A Systematic Study by the Extended ONIOM (XO ... - ACS Publications

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Exploring the Sodium Cation Location and Aluminum Distribution in ZSM-5: A Systematic Study by the Extended ONIOM (XO) Method Zhen-Kun Chu,† Gang Fu,† Wenping Guo,† and Xin Xu*,†,‡ †

State Key Laboratory of Physical Chemistry of Solid Surfaces, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China ‡ Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, MOE Key Laboratory for Computational Physical Science, Department of Chemistry, Fudan University, Shanghai 200433, China

bS Supporting Information ABSTRACT: There exist 12 crystallographically distinct Al-sites in the ZSM-5 zeolite, associated with which there are various Na-sites. Understanding their locations, while being the key to the understanding of the catalytic properties of this material, remains a great challenge in both experiment and theory. We present here a theoretical survey of the Na+ location along with the Al distribution in ZSM-5 by using hybrid methods, ONIOM (our Own N-layer Integrated molecular Orbital molecular Mechanics) as well as the newly developed extended ONIOM (XO) (Guo, W. P.; Wu, A. A.; Xu, X. Chem. Phys. Lett. 2010, 498, 203
208) method. The reliability and efficiency of different methods/models have been systematically tested. Using the T1 Al-site as an example, our calculations demonstrate that the high-level layers of ONIOM models have to include all rings around the [AlO4] tetrahedron to have reliable coordination structures and energetics of different Na-sites, while XO can provide reliable results with 60% savings of computational time as compared to that of ONIOM. Our XO calculations reveal that, in most Al-sites, Na+ preferentially occupies the six-membered-ring sites, and the most favorable Al-sites along with the Na-sites are T8/M6, T10/Z6, and T4/Z6. Conversely, those Al-sites only surrounded by five-membered rings, such as T6 and T3, are predicted to be energetically unfavorable.

1. INTRODUCTION Metal-cation-exchanged zeolites are of great interest for their broad use in heterogeneous catalysis.1,2 It has been well documented that the catalytic performance of zeolites for a given reaction is significantly influenced by the location of the extraframework metal cations.2 As the metal cation serves as a compensating ion for the negatively charged [AlO4], its location is, therefore, associated with the aluminum distribution. Thus, finding the metal cation locations along with the aluminum distributions is a prerequisite for the understanding of the catalytic properties of zeolites at the molecular level. It is a great challenge to locate the Al distribution and the corresponding extraframework metal cation position through crystallographic techniques.3,4 This is especially true for a zeolite with a high silicon to aluminum ratio, such as ZSM-5. First, the concentrations of aluminum and extraframework cations in highsilica zeolites are too low to distinguish. More severely, their distribution in different unit cells is usually nonuniform, i.e., lacking of real periodicity. This calls for help from other techniques such as UV
vis spectroscopy,5
10 FTIR spectroscopy,8
14 microcalorimetry,12
14 NMR spectroscopy,15 electron spin resonance (ESR) spectroscopy,16
19 extended X-ray absorption fine structure (EXAFS) spectroscopy,18
22 and the computational methods. Indeed, sophisticated quantum chemical calculations have r 2011 American Chemical Society

already provided much valuable information on the structural, electronic, and spectroscopic properties for metal cations in zeolites and have shed light on the structure
property relationship at the molecular level.23
27 For theory to play a decisive role, the method employed has to be reliable and efficient. Taking the Na+ location in ZSM-5 as an example, there exist 12 crystallographically distinct T-sites (see Figure 1) in the zeolite framework, where T stands for a tetrahedron of [SiO4] or [AlO4].2 Hence, there are 12 unique ways where [SiO4] can be substituted by [AlO4] to form 12 distinct Al-sites in ZSM-5. Furthermore, there are several plausible Na+ locations (Na-sites) associated with every Al-site whose energy differences are within several kilocalories per mole. For the T1 Al-site, we have previously located four probable Na-sites, namely, Z6, M7, I2, and I3 (see Figure 1).28 Here Z6 denotes the cation site on top of the six-membered ring (6MR) in the zigzag channel, while M7 represents the site on top of 6MR in the main channel with an additional [SiO4] at the bottom of the ring. I2 and I3 denote the sites located at the intersection of the main and zigzag channels, at which Na+ is coordinated to two or three Received: February 14, 2011 Revised: June 11, 2011 Published: June 29, 2011 14754

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Figure 1. Structure of ZSM-5 (orthorhombic) and labels of its 12 crystallographically distinct T-sites as well as the location of the four Na-sites (Z6, M7, I2, and I3) with T1 substituted by Al. Z6 represents a Na-site in which Na+ locates on the six-membered ring in the zigzag channel running parallel to [100]. M7 indicates that Na+ locates on top of the six-membered ring with an additional [SiO4] at the bottom in the main channel running parallel to [010]. I2 and I3 indicate that Na+ is not on the top of any ring, but only coordinates to two or three O atoms of [AlO4].

oxygen atoms of [AlO4], respectively. In that benchmark study, various cluster models with sizes ranging from 3T to 192T have been examined.28 A 75T cluster model was found to provide a reliable local geometry and stability sequence for all four probable Na-sites for the T1 Al-site. On the basis of this finding, a general scheme to set up suitable cluster models for metal cation location calculations in zeolites was proposed, where so-called C-5-type models can be constructed by allowing all atoms on the rings around the Al-site to relax during the geometry optimization and then expanding the region by another three shells of Si atoms.28 Such C-5-type models will serve as guidelines in this study to investigate various Na-sites associated with all 12 distinct Al-sites in ZSM-5. It has to be emphasized that quantum chemical calculations by using the C-5-type models are computationally very demanding. At the level of B3LYP/6-31G*, a geometry optimization job for the C-5-type models for the T1 Al-site (75T) usually requires more than 20 days on a modern dual-quad-core PC server.28 The sizes of the C-5-type models for other Al-sites are even larger (e.g., 146T for the T12 Al-site; see the Supporting Information for details). Such an expensive calculation cannot be adopted for routine use. In this regard, hybrid methods, which divide the whole system into different regions and deal with them with different levels of theories, have shown great promise. As one of the most popular hybrid methods, ONIOM (our Own N-layer Integrated molecular Orbital molecular Mechanics), developed by Morokuma and co-workers,29
32 has been widely employed to explore the zeolite systems. It is generally accepted that the state-of-the-art of ONIOM calculation relies on how to choose the high-level layer.33 In earlier studies, the highlevel layer in the zeolite system usually included a few T-sites (3T
6T) for efficiency.34
37 Previously, we have performed a systematic investigation on the effect of high-level layer selection in ONIOM with a series of nT@75T models for Na+ at the M7 location associated with the T1 Al-site (c.f. Figure 1).38 Our results demonstrated that reliable prediction of the Na
O coordination structure demands a much bigger high-level layer (22T
33T), while small high-level layers such as 7T always lead to a poor structure. Hence, there is a need to increase further the efficiency of the ONIOM model without retreating to a too small high-level layer at the expense of reliability.

Very recently, an extended ONIOM method, XO for short,39 was developed in our group. Unlike the ONIOM method, both overlapping and onionlike structures can be used, and models can be treated at different levels or the same level of theory, allowing a flexible way of partitioning and combining various levels of theory at will in XO (cf. Figure 2). Representative studies of NH3 adsorption on acidic site of mordenite zeolite demonstrated its efficiency in alleviating the ONIOM boundary errors and its robustness of being less sensitive to the choice of the low level. The XO method showed an improvement over the ONIOM method in providing more accurate geometries in a more effective way.39 In this work, we have performed a thorough investigation on various Na+ locations along with all 12 Al-sites in ZSM-5 zeolite. After a brief introduction of the computational methods and models, we will use Na-sites on the T1 Al-site as an instructive case to test the performance of a series of ONIOM models as well as the newly developed XO method. After demonstrating the reliability and efficiency of the XO method, we will then employ it to explore the location of Na+ and the distribution of Al on all 12 distinct T-sites throughout ZSM-5. The potential role that XO may play in complicated catalytic systems is thus highlighted.

2. COMPUTATIONAL METHODS AND MODELS 2.1. ONIOM. Figure 2 schematically depicts a two-layered ONIOM (i.e., ONIOM2) calculation. Here “High” and “Low” refer to the high and low levels of the theoretical method, respectively; while “Model” and “Real” refer to the model and real systems, respectively.29 Previously, we have found that the C-5 cluster (75T; see Figure 3) can nicely account for the longrange interaction for the T1 Al-site of ZSM-5,28 which gives a good choice for the “real system” in our ONIOM calculations for this Al-site. On the other hand, the smaller C-1
C-4 types of clusters, employed in our earlier work,28 can be used as the highlevel layers. The details of the construction rules for various cluster models (C-1
C-5) can be found in ref 28. The resultant ONIOM models are named O-1
O-4, respectively. Figure 3 illustrates the O-1
O-4 models for the I3 Na-site associated with the T1 Al-site. Noteworthily, a similar ONIOM scheme has been successfully used to explore the adsorption of 14755

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Figure 2. Computational schemes of the ONIOM2 and XO2 methods.

Figure 3. O-1
O-4 ONIOM models for the I3-site at the T1 Al-site using the C-5 cluster (75T) as the real system and different high-level layers (4T, 14T, 17T, and 33T; for simplicity, all H atoms for termination of the high-level clusters are omitted).

the M7 Na-site associated with the T1 Al-site.38 It should be pointed out that high-level layers of O-1
O-3 are too small to accommodate all Na-sites and different cluster models have to be adopted as the high-level layer to simulate different Na-sites, while when the high-level layer is enlarged to O-4, the high-level region can cover all different Na-sites simultaneously. During the geometry optimization with our ONIOM models, all [SiO4] groups on the three rings around [AlO4] (as well as the central [AlO4] itself and Na+) are allowed to relax. Other atoms are fixed on their crystallographic positions.40 Previously, we have examined the basis set effects and found that B3LYP41
43 in conjunction with 6-31G*44
46 was able to give a reliable coordination structure and relative stability sequence for different Na-sites for the T1 Al-site.28 Hence, in our present ONIOM calculations, B3LYP/6-31G* is used as the high-level method. For the low-level method, we adopt the HF/ STO-3G method. Therefore, the whole ONIOM scheme is denoted as ONIOM2 (B3LYP/6-31G*:HF/STO-3G). All calculations are performed by using the Gaussian 03 package.47 2.2. XO. XO is a natural extension of the ONIOM method based on the inclusion
exclusion principle (IEP) in combinatorics and makes use of the philosophy of divide-and-conquer.39 In this way, the whole system can be viewed as a union of several subsystems, recovered by including all subsystems and then excluding the intersections among them. Both ONIOM and XO are based on extrapolation schemes, where the full cluster method (Real@High) places the upper limit on the accuracy.

A schematic diagram of a two-level XO (i.e., XO2) is also shown in Figure 2, where the high-level layer of ONIOM2 is further divided into two smaller fragments (i.e., Frag 1 and Frag 2). According to IEP, the XO energy finally consists of six terms. In this way, the computational time can be significantly reduced, because it avoids calculation of E(Model@High) of ONIOM2, which can become very expensive when a huge highlevel layer is necessary. In addition, each of the six terms can be calculated in parallel to further accelerate the calculation. Figure 4 illustrates the building blocks of the XO2 model for the I3 Na-site associated with the T1 Al-site. Similar to the ONIOM2 calculations, the 75T cluster is adopted here as the “real model”, treated at the low level of HF/STO-3G. Instead of directly using O-4 (high-level layer 33T), XO2 starts from the O-2 high-level layer of 14T (see Figure 4a, depicted in ball-andstick format) and then expands to O-4 by adding patch models along the high/low-layer border. A 5T model is shown in Figure 4d, and eight such 5T patch models are used altogether, whose distributions are labeled in green as represented in Figure 4b. As we are interested in the Na+ location, a special patch model is designed for the border Si that directly connects to [AlO4] (labeled as brown in Figure 4b). This patch as shown in Figure 4c is an 8T model, consisting of seven [SiO4] groups and [AlO4]
plus Na+. Hence, in XO2, the high-level layer of the O-4 model is composed of one 14T central fragment shown in Figure 4a, as well as one 8T (Figure 4c) and eight 5T (Figure 4d) patch models, treated at B3LYP/6-31G*. We emphasize that the XO scheme provides a flexible way to set up the high-level layer for different Na-sites. For example, a smaller central fragment may be used for some Na-sites, where all border Si atoms directly connected to [AlO4] are patched with 8T models, while others are patched with 5T models. Such XO calculations were accomplished by using the program xo-tools developed in our laboratory and implemented through the external mechanism of Gaussian 03.39,47 Either the ONIOM or XO method is used here for geometry optimizations, as geometry optimizations are most time-consuming. For better accuracy, the final energies reported here are all based on the single-point energy calculations at the level of B3LYP/6-31G* on top of the optimized geometries with either ONIOM or XO.

3. RESULTS AND DISCUSSION 3.1. Performance of the ONIOM Method. First, the performances of the O-1
O-4 ONIOM models on the geometry optimization as well as the relative stability comparison of the 14756

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Figure 4. Building blocks of the XO2 model for the I3 Na-site at the T1 Al-site. (a) 75T real model and 14T central fragment. (b) Distribution of the patch models. Green balls stand for the locations of the 5T patches, and the brown one stands for the 8T patch. (c) 8T patch for [SiO4] that connects directly to [AlO4]. (d) 5T patch for [SiO4] that does not directly connect to Al. (For simplicity, all H atoms for termination of the patch models are omitted.)

Table 1. MADs of the Optimized Na
O Bond Lengths (Å) for Four Na-Sites Associated with the T1 Al-Site by Different ONIOM Models as Well as the XO Method Na-site

O-1

O-2

O-3

O-4

XO

Z6

0.126

0.121

0.036

0.030

0.031

I2

0.083

0.025

0.011

0.007

0.009

M7

0.449

0.043

0.035

0.013

0.024

I3

0.078

0.008

0.030

0.030

0.022

charge can be delocalized to a large extent. Therefore, the optimized structures are generally improved. To assess the stability of different Na-sites for the T1 Al-site, the relative energy (ΔE) has been calculated using the singlepoint energies of the full 75T models for each Na-site at the level of B3LYP/6-31G* with the optimized structures by using O-1
O-4. For example, ΔE of the I3 Na-site at the T1 Al-site is defined as ΔEðT1=I3Þ ¼ ½EAl

Naþ ðT1=I3Þ
EAl

Naþ ðT1=Z6Þ

ð1Þ

+

four Na adsorption sites associated with the aluminum-substituted T1-site are systematically tested. Table 1 summarizes the mean absolute deviations (MADs) of the optimized Na
O bond lengths for different models. Here the values from the full 75T cluster model at B3LYP/6-31G* are used as the references.28 Our calculations demonstrate that the O-1 model always leads to large errors for the Na
O bond lengths. This finding casts some doubt on previous ONIOM calculations in which the high-level layer usually consisted of 3T
6T.34
37 With an increase of the size of the high-level layer, the MADs of the bond lengths remarkably decrease. Especially, when the O-3 or O-4 model is employed, the predicted Na
O distances compare well with those of the reference model, with the MADs being less than 0.04 Å. As for the Na-ZSM-5 system, the zeolite framework formally carries a negative charge, and it is reasonable to expect that this charge is actually delocalized to some extent, rather than localized on the [AlO4] unit. On the other hand, in setting up the ONIOM models with small highlevel layers, such as O-1 and O-2, the Si
O bonds close to [AlO4] have to be cut off and terminated by O
H or Si
H. This leads to an artificial boundary, and the negative charge is therefore constrained in a small region, resulting in an unreasonable electronic structure, which in turn leads to a poor geometry. By contrast, as the high-level layer is enlarged, the boundary becomes farther away from the core area of the Na+ location. The electronic structure of the Na-site is less affected by the boundary, and the

Here the subscript Al

Na+ represents the optimized full 75T models for different Na-sites. The Z6 Na-site is used as the reference, as it is the most stable Na-site associated with the T1 Al-site, concluded in ref 28. Table 2 lists ΔE of I2, M7, and I3 with respect to Z6 from O-1 to O-4. Again, the values from the C-5 cluster model (75T) are used as references. O-1 largely overestimates the stability of the I2 Na-site (ΔE =
1.6 kcal/mol), erroneously putting I2 as the most stable. The calculated ΔE values for M7 and I3 from O-1 are in good accordance with the reference data. Such seemingly good results have to be interpreted as a result of fortunate error cancellation, as O-1 is shown to give generally poor results for the Na
O coordination structures. Even though O-1 is appealing for its speed, this model has to be used with great caution, as the favorable error cancellation for I3 and M7 cannot be guaranteed in other sites. Though being better in Na
O coordination structure optimizations, O-2 and O-3 fail badly in calculating ΔE. They erroneously predict the sequence of ΔE for I2, M7, and I3, leading to MADs of 3.0 and 3.8 kcal/mol, respectively. These are even worse than that of O-1 (1.9 kcal/ mol). They give an indication that the high-level layer of O-2 and O-3 is still not big enough. Indeed, all models from O-1 to O-3 adopt different regions treated at a high level theory for different Na-sites; thus, they encounter different high
low boundaries, and the resultant errors are difficult to cancel out. Encouragingly, by incorporating all possible Na-sites together in the high-level 14757

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Table 2. Relative Stability of I2, M7, and I3 with Respect to Z6 (kcal/mol) by Using the O-1
O-4 ONIOM Models, XO, and the 75T Full Cluster Modela b

Table 3. Relative Stability of Different Na-Sites Associated with All 12 Distinct Al-Sites in ZSM-5 Al-site

ΔEb

Na-site

CNa

Z6

3

0

I2 M7

2 4

2.6 4.6

Al-site

Na-site

CNa

ΔEb

T7

M7

4

0

T8

M6 M6

4 4

0.6 0

c

method

I2

M7

I3

MAD

time (s)

O-1


1.6

3.4

5.4

1.9

567 (454)

O-2

7.2

2.6

8.4

3.0

1015 (556)

O-3

8.4

5.0

11.0

3.8

1353 (882)

O-4

2.9

4.6

5.4

0.1

3995 (3474)

XO 75T

2.6 2.9

4.6 4.5

5.0 5.5

0.3

1570 (559) 14636

T1

T2

a

The CPU time for one-step force construction in geometry optimization of the I3 Na-site with different methods in serial (parallel) calculations is also presented. b MAD (kcal/mol) for the relative energies (ΔE) with respect to the results from the 75T full cluster models at B3LYP/6-31G*. c Jobs run on a cluster made of dual-processor Intel Xeon 5345
2.33 GHz Clovertown computers loaded with 8 GB of memory and 146 GB of disk space. ONIOM jobs are run in serial with standard Gaussian 03.47 XO jobs are run either in serial or in parallel.39 The parallel time is indicated by the CPU time consumed for the force construction in the most time-consuming fragment.

layer, O-4 well reproduces ΔE with an MAD of only 0.1 kcal/mol, as compared to the reference data. Such a good agreement in ΔE, in conjunction with its good performance in geometry, confirms the reliability of O-4 in Na+ location prediction. Table 2 also summarizes the CPU time consumed in one step of the force construction in geometry optimization for the I3 Nasite. The number in parentheses indicates the CPU time for the force construction for the most time-consuming fragment. O-1 is certainly the fastest; unfortunately, it is also the least reliable for its poor geometry. As compared to the 75T reference model, O-4 is also rather efficient. For the CPU time used, O-4 requires 3995 s while 75T needs 14636 s. This indicates more than 70% CPU time could be saved with O-4. Thus, the present study solidifies the previous finding concerning the M7 Na-site associated with the T1 Al-site38 that ONIOM with the O-4 model is reliable and rather efficient for the prediction of Na-site coordination geometries. 3.2. Performance of the XO Method. It should be pointed out that O-4 is still not cheap enough. Especially, when we are ambitious to obtain the whole scenario of Na+ locations associated with various Al-sites in ZSM-5, O-4 turns out to be unaffordable. As shown in Table 2, when O-4 for the I3 Na-site is employed, more than 85% CPU time is paid to the high-level calculation (Model@High, 3474 s). One of the possible solutions is to further divide the high-level layer into several fragments, which is actually a key idea of the XO method.39 Table 1 lists MADs of the optimized Na
O bond lengths by using the XO method. It is clear that the predicted Na
O distances by the XO method are significantly better than those of O-1
O-3, being comparable to those of O-4. Clearly, a reasonable structure is a prerequisite for a reliable energy. Indeed, we see that ΔE by XO is nearly the same as those from the 75T reference, with a small MAD of 0.3 kcal/mol. Significantly, as illustrated by the data in Table 2, the CPU time consumed by XO is only about two-fifths of that by O-4 (1570 vs 3995 s). Furthermore, as all fragments in XO are independent of each other, the calculations can be effectively parallelized. The time actually consumed for our parallel implementation of an XO job is only 559 s, as indicated by the CPU time for the force construction in the most time-consuming fragment. This is

T3

T4

T5

T6

I3

3

5.0

M5

4

6.7

I20

3

0

M7

4

10.9

M5

4

2.2

M6

5

0

Z5

3

5.0

I3

3

2.7

Z5

3

9.6

I3

3

3.4

I20

3

0

T10

Z6

3

0

I3 I20

3 3

1.6 1.6

T11

I2 M6

2 4

4.2 0

Z6

3

0

M7

2

5.1

Z10

2

8.2

M5

3

6.8

Z5

3

9.3

Z10

3

0

Z6

2

0

M6

3

5.3

I2

2

1.2

M5

3

10.7

M7

2

6.1

I2 Z5

2 3

0 1.3

I3

3

1.6

M5

3

1.9

T9

T12

a

A 2.73 Å distance48 is used as a criterion to assign the Na
O CN. b In kilocalories per mole.

comparable to the time for the O-1 calculation (567 s) with standard Gaussian 03 to run all ONIOM fragments sequentially. These findings indicate that the newly developed XO is very costefficient, which holds great promise in modeling complicated system such as zeolites. 3.3. Na+ Location at All Other T-Sites. Taking advantage of XO, we can conveniently explore the Na+ location sites at 11 other distinct Al-sites. For each T-site substituted by Al, all the probable Na-sites are considered. The symbols (Mn, Zn, and In) for Na-sites are similar to those used for the T1 Al-site. Table 3 summarizes the relative stability of Na-sites for each of the 12 T-sites in ZSM-5. The details of the coordination geometries are provided in the Supporting Information. The general trends are summarized as follows: (1) The coordination of Na+ is flexible, with the coordination number (CN) varying from 2 to 5 within the Na
O bond distance of 2.73 Å.48 (2) For most T-sites other than T2, T3, T6, and T12, the most favorable Na-site is on top of the 6MRs, such as Z6, M7, and M6. Especially, for T1, T4, T5, and T10, Na+ tends to sit atop the same type of Z6 ring (cf. Figure 5a), while for T8, T9, and T11, Na+ shares a common type of M6 ring (cf. Figure 5b). (3) The most stable Na-site for T12 is predicted to be Z10 (cf. Figure 5d), which consists of two five-membered rings and shall be the probable site for a divalent cation such as Co2+.10 (4) The I20 Na-site is calculated to be the most favorable for T2 and T3, while the I2 Na-site is found for T6. The differences between I2 and I20 lie in their coordination structures. The I20 Na-site not only involves two O atoms of [AlO4], but also includes another O atom of the adjacent [SiO4] (cf. Figure 5c). (5) The sites on all four- or fivemembered rings for all T-sites are found to be energetically unfavorable for Na+. 14758

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Table 4. Preferred Na-Sites and Relative Stability for Al Substitution of the 12 Distinct T-Sites in ZSM-5 Zeolite ΔEloca

ΔErelb

ΔEv-intc

Al-substituted T-site

most stable Na-site

T1

Z6

4.8

4.8

0.0

T2 T3

I20 I20

3.2 12.5


3.1 4.5

6.3 8.0

T4

Z6

2.8

4.1


1.3

T5

Z6

6.6

5.9

0.7

T6

I2

15.6

11.2

4.4

T7

M7

6.4

3.6

2.8

T8

M6

0.0

0.0

0.0

T9

M6

6.5

3.6

2.9

T10 T11

Z6 M6

1.0 7.0

2.8 6.4


1.8 0.6

T12

Z10

6.4

5.2

1.2

a

Figure 5. Local geometric structures for some preferred Na-sites in ZSM-5: (a) T1/Z6 (T1 denotes the T1 Al-site, and Z6 stands for the location site for Na+), (b) T8/M6, (c) T2/I20 , (d) T12/Z10.

The above trends for the Na-site stability may be understood in two aspects: the flexibility of the zeolite framework and the binding affinity of each individual site. 6MRs, such as Z6 and M6, bear very flexible structures. Thus, it is much easier for them to deform into an appropriate configuration to bind Na+ than it is for 5MRs or 4MRs. Furthermore, 6MRs have higher binding affinities than other sites, offering an accommodation for Na+ where the coordination number is generally 3
4. By contrast, there are only two O atoms available in the I2-site. In the next section, the effect of these two factors will be quantitatively evaluated through the decomposition of the cation location energy28 (Eloc for short). Previously, Kucera et al.48 studied the Na+ location for different Al-sites in ZSM-5 by using QM-pot49 as well as the interatomic potential function (IPF) method. In their QM-pot calculations, the size of the QM region ranged from 4T to 10T, which is similar to that of our O-1 model. The authors suggested that both the 6MR and I2 were important. Especially, when the substituted Al atom was on the corner of the 6MR (i.e., T2, T5, and T12 Al-sites), the I2 Na-site was found more stable.48 However, our calculations suggest that 6MRs are generally favored over I2 except for the T6 Al-site, around which the 6MR is not available. In addition, we find that many Na-sites assigned to I2 in ref 48 will convert to I20 if the inner region is enlarged. The latter configuration benefits from gaining an additional Na
O interaction with an O in the adjacent [SiO4]. 3.4. Aluminum Distribution on the 12 Distinct T-Sites. It should be noted that zeolites are usually synthesized under hydrothermal conditions from solutions of sodium aluminate, sodium silicate, or sodium hydroxide while other forms of zeolites can be obtained by ion exchange afterward.50 Thus, to understand the Al distribution at the molecular level, knowledge of the thermodynamics of different Al-substituted sites in Na-form zeolite is very helpful. In our previous work, the cation location energy (Eloc) was introduced to compare the relative stabilities of different Na-sites for a given T Al-site,28 where, for instance, Eloc for the I3 Na-site associated with the T1 Al-site is expressed as Eloc ðT1=I3Þ ¼ EAl

Naþ ðT1=I3Þ
ESi ðT1Þ

ð2Þ

Relative cation location energies (kcal/mol) with respect to T8/M6. b Relative relaxation energy (kcal/mol) with respect to T8/M6. c Relative vertical interaction energies (kcal/mol) with respect to T8/M6.

Here the subscript Si represents a siliceous cluster before Si
Al substitution. Noteworthily, Eloc can also be conveniently applied to assessment of the relative stability for Al substitution of different T-sites. To elucidate the origin of the stability sequence, we decompose Eloc into the relaxation energy (Erel) and the vertical interaction energy (Ev-int). Here Erel and Ev-int are defined as Erel ¼ ½EAl

0 þ ENaþ 
ESi

ð3Þ

Ev-int ¼ EAl-
Naþ
½EAl

0 þ ENaþ 

ð4Þ

where the subscript “Al

0” represents the Al-substituted model obtained from the Al

Na+ model by simply removing the Na+ cation with no further relaxation of the structure. Hence, Erel consists of two contributions: one comes from the Si
Al substitution energy, and the other reflects the local structure relaxation to prepare the accommodation for Na+. We also introduce Ev-int, which represents the energy required by vertically detaching a Na+ from the Al

Na+ model. Table 4 summarizes the relative energetics for all the 12 T-sites, where the T8 Al-site is used as the reference, as we find that this site is the most preferable Al substitution site in ZSM-5. From Table 4 it can be seen that, among all 12 T-sites, T10 and T4 are also among the most favorable sites for Al substitution with a ΔEloc of less than 3.0 kcal/mol. These sites shared a common feature in that Na+ is adsorbed on the 6MR, such as M6 and Z6. Detailed analyses reveal that these favorable T-sites are characterized by a relatively small Erel in conjunction with a negative Ev-int. This indicates that 6MR sites not only have a smaller structural constraint, but also provide a comfortable environment for Na+ bonding. On the contrary, T3 and T6 are found to be the least favorable for Al substitution. In these cases, the central Al atom is surrounded only by five-membered rings, with no 6MR being available. Indeed, the data in Table 4 show that T6 bears the largest Erel while T3 has the most positive Ev-int. The situation for T2/I2 is somewhat different. Its relaxation energy is the most favorable (ΔErel =
3.6 kcal/mol), which unfortunately has to compensate for its unfavorable Ev-int (ΔEv-int = 6.3 kcal/mol). 14759

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The Journal of Physical Chemistry C Previously, the semiempirical MNDO method and cluster models with sizes of 50 atoms have been used to explore Al substitution for the 12 distinct T-sites in ZSM-5.51 Proton was used as the compensating ion. A different stability sequence as well as a narrower energy gap among different Al-substituted sites was obtained. This may be reasonable, as proton adsorption is a more localized phenomenon than that of Na+. This indicates that when precursor salts with different cations are introduced in the synthesis stage, zeolites with different Al distributions can be synthesized. It should be noted, to elucidate the real Al distribution of a zeolite, the kinetic factors should also be taken into account, in addition to the thermodynamic calculations performed here.

4. CONCLUSIONS In this study, we have systematically tested the performance of different hybrid methods, such as ONIOM and XO. Due to its reliability and efficiency, we have employed XO to explore Na+ locations throughout all 12 distinct aluminum substitution sites in ZSM-5. The main conclusions can be summarized as follows: 1. Our calculations show that the success or failure of ONIOM models critically depends on the selection of the high-level layer. Both O-1- and O-2-type models provide poor geometric structures due to the serious boundary effects. Although the O-3 model starts to give reasonable Na
O distances, its energetics for various Na-sites still suffer from considerable errors. It is only up to O-4 to include all rings around the [AlO4] tetrahedron, which provides reliable optimized geometries and, at the same time, good energetics. With respect to the reference model, O-4 can reduce the CPU time by more than 70% for geometry optimization. 2. Although rather efficient compared to the full cluster model, the O-4-type model is found to still be quite expensive to go through all Na-sites for all T-sites, and more than 85% CPU time is paid to the high-level calculations. Taking advantage of XO, the high-level layer of an ONIOM model is further divided into smaller fragments. Such a divide-and-conquer method makes geometry optimization efficient and easily parallelized. Test calculations demonstrate that a parallelized XO can lead to accuracy of O-4 at the expense of O-1, which is about 1/25 of the CPU time for geometry optimization using the full cluster model (e.g., 75T for the T1 Al-site). 3. Our XO calculations disclose the most favorable Na-sites for all 12 distinct Al substitution T-sites. It is found that, for Na-sites, six-member-ring sites are dominant (T1, T4, T5, T7, T8, T9, T10, T11), followed by I20 (T2 and T3), I2 (T6), and Z10 (T12). This allows us to further compare the relative stabilities of different Al substitution sites. Our calculations reveal that Al substitutions on T8-, T10-, and T4-sites are energetically more favorable than on other sites. Thus, we predict that such sites are preferentially occupied by an Al atom during the synthesis process using Na+ as the compensating cation. Our calculations demonstrate that XO can provide accurate geometries in a more efficient way. We suggest that fast screening of complicated catalysts can be facilitated by using the newly developed XO method. Indeed, XO can be easily extended to calculate properties such as vibrational frequencies and NMR chemical shifts. Such results will be reported in due time.

ARTICLE

’ ASSOCIATED CONTENT

bS

Supporting Information. Detailed coordination geometries of the probable Na-sites and the real models of the XO calculations for T1
T12 Al-sites. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected], [email protected].

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