On the structure and stability of Ti-zeolites. A comparison
of cluster and periodic ab initio calculations (*)
C. M. ZICOVICH-WILSON(**) and R. DOVESI
Dipartimento di Chimica Inorganica, Chimica Fisica e Chimica dei Materiali Università di Torino - via P. Giuria 5, I-10125 Torino, Italy
(ricevuto il 28 Febbraio 1997; approvato l’8 Maggio 1997)
Summary. — A periodic Hartree-Fock study of Ti-containing zeolites was performed. The zeolitic framework was modeled by means of the chabazite structure. Two framework compositions were considered (TiO( Si1Ti ) 40 and 0.5) and the corresponding periodic structures were optimized in order to estimate the geometric and energetic features of the Ti sites. Cluster models were also considered for comparison. It arises that the main structural distortion of the zeolite lattice upon SiOTi substitution comes from the increment of the T-site volume. From the obtained results, the limitations of the different models are discussed.
PACS 71.15 – Methods of electronic structure calculations. PACS 01.30.Cc – Conference proceedings.
1. – Introduction
The synthesis in 1983 of the first zeolite with titanium atoms in the framework, Ti-silicalite-1 or TS-1 [1], has introduced the use of Ti-zeolites as selective and efficient heterogeneous oxidizing catalysts. Selective oxidation of unsaturated organic compounds can be performed by using Ti-zeolites with aqueous hydrogen peroxide and this possibility, which is of great interest for industry and fine chemistry [2], has stimulated the synthesis of new Ti-zeolites with different selectivity behavior [3].
Zeolite frameworks consist of corner-shared TO4tetrahedra, where T is usually a Si or Al atom. In the case of Ti-zeolites, a fraction of the T sites is occupied by Ti atoms [2, 4]. In spite of the recent advances in the physico-chemical characterization of the Ti-sites, the local structure and siting of Ti atoms in the zeolite framework are still subject of discussion.
(*) Paper presented at the “First International Workshop on Reactivity of Oxide Materials. Theory and Experiment”, Como, 8, 9 November 1996.
(**) On leave from: Instituto de Tecnología Química, UPV-CSIC, Av. Naranjos s/n, 46071 Valencia, Spain.
In the last years only a few ab initio calculations on Ti-zeolites have been reported [5]. In all cases the cluster model was used to represent the Ti site and its environment. Recently a preliminary study of the electronic and structural aspects related to the presence of framework Ti-sites in zeolites was performed by means of ab
initio periodic calculations [6]. The present work is a continuation of such a study, and
is aimed to provide some new information concerning the structural features of Ti-sites in zeolites. Clusters with different boundary geometrical constrains were used together with periodic models to elucidate the limits and merits of each kind of approach.
2. – Models and methods
In the present work, we consider a chabazite structure in which one out of two silicon atoms of the framework are substituted by titanium atoms. After substitution, only a mirror plane is lost with respect to the pure Si-chabazite structure (space group
R 3 m) and the symmetry becomes R 3 (6 point symmetry operators). In spite of the high
Ti concentration, each Ti atom is therefore surrounded by four Si atoms as second neighbours, and the minimal distance between a pair of Ti atoms is 4.7 Å. Only six non-equivalent atoms occur in the structure: one Ti, one Si, and four O that correspond to the four non-equivalent oxygens of Si-chabazite. This structure will be indicated as PTi and the pure Si-chabazite as PSi.
A model cluster, shown in fig. 1, was also considered for calculations. It consists of a central T site (T=Si or Ti) surrounded by the first 3 shells of neighboring atoms
occurring in the chabazite framework. Depending on whether T=Si or Ti, the starting geometry for cluster optimizations (see details below) can be taken either from PSi or
PTias reference periodic systems. In this work, 3 different series of cluster calculations were performed by combining such conditions, namely C(PSi)Si, C(PSi)Tiand C(PTi)Ti. In the above notation, the reference periodic model and the central T atom are indicated between the brakets and in the last subindex, respectively. For instance, C(PSi)Ti is a cluster with T 4 Ti whose starting geometry is taken from PSi. As shown in fig. 1, the «dangling» bonds resulting from the broken connection with the rest of the structure were saturated by hydrogen atoms[7].
Periodic and cluster calculations were carried out within the Hartree-Fock approximation using the CRYSTAL95 [8] and the GAUSSIAN92 [9] codes, respect-ively. The basis set and the computational conditions for periodic and cluster calculations are described in ref. [6]. Geometry optimizations in the periodic systems have been carried out by using a modified Polak-Riviere algorithm [10] in which the gradients are calculated numerically. For clusters, the standard analytic gradient techniques implemented in the GAUSSIAN92 code [9] have been used.
In the periodic models, the neighboring atoms of each T site are symmetry constrained starting from the second shell of neighbors. Therefore, whereas the four oxygens surrounding each cation are inequivalent in both PSi and PTi, the cations belonging to the second shell are symmetry-equivalent, and such a restriction was kept in geometry optimizations. The other shells are constrained depending on the space symmetry group of the models, i.e. in PSi all tetrahedral positions are symmetry-equivalent while in PTithey split into two inequivalent positions.
As regards the clusters, no symmetry constrain was imposed. However, in order to keep in any way the mechanical limitations of the actual solid structure, the oxygens of the OH groups (third shell around T) were constrained to remain at the same relative positions as the corresponding O atoms in the optimized periodic models. In addition, clusters were optimized by using two different relaxation criteria. In the first one, only the T atom and its first neighbors were relaxed while the remaining atoms were kept at their original position in the periodic reference structure. This optimization scheme will be labeled with the extension .I after the model symbol, for instance: C(PSi)Si.I. Calculations were also performed in which the system was relaxed up to the second shell of neighbors around T. The extension .II is added in this case for the notation. As regards the border H atoms, they were fixed in all cases at their original position corresponding to an OH distance of 0.98 Å and a SiOH angle of 1307 with respect to the starting Si positions.
3. – Results and discussion
In table I the energy and the range of variation of the relevant geometry parameters of the various models are listed. The substitution of a Si by a Ti inside the zeolite framework leads to an increment of the site volume due to the change on the TO distance from 1.61 to 1.79 Å as one can see in the case of models PSiand PTi. This bond length increment is associated to a simultaneous opening of the TOSi angle. Indeed, from the periodic calculations, the optimized lattice parameter for PTi is 9.94 Å, while for PSi is 9.36 Å and this indicates that the site volume increases by 27 Å3 after substitution. This is consistent with experimental XRD data from which it turns out that the cell volume increases linearly as the framework Ti content does [2].
Table I. – Energy and optimized geometry parameters. Model Energy (Hartree) D Esubst (kcal P mol21) Geometry parameters dTO(Å) dOSi(Å) aTOSi(7) PSi 2 5264.6732 — 1.61–1.62 1.61–1.62 148–154 PTi 2 8620.9913 35 1.78–1.79 1.61–1.63 150–157 C(PSi)Si.I 2 2648.7636 — 1.62 1.60–1.61 149–153 C(PSi)Si.II 2 2648.7643 — 1.62 1.60–1.61 150–153 C(PSi)Ti.I 2 3208.1216 54 1.73–1.75 1.55–1.57 138–149 C(PSi)Ti.II 2 3208.1314 47 1.74–1.76 1.56–1.58 142–150 C(PTi)Ti.I 2 3208.1620 28 1.78–1.81 1.60–1.61 152–156 C(PTi)Ti.II 2 3208.1630 27 1.78–1.81 1.60 152–156
The expansion of the tetrahedral site upon Ti substitution is the dominant feature with respect to other relaxation modes of the environment. Cluster optimizations with T 4 Ti and the border atoms fixed at the same positions as in PTi, C(PTi)Ti.II and
C(PTi)Ti.I, lead to geometries that are very close to that of the periodic structure. Relaxation of the second shell (model C(PTi)Ti.II) does not yield an important energy gain ( 1 kcal Q mol21). A similar behavior is observed in going from C(P
Si)Si.I to
C(PSi)Si.II. This means that the TO4 geometries obtained from periodic optimizations are not very strained, despite symmetry equivalences have been imposed on neighboring atoms. In such a way, the additional relaxation allowed in the cluster models introduces only minor changes in the local geometry of the T-site. This is confirmed by the fact that the energy change for clusters C(PSi)Si.II and C(PTi)Ti.II when relaxing the systems from the initial periodic-like structure to the equilibrium geometries is rather small (0.9 and 1.6 kcal Q mol21, respectively). As regards the geometry of the TO4 tetrahedra, it should be noticed that the ranges of OTO angles are nearly the same in periodic and cluster models (107–1117 and 105–1157, for OSi× O and O Ti× O, respectively). The optimized TiO4 tetrahedron is only slightly distorted (apart from the modification of the Ti-O distance) with respect to the SiO4one.
On the other hand, when the model cluster is designed without taking into account the volume expansion of the T-site, as in C(PSi)Ti, the structure is strongly strained as it can be deduced from the energies listed in table I. This is the reason why in the
C(PSi)Ti(.I, .II) models, the TO distances and TOSi angles are rather shorter than in the case of PTi and C(PTi)Ti. Table I also shows that a large energy difference holds between the two relaxation schemes (I and II), which is associated to relevant geometry changes. This is a consequence of the strain imposed by the position of the boundary atoms, that forces the system to be in a compressed configuration. The energy change related to the volume expansion of the Ti-site from PSi to PTi -like geometry, can be estimated from table I in about 2 20 kcalQmol21.
The substitution energy (D Esubst in table I) was calculated according to the following ideal reaction:
SiO2( Si-Cha ) 1TiO2( Rut ) KSiTiO4( Ti-Cha ) ,
where TiO2(Rut) is the rutile structure [6]. From our results D Esubstis about 35 kcal Q
calculations is small (7 kcal Q mol21) and it may be mainly attributed to the effect of the boundary conditions and environment on the electronic structure of each model. It probably occurs that the cluster approach underestimates the substitution energy because it does not take account for the Madelung potential of the lattice. On the other hand, the periodic approach may overestimate the substitution energy owing to the high Ti concentration in the model. Nevertheless, as it turns out from periodic calculations on zeolites with different Ti content [11], the interaction between neighboring Ti sites is not relevant compared to the framework strain associated to the presence of an isolated Ti-site.
In conclusion, from this study one can state that the main structural change produced by the substitution of a Si atom by Ti inside the zeolite framework comes from the increment of the volume of the TO4 tetrahedron. The geometrical perturbation produced by the site expansion propagates beyond the third coordination sphere around the position where Si-by-Ti substitution was done as it can be deduced from comparison of periodic and boundary constrained cluster model optimizations. The
increment of the T-site volume can be estimated in 27 Å3 and the energy change
associated to the expansive relaxation is about 220 kcalQmol21.
The present results also indicate that model clusters must be used with caution in this case, due to the difficulty to a priori define proper boundary conditions in order to take into account the framework mechanical restrictions. On the other hand, it is well known that artificial distortions may occur when optimizations of open zeolitic clusters are performed without any geometry constrain (see [7] and references therein). As regards the periodic model approach, the chabazite structure with SiOTi 4 1, despite its unrealistic high Ti content and geometry constrains imposed by symmetry, has shown to provide a reasonable description of the geometrical features of framework Ti-sites in zeolites.
* * *
CZ thanks the Spanish “Ministerio de Educacion y Ciencia” for grant. RD thanks Italian CNR and “Ministero dell’Università e della Ricerca Scientifica e Tecnologica (MURST)” for financial support.
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