J . Phys. Chem. 1991, 95. 10031-10036
of thermally induced stacking disorders observed by Srarby et al.I3 In that work,I3 less than 10%conversion of a VPI-5 sample into AIPO4-8 resulted in a loss of 80% of the adsorption capacity for hexane and cyclohexane. Alternatively, the 0.83-nm pore opening could as well be an intrinsic property of the anhydrous form, reflecting strong deformation of some of the 18-membered rings in absence of pore filling. It may, therefore, be difficult to exploit the 1.2-nm molecular sieving potential of VPI-5. VPI-5 activated by heating to 623 K in vacuum adsorbs triisopropylbenzene molecules, having a kinetic diameter of 0.85 nm.” The present data on argon adsorption suggest that this kinetic diameter may be close to the rejection size of the anhydrous form of VPI-5. Conclusions
In situ high-temperature XRD of VPI-5 previously degassed a t low temperature indicates that its transformation into an AIP04-8 phase can be inhibited and that the VPI-5 topology exists at high temperatures. Fast calcination of hydrated VPI-5, however, shows an irreversible and complete transformation into AIP04-8. 31P MAS N M R indicates the presence of specific sets of resonance lines, which can be assigned with the help of *’AI MAS NMR to the existence of specific phases: VPI-5 dihydrate, VPI-5 monohydrate, VPI-5 dehydrate, A1P04-8 dihydrate, AlP04-8 dehydrate. MAS NMR, therefore, allows one to monitor the
10031
exact composition of a given sample. VPI-5 samples with a degree of hydration between mono- and dihydrate readily undergo phase transformations into A1P04-8. This process occurs already to room temperature but is rather slow. 31P MAS NMR shows that, during hydration of a sample of VPI-5 that is partially transformed into AlP04-8, first the latter part is hydrated. Upon further equilibration, the A1P04-8 part is dehydrated again at the expense of the hydration of the VPI-5 part. This is explained by the preferential formation of AlP04-8 at the external rim of the VPI-5 crystals. With ‘29XeNMR the pore size of VPI-5 predicted by its topology is measured, while with dynamic Ar adsorption measurement values of 0.83 and 1.1 nm are obtained. It is concluded that dehydrated phase-pure VPI-5 shows pore entrance narrowing. One possible explanation is that the pore mouth restriction is a result of a phase transition into AlP04-8 starting from the external rim of the VPI-5 crystals. The 0.83-nm pore opening could as well represent the deformation of some 18-membered rings in absence of pore filling. Acknowledgment. J.A.M. and P.J.G. ackowledge the Flemish National Fund for Scientific Research for research positions. Sponsoring of this research by the Belgian Government in the frame of a Concerted Action (GOA) and by NFWO-FNRS is highly appreciated. Registry No. 129Xe,13965-99-6; Ar, 7440-37-1.
Ab Inltio Quantum Chemical Calculations of Aluminum Substitution in Zeolite ZSM-5 Aileen E. Alvarado-Swaisgood,* Mark K. Barr, Amoco Oil Company, Amoco Research Center, P.O.Box 301 1 , Naperville, Illinois 60566
P. Jeffrey Hay, and Antonio Redondo* Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (Received: May 7, 1991)
We have performed ab initio quantum mechanical calculations in monomeric clusters modeling the 12 different T sites of zeolite ZSM-5. By comparing the results of calculations that use minimum basis sets with those that employ valence double-{ bases, we conclude that minimum basis sets are unreliable for predicting relative replacement energies for the substitution of silicon by aluminum atoms at the T sites of the zeolite. From these calculations, we also conclude that small differences in the bond lengths and angles can significantly alter the order of the sites with respect to the replacement energies. From calculations using valence double-c basis sets on T(OH)4 monomers, we conclude that, in the absence of protons or other ions, the most favorable sites for AI substitution in zeolite ZSM-5 are the T6, TI*,and T9sites, whereas the least favorable site is Tp. However, the least favorable and most favorable sites only differ by 3.3 kcal/mol. We also present a simple empirical model that is capable of reproducing the results of the ab initio calculations. This model gives the replacement energy in terms of the bond lengths and bond angles about each site.
1. Introduction We have undertaken a theoretical study of some of the catalytic properties of zeolites. In the first phase of this study, we are concerned with the characteristics of acid sites in zeolites and zeolite ZSM-5 in particular. In the present paper, we report studies of the energetics of the substitution of silicon atoms by aluminums in the framework of zeolite ZSM-5. These studies have been carried out using ab initio Hartree-Fock wave functions in small clusters that model the zeolite framework. In addition to the calculated relative substitution energies for the different sites, we also present an empirical model that reproduces the results of these a b initio calculations. A number of quantum chemical studies have been carried out on zeolites using clusters of atoms to model relevant portions of the zeolite framework. Some of these studies have employed semiempirical methods,’ such as the extended Hackel and complete
0022-3654/91/2095-1003 1$02.50/0
neglect of differential overlap methods; other calculations have used a b initio techniques,’ such as the self-consistent-field Hartree-Fock method. Although the latter approach is more reliable than the former, it is more demanding in terms of computational resources. The basic theoretical technique we have employed in the calculations reported herein is the ab initio Hartree-Fcck method. To date, many of the ab initio studies on zeolites have employed minimum basis sets.* While minimum basis sets are compact, they have the disadvantage that they lack flexibility in the description of the wave functions. This is particularly apparent when (1) Sauer, J. Chem. Rev. 1989, 89, 199 and references therein. (2) Reviews of the nomenclature and techniques of quantum chemical calculations can be found in: Goddard 111, W. A,; McGill, T.C . J . Voc. Sci. Technol. 1979. 16, 1308. Gibbs, G. V. Am. Mineral.1982,67,421. Lasaga, A. C.; Gibbs, G. V. Am. J . Sci. 1990, 290, 263.
0 1991 American Chemical Society
10032 The Journal of Physical Chemistry, Vol. 95, No. 24, 1991
different geometries are compared. Minimum basis sets typically are not capable of accommodating large variations in bond angles and bond lengths, thus leading to poorer results than those obtained with larger basis sets. Because of these considerations, the initial part of our study compares the results of minimum basis set calculations for the energy of substitution of silicon by aluminum in the different sites of zeolite ZSM-5 with corresponding calculations that employ valence double-{basis sets.) In such a basis set, the single-particle functions of the valence shell are described using twice as many basis functions as in the minimum basis sets. While valence double-{ basis sets are not optimum, they represent the smallest basis sets that have enough flexibility to reliably describe different bonding configurations with the same basis set. Calculations comparing minimum to valence double-{ basis sets are described in section 11. In section 111 we report on an empirical model that reproduces the results of the a b initio calculations. Finally, section IV summarizes our conclusions.
11. Replacement Energy of Silicon by Aluminum in Zeolite ZSM-5 A. Comparison between Minimum and Valence Double-{ Basis
Sets. We have carried out a b initio Hartree-Fock calculations using monomeric T(OH)4 clusters, where T stands for either Si or AI. The T and oxygen atoms were positioned according to their location in the framework of zeolite ZSM-5 from the crystal structure of van Koningsveld et al.: published in 1987. This structure represents the most accurate determination based on the reported refinement parameters. Earlier structures were reported by Olson et aL5in 1981, Lermer et a1.6 in 1985, and Chao et al. in 1986.' As discussed below, significant differences in the relative T(OH)4energies and in AI/Si substitutional energies can be obtained, depending on which crystal structure is used to construct the monomeric cluster. An important point to be noted here is that these calculations do not include protons or other counterions. This means that, although the information they provide is valuable in establishing substitutional trends in the zeolite, it is possible that experimental results lead to somewhat different trends because real systems always have counterions associated with the substitution of silicons by aluminums. The two main basis sets used in these calculations were the STO-3G minimum basis set* (denoted STO-3G hereafter) and the valence double-{ (VDZ) set.9 In the VDZ set, the core electrons of silicon and aluminum are replaced by an effective core potential (ECP).IO To check the validity of the ECP, additional all-electron calculations were performed in a third basis set, a full double-{ (DZ) basis, in which all electrons were explicitly treated.g For the clusters we considered, the relative AI/Si replacement energies differed by at most 0.1 kcal/mol between the ECP-VDZ and all-electron DZ calculations. All calculations reported here were carried out at the self-consistent-field Hartree-Fock level using the MESA electronic structure codes." Hydrogen atoms were used to form covalent bonds to what otherwise would have been dangling bond orbitals on the oxygens. The clusters are neutrally charged when T is a silicon atom and have a charge of -1 when T is an aluminum atom. The H atoms used to terminate the clusters were placed either (a) at the lattice (3) These sets are also known in the literature as split-valence sets. (4) van Koningsveld, H.; van Bekkum, H.; Jansen, J. C. Acta Crystallop. 1987, 843, 127. (5) Olson, D. H.; Kokotailo, G . T.; Lawton, S . L.; Meier, W. M. J . Phys. Chem. 1981,85, 2238. (6) Lermer, H.; Draeger, M.; Steffen, J.; Unger, K.K. Zeolites 1985, 5 , 131. (7) Chao, K. J.; Lin, J. C.; Wang, Y.;Lee, G. H. Zeolites 1986, 6, 35. (8) Hehre, W. J.; Stewart, R. F.;Pople, J. A. J . Chem. Phys. 1969, 51, 2657. Hehre, J. W.; Ditchfield, R.; Stewart, R. F.;Pople, J. A. J. Chem. Phys. 1970, 64, 5142.
(9) Dunning, Jr., T. H.; Hay, P. J. In Modern Theoretical Chemistry; Schaefer 111, H. F.. Ed.; Plenum: New York, 1977; Vol. 3, p 1. (10) Wadt, W. R.; Hay, P. J. J . Chem. Phys. 1985, 82, 284. ( I I ) Saxe, P. W.; Martin, R. L.; Lengsfield, 111, B. H.; Page, M.Molecular Electronic Structure Applications program, 1987, unpublished.
Alvarado-Swaisgood et al. TABLE I: Replacement Energies of Silicon by Aluminum for Monomeric Clusters Modcliq-thc T Sites of &Ute ZSM-9 STO-3G VDZ VDZ 1.o
1.3
-0.8 0.5 -1.2 0.5
1.4
TI
T2 7.3
T4
T5
3.6 2.0 1.1
1.2 1.1 3.3 1.5 0.8
-6.2 -9.9 -5.6 -3.5 -3.5
T6
0.0d
0.v
0.N
0.0
T7 TS T9
1.4
2.4
1.9
-5.2
0.0 -4.2 -0.3 -2.6 -1 1.6
TI0
TI, TI2
1.6
1.1
1.4
0.6
0.4
0.8 -0.5 0.3
1.3 2.3
0.7 1.7 0.2
-2.0
0.4
"All energies are in kcal/mol and are referenced to the T, site. bSee Figure I . CReference 12. dTotal energy of Si(OH), cluster, -582.5 I9 73 hartrees; total energy of AI(OH), cluster, -535.920 80 hartrees; energy of Si4+, -281.995 69 hartrees; energy of AI3+, -237.256 54 hartrees. CTotalenergy of Si(OH)4cluster, -305.001 42 hartrees; total energy of AI(OH), cluster, -303.180 81 hartrees; an effective core potential was used to replace the cores of silicon and aluminum. ,Total energy of cluster, -305.607 85 hartrees; total energy of AI(OH), cluster, -303.815 35 hartrees; an effective core potential was used to replace the cores of silicon and aluminum. ZSM-5 1907
Q
w 015
Figure 1. Numbering scheme for the atoms in zeolite ZSM-5.
positions of the Si atom they were replacing (HI*,), with a corresponding 0-HI,, distance of ca. 1.6 A, or (b) at a distance of 0.95 A (H,J, corresponding to the 0-H bond distance in water. The results of the comparisons between the minimum and double-t basis sets are summarized in Table I, where we show the replacement energy in kcal/mol for the substitution of silicon by aluminum at each of the different T sites. The relative positions of the atoms in these sites are shown in Figure 1. Column 2 of Table I reports the results of our calculations for the minimum basis set, whereas columns 3 and 4 show the corresponding results for the valence double-t basis. The last column shows the results of the STO-3G calculations by Fripiat et al.,'* which will be discussed in the next subsection. All replacement energies have been referenced with respect to the values at the T6 site, which we have found to have the lowest replacement energy. The replacement energies shown in Table I were obtained from the following expression AEi = [E(Ti(AI)) - E(T,(Si))] - [E(T6(Al)) - E(T,(Si))] where AEi is the replacement energy for the ith T site. A comparison of the STO-3G and the VDZ results shows that the two basis sets lead to a completely different ordering of the sites with respect to their AI/Si replacement energies. Whereas the minimum basis set favors T8 as the most favorable site for (12) Fripiat, J. G.; Berger-Andre, F.; Andrb, J.-M.; Derouane, E. G. Zeolites 1983, 3, 306. Derouane, E. G.; Fripiat, J. G . Zeolites 1985, 5, 165.
The Journal of Physical Chemistry, Vol. 95, No. 24, 1991 10033
Aluminum Substitution in Zeolite ZSM-5
A
Bond-Length Contribution
AllSi ReplacementEnergy
-
1 1
2
3
4
5
6
7
6 T site
9
1
0
1
1
1
2
I
2
3
(b)
4
5
6
7 T site
8
I
9 1 0 1 1 1 2
T-0-T Angle Contribution
n
I
Figure 2. AI/Si replacement energies (from monomer calculations) for the 12 T sites of zeolite ZSM-5: solid line, VDZ basis set; dashed line, STO-3G basis.
-
1
z 4
4
I
2
3
4
5
6 7 T site
8
9 1 0 1 1 1 2
Figure 4. (a) Bond-length and (b) T-O-T angle contributions to the AI/Si replacement energy for the VDZ and STO-3G basis sets.
U
E
I 1
I 2
I 3
I 4
5
1
2
3
4
5
7
8
8 1 0 1 1 1 2
6 7 T site
8
9 1 0 1 1 1 2
6
16-
-
m Y
> 120 W w
8-
E 4
4-
u
n-
"
Figure 3. Relative energies for the monomeric T(OH)., clusters: (a) T = Si; (b) T = AI. All energies are referenced to that of the respective T6cluster. Solid lines, VDZ calculations; dashed lines, STO-3G calculations.
substitution of the silicon by an aluminum, the valence double-{ basis shows that the site with the lowest replacement energy is the T6 site. Both basis sets lead to essentially the same range of replacement energies, namely, approximately 3.5 kcal/mol. The differences between the relative orderings of the sites are shown in Figure 2, where we plot the replacement energies for the two basis sets for the different T sites. The total energies (relative to the T6 site) for the minimum basis and the valence double-{ basis, for the Hlatgeometry, are shown in Figure 3 for the 12 different clusters modeling zeolite ZSM-5. These energies were calculated using the expression = E,(T) - E6(T), where T is either Si or Al, and E, is the total energy of the cluster modeling the ith site. Figure 3a plots the relative energy when the T site is occupied by a silicon atom. Figure 3b reports the corresponding values for the clusters containing aluminum atoms. In this case, the discrepancies between the two basis sets are less pronounced thanfor the replacement energies. The most obvious difference occurs at the T8 site, which is among the less stable sites for the STO-3G basis, but not so for the valence double-f basis set. In addition, the STO-3G basis leads to relative energies in a range (17.6 kcal/mol) somewhat larger than that of the valence double-f basis set (1 5.2 kcal/mol). To further investigate the origin of the differences between the minimum and valence double-{ basis sets, we carried out additional calculations to separate the effect of variations in the bond lengths from those of variations in the angles. These calculations consisted of separate studies on the molecules Si(OH)4and AI(OH),, where
only the T-O bond length was varied. From them, a contribution to the substitutional energy due to the T-0 bond lengths was estimated. Because of their relevance to the empirical model introduced in section 111, we defer a detailed discussion of these calculations until then. In the present section we will restrict ourselves to reporting the results relevant to the differences between the VDZ and STO-3G basis sets. Figure 4a presents a comparison of the bond-length contributions to the AI/Si replacement energy for each of the individual T sites of zeolite ZSM-5. For ease in the comparison, all energies are referenced to site T6. This figure shows that if the Al/Si substitutional energy were only due to variations in the T-0 bond lengths between the different sites, then the two basis sets would lead to exactly the same ordering; namely, the most favorable site for the aluminums would be the T6 site, whereas the T3 site would be the least favorable one. To estimate the contribution of the variations in the angles among the 12 sites, we subtracted the contributions due to the bond lengths from the actual calculated substitutional energies (cf. Figure 2). The results are reported in Figure 4b, where we can see that the minimum basis set leads to site orderings that are quite different from those found for the valence double-{ basis set. These results show that the main deficiency of the minimum basis set rests in their lack offlexibility for the proper description of variations in the bond angles. The most striking conclusion from these comparisons is that the minimum basis sets are unreliable for predicting trends among the replacement energies for the different T atom sites in zeolites. For individual sites, the difference between the replacement energy calculated with the minimum basis set and that calculated with the valence double-{ basis is as much as 3.6 kcal/mol. This result has important implications when interpreting previously published ab initio calculations on zeolites because many of them have employed minimum basis sets.13 These results are also consistent with previous reports indicating the valence double-{ basis sets perform better than minimum basis sets for bond lengths and force ~0nstants.l~The importance of flexible basis sets for the de(13) Hass, E. C.; Mezey, P. G.; Plath, P. J. J. Mol. struct. (THEOCHEW 1981, 76,389; 1982,87, 261. Sauer, J.; Engelhardt, G. 2. Nuturforsch. 1982, 37A, 277. Reference 7 . Geisinger, K. L.; Gibbs, G. V.; Navrostsky, A. Phys. Chem. Miner. 1985, 11, 266. Derouane, E. G.; Fripiat, J. G. J. Phys. Chem. 1987, 91, 145. (14) Binkley, J. S.; Pople, J. A.; Hehre, W. J. J. Am. Chem. SOC.1980, 102,939. Pople, J. A.; Schleger, H. B.; Krishnan, R.; Defrees, D. J.; Binkley, J. S.; Frisch, M. J.; Whiteside, R. A. In?. J. Quantum Chem. 1981, SlS, 269. Gordon, M. S.; Binkley, J. S.; Pople, J. A.; Pietro, W. J.; Hehre, W. J. J. Am. Chem. Soc. 1982, 104, 2797.
Alvarado-Swaisgood et al.
10034 The Journal of Physical Chemistry, Vol. 95, No. 24, 1991
scription of the T-O-T angles in silicate systems has also been noted previou~ly.~~ From the valence double-f calculations we conclude the following: (1) the variations of values for the replacement energy of silicons by aluminums have a narrow range, with the largest difference being 3.6 kcal/mol between the T3 and T6 sites; (2) the clusters do not exhibit striking differences between the total energies for the VDZ and STO-3G basis sets; for example, the relative energies between the most stable site, T,, and the least stable site, T3, are within a range of 1 1.6 kcal/mol for the silicon clusters and 15.2 kcal/mol for the AI clusters; (3) the most favorable sites for AI substitution are T6, T12,and T9, all within 0.6 kcal/mol of each other; (4) the least favorable site for AI substitution is T3. B. Comparisonwith Previous Work. In a previous study, Fripiat et al.I2 carried out molecular orbital calculations using the selfconsistent-field Hartree-Fock approach to study monomer and dimer clusters modeling zeolite ZSM-5. Like ours, their main objective was to investigate the relative stability of different T(OH)4 monomers, where T stands for Si or AI. In the calculations that are most relevant to the subject of the present work, they employed monomeric T(OH)4 clusters, where the T and oxygen atoms were positioned according to their location in the framework of zeolite ZSM-5.16 Hydrogen atoms located at the nearest-neighbor T sites (Hlat)were used to form covalent bonds to what otherwise would have been dangling bond orbitals on the oxygens. As in our case, their clusters are neutrally charged when T is a silicon atom, and they have a charge of -1 when T is an aluminum atom. Fripiat et al. used minimum basis sets of the STO-3G type to calculate the replacement energy of silicon by aluminum in the 12 different sites of zeolite ZSM-5. Their choice of this basis set was imposed by computational constraints. Some comparisons between this and two other basis sets are reported by these authors. Their results for the T2 and T8 sites of zeolite ZSM-5 indicate that the use of the STO-3G basis with polarization functions of d type or of the more flexible 6-21G basis sets simply produce a shift of the energies by an approximately constant value. This would mean that the STO-3G minimum basis set is capable of giving reliable results for the trends in the relative energies for the replacement of silicon by aluminum. In view of the results presented here, this conclusion appears to be somewhat optimistic. In fact, their own results showI2 that whereas the replacement energy of the T8 site, with respect to the T2 site, is 10.0 kcal/mol for the STO-3G basis, it is 14.4 kcal/mol for the 6-21G basis. This discrepancy is not negligible considering that they estimate their uncertainty to be approximately 3 kcal/mol. An important point in the comparison of their results with ours is evident from columns 2 and 5 in Table I. Clearly, our STO-3G calculations, with the same basis set Fripiat et al. employed," do not lead to the same ordering of the T sites with respect to silicon substitution by aluminum. This discrepancy stems from the fact that we employed a different X-ray refinement4 of the crystal structure of zeolite ZSM-5 than they did.s This is a crucial point that merits emphasis. Dramatically different results can be obtained between ab initio calculations that differ by relatively small amounts in the geometric arrangement of the atoms. For example, the range of T-O bond lengths for the structure obtained by Olson et aL5 is 1SO-1.67 A, whereas the more recent refinement of van Koningsveld et a1.4 reports a narrower range of 1S67-1.605 A. Similarly, the 0-T-0 angle ranges are 96-129O for the structure of Olson et al. and 106-1 12' for that of van Koningsveld et al. A specific instance of the importance of small variations in (15) Mortier, W. J.; Sauer, J.; Lercher, J. A.; Noller, H. J . Phys. Chem. 1984,88,905. OKeefe, M.; DomengEs, B.; Gibbs, G. V. J. Phys. Chem. 1985, 89, 2304. Reference 1 . (16) Reference 4; notice that this is an earlier X-ray structure than the one we employed in our calculations. (1 7) To make sure these comparisons were valid, we repeated the calculations using the geometries employed by Fripiat et al. for two of the T sites and obtained the same values they did.
STO-3G (Hlat,1987)
(b)
30 20 10
0 30 20 10
n
1
2
3
4
5
6 7 T site
8
9 1 0 1 1 1 2
Figure 5. Aluminum occupancy statistical distributions at T = 150 "C: (a) STO-3G calculations of Fripiat et al. (1981 structure, HI& (b) STO-3G calculations (1987 structure, HI& (c) VDZ calculations (1 987 structure, Hlat);(d) VDZ calculations (1 987 structure, Hw).
geometry can be seen in the results for the T8 site. Our STO-3G calculations show this site to be the most favorable one for aluminum substitution (see Table I), 2.3 kcal/mol better in the replacement energy than the TI2site. Fripiat et al. found this site to have a replacement energy 11.6 kcal/mol above that of the T I 2site. If we now consider the T-0 bond lengths for the T8 site, we find that Olson et al. give the following values: 1.58, 1.63, 1.52, and 1.53 A. On the other hand, van Koningsveld et al. reported the values 1.586, 1.588, 1.583, and 1.577 A. Clearly, the differences (as much as 0.06 8) can easily account for the discrepancies in the two calculations.18 One way to emphasize the differences between the different calculations described above is to examine the distributions for aluminum atom occupancy that each calculation predicts. To do this, we assume that the relative probability of finding the ith site occupied by an aluminum atom at absolute temperature Tis only given by the Boltzmann distribution, exp(-AEi/k7')/Z, where Mi is the replacement energy of the ith site and 2 is the partition function. Of course, this ignores the kinetics and the effect of protons or other counterions, but it illustrates the differences between the calculations. Figure 5 shows the percentage of aluminum atoms found in each of the 12 T sites, for T = 150 OC, a typical synthesis temperature for zeolite ZSM-5. The distribution obtained from the calculations of Fripiat et al. is shown in Figure 5a. The corresponding distribution for our minimum basis set calculations with the 1987 geometry of van Koeningsveld et al. is reported in Figure 5b. Figure 5c,d shows the distributions obtained from our valence double-f results using the 1987 X-ray structure; Figure 5c is for the case when the capping hydrogens are at the lattice positions while Figure 5d corresponds to the case when the oxygen-hydrogen bond lengths are similar to those of water. Comparing parts a and b of Figure 5, we notice that while the calculations of Fripiat et al. predict that only the TI2and T2 sites would be effectively occupied by aluminums, our identical calculation, but using a more recent geometry, shows that practically all 12 sites are occupied. A comparison between parts b and c shows that the minimum and valence double-{ basis sets lead to different distributions. Finally, a comparison between parts c and d shows that changing the oxygen-hydrogen bond length does not significantly alter the aluminum distribution^.'^ ( 1 8) For an example of how important these differences can be, see Table 111.
The Journal of Physical Chemistry, Vol. 95, No. 24, 1991 10035
Aluminum Substitution in Zeolite ZSM-5 4.5
TABLE II: Average Bond Lengths and Angles for the 12 T Sites in Zeolite Z S M - 9 T site RT4 LO-T-O fl-0-T 152.72 TI 1 S879 109.45
AI/Si Replacement Energy
4.0
VDZ + d VDZ
3.5
E 3.0 -. Y
$
2.5
T2
2.0
T4
1.5
TS
T3 T6
1.o
T7 Tll T9 TI0
0.5 n
1
2
3
4
5
6
7
8 9 T site
1
0
1
1
1
2
TI I
Figure 6. Comparison of AI/Si replacement energies (1 987 structure, H,) obtained using the VDZ basis with d-type functions at the T site and the VDZ basis set.
C. Effect of d-Type Basis Functions. To investigate the effect of d-type functions in the AI/Si replacement energies, we carried out a set of monomer calculations using the VDZ basis augmented by one set of d functions located at the T site. As in the calculations reported in Table 1, we performed calculations in both the Si(OH), and AI(OH),- clusters using hydrogens located at 0.95 A (H,) from the oxygens. A single set of d-type functions was added to the AI (Gaussian exponent of 0.4) and Si (Gaussian exponent of 0.5) atoms. Except for the addition of the d functions at the T site, these calculations were identical to those of the fourth column of Table I. Figure 6 reports the values of the AI/Si replacement energies obtained when the d functions are present at the T site. For comparison, the values for the plain VDZ basis (see Table I) are also shown in the figure. Although the d functions introduce minor differences in the absolute values of the replacement energies, the ordering of the sites with respect to A1 substitution is the same as that found for the VDZ basis. Therefore, we conclude that, in the interest of keeping the computational cost down, the inclusion of d-type functions in the basis sets is not as essential as the inclusion of a double-r description of the valence shells. 111. An Empirical Model for the Calculation of the Replacement Energies
The understanding of the results of the ab initio calculations can be aided by the construction of a physical model of an empirical nature. Accordingly, we have analyzed our results in light of such a simple model. Instead of using the valence double-f results presented in column 3 of Table I, we repeated the calculations, but instead of locating the hydrogens at the positions of the nearest-neighbor T sites, we placed them along the direction of the @T bonds at a distance of 0.95 A from the oxygen atoms (H,). Those energies are shown in colum 4 of Table I. The first thing that comes to mind when considering an empirical model for the replacement energy of silicon by aluminum in the zeolite is the geometric environment around the T atoms. The covalent radius of silicon is20 1.17 A, and that of aluminum is 1.26 A. Because AI atoms are larger that Si atoms, one would expect that a general trend would be that the sites with larger average T-O bond lengths are more favorable to the replacement than sites with smaller values. Table 11 shows the average geometric factors around each one of the 12 T sites of zeolite ZSM-5. Column 2 reports the average T-0 bond lengths (in angstroms), while columns 3 and 4 show the average 0-T-0 and T-0-T angles (in degree^).^ Looking at Tables 1 and 11, we see that the AI/Si substitution energy is related to the size of the cavity. Sites T9, T6, and T,2 have the largest average T-0 bond lengths and exhibit the lowest replacement energies. Alternatively, the shortest average bond ~~
(19) It should be pointed out that the reactivity of a given site is not
necessarily related to its aluminum occupancy. It is possible that sites whose AI occupancy is small are more catalytically active than sites with larger occupancies . (20) Mason, J. J . Chem. Educ. 1988, 65, 17.
7-12
1 S852 1 S800 1.5830 1 S882 1.5903 1.5855 1.5833 1.5912 1.5890 I S834 1.5902
109.46 109.46 109.47 109.46 109.45 109.48 109.47 109.45 109.47 109.47 109.46
159.09 158.99 161.48 154.60 153.46 152.30 162.83 150.5 1 153.03 159.3 1 153.00
ODistances are in angstroms and angles in degrees. All geometries are taken from ref 4.
distance occurs at site T3, the site that is most unfavorable for AI/% substitution. However, this picture is incomplete because the difference between the average bond lengths around sites T9 and T6 is not consistent with the difference of 0.4 kcal/mol in their replacement energies. Thus, the replacement energy is not a monotonic function of the average T-O bond length. Thus, our model must become more complex. One could, for example, start to look for differences between the individual bond lengths instead of their averages. To keep the model as simple as possible, we have .taken a different approach. Before proceeding with the model, we note that our calculations simply consisted of a replacement of the silicon atom by an aluminum atom, leaving the geometry of the cluster unchanged. This means that the energies quoted in Table I do not include any atomic relaxation around the T sites after the silicons have been substituted by aluminums. Thus, our model will not include such relaxations. To go beyond the dependence on the average bond length, we made two basic assumptions. First, we assumed that the discrepancies we have pointed out are caused by differences in the angles formed by the atoms at the T sites. The second assumption is that the 0-T-0 angles are much less important in the contributions to the replacement energies than the T-0-T angles are. This assumption is consistent with the fact (cf. Table 11) that the range of variations for the average T-0-T angles is 150.5-162.8', whereas the average 0-T-O angles are practically constant from site to site. Ostensibly, our simple model is set by the discussion above. The replacement energy should have the form AEmde, = AE(r) + A E ( 8 ) where AE(r) is the contribution of the average bond length, r, and AE(8) is the contribution of the average T-O-T angle, 8. In its simplest form-the form we actually used-the model assumes that both of these terms are linear in their respective variables.21 Thus AE(r) = A, + B y , AE(8) = AB B&I
+
where A,, B,, AB,and Bo are constants. To calculate the constants we proceeded as follows. To ascertain the contribution of the average bond length, we performed a separate set of calculations on the molecules Si(OH)4 and Al(OH),-, using the angles and 0-H bond lengths found in or(21) Note that this approximation is for the energy difference between the AI and Si monomers. The respective total energies of the clusters cannot be
approximated by linear expressions, requiring at least quadratic terms. The linear approximation for the energy difference works well because both the Si and AI clusters have approximately the same second derivatives. Indeed, from Table I11 one obtains good quality fits to the total energies of the clusters using second-degree polynomials in r. For the VDZ basis, the least-squares fit to the Si(OH)4total energies is -289.61 1 - 8.254r + 2.4389. whereas for the AI(OH), monomer the fit to the total energy is given by -295.282 9.603r + 2.679r2,leading to very similar second derivatives. Almost exact fits are obtained if one uses cubic polynomials.
Alvarado-Swaisgood et al.
10036 The Journal of Physical Chemistry, Vol. 95, No. 24, 1991
TABLE III: TOW Entrgies' of tbe Si(OH), .ad Ai(0H)i Clusters (Columns 2-5 in hartrees, Columns 6 and 7 in kcal/mol Referenced to the Value at 1.80 A) as a Function of the T-O Bond Length (in A) Si(OH)4 AI(0H)L PEW rT-0
VDZ
1S O
-305.497 20 -305.55244 -305.584 21 -305.597 42 -305.595 99 -305.583 15 -305.561 52 -305.533 25 -305.500 08
1.55 1.60 1.65 1.70 1.75
1.80 I .85 I .90
VDZ
STO-3G -583.27472 -583.31982 -583.342 50 -583.347 41 -583.338 22 -583.31789 -583.288 77 -583.252 79 -583.21 1 52
VDZ
STO-3G -536.548 46 -536.621 15 -536.66845 -536.695 26 -536.705 41 -536.702 23 -536.688 08 -536.665 12 -536.63508
-303.648 73 -303.73409 -303.79508 -303.836 57 -303.862 41 -303.875 66 -303.878 77 -303.873 71 -303.862 09
STO-3G 79.79 61.48 46.03 32.29 20.1 1 9.39
103.99 85.09 66.76 49.01 31.01 15.53
0.00
0.00
-14.57 -28.08
-8.17 -1 5.22
"An effective core potential has been used in both the Si and AI atoms for the VDZ calculations; thus, an energy of 44.739 15 hartrees (corresponding to the difference between the Si and AI cores) must be included in the calculations of the AI/Si substitution energies; see ref 9 and footnote d to Table 1.
TABLE IV: Contributions to the Replacement Energy from A E ( r ) and A E ( 0 ) (All Energies In kcal/mol; VDZ Calculations) T site AE(r) AE(0) AE,d, AEAllsi 0.87 1.86 3.75 2.66 0.76 0.00 1.75 2.55 -0.33 0.47 2.51 0.04
0.30 -0.8 1 -0.80 -I .23 -0.03 0.17 0.38 -1.47 0.69 0.25 -0.85 0.25
1.2 1.1 3.0 1.4 0.7 0.2 2. I 1.1 0.4 0.7 1.7 0.3
1.2 1.1 3.3 1.5 0.8 0.0 1.9 1.1 6.4 0.7 1.7 0.2
thosilicic acid by Sauer.22 We varied only the T-O bond length (uniformly for all four bonds) and calculated the total energy of the cluster, leading to the results found in Table 111. The last two columns of Table I11 are obtained by subtracting the total energy of the Si(OH)4 cluster from that of the AI(OH),cluster. A least-squares fit to the values between r = 1.50 and 1.70 A gives the followin parameters: A, = 649.7 kcal/mol and B, = -364.08 kcal/(mol. ) for the valence double-{calculations; the corresponding values for the minimum basis set are A, = 5 16.7 kcal/mol and B, = -293.1 kcal/(mol*A). Using the average bond lengths shown in Table 11, we obtained the values of M ( r ) shown in column 2 of Table IV for each one of the 12 T sites of zeolite ZSM-5. To obtain the average T-O-T angle contribution to the replacement energy, we picked two sites, T8 and T9, to fit the values of ABand Bo. These sites were chosen because they correspond to the sites with the largest and smallest angles 6' (cf. Table 11). We first calculated the difference between the calculated replacement energies, 1.1 and 0.4 kcal/mol (for the VDZ calculations) for the T8 and T9 sites, respectively, and the values of AE(r), namely, 2.32 and -0.30 kcal/mol (see Table IV). This leads to values of -1.24 and 0.66 kcal/mol for the contribution to AE(6') for these two sites. From these two energies and the average angles shown in Table 11, we obtained the parameters AB= 27.0781 kcal/mol and Bo = -0.175325 kcal/(moldeg). The values of hE(c9) obtained from these parameters for the other T sites are also shown in the third column of Table IV. The results of the model are shown in column 4 of Table IV and can be compared with the ab initio values, shown in the last column. An equivalent comparison is shown in Figure 7. By choice, sites T8 and T9 agree exactly. The agreement for the sites not used in the fits is excellent. These results support the assumption upon which the model is based. In particular, they indicate that a simple physical model can account for the results
1
(22) Sauer, J. J . Phys. Chcm. 1987, 91, 2315. The 0-H torsional angles were arbitrarily held fixed at Oo.
3.5
c
1
Ai/SI Substitutional Energy
2
3
4
5
6 7 T site
8
9 1 0 1 1 1 2
Figure 7. Comparison of AI/Si replacement energies (1987 structure,
Hw):solid line, ab initio results; dashed line, empirical model. of the quantum mechanical calculations. We should emphasize again that the results of the a b initio calculations and the subsequent simple model presented above are valid only for the substitution of silicon by aluminum in the absence of counterions. Although very useful in the further interpretation of real systems, more meaningful comparisons with experimental results should await more complete calculations in which counterions are properly included.
IV. Conclusions We have performed ab initio quantum mechanical calculations in monomeric clusters modeling the 12 different T sites of zeolite ZSM-5. By comparing the results of calculations that use minimum basis sets with those that employ valence double-{ basis sets, we conclude that minimum basis sets are unreliable for the prediction of relative replacement energies for the substitution of silicon by aluminum atoms at the T sites of the zeolite. From these calculations, and upon comparison with similar calculations carried out with a slightly different geometry, we also conclude that small differences in the bond lengths and angles can significantly alter the order of the sites with respect to the replacement energies. From the calculations using valence double-{ basis sets and the latest refinement of the ZSM-5 X-ray structure, we conclude that the most favorable sites for A1 substitution in zeolite ZSM-5 are T,,TI2,and T,; the least favorable site is TB. We also introduced a simple empirical model that is capable of reproducing the results of the a b initio calculations. From the agreement between this simple model and the calculated replacement energies, we conclude that the most important effects in the substitution of silicons by aluminums in the T sites of zeolite ZSM-5 are due to the T-O distances and the T-O-T angles. Acknowledgment. Portions of this research (P.J.H. and A.R.) have been carried out under the auspices of the U.S. Department of Energy, Advanced Industrial Concepts Division, Catalysis/ Biocatalysis Program. A.E.A.-S. and M.K.B. were supported by Amoco Corporation's Synthetic Fuel Department.
