Journal of Molecular Catalysis, 57 (1989)
125
125 - 137
GEOMETRIC FACTORS IN DEHYDRATION OF ALCOHOLS ON ALUMINA: COMPARISON OF ACCESSIBILITY OF LEWIS AND BRiiNSTED ACID SITES ON (100) SURFACE TU CUONG and J&I SEDLACEK Institute of Chemical Process Fundamentals, Prague 6 - Suchdol (Czechoslovakia) (Received October 12,1988;
Czechoslovak Academy
of Sciences,
16502
accepted January 6, 1989)
Summary Geometric conditions for interaction of an alcohol molecule with (100) surface of o-alumina were studied using computer models. The requirement of two-point adsorption of the alcohol via its hydroxyl group and its flhydrogen on a pair of surface acidic and basic sites results in strong dependence of the reaction course on the geometric factor. Steric hindrances greatly influence reaction selectivity. The steric demands of the two-point adsorption state increase rapidly in the product series l-alkene, cisS-alkene and trans-2-alkene. Adsorption on Bronsted acid sites (surface hydroxyl groups) is much easier than adsorption on Lewis acid sites (aluminium cations).
Introduction The molecules of all reacting components are freely moving in homogeneous reactions occurring in the liquid or gas phase: molecules may always collide in the proper way to enable chemical reaction to occur. For this reason, reactivity in the homogeneous phase is governed by the quality (density and shape) of the electron cloud of reactants, i.e. by electronic factors. A substantionally different situation occurs in reactions on a gassolid or on a liquid-solid interface: active sites are fixed on the surface and their configuration is rather rigid. This also holds true for catalyzed reactions. Molecules are adsorbed by at least one bond to the catalyst surface in any heterogeneously catalyzed process. Moreover, it seems that interaction with more than one surface atom is needed for most known reactions. A series of questions arises concerning the action of such multiatomic (multiplet) sites in heterogeneous catalysis: (a) Do two atomic (or multiatomic in general) sites exist with a distance matching the distance of reacting atoms in the reactant molecule? 0304-5102/89/$3.50
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(b) If so, does the character of the surface in the neighborhood of the convenient site ensemble allow access of the molecule to the surface? (c) How does interaction with the surface influence the configuration of the adsorbed molecule, and how does this interaction reflect upon the selectivity of formation of various reaction products? It is possible to answer these questions on inspecting thoroughly the geometric conditions of interaction of both partners, i.e. by considering the so-called geometric factor in heterogeneous catalysis. Both electronic and geometric factors in catalysis have a common basis. All interactions and all structural changes taking place in the course of chemical reaction are connected inseparably with changes in the total energy. The energy profile along the reaction coordinate originates from atomic core repulsion and, above all, from valence electron interaction. Generally, this problem can be solved with the aid of quantum chemical calculations. However, the application of quantum chemistry in heterogeneous catalysis is a highly complicated problem. The special conditions of heterogeneous reactions help avoid the difficulties of quantum chemical procedures, which employ for some purposes much simpler geometry estimations. Investigation of total energy changes during the reaction may be substituted by inspection of the geometric conditions. This survey reveals whether the structure and the flexibility of the given system allow, in principal, the interaction needed for completion of the reaction process. Geometric estimation gives semiquantitative results at most, which is not comparable with the predictive power of quantum chemistry. Nevertheless, the geometric factor calculations often reflect very well the characteristic features of a heterogeneous reaction, which, together with their relative simplicity, gives them a definite validity. Recently, increasing attention has been paid to the geometric factor. Its importance was revealed by Balandin [l, 21, the author of multiplet theory. Since that time, it has been clear that geometry may play an important role in heterogeneous catalysis [3] but there was no usable procedure on hand. Recently, the application of modem physical methods [4] (e.g. LEED, ESCA and Auger electron spectroscopy) has increased the amount of data regarding the structure of catalyst surfaces. The new information renders it possible to discuss the importance of the geometric factor in catalysis by metals [5,6] as well as in catalysis by polar catalysts, namely in oxidation processes [ 7,8] and in acid-base catalysis [9,10]. In our laboratory, the role of the geometric factor in alumina-catalyzed alcohol dehydration was studied using computer models [ll]. This study was based on the supposition that surface hydroxyl groups, i.e. Bronsted acid sites, are engaged in this reaction [ 121. But recent experiments carried out in a nonstationary regime [13] have suggested that the idea of adsorption on surface aluminium cations, i.e. on Lewis acid sites, may not be easily rejected. The aim of the present study is to investigate geometric conditions of the alcohol molecule in interaction with all possible sites of the (100) surface of y-alumina.
127
Methods The geometric conditions for alcohol dehydration were studied using computer models. Two-point adsorption on a pair of surface acidic and basic sites was considered as the limiting step [ 141 in the elimination reaction, in which two bonds of the alcohol molecule (C,-O and CP-H) are broken and an alkene molecule is formed. Simultaneous interaction between an alcohol molecule and a bipolar catalytic site is a necessary requirement in the concerned elimination proceeding by an E2-like mechanism. Even in successive cleavage of the two key bonds by El- or ElcB-like mechanisms, the molecule passes through the stage in which it is adsorbed on two sites. During breaking of the first bond, the remainder of the molecule must be bonded to ensure its continued adsorption. In general, it can be expected that steric interaction between reactant and catalyst plays a more important role in two-point adsorption compared to the one-point case. Therefore, we based the geometric factor estimation on the two-point adsorption, regardless of details of the key bond-fission timing. In our computer models, the alcohol molecule is bonded by the free electron pair of its oxygen atom to a surface acid site, i.e. to a surface hydroxyl group or to a surface aluminium cation, and by a hydrogen bridge (including P-carbon hydrogen) to a surface basic site, i.e. to an oxygen anion. Both energetically favourable configurations of the alcohol molecule pertinent to anti and syn elimination reaction modes were considered [15]. Standard bond lengths and tetrahedral bond angles were used (O-H 96 pm, C-H 109 pm, C-O 143 pm, C-C 154 pm [16]) in construction of the models. The hydrogen-bridge bond equaled 160 pm [ 171. The distance AI-O (202.5 pm) was determined from ~-alumina density, respecting the fee symmetry of its crystal lattice. With the exception of the C,-O bond, dihedral angles in the alcohol molecule corresponded to the staggered conformation. In the syn elimination models, the conformation along the C,-C, bond was eclipsed. It has already been shown [ 10,111 that an alcohol molecule can be adsorbed on a pair of surface sites whose mutual distance lies within a certain interval. Under accepted structural assumptions and with surface hydroxyl groups as the catalytic acidic sites, this interval spans the range 101 -560 pm for syn elimination and 557 - 671 pm for anti elimination. Similarly, suitable distances for surface aluminium cations as acidic sites range from 134 to 508 pm and from 533 to 628 pm for syn and anti elimination, respectively (see Fig. 1). Adsorption of all alcohols with the formula HOR,R,C,-C,R,R,H was considered where substituents R1 , Rz, R3 and R4 are methyl groups and/or hydrogen atoms in all possible combinations. The (100) surface of y-alumina was modeled by a cluster of size 6 X 6 atoms composed of three layers: (i) the coverage layer, formed by hydroxyls and by oxygen anions, (ii) the surface layer, composed of oxygen anions and aluminium cations situated in
128
Al
0
Fig. 1. Schemes illustrating change in distance of acidic (aluminium cation) and basic (oxygen anion) catalytic site on rotation around the Q-0 bond of the alcohol molecule for anfi (a) and syn elimination (b) reaction modes. Presented conformations correspond to the minimum (r,i,) and maximum (rmax) possible distances between both catalytic sites.
octahedral positions of the fee oxygen atom matrix, and (iii) the subsurface layer, of the same composition as the surface one. Vacancies of various types, in hydroxyl coverage as well as in the surface layer, were taken into account. The calculation procedure consisted of three stages, described in detail previously [lo]: Firstly, the alcohol molecule is constructed with a structure fitting the distance of the catalytic sites chosen for adsorption modeling. Then the molecule is transferred onto the surface model and, finally, its position with respect to the catalyst is optimized. During the optimization, the geometric interaction between the molecule and the surface is minimized, i.e. the distance at the point of closest contact of both partners is maximized. In this study, the reactant-catalyst distance is defined as the distance between the centres of the two closest atoms of the reactant and of the catalyst, from which the sum of the radii of these atoms is subtracted. As in our previous studies [lo, 111, the radii of the atoms were chosen so that the atoms connected via a chemical bond may be in touch. The above radii differ significantly from the ionic radii [18] widely used in depicting crystal structures. Their values are very close to the valence radii [19] with which they have a similar definition. The sum of the so-defined radii of the two atoms corresponds to the length of their chemical bond, and in this study it is understood to be the minimal distance to which both atoms can approach each other. Results y-Alumina is a rather hydrophilic oxide. Due to this fact, its surface always bears a certain amount of dissociatively adsorbed water [20]. Figure 2 shows the (100) y-alumina surface in two extreme situations: the com-
(a)
(b)
Fig. 2. Top view on the model of completely hydroxyl-covered (a) and entirely dehydrated (b) (X00) surface of y-alumina. (Valence radii shown: (0) Al, (@) 0.)
(a)
(b) Fig. 3. Schematic representation of Bransted acid site involving catalytic ensembles found on the (100) y-alumina surface (a) in syn elimination distance range (101 - 560 pm) and (b) in anti elimination distance range (557 - 671 pm).
pletely hydroxyl-covered surface and the entirely dehydrated one. The real composition of the catalyst surface depends on its p~treatment as well as on the conditions of the reaction process itself, because water is produced during the alcohol decomposition under study [223. Firstly, the adsorption on Briinsted acid sites, i.e. molecular adsorption on hydroxyls of the (100) surface, was modeled. These sites are situated in the coverage layer exclusively. Basic sites (oxygen anions) lying in both the coverage and surface layers were considered (unlike our previous study [ 1lJ where the basic sites from only the coverage layer were taken into account). In the ranges of distances suitable for two-point adsorption, we found four and three types of surface site ensembles pe~~rng to syraand anti eliminations, respectively (see Fig. 3). The characteristics of these ensembles are listed in Table 1. It is easy to see that the catalytic ensembles differ in their
130 TABLE 1 Characteristics of Bronsted acid site involving catalytic ensembles found on (100) surface of y-alumina (see Fig. 3) Ensemble type
Identifier
Acidic sitea
Basic sitea
Distance (pm)
vn
Sl-OH S2-OH S3-OH S4-OH Al-OH A2-OH A3-OH
Ic3 Ic3 Ic3 Ic3 Id2 Id2 Id2
11~4 Id4 Ic5 IId Ib4 IId Ic5
266 286 405 496 573 640 640
syn syn syn anti anti anti
Vite label structure: Roman numeral-letter-number which denotes layer, file and row, respectively. Layers are numbered downwards and rows backwards (i.e. I and II indicate the coverage and the surface layers, resp.); files are labelled going from left to right.
distance, on the other hand, and in their location, on the other. While the hydroxyl groups (Bronsted acid sites) are situated within the coverage layer exclusively, the oxygen anions (basic sites) are found in both the coverage and surface layers. The results of modeling alcohol adsorption on these ensembles are summarized in Table 2. In the first place, we can compare the syn and anti elimination reaction modes. It is seen that steric hindrances are generally less significant in the syn elimination structures. The steric demands of various reaction products decrease in the series trans-1,2-dialkylethylene > l,ldialkylethylene > cis-1,2dialkylethylene > monoalkylethylene > ethylene, as shown most distinctly by adsorption on the A2-OH ensemble. Steric interaction may be reduced substantially by withdrawal of some of the surface hydroxyl groups lying in close proximity to the catalytic ensemble. Again, anti elimination structures need more free space, i.e. higher occurrence of vacancies in the hydroxyl coverage. Adsorption on the A2-OH ensemble even necessitates a vacancy in the surface layer. This means that the absence of one aluminium atom is needed. The alcohol molecule can be adsorbed on the (100) r_alumina surface in a dissociative way, i.e. on a surface aluminium cation playing the role of a Lewis acid. This mode of adsorption was also modeled. Aluminium cations, in contrast to surface hydroxyl groups, are situated deeper in the (100) surface. We have found four syn and two anti elimination ensembles involving Lewis acid sites (see Fig. 4), specified in Table 3. The results of calculations for the two-site dissociative adsorption of alcohols are presented in Table 4. As for molecular adsorption, the syn elimination reaction mode is distinctly less sterically demanding. The Al-Al ensemble is inaccessible to the alcohol molecule, even if two surface atoms (oxygen and aluminium) are missing in the neighborhood. The same trend in steric demands for formation of various reaction products is manifested as in
131 TABLE
2
Results of calculations modeling geometric factors in molecular adsorption on the catalytic ensembles involving Brijnsted acid sites, i.e. surface hydroxyl
of alcohols groups
Ensemble
Vacancya
Alcoholb
ProductC
Sl-OH
Ib4 Ib4, c5
MMHM MMHM
T T
17 25
S2-OH
-
MMMM MMMH
T T
119 124
S3-OH
-
MMMM MMMH MMMM MMMH
T T T T
67 108 111 116
Id4, e5, c5, d6
MMMM MMMH MMMM
T T T
5 23 63
Al-OH
Ic3 Ic3 Ib2, c3, d4 Ib2, c3, d4
MMHH HMMH MMMH HMMH
D C T C
16 27 27 41
A2-OH
IId4, IId4, IId4, IId4, IId4, IId4, IId4, IId4,
HMMM HHMM HMMH HHHM HHHH HMMM HHMM HMMH
T D C M E T D C
5 7 21 27 36 5 7 36
HMMH HMMM HMMH
C T C
25 51 67
Id4, b4 Id4, b4 S4-OH
A3-OH
-
Id4 Id4 Id4 Id4 Id4 Id4, e5, c5 Id4, e5, c5 Id4, e5, c5
Ic3, d4, b4 1~3, d4, b4
Distanced (pm)
aVacant positions in the catalyst model. bDefinition of the alcohol molecule structure HORrR&,-CpRsR$I: M and H indicate methyl and hydrogen in place of substituents Rt ,Rs, R3 and R4. CSpecification of possible product: T = tmns-1,2_dialkylethylene, C = cis-1,2-dialkylethylene, D = l,l-dialkylethylene, M = monoalkylethylene and E = ethylene. dQuantity accepted in this study as a measure of extent of steric hindrance: i.e. the distance alcohol molecule-catalyst at the point of the closest contact of both partners.
molecular adsorption on a Briinsted acid site: truns-1,2dialkylethylene > l,ldialkylethylene > ck-1,2dialkylethylene > monoalkylethylene > ethylene. Generally, the geometry is more strained in structures modeling alcohol adsorption on catalytic ensembles involving aluminium cations (Lewis acid sites), which is clearly seen upon comparison of data (i.e. distances, products and vacancies) from Tables 2 and 4.
132
(b) Fig. 4. Schematic representation of Lewis acid site involving catalytic ensembles found on the (100) ‘y-alumina surface (a) in syn elimination distance range (134 - 508 pm) and (b) in anti elimination distance range (533 - 628 pm). TABLE 3 Characteristics of Lewis acid sites involving catalytic ensembles found on the (100) surface of y-alumina (see Fig. 4) Ensemble type
Identifier
Acidic sitea
Basic sitea
Distance (pm)
vn
Sl-Al S2-Al s3-Al S4-Al Al-Al A2-Al
11~3 11~3 11~3 11~3 IIdP IId
11~4 Id4 IId Ic5 IId Ib4
203 351 453 453 608 608
syn syn syn
anti anti
aFor site label explanation see footnote Table 1.
Discussion Alcohol dehydration has been studied experimentally for several decades and still its reaction mechanism is not quite clear. Heterogeneously catalyzed dehydration exhibits two interesting phenomena [14,22 - 241: (i) antiperiplanar conformation of the hydroxyl group and P-hydrogen of the molecule in the transition state and (ii) the prevailing formation of the thermodynamically disfavoured cis alkene. The anti elimination reaction mode is well known from homogeneously catalyzed reactions. It was shown that this phenomenon is based on energetical reasons which can be understood in terms of quantum chemistry [25]. In heterogeneously catalyzed alcohol dehydration, the question arises as to how the P-hydrogen gets to the catalyst surface while maintaining the antiperiplanar conformation of the transition state [ 14,261.
133 TABLE 4 factor in dissociative adsorption of alcohols Results of calculations modeling geometric cation (for on the catalytic ensembles involving Lewis acid site, i.e. surface aluminium shown, see footnotes Table 2) explanation of notation used and meaning of quantities Ensemble
Vacancy
Alcohol
Product
Distance (pm)
Sl-Al
Ic3 Ic3 Id2, c3, d4
MMMM MHHM MHMM
T C T
12 40 51
S2-Al
Ic3 Ic3 Ic3 Id2, Id2, Id2, Id2,
MHMM MMHM MHHM MMMM MMHM MHMM MHHM
T T C T T T C
10 12 59 23 27 49 71
b2, b2, b2, b2,
c3 c3 c3 c3
s3-Al
11~4, Id4 IIca, Id4 11~4, 1~3, d4
MMMM MHMM MMMM
T T T
2 18 18
S4-A1
Ic3 Ic3 Id2, c3, d4 Id2, c3, d4 Id2, c3, d4
MMMM MMHM MMMM MHMM MHHM
T T T T C
8 38 46 50 71
Al-Al
IId3, d4
-
-
-
A2-Al
11~3, 1~3 IIc3,Ic3, d2, b2, d4 IIc3,Ic3, d2, b2, d4 IIc3,Ic3, d2, b2, d4
HHMM HHMM MHHM HHHM
D D C M
1 8 52 58
Knijzinger et al. [14] were probably the first who recognized intuitive ly the possibility of two-point adsorption of the alcohol molecule with internal structure leading to anti elimination, and the close connection between the structure of this adsorption complex and the non-equilibrium composition of elimination products. The results of the present study support their hypothesis by successful construction of a series of models of an alcohol molecule adsorbed on two surface sites via its hydroxyl group and its P-hydrogen simultaneously. All the structures found in our modelling were constructed assuming ideal geometry of the alcohol molecule (i.e. no distortion of ideal angles was needed), which is a very encouraging finding. Both syn and anti elimination structures are possible. From the geometric point of view, the syn elimination is more comfortable than the anti elimination, which is illustrated by Figs. 5 and 6 depicting adsorption on S2-OH and A3-OH surface en-
134
Al
0
C
H
Fig. 5. View of the model 2,3-dimethyl-2-butanol molecule adsorbed on the S2-OH catalytic ensemble. No vacancy in the catalyst model needed, trans-2-butene may be formed. (The set of circles shown at the bottom of the figure designates the atoms and size scale used in this and later figures.) Fig. 6. View of the model 2-butanol molecule adsorbed on the A3-OH catalytic ensemble. No vacancy in the catalyst model needed, at most cis-2-butene may be formed.
Fig. 7. View of the model 2-methyl-2-butanol molecule adsorbed on the Sl-OH catalytic ensemble. One vacancy in the coverage layer of the catalyst model needed, Pans-2-butene may be formed. Fig. 8. View of the model 2-butanol molecule adsorbed on the A2-OH catalytic ensemble. Two vacancies in the coverage layer of the catalyst model needed, at most c&2butene may be formed.
sembles. Steric interaction increases if the molecule is bonded more tightly to the surface, which may be caused by a deeper position of the engaged adsorption sites. This effect is produced as soon as at least one of the pair of sites moves from the coverage into the surface layer. This is shown in Figs. 7 and 8 displaying the adsorption on Sl-GH and A2-GH ensembles. The idea of the importance of aluminium cations as acidic catalytic sites and the idea of dissociative adsorption via the formation of alkoxide species were revived in connection with some recent experiments carried out in our laboratory [13,16]. This is why we also tried to construct models of adsorption of this type. Generally, small cations are not present in the coverage layer of polar solids, due to energetically conditions, and this layer is preferentially composed from anions which are usually larger. (With increasing size of an ion, the electric potential on its surface decreases, resulting in higher stability of this ion when located on a solid surface). It follows
135
Fig. 9. View of the model 2,3-dimethyl-2-butanol molecule adsorbed dissociatively on the Sl-Al catalytic ensemble. One vacancy in the coverage layer of the catalyst model needed, trans-2-butene may be formed. Fig. 10. View of the model 2-butanol molecule adsorbed dissociatively on the A2-Al catalytic ensemble. Four vacancies in the coverage layer and one vacancy in the surface layer of the catalyst model needed, at most cis-2-butene may be formed.
from this fact that in all structures which model adsorption on surface ensembles including an aluminium cation, at least one site is situated in the surface layer. This results in a considerable increase in steric interaction between the alcohol molecule and catalyst surface found in our models of adsorption (see Figs. 9 and 10). For Lewis sites, as for BrSnsted ones, syn elimination is sterically less demanding than anti elimination, which is also illustrated by Figs. 9 and 10. We have demonstrated how the steric interaction depends on the depth of surface site location. Let us now explain why this interaction is larger for anti elimination structures than for syn elimination ones. Figures 11 and 12 show side views of the alcohol molecule adsorbed on surface ensembles characterized by various internal distances. All types of site ensembles differing in internal distance are pictured. It is quite easy to see that while syn elimination structures are rather expelled from the space between both catalytic sites, the situation for anti elimination is quite different. In spite of the significantly longer distance between both sites, the molecule is stretched and pulled into the space between the sites. But on a regular catalyst surface, some atoms of the solid are laying in this space. The steric interaction between them and the alcohol molecule is usually large enough to make adsorption difficult or impossible. An important result of our study is the finding that product selectivity of alcohol dehydration is controlled by steric interaction between bulky substituents of the molecule and the catalyst surface. Anti elimination structures show a pronounced preference for cis over trans alkene formation, while in syn elimination this effect is apparent only in case of adsorption on Lewis sites. This finding explains the frequently observed high selectivity for cis alkene production, We may summarize our work as follows: (a) Two-point adsorption of an alcohol molecule (via its hydroxyl group and its p-hydrogen) on the (100) y-alumina surface is possible without distortion of the molecule on ensembles including BrSnsted as well as Lewis acid sites.
136
(b)
(a)
Fig. 11. Side view of 2,3-dimethyl-2-butanol molecule interacting with catalytic ensembles involving a Bronsted acid site (hydroxyl group) at various distances from a basic site: (a) 286 pm, (b) 405 pm, (c) 496 pm, (d) 5’73 pm and (e) 640 pm.
(a)
(b)
(cl
(d)
Fig. 12. Side view of alkoxide anion of 2,3-dimethyl-2-butanol molecule interacting with catalytic ensembles involving a Lewis acid site (aluminium cation) at various distances from a basic site: (a) 203 pm, (b) 351 pm, (c) 453 pm and (d) 608 pm.
(b) The steric interactions between the molecule and catalyst surface are remarkably larger for Lewis sites than for BrSnsted ones, due to the location of the cations deeper in the surface layer than hydroxyl groups. (c) The steric hindrances for anti elimination structures are larger than those for syn elimination, due to longer internal distances in the catalytic ensembles, leading to closer contact between reactant and site. (d) The location of adsorption sites from the coverage layer into the surface layer is followed by a rapid increase in steric hindrances. (e) The specific situation at the site of contact of alcohol molecule with catalyst surface controls the selectivity of the reaction with respect to its products. In particular, steric demands on cis alkenes formation are significantly smaller than those on tram alkanes formation. Our present study is based on the (100) surface of y-alumina. Because the real catalyst does not expose this face on its surface only, a question about the general validity of our conclusions arises. Therefore, modeling of alcohol adsorption on other low-index surfaces is in progress. Preliminary results show trends similar to those presented in this paper.
137
References
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
A. A. Balandin, Z. Phys. Chem., B2 (1928) 289; ibid., 83 (1929) 167. A. A, Balandin, Adv. Catal., 19 (1969) 1. R. H. Griffith, Adu. CataZ., 1 (1948) 91. D. Lichtman, in A. W. Czanderna (ed.), Methods of Surface Analysis, Methods and Phenomena: Their Applications in Science and Technology, Elsevier, Amsterdam, 1975, Vol. 1, p. 39. W. F. Libby, Catal. Rev. Sci. Eng., 23 (1981) 615. F. Garin, S. Aeiyach, P. Legare and G. Maire, J. Catal., 77 (1982) 323. J. Ziolkowski, J. CataZ., 84 (1983) 317. J. C. Volta, J. M. Tatibouet, C. Phichitkul and J. E. Germain, Proc. 8th Int. Congr. Catal., Berlin, 1984, Verlag Chemie, Weinheim, 1984, Vol. IV, p. 451. S. Kasztelan, H. Toulhoat, J. Grimblot and J. P. Bonnelle, Appl. Catat., 13 (1984) 127. J. Sedlii?ek, Collect. Czech. Chem. Commun., 46 (1981) 2466. J. SedllEek, J. Catal., 57 (1979) 208. H. Knozinger, Angew. Chem., 80 (1968) 778. V. Moritvek and M. Kraus, J. Catal., 87 (1984) 452. H. Kniizinger, H. Biihl and K. Kochloefl, J. CataZ., 24 (1972) 57. J. SedlaEek and M. Kraus, React. Kinet. Catal. Lett., 2 (1975) 57. J. A. Pople and M. S. Gordon, J. Am. Chem. Sot., 89 (1967) 4253. F. Steinbach and H. D. MiYIer, Z. Phys. Chem. (Frankfurt am Main), 84 (1973) 277. A. F. Wells, Structural Inorganic Chemistry, Oxford Univ. Press (Clarendon), London, 1962, p. 52. A. F. Wells, Structural Inorganic Chemistry, Oxford Univ. Press (Clarendon), London, 1962, p. 66. T. Morimoto, M. Nagao and J. Imais, Bull. Chem. Sot. Jpn., 44 (1971) 1282. H. Pines and J. Manassen, Adu. Catal., 16 (1966) 49. D. Dautzenberg and H. Knozinger, J. Catal., 33 (1974) 142. G. Forster, H. Noller and K. Thomke, J. Catal., 44 (1976) 492. B. H. Davis, J. Catal., 58 (1979) 493. J. SedIlEek, Collect. Czech. Chem. Commun., 42 (1977) 2027. V. Moravek, React. Kinet. Catal. Lett., 30 (1986) 71.