J. Phys. Chem. 1988, 92, 6705-6709
6705
Nevertheless, the differences between the spectra of the calcined samples exposed or not to wet atmosphere can lead to relative estimations of the tetrahedral species. It is obvious that the tetrahedral species content is much more important in the HSA sample than in the calcined B sample. A further study with various vanadium coverage, in correlation with the selective catalytic properties, is in progress.
W, or V for well-dispersed supported catalysts, by using laser Raman spe~troscopy,~~,~’ and thus this work shows that wide-line N M R can supply very fine information about vanadium catalysts also. In particular, it shows that the tetrahedral species seem to be able to bind preferentially with the silica in our preparation conditions. Furthermore, a more important distortion of the tetrahedral species is still visible in the spectra of the calcined B sample in wet air (Figure 6b). Consequently, a chemical simulation with the mechanical mixtures of calcined (b) V20, and N H 4 V 0 3 is not as good as in the case of the dried sample.
Acknowledgment. We are indebted to S. Kasztelan for valuable discussions and preparation of the HSA sample. We thank also B. Mouchel, R. Guillemand, J. P. Amoureux, and L. Gengembre for their helpful contributions in N M R and XPS experiments. Registry No. 51V,7440-62-2; vanadium oxide, 11099-1 1-9.
(35) Payen, E.; Kasztelan, S.;Grirnblot, J.; Bonnelle J. P. J . Raman Spectrosc. 1986, 17, 233.
Determination of Structure and Acidity Scales in Zeolite Systems by ab Initio and Pseudopotential Calculations E. Kassab, K. Seiti, and M. Allavena* Dynamique des Interactions MolPculaires, E R 271 du CNRS, UniversitP Pierre et Marie Curie, Tour 22, 4 Place Jussieu, 75252 Paris Cedex 05, France (Received: January 7, 1988)
SCF ab initio calculations at the 6-31G level have been used to investigate the structure of several aggregates simulating some of the proton donor sites within faujasite-type zeolites. The Si(OH),,, H3SiOHAlH3,and (OH)3SiOHAI(OH)3clusters have been successively examined. Deprotonation energies and charge distributions are determined at a higher level by using a 6-31G basis set augmented with polarization and diffuse functions. The results are compared with values obtained by using pseudopotential methods. The small differences between the two sets of results demonstrate that comparable accuracy should be expected from both procedures. Finally, deprotonation energies of (OH)ST10HT2(OH)3aggregates (TI, T2 = AlSi, BSi, GaSi; AlGe, BGe, GaGe) are calculated by using pseudopotential methods and compared with the results given by the semiempirical MNDO method. In some cases ab initio SCF calculations were also performed. The results confirm that the inclusion of boron atom lowers the acidity as already demonstrated by experimental investigation. The effects due to the inclusion of Ga are discussed and compared to available experimental data.
Introduction Zeolites are porous minerals’ commonly used in the oil industry as molecular sieves and catalytic materials. Their microscopic crystalline structure has been extensively studied by X-ray diffraction, but the mechanism of their interaction with host molecules is not as well understood and still poses some puzzling questions. In particular, the determination of the factors that control the acidity of these materials leads to ambiguous results. Moreover, the research for improving the performance of zeolites as catalytic agents is very active. These materials are then still a challenge for chemists, and they also have become a subject of interest for quantum chemists. The number of papers recently published in this field is growing very rapidly. Recent publications show that semiempirica12” and small basis set ab i n i t i ~ ~ * ’ - ’ ~ (1) Breck, D. W. Zeolite Molecular Sieves; Wiley: New York, 1974. (2) Mezey, P. G. In Catalytic Materials: Relationship between Structure and Reactivity; Whyte, Jr., E., Dalla Betta, R. A., Derouane, E. G., Baker, R. T. K., Eds.; ACS Symposium Series 248; American Chemical Society: Washington, DC, 1984; p 145. (3) Mortier, W. J.; Geerlings, P.; Van Alsenoy, C.; Figeys, H. P.J. Chem. Phys. 1979, 83, 855. (4) Beran, S. Z . Phys. Chem. 1982, 133, 37. (5) Beran, S. In Structure and Reactivity of Modified Zeolites; Jacobs, P. A., et al., Eds.; Elsevier: Amsterdam, 1984. (6) Senchenya, I. N.; Kasansky, V. B.; Beran, S.J. Phys. Chem. 1986,90, 4857. ..
(7) Mortier, W. J.; Sauer, J.; Lercher, J. A,; Noller, H. J . Phys. Chem. 1984, 88, 905.
0022-3654/88/2092-6705$01.50/0
calculations are still in competition in this area. However, the use of these theoretical tools for the determination of electronic or vibrational properties of small clusters, which are supposed to reproduce the local properties of zeolites, gives rise to at least two basic questions: (i) the reliability of these calculations and (ii) the ability of small clusters to simulate the real environment of the catalytic site considered. These questions, though very general, should be addressed before too much effort is expended on such calculations. The review recently given by Dewar” concerning the use of small basis set a b initio calculations generates some concern with respect to using this procedure. The argument that only trends are being searched for using any theoretical method is not really convincing when the number of cases examined is too small. The objective of the present work is to investigate the acidity of the faujasite-type zeolite. The term acidity is used here in the Bronsted sense, Le., the aptitude of the system to lose a proton. The quantity directly related to this concept is the deprotonation energy, evaluated here by using both ab initio and pseudopotential (8) Fripiat, J. G.; Galet, P.; Delhalle, J.; AndrC, J. M.; Nagy, J. B.; Derouane, E. G. J . Phys. Chem. 1985,89, 1932. (9) Sauer, J. Acta Phys. Chem. 1985, 31, 19. (10) Derouane, E. G.; Fripiat, J. G. J . Phys. Chem. 1987, 91, 145. (1 1) Pelmenshchikov, A. G.; Pavlov, V. I.; Zhidornirov, G. M.; Beran, S. J . Phys. Chem. 1987, 91, 3325. (12) (a) Sauer, J. J . Phys. Chem. 1987, 91, 2315. (b) Sauer, J. Chem. Phys. Lett. 1983, 97, 275. (13) Dewar, M. J. S . J . Phys. Chem. 1985,89, 2145.
0 1988 American Chemical Society
6706 The Journal of Physical Chemistry, Vol. 92, No. 23, 1988
methods. We will show that good quality ab initio calculations can be done on clusters of various sizes. We also show that some computed local properties are basis-set dependent. The results of our best ab initio calculations are compared to pseudopotential results. Terminal and bridged (HO),SiOHAI(OH), sites are examined. Results concerning this latter cluster are compared with data obtained from the H3SiOHA1H3aggregate. Finally, using the largest cluster (H0)3SiOHA1(OH),, deprotonation energies are calculated when the atom pairs AlSi are substituted by BSi, GaSi, AIGe, BGe, and GaGe. These results allow us to discuss how acidity may be affected by local environment. Referring to the second question mentioned above, in part 2 of this work (to be published) an appropriate treatment will be proposed taking into account the cage effect, i.e., effect of the electrical field due to the presence of ionic charges in the zeolite frame, on deprotonation energy and related quantities. Method of Calculation Ab initio LCAO-MO-SCF calculations have been performed with the MONSTERGAUSSI4 program using a standard 6-31G basis set. In some cases, extended basis sets were used by introducing polarization and diffuse functions. We successively used standard basis sets augmented by (i) polarization functions on every atom (6-31G**), (ii) diffuse function with a single optimized exponent on the bridged oxygen atom (6-3lG+D,a(D)=O.O63), and (iii) polarization functions on every atom and the same single diffuse function on the bridged oxygen atom (6-31G**+D). However, for the larger cluster examined, polarization functions are restricted to the Si, Al, and 0 bridged atoms (6-31G(")+D). Compared to other available smaller sets of functions, the 6-31G basis has the advantage of giving a better representation of charge distribution. The pseudopotential technique used here has been developed by Durand and Barthelat.ls The basic idea of a pseudopotential method is to simulate the effect of core electrons with an analytical potential fitted to ab initio calculations. Among the various pseudopotential methods proposed recently, the Durand and Barthelat method seems particularly well adapted to reproduce all-electron ab initio results. This method has been used here with a double-{-type basis set function without polarization or diffuse functions. Strictly speaking, the method should be less timeconsuming than all-electron ab initio methods. Unfortunately, with the computational version actually available the inverse was obtained. One of the reason explaining this behavior is that in our ab initio calculations, the s-p constraint was systematically applied and this reduces significantly the number of computed two-electron integrals. The usefulness of the pseudopotential method is manifested only in the calculation of systems including gallium and germanium atoms. In these cases the number of orbitals was larger than the number of orbitals allowed in our ab initio program. Finally, the semiempirical MND0I6 method has been used in some cases in order to compare with ab initio and pseudopotential results. These calculations were carried out with the ab initio optimized geometries. Structure of the Active Site The zeolite faujasite' is an aluminosilicate frame organized as a three-dimensional structure (space group Fd3m) whose unit cell is cubic. This cell has very large dimensions (unit cell constant, a = 24.67 A) and contains 192 (Si,AI)O, tetrahedra. The framework structure is illustrated in Figure la. This structure is a diamondlike array of linked octahedra which are connected (14) Peterson, M. R.; Poirier, R. A. Department of Chemistry, University of Toronto, Version 1983. For a discussion of the optimization methods in this program, see: Peterson, M. R.; DeMarE, G. R.; Csizmadia, I. G.; Strausz, 0. P. Theochem 1983, 92, 239 and references cited therein. ( 1 5 ) Durand, Ph.; Barthelat, J. C. Theor. Chim. Acta 1975, 38, 283. (16) (a) Davis, L. P.; Guidry, R. M.; Williams, J. R.; Dewar, M. J. S.; Rzepa, H. S.J . Comput. Chem. 1981,2,433. (b) Dewar, M. J. S.; Mc Kee, M. L.; Rzepa, H. S. J. Am. Chem. SOC.1978, 100, 3607.
Kassab et al. a - Framework structure
rn -Truncated octahedron Hexagonal prism ( D 6 R )
Figure 1. (a) Framework structure. (b) Representative clusters for a hydroxyl group in the bridged position: (I) H,SiOHAIH,; (11) (OH),-
SiOHAI(OH),. through the 6-membered rings. Hexagonal prisms (D.6.R) assure the linkage between adjoining truncated octahedra. The domain of interest, Le., the active site where proton exchange may be located, is restricted to a small area which has been enlarged in Figure lb. The first crude approximation introduced in the work presented here is to assume that the proton-exchange process that we are interested in is entirely determined by the local structure which can be restricted to the first or eventually second shell of atoms surrounding the 0-H proton donor group. Furthermore, two situations have to be distinguished according to the position occupied by the oxygen atom: either in a bridged position (0atom bonded to both Si and A1 atoms) or in a corner position (0atom bonded to only one heavy atom (Si or AI)). The next step in the modeling process consists of isolating a neutral cluster from the rest of the bulk structure. If we consider the smallest unit, SiOH-AI, the six bonds issued from Si and AI atoms are unsubstituted, and neutralization can be obtained by bonding with H atoms. This procedure is not quite satisfactory and has already been discussed at length.!' The polarizability and electronegativity of the H atoms are different from the oxygen atoms they model. Consequently, this may affect the electronic distribution in the Si-OH-A1 unit. Exact compensation between atomic charges is then not well balanced and may be a poor approximation of the real charge distributions in this Si-OH-A1 unit. The magnitude of these effects using the same basis set are different according to the quantity considered. The atomic charges on certain atoms may be sensitive to substituent effect. The energy of a subsystem (like the hydroxyl group) embedded in the bulk is less affected. In Figures 1b and 2 are depicted the clusters corresponding to an hydroxyl group in a bridged or corner position. Their structures are partially optimized at the 6-31G level. S i ( O H ) , Group (Figure 2 ) . The minimization of the ground-state energy of Si(OH), is performed by taking into account a certain number of symmetry constraints. For modeling purposes the Si03H3subgroup is restrained to C3, symmetry and only three geometrical parameters are optimized: r(Si-O), r(OH), and LOSiO. The imposition of &OH at 180' is done only (17) Chen, 2.; Wang, Z.; Hong, R.; Zhang, Y. J . Catal. 1983, 79, 271.
The Journal of Physical Chemistry, Vol. 92, No. 23, 1988 6707
Structure and Acidity Scales in Zeolite Systems
Figure 3. The four basic configurations of the H3SiOHAIH3cluster. TABLE 11: Optimized Molecular Geometry of H3SiOHAIH3 and (OH),SiOHAI(OHL Complex and Their Anions"
H3SiOHAIH3, (H3SiOAIH3)-b
(OH),SiOHAI(OH),, ((OH)3SiOAl(OH)3)-c
SiH,
Si(OH),
r(Si-H)
147.9 (150.5)
r(Si-H)
147.1 (150.5) 104.5 (114.2) 108.5 (114.2) 112.2
r(Si-0)
1
1
Si04H4
LOSiH
Figure 2. Hydroxyl group in the terminal position: TABLE I: Molecular Geometry of Si(OH), Complex STO-3Gb 4-31Gb 6-31Gb 6-31G*'
symmetry r(Si-0) r(O-H) LSiOH LOSiO r(Si-0) r(0-H) &OH
DZd 165.7 98.1 108 109
Dtd
s4
163 93.8 140 140
163.5 94.7 117 117
s4
163 94.7 117.12 115.80
LOSiH 6-31Gd
cs
162.5 93 18OC 108.88 166.9 94.2 132.30
Distances in pm, angles in deg. bReference 12b. cReference 12a. dThis work. CFixedvalue.
so that optimization of the larger unit can be accomplished within the financial means available. One of the OH bonds is considered as the terminal group and three more parameters are needed to fix its geometry assuming that the terminal H atom is in one of the OSiO planes. These coordinates are r(Si-O), r(0-H) and the angle &OH. All together six geometrical parameters are optimized. For the anion (SiO,H,)- this number is reduced to four. This above calculation differs from previous studies on orthosilicic acid7*9s18 where all 0-H groups play an equivalent role. In the present case the three LSiOH bond angles are assumed equal to 180° for electronegativity modeling purposes. The imposed pyramidal structure is supposed to simulate the bulk medium to which the unsymmetrical OH is attached. Results are reported in Table I. H3Si-OH-AIH, Group (Figure Zb). This structure has already been investigated by Mortier et aL7 at the 3-218 level and more recently by Sauer'* at the 6-31G* level. In order to calibrate our results, we have recalculated this structure using the same symmetry constraints in order to diminish the number of independent geometrical parameters. This commonly adopted model is built from a reference plane (P) determined by the atoms Si, 0, and A1 (Figure 3). It is assumed that the 0-H bridged bond remains in that plane. Furthermore, both the SiH, and AlH, groups are represented by two distinct tetrahedra having one SiH (or AIH) bond in the reference plane, but with the three summit angles identical. Four situations can be distinguished according to the values of the dihedral angles (Si and AI) formed between the planes HSiO or OAlH and the reference plane. Taking into account these constraints, the number of independent geometrical parameters is reduced to 15: the two (Si-H) distances and the (18) Hess, A. C.; Mc 90, 566 1.
LHSiH
Millan, P. F.; O'Keeffe, M. J. Phys. Chem. 1986,
161.1 (165.0)
Si(OH)3 LOSiO
106.9 (112.8) 93.3d
r(0-H) AIH,
AI(OH)I
r(AI-H)
162.2 (1 66.5)
r(AI-H)
161.1 (166.5) 96.8 (1 10.0) 102.7 (1 10.0) 117.3
LOAlH LOAIH LHAlH
r(Al-0)
169.3 (173.3)
LOA10
101 (108.3) 93.1d
r(0-H) r(Si-0) r( AI-0)
LSiOH LSiOAl r(0-H)
173.4 (161.7) 192.7 (175.6) 119.6
r(Si-0)
130.7 (1 80.0) 96.7 (-)
LSiOAl
r(A1-0)
LSiHO
r(0-H)
173.4 (160.6) 197.6 (1 77.1) 117.6 (91.8) 134.2 179.3 95.6 (m)
"Distances in pm, angles in deg. b3-21G calculations. c6-31G calculations. dFixed values. two LHSiH angles for the SiH3 pyramid as well as similar quantities for the A1H3group. Next, six coordinates are required to specify the positions of the atoms in the central group (SiOHAl), Le., the r(Si-0) and r(A1-0) distances, both angles &OH and LAIOH, and finally the r(0-H) distance. Total energy for configuration d (Figure 3) has been reported by Mortier et aL7 By use of the 6-31G basis set and the geometrical parameters given by Mortier, the energy of the three other configurations have been recalculated as well as the energy of their anions. (OH),Si-OH-AI(OH), Group (Figure Ib). This cluster is built starting with model d in Figure 3, where terminal H atoms have been replaced by hydroxyl groups (Figure 4). It is assumed that the nonbridged O H units in the SiOH or (AlOH) groups are linear. This choice is certainly arbitrary. It can be argued that this simulates some sort of environmental effect. However, since the main objective of our calculations is to evaluate a difference (Le., the DE) between some molecular species and their anions,
6708
The Journal of Physical Chemistry, Vol. 92, No. 23, 1988
Kassab et al.
TABLE 111: Deprotonation Energies (in kJ/m) for the Si(OH),, H@iOHAIH3, and (OH)$iOHAI(OH), Complexes 3-21G 6-31G 6-31G* 6-31G** 6-31G+D 6-31G(**) 1606.1 1 1631.26 1650.64
6-31G(**)+D
H3SiOHAIH3 a b C
d
(OH)3SiOHAI(OH)3
1354.75 1350.42 1355.59 1356.28
1358.72 1354.31 1359.83 1360.03 1384.22
1376.16
1411.12
1404.79
TABLE I V Charge Distribution in SitOH).,
0 H
Si
Figure 4. Set of coordinates and symmetry constraints in (OH)@OHA1(OH)3cluster (case d of Figure 3).
the conformation of the terminal SiOH (or AlOH) groups which are kept identical in both the neutral and charged species should have no or little influence on the result. Furthermore, the OH distances are kept fixed and their values are taken from the optimization of the Si(OH)4 and AI(OH)4 groups, respectively. Finally, the two end tetrahedra Si(OH)3 and Al(OH)3 are represented by two rigid C3, groups whose symmetry axes lie along the S i 0 and A10 bonds, respectively. The result of our optimization is compared (Table 11) to the data given by Mortier et al.' for the H3SiOHAlH3 cluster. Comparison is not straightforward since in our case some symmetry restraints have been imposed, increasing the rigidity of the structure, whereas the larger basis set used in the calculation usually leads to a more flexible structure. Comparison cannot be made with the structure of terminal groups. In the central group, the S i 4 bond is less affected than the A 1 4 one, the latter being increased by 5 pm. The LSiOAl bond angle is also more open. It is also remarkable that the hydroxyl bond distance is quite stable.
Calculation of the Deprotonation Energy The deprotonation energy (DE) is defined as the difference between the energies of the neutral and deprotonated aggregates. As previously mentioned, this quantity is a measure of acidity in the Bronsted sense.lg The DE has been evaluated at various levels of treatment and, when data are available, will be compared to previous results. In all cases, anion and parent systems were both optimized. The results are given in Table 111. For the Si(OH)4 cluster, the best calculation (6-31 G**) leads to a value of 1650 kJ/mol. In the second case of (H3Si4H-A1H3), the four configurations have been considered; in all cases the values are very close, ranging from 1350 to 1360 kJ/mol, with average values of 1351 kJ/mol (3-21G calculation) and 1358 kJ/mol (6-31G calculation). Finally, for the largest cluster (OH)3SiOHAl(OH)3, the 6-31G calculation leads to 1384 kJ/mol whereas with the (6-31G**+D) basis set, one obtains 1404 kJ/mol. From these results some conclusions may be drawn. (19) Bell, R. P. In The Proton in Chemistry: Cornel1 University Press: Ithaca, NY, 1959.
6-31G -0.99 0.45 2.29
6-31G* -0.88 0.47 1.65
6-31G** -0.77 0.36 1.64
(i) As previously stated,' it is found that the bridged proton is more acidic than the terminal group. (ii) The enrichment of basis set with polarization functions does not qualitatively reverse these results. For example, in the case of Si(OH)4 the difference between the values obtained with 6-3 1G and 6-31G** basis sets is of the order of 44 kJ/mol (0.5 eV). It is less in the other cases. (iii) Deprotonation energy is sensitive to the size of the cluster. In passing from (H3SiOHA1H3) to (OH)3SiOHA1(OH)3 the deprotonation energy varies by 24 kJ/mol(O.25 eV) when 6-31G basis set is used. This variation gives a quantitative indication of how the properties of the hydroxyl group are affected and correlated to the structure of the host cluster.
Charge Distribution The Mulliken atomic charges are given in Tables IV and V for the complexes studied, but only for the relevant atoms. Charges on frontier atoms have not been included since they are physically meaningless. In all cases it is seen that charges are rather sensitive to the quality of the basis set and then should be considered with care when used as indicators. With respect to cluster size, charges on the hydroxyl group atoms are the most stable, whereas frontiers effects are large on the Si and A1 atoms (Table V). In both cases, the basis set refinement leads to a redistribution of charges among the atoms of the molecular system. Effect of Local Environment on Deprotonation Energy As stated under Calculation of the Deprotonation Energy, deprotonation energy appears to be a rather local property loosely correlated to the size and form of the representative cluster. This statement immediately gives rise to the question of how the deprotonation energy would react to a modification of the close environment of the hydroxyl group, Le., if the pair Si,A1 is substituted by a different pair of atoms such as BSi, GaSi, .... This problem is directly related to an active area of experimental research in the field of synthetic zeolites. A first attempt in that direction can be traced back to the pioneering work of Goldsmith20 in 1952, who substituted A1 by Ga in order to obtain the thomsonite. Since then numerous results have been accumulated and the substitution of Si or A1 by Ge or B and Ga ... have been reported.*' Starting with a basic structure (OH)3TiOHT2(OH)3made of two distinct tetrahedra bonded via the hydroxyl group, the deprotonation energy has been recalculated for the pairs BSi, GaSi, AlGe, BGe, and GaGe. Results are shown in Table VI. The calculations are performed with the pseudopotential method. Comparison with ab initio results (cases of SiAl and SIB) demonstrates the validity of the pseudopotential results, which exhibit very close absolute values and a trend similar to the one given by ab initio. Finally, some values are evaluated with the help of the semiempirical MNDOi6method. Discrepancies with ab initio values are as large as expected, but above all the trends depicted (20) Goldsmith, J. R. Min. Mag. 1952, 29, 952. (21) Guth, J. L.; Caullet, Ph. J . Chim. Phys. 1986, 83, 155 and references herein.
The Journal of Physical Chemistry, Vol. 92, No. 23, 1988 6709
Structure and Acidity Scales in Zeolite Systems
TABLE V Charge Mstribution in HfiiOHAIH3 and (OH)fiiOHAI( OH)3 Complexes
HISiOHAIH7
0 H A1
Si 0 H A1
(OH)3SiOHAI(OH)3
3-21G
6-31G
6-31G+D
6-3 lG(**)
6-31G(**)+D
-0.93 0.46 0.82 1.20
-1.10 0.50 0.90 1.21 -1.08 0.50 2.0s 2.39
-1.50 0.54 2.02 2.76
-0.97 0.52 1.46 1.72
-1.40 0.57 1.46 2.10
Si TABLE V I Deprotonation Energies of (OH)3T,0HT2(OH)3 Complex, for TI-= AI, B, and Gaand T2= Siand Ge'
r(O-T,) r(O-Tz) LTIOTZ A(1) A(3)
SiAlb
SiBb
SiGa
GeAl
GeB
GeGa
173 163 131.5 1320.9 1337.6 1220.6
146 163 134.6 1379.4 1400.3 1224.7
180 163 134.8 1304.2
173 169 134.8 1316.7
146 169 135 1379.4
180 169 135 1300
844.4
1228.9
"Distances (r) in pm, L(T,0T2)in deg, and deprotonation energies in kJ/mol. Superscript i is read (1) pseudopotential method, (2) ab initio, and (3) semiempiricalmethod MNDO. The geometry adopted for the pseudopotential calculation (two perfect tetrahedra) was also used in cases 2 and 3. bAb initio calculations at the 6-31G level. by both ab initio and pseudopotential values are not reproduced.
Discussion and Conclusion From the tendency displayed by the calculated deprotonation energy as shown in Table VI, some information can be deduced concerning the acidic properties of the site considered. (i) For any of the two four-coordinated atoms involved (Si or Ge) the substitution of AI by B corresponds to a net decrease of the acidic strength. (ii) The substitution of Ga, under the same conditions, leads to an inverse effect but of a much smaller amplitude. As expected, the acidic strength is primarily controlled by the electron-deficient atom (B, Al, Ga) and unaffected by substitution of the four-coordinated atom. According to these results the acidic scale would be in the order B
