.In the following section of the manuscript, we consider whether and how the adsorption of probe molecules can help to determine the strongest acidic sites in the described developed models.The probe molecules are generally considered in the order of decreasing acid strength of their conjugated acids.Figure 4 reveals energy of adsorption of acetonitrile over all the different Brønsted acid sites in the zeolite beta model HAlbea221c.Acetonitrile is a prominent probe molecule because it is a linear molecule and interacts with the zeolite framework only with its nitrogen atom of the nitrile group.As we can see, the strongest interaction of acetonitrile was exhibited for the acid sites T7 HO490 and T2 HO95, and to a smaller extent, T6 HO495 and T9 HO421, while the weakest interaction was seen for the sites T6 HO341 and T9 HO53.According to the second computational method, the strongest interaction was observed with the sites T7 HO490 and T9 HO426 and the weakest interaction was obtained with the site T4 HO338.In the following section of the manuscript, we consider whether and how the adsorption of probe molecules can help to determine the strongest acidic sites in the described developed models.The probe molecules are generally considered in the order of decreasing acid strength of their conjugated acids.Figure 4 reveals energy of adsorption of acetonitrile over all the different Brønsted acid sites in the zeolite beta model HAlbea221c.Acetonitrile is a prominent probe molecule because it is a linear molecule and interacts with the zeolite framework only with its nitrogen atom of the nitrile group.As we can see, the strongest interaction of acetonitrile was exhibited for the acid sites T7 HO490 and T2 HO95, and to a smaller extent, T6 HO495 and T9 HO421, while the weakest interaction was seen for the sites T6 HO341 and T9 HO53.According to the second computational method, the strongest interaction was observed with the sites T7 HO490 and T9 HO426 and the weakest interaction was obtained with the site T4 HO338.

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If we compare the strongest acid sites with the strongest adsorption of acetonitrile, we can conclude that only partial agreement is reached; the sites T2 HO95 and T6 HO495 are both strong acids and both showed large acetonitrile adsorption energy.No agreement was observed for the weakest acid sites and the lowest energy of adsorption.For the second computational method used, a slightly better agreement was reached; the strongest acid sites T9 HO426 and T7 HO490 produced larger acetonitrile energy of adsorption, while the weakest acid site T4 HO338 agreed well with the lowest adsorption energy over it.Therefore, acetonitrile adsorption provided partial information on the strongest and weakest acid sites.However, the strongest acid sites T1 HO94 and T2 HO95 were both elusive in their identification by the second computational method, while the site T2 HO95 was correctly identified by the first computational method.
The next probe molecule that was applied for testing the acid sites was dimethyl sulfide.According to the results observed in Figure 5A, the largest interaction energy was for the acid sites T6 HO495 and T7 HO490, and the weakest binding energy was for the sites T1 HO67, T2 HO95, and T4 HO305.For the second applied computational method, the largest binding energy was for the sites T7 HO490, T1 HO94, and T9 HO421.The weakest interaction was seen for the sites T6 HO341, T8 HO470, T1 HO67, T4 HO305, and T4 HO338.
For the DMS adsorption, again only strong acid site T6 HO495 was able to be identified by the first method, and the strongly acidic site T1 HO94 was identified.T4 HO338 was correctly identified as the weak acid site.If we compare the strongest acid sites with the strongest adsorption of acetonitrile, we can conclude that only partial agreement is reached; the sites T2 HO95 and T6 HO495 are both strong acids and both showed large acetonitrile adsorption energy.No agreement was observed for the weakest acid sites and the lowest energy of adsorption.For the second computational method used, a slightly better agreement was reached; the strongest acid sites T9 HO426 and T7 HO490 produced larger acetonitrile energy of adsorption, while the weakest acid site T4 HO338 agreed well with the lowest adsorption energy over it.Therefore, acetonitrile adsorption provided partial information on the strongest and weakest acid sites.However, the strongest acid sites T1 HO94 and T2 HO95 were both elusive in their identification by the second computational method, while the site T2 HO95 was correctly identified by the first computational method.
The next probe molecule that was applied for testing the acid sites was dimethyl sulfide.According to the results observed in Figure 5A, the largest interaction energy was for the acid sites T6 HO495 and T7 HO490, and the weakest binding energy was for the sites T1 HO67, T2 HO95, and T4 HO305.For the second applied computational method, the largest binding energy was for the sites T7 HO490, T1 HO94, and T9 HO421.The weakest interaction was seen for the sites T6 HO341, T8 HO470, T1 HO67, T4 HO305, and T4 HO338.For the DMS adsorption, again only strong acid site T6 HO495 was able to be identified by the first method, and the strongly acidic site T1 HO94 was identified.T4 HO338 was correctly identified as the weak acid site.The next probe molecule for this study is dimethyl sulfoxide.Figure 6A shows the energy of interaction between this probe molecule and acid sites in zeolite beta computed by the first method.Its strongest adsorption was obtained for the sites T9 HO421, T8 HO465, and T1 HO94.The weakest interaction was obtained for the sites T1 HO12, T2 HO149, T2 HO167, and T4 HO338.According to the second method of computation, results of which are shown in Figure 6B, the largest adsorption energy was for the sites T3 HO13, and T7 HO490, and the lowest adsorption energy was for the sites T4 HO338, T8 HO470, and T9 HO426.Generally speaking, the multigrid settings 5/600/50 provide more dependable results since the denser grid provided more precise results, and these results are more trustworthy.Dimethyl sulfoxide is closer in acid strength to the acid strength of zeolite beta acid sites, and the extent of proton transfer reflects how acid strength of DMSO relates to the acid strength of zeolite acid sites.Next, we compared the results of DMSO adsorption with the acid strength obtained in Figure 3A.The strongest acid sites were T1 HO94, T2 HO95, and T6 HO495 for the first computational method.As we can observe, the site T1 HO94 was identified correctly from the adsorption energy of DMSO.The weak- The next probe molecule for this study is dimethyl sulfoxide.Figure 6A shows the energy of interaction between this probe molecule and acid sites in zeolite beta computed by the first method.Its strongest adsorption was obtained for the sites T9 HO421, T8 HO465, and T1 HO94.The weakest interaction was obtained for the sites T1 HO12, T2 HO149, T2 HO167, and T4 HO338.According to the second method of computation, results of which are shown in Figure 6B, the largest adsorption energy was for the sites T3 HO13, and T7 HO490, and the lowest adsorption energy was for the sites T4 HO338, T8 HO470, and T9 HO426.Generally speaking, the multigrid settings 5/600/50 provide more dependable results since the denser grid provided more precise results, and these results are more trustworthy.Dimethyl sulfoxide is closer in acid strength to the acid strength of zeolite beta acid sites, and the extent of proton transfer reflects how acid strength of DMSO relates to the acid strength of zeolite acid sites.Next, we compared the results of DMSO adsorption with the acid strength obtained in Figure 3A.The strongest acid sites were T1 HO94, T2 HO95, and T6 HO495 for the first computational method.As we can observe, the site T1 HO94 was identified correctly from the adsorption energy of DMSO.The weakest acid site T4 HO338 was also identified correctly.For the second method of computation shown in Figure 3B, the strong acid sites were T1 HO94, T2 HO95, T9 HO496, and T3 HO 241.The weakest sites were T4 HO338, T8 HO465, and T8 HO470.Among these strong acid sites, T1 HO94 was identified correctly from the DMSO adsorption.The weakest acid site was T4 HO338, which was also identified correctly.Therefore, again, adsorption of the probe molecule DMSO allowed only partial correct identification of the strongest and the weakest acid sites.The next studied probe molecule with even weaker acid strength of its conjugated acid was isothiazole.This molecule becomes protonated at the nitrogen atom and since it attracts protons relatively strongly, the acid strength of iTA conjugated acid was weaker as compared with all previously considered probe molecules.Figure 7A demonstrates adsorption energy of iTA to all Brønsted acid sites of the HAlbea221c model.According to the first computational method, the strongest interaction was obtained for the acid site T9 HO421, while there were plenty of sites with weak interaction with iTA probe molecule.Among such weakly interacting sites was T4 HO338.Therefore, the iTA adsorption allowed identification of the weakest acid site T4 HO338.For the second computational method, results of which are shown in Figure 7B, the strongest adsorption was seen for the sites T3 HO13 and T7 HO490.The weakest adsorption was obtained for the sites T4 HO338, T8 HO470, and T9 HO426.Again, adsorption of the probe molecule allowed for the identification of the weakest acid site T4 HO338, while the strongest acid sites eluded their identification.The iTA molecule is a cyclic molecule, and its close interaction with the acid sites located pinned to the zeolite pore wall required distortion of the OH group so that the interaction could proceed effectively.The same was also valid for the interaction with the other probe molecules, not excluding the simplest linear molecule acetonitrile.Normally, the nitrile group of acetonitrile interacts with the OH group in such a way that the OH ··NCCH3 moieties form a linear complex.However, if steric hindrances are present, the adsorption complex deviates from the linear form, and this results in a decrease in the interaction energy.To conclude, specific chemical interactions between iTA and the zeolite surface masked the identification of the strong acid sites.The next studied probe molecule with even weaker acid strength of its conjugated acid was isothiazole.This molecule becomes protonated at the nitrogen atom and since it attracts protons relatively strongly, the acid strength of iTA conjugated acid was weaker as compared with all previously considered probe molecules.Figure 7A demonstrates adsorption energy of iTA to all Brønsted acid sites of the HAlbea221c model.According to the first computational method, the strongest interaction was obtained for the acid site T9 HO421, while there were plenty of sites with weak interaction with iTA probe molecule.Among such weakly interacting sites was T4 HO338.Therefore, the iTA adsorption allowed identification of the weakest acid site T4 HO338.For the second computational method, results of which are shown in Figure 7B, the strongest adsorption was seen for the sites T3 HO13 and T7 HO490.The weakest adsorption was obtained for the sites T4 HO338, T8 HO470, and T9 HO426.Again, adsorption of the probe molecule allowed for the identification of the weakest acid site T4 HO338, while the strongest acid sites eluded their identification.The iTA molecule is a cyclic molecule, and its close interaction with the acid sites located pinned to the zeolite pore wall required distortion of the OH group so that the interaction could proceed effectively.The same was also valid for the interaction with the other probe molecules, not excluding the simplest linear molecule acetonitrile.Normally, the nitrile group of acetonitrile interacts with the OH group in such a way that the OH ••NCCH3 moieties form a linear complex.However, if steric hindrances are present, the adsorption complex deviates from the linear form, and this results in a decrease in the interaction energy.To conclude, specific chemical interactions between iTA and the zeolite surface masked the identification of the strong acid sites.The following probe molecule studied here was pyridine.The pyridine molecule possesses rather strong basic character, and, therefore, its conjugated acid is rather weak.Thus, it attracts protons from the zeolite acid sites strongly and less selectively.From Figure 8A, one can deduce that the strongest Py adsorption was attained for the sites T1 HO67 and T8 HO303.The weakest interaction was for the sites T2 HO127 and T3 HO13.Comparison with the acid sites strength in Figure 3A shows that the strong and weak acid sites could not be identified from the pyridine adsorption.According to the results of the second computational method shown in Figure 8, the largest adsorption was attained for the sites T9 HO57 and T7 HO201.The weakest interaction was for the sites T6 HO341, T2 HO95, and T4 HO338.In this case, T4 HO338 was correctly identified as the weakest acid site, while other sites were not identified correctly.Pyridine is a bulky molecule that barely suits into the pores of zeolite beta.Therefore, its The following probe molecule studied here was pyridine.The pyridine molecule possesses rather strong basic character, and, therefore, its conjugated acid is rather weak.Thus, it attracts protons from the zeolite acid sites strongly and less selectively.From Figure 8A, one can deduce that the strongest Py adsorption was attained for the sites T1 HO67 and T8 HO303.The weakest interaction was for the sites T2 HO127 and T3 HO13.Comparison with the acid sites strength in Figure 3A shows that the strong and weak acid sites could not be identified from the pyridine adsorption.The following probe molecule studied here was pyridine.The pyridine molecule possesses rather strong basic character, and, therefore, its conjugated acid is rather weak.Thus, it attracts protons from the zeolite acid sites strongly and less selectively.From Figure 8A, one can deduce that the strongest Py adsorption was attained for the sites T1 HO67 and T8 HO303.The weakest interaction was for the sites T2 HO127 and T3 HO13.Comparison with the acid sites strength in Figure 3A shows that the strong and weak acid sites could not be identified from the pyridine adsorption.According to the results of the second computational method shown in Figure 8, the largest adsorption was attained for the sites T9 HO57 and T7 HO201.The weakest interaction was for the sites T6 HO341, T2 HO95, and T4 HO338.In this case, T4 HO338 was correctly identified as the weakest acid site, while other sites were not identified correctly.Pyridine is a bulky molecule that barely suits into the pores of zeolite beta.Therefore, its According to the results of the second computational method shown in Figure 8, the largest adsorption was attained for the sites T9 HO57 and T7 HO201.The weakest interaction was for the sites T6 HO341, T2 HO95, and T4 HO338.In this case, T4 HO338 was correctly identified as the weakest acid site, while other sites were not identified correctly.Pyridine is a bulky molecule that barely suits into the pores of zeolite beta.Therefore, its interaction with the acid groups was strongly affected by the steric effects, and the results reflect not only the protonation energy but also configuration adjustment energy.
The next probe molecule considered in this study was tetrahydrofuran, which possesses relatively strong acid strength of its conjugated acid.Figure 9 demonstrates the results of interaction of this probe molecule with all the Brønsted acid sites in the HAlbea221c model with diverse configurations of acid sites adjacent to different T sites substituted with Al atoms.Figure 9A shows the results of interactions computed by the method PBE-D3 basis set TZV2P and multigrid settings 5/400/50.The strongest interaction of THF was obtained with the sites T9 HO421, T9 HO426, and T8 HO465.These sites do not represent the strong acid sites.The lowest adsorption energy was observed for the sites T2 HO127 and T9 HO53.These sites do not represent weak acid sites in the HAlbea221c.For the computational method PBE-D3, multigrid settings 5/600/50, and basis set TZVP (Figure 9B), the largest adsorption energy was seen for the sites T9 HO426 and T7 HO490.These sites do not represent strong acid sites.The weakest adsorption was observed for the acid sites T8 HO465, T4 HO338, T5 HO366, and T8 HO470.All of these sites except T5 HO366 represent weak acid sites in the structure of HAlbea221c.For the THF molecule, protonation from the acid sites took place at the oxygen atom of this molecule.This molecule is relatively bulky, and some steric hindrances also had an influence on the interaction of this molecule with the acid sites.Some acid sites had OH groups aligned closer to the surface of the zeolite pore wall.Thus, structural deviations took place for the deprotonation to occur.The same was also valid for other bulky probe molecules, such as pyridine.To conclude, THF molecule provided one of the best results for the identification of weak acid sites.
Catalysts 2023, 13, 833 9 of 15 interaction with the acid groups was strongly affected by the steric effects, and the results reflect not only the protonation energy but also configuration adjustment energy.
The next probe molecule considered in this study was tetrahydrofuran, which possesses relatively strong acid strength of its conjugated acid.Figure 9 demonstrates the results of interaction of this probe molecule with all the Brønsted acid sites in the HAl-bea221c model with diverse configurations of acid sites adjacent to different T sites substituted with Al atoms.Figure 9A shows the results of interactions computed by the method PBE-D3 basis set TZV2P and multigrid settings 5/400/50.The strongest interaction of THF was obtained with the sites T9 HO421, T9 HO426, and T8 HO465.These sites do not represent the strong acid sites.The lowest adsorption energy was observed for the sites T2 HO127 and T9 HO53.These sites do not represent weak acid sites in the HAl-bea221c.For the computational method PBE-D3, multigrid settings 5/600/50, and basis set TZVP (Figure 9B), the largest adsorption energy was seen for the sites T9 HO426 and T7 HO490.These sites do not represent strong acid sites.The weakest adsorption was observed for the acid sites T8 HO465, T4 HO338, T5 HO366, and T8 HO470.All of these sites except T5 HO366 represent weak acid sites in the structure of HAlbea221c.For the THF molecule, protonation from the acid sites took place at the oxygen atom of this molecule.This molecule is relatively bulky, and some steric hindrances also had an influence on the interaction of this molecule with the acid sites.Some acid sites had OH groups aligned closer to the surface of the zeolite pore wall.Thus, structural deviations took place for the deprotonation to occur.The same was also valid for other bulky probe molecules, such as pyridine.To conclude, THF molecule provided one of the best results for the identification of weak acid sites.At the end of this study, we considered the molecule that is most often used for the TPD studies of acid sites in zeolites.Ammonia is a strongly basic molecule that interacts easily with all Brønsted acid sites in zeolites.Figure 10 demonstrates adsorption energy of ammonia over all acid sites in zeolite beta model HAlbea221c.The strongest adsorption was observed for the sites T9 HO426, T9 HO421, T9 HO57, T7 HO490, T7 HO201, T4 HO305, and T1 HO94.Among these acid sites, the site T1 HO94 was correctly identified as the strong acid site.The rest of the found sites represented average acid strength.Weak adsorption of NH3 was observed for the sites T8 HO465, T6 HO341, and T4 HO338.Among these sites, T8 HO465 and T4 HO338 represented weakest acid sites.Therefore, ammonia adsorption allowed for the correct identification of several strongest and At the end of this study, we considered the molecule that is most often used for the TPD studies of acid sites in zeolites.Ammonia is a strongly basic molecule that interacts easily with all Brønsted acid sites in zeolites.Figure 10 demonstrates adsorption energy of ammonia over all acid sites in zeolite beta model HAlbea221c.The strongest adsorption was observed for the sites T9 HO426, T9 HO421, T9 HO57, T7 HO490, T7 HO201, T4 HO305, and T1 HO94.Among these acid sites, the site T1 HO94 was correctly identified as the strong acid site.The rest of the found sites represented average acid strength.Weak adsorption of NH 3 was observed for the sites T8 HO465, T6 HO341, and T4 HO338.Among these sites, T8 HO465 and T4 HO338 represented weakest acid sites.Therefore, ammonia adsorption allowed for the correct identification of several strongest and weakest acid sites.For the ammonia molecule, adsorption reflected not only direct interaction with the acid sites but also numerous interactions with the neighbor oxygen atoms in the walls of the pores of zeolite beta.Ammonia can form monodentate, bidentate, and tridentate complexation with the oxygen atoms in the zeolite pore walls.These interactions strongly affected the results obtained from the TPD experiments.Therefore, despite the popularity of this molecule for the acid sites studies, it was not fully suitable for obtaining results regarding the acid strength of sites in zeolites.

A B
Catalysts 2023, 13, 833 10 of 15 weakest acid sites.For the ammonia molecule, adsorption reflected not only direct interaction with the acid sites but also numerous interactions with the neighbor oxygen atoms in the walls of the pores of zeolite beta.Ammonia can form monodentate, bidentate, and tridentate complexation with the oxygen atoms in the zeolite pore walls.These interactions strongly affected the results obtained from the TPD experiments.Therefore, despite the popularity of this molecule for the acid sites studies, it was not fully suitable for obtaining results regarding the acid strength of sites in zeolites.Further, it deserves considering the ranges of adsorption energy obtained for different probe molecules and by the different computational methods.Table 1 provides information regarding the energy of adsorption for all the studied probe molecules.As we can observe, the smallest adsorption energy was present for adsorption of acetonitrile.This is related with the smallest basicity of the nitrogen atom in the cyano group.Dimethyl sulfide had a bit larger adsorption energy followed by stronger adsorbed dimethyl sulfoxide.Pyridine had the largest heat of adsorption, while tetrahydrofuran had a moderate heat of adsorption comparable to that of tetrahydrofuran.It is interesting to compare the computed energy of adsorption to the experimentally available published Further, it deserves considering the ranges of adsorption energy obtained for different probe molecules and by the different computational methods.Table 1 provides information regarding the energy of adsorption for all the studied probe molecules.As we can observe, the smallest adsorption energy was present for adsorption of acetonitrile.This is related with the smallest basicity of the nitrogen atom in the cyano group.Dimethyl sulfide had a bit larger adsorption energy followed by stronger adsorbed dimethyl sulfoxide.Pyridine had the largest heat of adsorption, while tetrahydrofuran had a moderate heat of adsorption comparable to that of tetrahydrofuran.It is interesting to compare the computed energy of adsorption to the experimentally available published values.Results of experimental studies are usually reported as heat (enthalpy) of adsorption.The adsorption process is expressed by the following equation.
Thus, energy of adsorption is ∆E = ∆H +RT, where R is the universal gas constant (8.314J/(K mol)), and T is the temperature of the adsorption process (K).The difference between the heat of adsorption and adsorption energy is below 8.1 kJ/mol for temperature below 700 K. Work [31] reports heat of adsorption of pyridine as −200 kJ/mol and from −145 to −160 kJ/mol for ammonia over HZSM-5 and mordenite.This agrees very well with our data in Table 1.Theoretical work [45] reports energy of adsorption of acetonitrile in the range from −46 to −80 kJ/mol for different zeolites, which is much smaller than reported in our study.This is related to the deficiencies in the method of computation used in the cited work.Study [28] reports experimentally observed NH 3 adsorption enthalpy from −145 to −175 kJ/mol for zeolites MFI, MOR, FER, and FAU, which also agrees well with the results of the present study.Liu et al. [51] computed adsorption energy for CH 3 CN in the range from −60 to −120 kJ/mol, for NH 3 in the range from −104 to −189 kJ/mol, and for pyridine from −144 to −270 kJ/mol for different zeolites.These computations are also in good agreement with our results.The results of Boronat and Corma [50] also do not differ significantly from our results; they computed adsorption energy for ammonia from −135 to −169 kJ/mol and for Py from −205 to −222 kJ/mol for MOR and MFI using PBE-D3 method.Therefore, the novel basis set applied in the present study demonstrated good performance, and the results obtained are well in line with the state-of-the-art results in the literature.
Herein, we discussed how adsorption energy correlated with the acid strength of Brønsted acid sites in zeolite beta and whether application of probe molecules could indeed provide information regarding the acidity of acid sites in zeolites.Acetonitrile allowed correctly identified five strongest and weakest acid sites.Dimethyl sulfide produced three correctly identified strongest and weakest acid sites.DMSO produced only two correctly identified sites, while pyridine and isothiazole provided only single correctly identified weakest adsorption sites.Tetrahydrofuran and ammonia adsorption resulted in three strongest and weakest sites each.Therefore, acetonitrile can be recommended as the best probe molecule to study the acid sites in zeolite beta.
The result that the acid strength did not correlate well with the heat of adsorption of molecules could not be easily confirmed or disproved experimentally.This is due to the difficulties in determining the acidity constant of zeolites.

Experimental Section
Model bea221c, which represents a fragment of zeolite beta modification A framework, was constructed from the bulk lattice of this material in a way as to include the main central straight pore and also four 6-membered rings in the center of the model.This sample was used previously in our study on acid sites using the previous generation of basis set [48]. Figure 11 represents views of the model in two projections.The structure of this zeolite contains main straight channels in direction [010] as well as side channels in direction [100].These channels are interconnected with zig-zag channels running along the direction [001] so that the entire structure contains a 3D system of interconnected pores that make molecules transport easier compared with other zeolites that have only unidimensional channels.The cell parameters for the structure were taken as a = 12.6320, b = 12.6320, c = 26.1860Å, and α = β = γ = 90 • .The supercell was constructed in such a way so that it had approximately the same size in all directions.
deprotonation energy (DPE) that is reversely related to acid strength of the Brønsted acid sites-the smaller the DPE, the larger the acid strength.
Thereafter, adsorption of a diverse set of bases was performed over every acid site to determine adsorption configuration and energy of adsorption.In experimental works, energy of adsorption of probe molecules is often used to obtain information regarding the acid strength of acid sites in zeolites.Here, we elucidated whether adsorption energy correlates with the acid strength and which factors other than acid strength determine adsorption energy.All computations were performed using CP2K [52] program package version 7.1 employing newer available basis set file BASIS_MOLOPT_UZH and potential file POTEN-TIAL_UZH.The purpose of utilization of these new basis sets and potential files is their testing and, to a degree, comparison with the previous results.The Gaussian and plane wave (GPW) approach was used [53].Multigrid settings were 5/400/50 and 5/600/50, the latter setting was determined to provide more convergence to the stable plateau of energy with respect to cutoff energy while requiring longer computational time.GGA functional PBE [54] was used in conjunction with DFT-D3 dispersion interaction correction [55].The basis set TZVP-MOLOPT-PBE-GTH-qX was used in combination with 5/600/50 and the TZV2P-MOLOPT-PBE-GTH-qX basis set was employed with the multigrid setting 5/400/50.All geometry and cell optimizations were performed without any restrictions, and the convergence criteria were set to be ten times stricter compared with the default program settings.

A B
Initial geometry for adsorption of molecules was set in such a way that the coordinating oxygen or nitrogen atom were directed towards to protons of OH groups, with the initial distance between these atoms being 2.5Å.All computations were performed using the computational facilities of Ohio Supercomputing Center (OSC) using 28 core single computing nodes.The structure of zeolite beta contained tetrahedral sites T1-T9 and the multiplicity of sites T1-T7 was 8, while T8 and T9 sites are present only in the number of 4 per each unit cell.There are very many T sites in the model bea221c, and we selected only single T sites of each type in the center of the model to minimize the boundary effects.
In our methodology, we first substituted bea221c with single Al atoms in different T sites to obtain negatively charged structure Albea221c -.Then, oxygen atoms adjacent to the Al atom were protonated to obtain structure HAlbea221c.All Al-substituted T sites had four oxygen atoms available for protonation, except sites T5 and T6, which had only three oxygen atoms at the surface; oxygen atoms inside the bulk of the pores were not considered for protonation.Following protonation, it was possible to determine the deprotonation energy (DPE) that is reversely related to acid strength of the Brønsted acid sites-the smaller the DPE, the larger the acid strength.
Thereafter, adsorption of a diverse set of bases was performed over every acid site to determine adsorption configuration and energy of adsorption.In experimental works, energy of adsorption of probe molecules is often used to obtain information regarding the acid strength of acid sites in zeolites.Here, we elucidated whether adsorption energy correlates with the acid strength and which factors other than acid strength determine adsorption energy.
All computations were performed using CP2K [52] program package version 7.1 employing newer available basis set file BASIS_MOLOPT_UZH and potential file POTEN-TIAL_UZH.The purpose of utilization of these new basis sets and potential files is their testing and, to a degree, comparison with the previous results.The Gaussian and plane wave (GPW) approach was used [53].Multigrid settings were 5/400/50 and 5/600/50, the latter setting was determined to provide more convergence to the stable plateau of energy with respect to cutoff energy while requiring longer computational time.GGA functional PBE [54] was used in conjunction with DFT-D3 dispersion interaction correction [55].The basis set TZVP-MOLOPT-PBE-GTH-qX was used in combination with 5/600/50 and the TZV2P-MOLOPT-PBE-GTH-qX basis set was employed with the multigrid setting 5/400/50.All geometry and cell optimizations were performed without any restrictions, and the convergence criteria were set to be ten times stricter compared with the default program settings.
Initial geometry for adsorption of molecules was set in such a way that the coordinating oxygen or nitrogen atom were directed towards to protons of OH groups, with the initial distance between these atoms being 2.5Å.All computations were performed using the computational facilities of Ohio Supercomputing Center (OSC) using 28 core single computing nodes.

Conclusions
The present study aimed to study zeolite beta interactions with a set of test molecules.In addition, the stability of different single Al-substituted zeolite beta modification A samples was computed, and acid strength of all possible protonated Brønsted acid sites was studied theoretically.Probe molecules were adsorbed over all the different acid sites in protonated zeolite beta samples with an aim to apply probe molecules for identification of strong and weak acid sites.
Relative stability of single Al-atom-substituted deprotonated samples of zeolite beta was different from our previous results.However, the most stable sites remained T5 and T6, which agrees with our data and the literature data.For the protonated samples, the highest stability was also observed for Al situated in sites T5 and T6, which also agrees well with the results of our previous study.The largest acid strength, i.e., the lowest deprotonation energy, was obtained for samples with Al in sites T1 and T2.The lowest acid strength was obtained for the sample with Al located in site T4.
Energy of adsorption of different test molecules was in agreement with the published results of experimental and theoretical computational studies.Correlation of acid site strength with energy of adsorption of all the test molecules was not generally observed.The results of computations depended strongly on the basis set used and multigrid settings for CP2K.Identification of sites with largest and smallest acidity was undertaken using adsorption energy of test molecules.Such an identification generally failed with only a few successful outcomes.Acetonitrile was the best molecule for acid sites characterization, while the traditionally used pyridine molecule allowed for the identification of only one weakest acid site.This result generally agrees with the previous computational studies.Therefore, the energy of adsorption of various molecules used in experimental TPD studies does not accurately evaluate acid sites strength.The new basis sets of CP2K contained in basis set file BASIS_MOLOPT_UZH can be recommended for use according to the good results in computing energy of adsorption.

Figure 10 .
Figure 10.Interaction of ammonia with single separate acid sites in zeolites beta as computed by DFT PBE-D3 using the following basis set and multigrid setting: basis set TZVP, multigrid 5/600/50.

Figure 10 .
Figure 10.Interaction of ammonia with single separate acid sites in zeolites beta as computed by DFT PBE-D3 using the following basis set and multigrid setting: basis set TZVP, multigrid 5/600/50.

Figure 11 .
Figure 11.Computational model bea221cof zeolite beta (framework BEA*) that was employed for modeling of Brønsted acid sites and their interaction with the probe molecules: (A)-view along [010] direction and (B)-view along [100] direction.

Figure 11 .
Figure 11.Computational model bea221cof zeolite beta (framework BEA*) that was employed for modeling of Brønsted acid sites and their interaction with the probe molecules: (A)-view along [010] direction and (B)-view along [100] direction.

Table 1 .
Ranges of the adsorption energy for different probe molecules.

Table 1 .
Ranges of the adsorption energy for different probe molecules.