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A theoretical investigation of the binding of TiCln to MgCl2
Surface Science 490 (2001) 237±250
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A theoretical investigation of the binding of TiCln to MgCl2 C. Martinsky a, C. Minot a,*, J.M. Ricart b a
Laboratoire de Chimie Th eorique, UMR 7616 CNRS, Universit e P. et M. Curie, Bo^õte 137 Tour 23-22, 4 Place Jussieu, Paris 75252 Cedex 5, France b Departament de Quimica Fõsica i Inorg anica i Institut d'Estudis Avancßats, Universitat Rovira i Virgili, Pcßa Imperial Tarraco, 1 43005 Tarragona, Spain Received 10 March 2001; accepted for publication 20 June 2001
Abstract The structure of the (0 0 0 1) surface of the a-MgCl2 crystal has been investigated using DFT-GGA periodic calculations. The calculated surface relaxation is in agreement with LEED measurements. Motivated for the use of MgCl2 as support for the Ziegler±Natta reaction, we have studied the adsorption of the catalyst (titanium chlorides as monomers or dimers) on the (1 0 0) and (1 1 0) MgCl2 surfaces. The structures of adsorbed species are close to those previously found on cluster models: bridging chlorine atoms connect the Ti to the Mg atoms and the systems remain in high spin states. The (0 0 0 1) surface is the most stable face of the a-MgCl2 crystal; however it is Cl-terminated and henceforth poorly reactive; it had been suggested to deposit metallic Mg in order to improve its reactivity. Our modelling explains the failure of this tentative; the interaction between the deposited metal and the surface is repulsive and uncharged Mg atom does not bind. Ó 2001 Elsevier Science B.V. All rights reserved. Keywords: Computer simulations; Molecular dynamics; Density functional calculations; Halides; Catalysis; Chemisorption
1. Introduction Magnesium chloride is often used as a catalyst support for the Ziegler±Natta polymerisation of a-ole®ns. Crystallographic faces of the magnesium chlorides dier by the nature of surface ions (Mg2 , Cl or both) and by their coordination: the small particles of titanium chloride bind in dierent ways in¯uencing the stereoselectivity of the polymerisation reaction. The index of isotacticity increases when an appropriate active site is exclusively prepared by the adsorption of the catalyst * Corresponding author. Tel.: +33-1-44272505; fax: +33-144274117. E-mail address: [email protected] (C. Minot).
on a well-de®ned crystallographic surface of the support. The most stable surface with saturated Mg atoms is not reactive since the steric hindrance prevent adsorption. The active sites are then thought to be located on the coordinatively unsaturated lateral faces [1]. However, sites of very low coordination could have the same activity on polymers of dierent topology and be inecient to control the stereospeci®city. The titanium chloride catalyst may coexist on the support with dierent oxidation states. The proportion of Ti4 varies according to experimental conditions [2±4]. It is generally believed that a large amount of Ti4 is associated with a large activity [5] and a poor stereospeci®cy. The stereoactive centres may represent only several percents of Ti in the catalyst [6].
0039-6028/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 9 - 6 0 2 8 ( 0 1 ) 0 1 3 7 3 - 5
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There is no direct proof of the location and on the nature of the active sites of the Ziegler±Natta catalyst at the atomic level [7]. The geometry of the active sites and their oxidation state are not perfectly known and only few surface determinations have been made [8,9]. The lack of information on the MgCl2 surface structure arises from the diculty in characterising insulators [10] due to their tendency to become charged under irradiation by an electron beam. Some EXAFS [11,12], XPS [13], EPR [4,13±16] and LEED [10] studies however lead to propositions. Ti is adsorbed as monomer or dimer; according to the conditions (the presence of a cocatalyst is necessary for the reaction) and it is partially reduced. The percentage of reduced Ti atoms varies. Some analyses [3] estimate that Ti2 represent 80% of the total titanium. In some EPR experiments [4] Ti2 and Ti3 species represent 8% and 38% of the content, a fraction of which is seen in EPR (that corresponding to monomeric complexes) while the other part, silent to EPR, is attributable to dimers. Superexchange of the Ti3 ions results in antiferromagnetism for the bridged complexes [17]. Calculations indeed always found high spin states [18] for the reduced species. A Cl content of 3.5 per Ti was observed [4], showing that some chlorine has desorbed and that a partial reduction had occurred. In the presence of methylp-toluate, 90% of the Ti4 is reduced [4] producing a multitude of Ti3 species [14]. This Ti3 species is supposed to have D3h symmetry with no other adjacent Ti3 in the vicinity [14]. EXAFS [11,12] agree to a predominant adsorption of TiCl4 with the formation of dimeric complexes; such species could be precursors of nonstereospeci®c sites, the active centres representing only several percents of Ti in the catalyst [6]. In summary, literature refers to many species on the surface, monomers and dimers, in dierent oxidation states. We have recently investigated the bonding and the reactivity of TiCln , TiCln 1 CH3 complexes and related dinuclear complexes [18,19] by means of quantum mechanic calculations using the density functional theory. The coupling of TiCln , (dimerisation, addition to TiCln 1 CH3 and complexation by the magnesium chloride) results from the donation of the electron pairs from the chlorine ligands to the metal atoms leading to bridging
structures (2 or 3 bridging Cls) as proposed from EXAFS [11,12]. The bridging structures arise from the formation of both Ti±Cl and Mg±Cl bonds and not from Ti±Cl bond only as was initially proposed [20]. Moreover, the alkyl groups could also bridge the two metal centres of the dinuclear complexes. In this paper, we present periodic DFT-GGA calculations for the MgCl2 surface, using the Vienna ab intio simulation program (VASP) method, and show that they reproduce the experimental relaxation of the (0 0 1) face (Section 3). Unfortunately, this surface, stable and eectively observed, is poorly reactive. All the surface atoms are chlorine atoms and the Mg atoms remain saturated (hexacoordinated) in the sublayer and poorly accessible. TiCl4 does not chemisorb on this Cl-terminated ®lm in UHV [21]. We therefore turn to other orientations to study the adsorption of small (TiCln )x units. In the Section 6, we will return to the possibility to add extra Mg atoms on the (0 0 0 1) surface to improve its reactivity. In Section 4, we will use a periodic approach to study, on the (1 0 0) and (1 1 0) surfaces, the adsorption of the structures previously obtained by means of cluster models. We show that adsorption of small particles of titanium chlorides always results from the donation of the electron pairs from the chlorine ligands to the metal atoms leading again to bridging structures. In the surfaces that we have considered, the chlorine atoms of the lattice are already bridging; when they bind to the titanium centre and form a new Ti±Cl bond, they become (l3 -Cl). When the chlorine atoms from the TiCln monomers bind to the magnesium centre (formation of a Mg±Cl bond), they become bridging (l2 -Cl). This description is in agreement with the models used for the Ziegler±Natta reaction [22] where the dominant species, TiCl4 or TiCl3 R, is considered. In the cases of dimers, the bridging chlorine atoms become (l3 -Cl). 2. Computational details All the calculations have been performed using the VASP [23±25]. The Kohn±Sham equations are solved with the generalised gradient approximation
C. Martinsky et al. / Surface Science 490 (2001) 237±250
(GGA) proposed by Perdew et al. [26,27]. Ultrasoft pseudopotential have been used [28,29] with the default parameters provided by the program; for the metal atoms we have chosen those which include functions that usually are considered in the core (3p for Ti) and that are supplied by the VASP basis set library. The unit cell is repeated in three directions. For the slabs, we have considered a cell vector perpendicular to the surface plane large enough to leave a signi®cant empty space between We have tested on MgCl2 successive slabs (11 A). and TiCln bulk that four k-points, associated to the in-plane periodicity, were enough to reach a 50 meV precision. For the adsorption of the monomeric species on the (1 0 0) surface, we have considered a three multilayer slab and a double unit cell (six MgCl2 per unit cell). The lowest multilayer was kept ®xed and the other relaxed. For the dimeric species, we have taken a two multilayer slab and a triple unit cell (again six MgCl2 per unit cell), only the upper multilayer being relaxed in this case. For the (1 1 0) surface, we have taken two multilayers and a double unit cell (four MgCl2 per unit cell) for the a and the b phases. The adsorption energies have been de®ned using the expression: Eads E A E MgCl2 E A= MgCl2 where A represents the adsorbate. Positive values correspond to exothermic adsorption.
3. The bulk and the main surface structures of MgCl2 MgCl2 exists as two crystalline forms: the ®rst one is the a-MgCl2 (R3m or P1) with the chloride anions organised in a face-centred cubic arrangement and the Mg cations in the octahedral interstices; the primitive cell is rhombohedric and the conventional cell hexagonal. It is more stable than the b-MgCl2 (Cm) with the chloride anions organised in a hcp arrangement. In the following, we will refer to the hexagonal cells for the two varieties. The two structures dier by the stacking of hexagonal layers: AbC BcA CaB. . . or AbC AbC AbC. . . for the a-MgCl2 and b-MgCl2 respectively. The (0 0 0 1) slabs are very stable. The building
239
Table 1 The calculated lattice parameters of the crystal structures compared with the experimental values [41] a-MgCl2 (calculated) a-MgCl2 (experimental) b-MgCl2 (calculated) b-MgCl2 (experimental)
a
c
u
3.634
17.755
0.257
3.59
17.59
0.256
3.700
5.873
0.231
3.66
5.80
0.240
E (eV) 10.823
10.799
The calculated energies for the optimised structures are given in eV.
unit, AbC, is made of three layers, a sandwich of two layers of Cl with a layer of Mg in the middle. The stacking of these units is made by van der Waals bonds and the cleavage between two units does not break any chemical bond. The 0 0 0 1 layers containing the Cl atoms are not equally spaced; the spacing is slightly shorter within the three layers than between them. 1 Calculated structural parameters and the cohesive energy are presented in Table 1. The a-phase is slightly more stable than the b-phase. Indeed, in this stacking, the closest Cl atoms from the next three layer are right above and below the magnesium atoms These atoms are labelled by the (dMg±Cl 4:48 A). same letter (underlined) in the sequence AbC BcA CaB. For a-MgCl2 , a clean slab was prepared by deposition on palladium [10] and the relaxation was studied by dynamical LEED. It was found that the epitaxy imposes a slight increase of the lattice parameter (3%) for the 0 0 0 1 surface. In the obtained model, we ®xed the cell vector to 3.635 A in the optimisation of the bulk; this represents a small increase relative to the experimental parameter of the bulk that corresponds to the epitaxy. The optimisation of a nine-layer slab reproduces the experimental relaxation. The spacing between the top six layers have been varied and that of the three lowest one have been kept ®xed. The spacing between the two Cl layers within the three-layer 1 1 2uc=3 and 2uc vs. 2uc=3 and 1 2uc for the aMgCl2 for the b-MgCl2 respectively (u from Table 1).
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Fig. 1. The 1 0 0 surface of the b-MgCl2 crystal.
the unit (®rst and second ones) are 2.72±2.74 A, exact values obtained from LEED [10]. The spacing between the two adjacent Cl layers (between vs. 3.13 A. the two ®rst three-layer units) is 3.15 A Let us note, however, that in spite of the excellent agreement for the upper layer spacing, we do not obtain pronounced variations relative to the bulk (expansion of the MgCl interlayer distance and contraction of the ClCl interlayer distance) if we
refer to the optimised values obtained for the aMgCl2 bulk (Table 1). The other cleavages lead to unsaturated Mg atoms. In b-MgCl2 , the Mg atoms at the (1 0 0) surface are pentacoordinated (Fig. 1). In the aMgCl2 species, the net cleavage leaves Mg atoms with dierent coordination (3, 5 and 6) but a reconstruction [20,30] leads again to pentacoordination (Fig. 2). This reconstruction is correctly reproduced by the slab optimisation. Other faces also lead to the coordination 5: the (1 0 4) and (1 0 1) surfaces that do not reconstruct [30]; however, since information on the their reactivity is missing, we have considered the (1 0 0) surface to study the reactivity on a pentacoordinated Mg atom. The (1 1 0) surface is promising for the potential reactivity since the coordination of the Mg atoms at the surface is lower (4 only); let us note however, that this goes along with a decrease of stereospeci®city due to the presence of two vacancies [31]; the stereospeci®city could be restored at the expenses of the reactivity by a poisoning eect when one of the vacancies is occupied by a ligand (a Lewis base as Ph2 Si(OMe)2 [32,33]). The adsorption sites for the a and b-MgCl2 are very similar, diering only by the repetition mode (Fig. 3). Thus, we have chosen the a phase to study the adsorption of the titanium chlorides thereon. There are some studies [34] on the adsorption of molecules on MgCl2 . Alcohols and esters form the most stable complexes on the (1 0 1) surfaces and it
Fig. 2. The 1 0 0 surface of the a-MgCl2 crystal after reconstruction.
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241
Fig. 3. (a) The top view of the (1 1 0) surface for the b-MgCl2 crystal. Atoms from p the surface layer are labelled by 0 and atoms from the ®rst sublayer are labelled by 1. The unit cell is shown; the cell vectors are a 3 and c. (b) The top view of the (1 1 0) surface for the a-MgCl2 crystal. Atoms from the surface layer are labelled by 0 and atomsfrom the by 1. The active sites are 1=2®rst sublayer are labelled p 1=2 2 2 . 2a if c a 83 very similar, however the unit cells dier. The cell vectors are, a 3 and 4a3 c9
has been shown that the binding bene®ts from Hbonding. Ketones are preferably coordinated to the (1 1 0) surface. For TiCln complexes, the common features of b-TiCl3 and MgCl2 suggest an easy interaction with a titanium in an octahedral environment; this has been proposed for a TiCl4 ± MgCl2 interaction from a cluster model approach [35]. 4. The adsorption of TiCln on MgCl2 on the (1 0 0) and (1 1 0) surfaces In this section, we present the adsorption of titanium chlorides (monomers, dimers and some methyl derivatives) on the (1 0 0) and (1 1 0) surfaces of MgCl2 . Clusters for the reference energies have been or more with the recalculated in boxes of 10 A geometries previously optimised [18,19] with the G A U S S I A N program [36] and reasonable basis sets
and pseudopotentials, using the Perdew±Wang 1991 density functional. The present structures of the monomeric TiCln complexes are close to those obtained with the G A U S S I A N program. TiCl2 is TiCl3 has D3h symmetry linear (dTi±Cl 2:21 A), (dTi±Cl 2:24 A) and TiCl4 is tetrahedral (dTi±Cl For the dimeric complexes, the best 2:19 A). structures obtained using the VASP program have two bridging chlorine atoms (l2 -Cl) instead of three. For (TiCl2 )2 and (TiCl3 )2 the structures ClTi(l2 -Cl)2 TiCl and Cl2 Ti(l2 -Cl)2 TiCl2 are lower in energy than the structures ClTi(l2 -Cl)3 TiCl and ClTi(l2 -Cl)3 TiCl2 by 4.4 and 5.9 kcal/mol respectively; they were higher by 15.9 kcal/mol and 3.1 kcal/mol using G A U S S I A N . The (TiCl4 )2 best structure obtained with the VASP code has also two bridging chlorine atoms (l2 -Cl); it is more stable by two kcal/mol than that with three asymmetrically bridging chlorine atoms described in Ref. [18]. The formation energy of the (TiCln )2 dimer decreases with n; these values calculated by VASP
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C. Martinsky et al. / Surface Science 490 (2001) 237±250
are smaller than those from Ref. [18] and decrease more rapidly (52.5, 28.8 and 7.9 kcal/mol for n 2, 3 and 4 respectively). 4.1. The adsorption of TiCl2 The addition of TiCl2 to a MgCl2 molecule (triplet state) builds three bonds: two Mg±Cl bonds and one Ti±Cl bond resulting in a Ti(l2 Cl)3 MgCl structure with the terminal ligand bound to the magnesium atom and not to the titanium atom; the Mg±Cl bond strength is larger than the Ti±Cl bond one [18]. The addition of TiCl2 on the (1 0 0) surface of b-MgCl2 also introduces three bonds: two Ti±Cl (found asymmetrical ± see the distances in Table 3) and one Mg±Cl; the titanium
atom becomes threefold coordinated, bound to one l3 -Cl and to two l2 -Cls (see Fig. 4) and is deprived of terminal ligand. The adsorption energy, 27.5 kcal/mol, is small compared with the interaction energy of the molecular system, 57.9 kcal/mol because of the constraint for the chlorine atoms that are also bound to the lattice. Another adsorption mode, with two new bonds only (one chlorine atom remaining in terminal position) is slightly above in energy (2.1 kcal/mol). The addition of TiCl2 to a-MgCl2 (1 1 0) results from the formation of four bonds (two Ti± Cl and two Mg±Cl; see mode L in Fig. 5). The binding energy is larger (Table 2). Another mode (mode A) with the formation of three bonds only is less favourable but with an adsorption energy
Fig. 4. The (1 0 0) face with a TiCl2 , a TiCl3 and a TiCl4 adsorbed. The binding introduces 2 Mg±Cl (the chlorine atoms from the complex become l2 ) and one Ti±Cl bond (the chlorine atom from the lattice becomes l3 ).
Fig. 5. The (1 1 0) face with adsorbed TiCl2 (left, above and below) TiCl3 (middle and right, above) and TiCl4 (middle and right, below) species.
C. Martinsky et al. / Surface Science 490 (2001) 237±250
(Eads 37.9 kcal/mol) larger than that on the 100 face. 4.2. The adsorption of TiCl3 and TiCl2 CH3 The Ziegler±Natta reaction is a polymerisation reaction; an alkyl ligand of increasing size is bound to the metal. The propagation steps adds a C2 unit to its length. For simplicity, we have modelled, in addition to pure chlorides, the alkylated species by methyl species. According to Corradini [1], TiCl3 complexes are adsorbed to form a fourfold coordinated nonstereospeci®c Ti centre on the 1 0 0 surface and a ®vefold coordinated stereospeci®c Ti centre on the 1 1 0 surface. On the (1 0 0) surface, we indeed obtain a fourfold coordination (one (l3 -Cl), two (l2 -Cl) and a terminal Cl; see Fig. 4). The adsorption mode is identical to that of TiCl2 except that there is an extra ligand (the terminal ligand) that is inactive relative to the adsorption; the same bonds are formed. The heat of adsorption and the distances are thus similar to that of TiCl2 (Tables 2 and 3). Next, we have replaced the terminal Cl ligand by a methyl group. The heat of adsorption is now 24.7 kcal/mol. Afterwards, we have replaced one of the (l2 -Cl) by a methyl group and obtained another isomer that is very close in energy (2.7 Table 2 Heat of adsorption in kcal/mol for the best mode of the TiCln monomeric complexes TiCl2 TiCl3 TiCl4 a
100
110
MgCl2 moleculea
27.5 23.3 3
46.1 32 31 (h 1=4)
57.9 62.7 44.4
From Ref. [18]
Table 3 for the adsorption of complexes on the 1 0 0 face Distances (A) (see labels in Fig. 4) TiCl1 TiCl2 TiCllattice MgCl1
TiCl2
TiCl3
TiCl4
2.30±2.31 ± 2.40 2.54±2.64
2.30±2.31 2.20 2.51 2.55±2.56
2.27 2.17 2.84 2.66±2.70
243
kcal/mol higher in energy). The methyl group can easily switch to the bridging position with the chlorine group. Thus, TiCl2 CH3 complexes behave similarly to TiCl3 complexes. On the (1 1 0) surface, we have optimised two adsorption modes, B and C (see Fig. 5). The best (mode B) is that proposed by Corradini where four bonds are formed (two Ti±Cl and two Mg±Cl). The Ti centre is ®ve-fold coordinated with a distribution: two l3 -Cl, two l2 -Cl and one terminal Cl. The heat of adsorption is 32 kcal/mol. In the mode C, three bonds are formed (two Ti± Cl and one Mg±Cl) and the Ti centre is also ®vefold coordinated with a dierent distribution: two l3 -Cl, one l2 -Cl and two terminal Cls. The heat of adsorption is 24.5 kcal/mol. The substitution of the terminal Cl by a methyl group leads to a structure with a heat of adsorption of 24.7 kcal/mol (on the (1 0 0) face). The TiCl3 adsorption on the MgCl2 surface appears to be similar to that for TiCl2 ; This fact was already found for the coupling with a MgCl2 molecule [18] (Table 4). 4.3. The adsorption of TiCl4 The TiCl4 is a closed shell molecule with a tetrahedral geometry; the distortion to a square planar geometry is expensive in energy (55.0 kcal/ mol). We ®rst searched for a tetrahedral precursor state (here referred as mode T) where the titanium atom remains tetravalent as proposed by Lin [20]. This model was considered by Potapov [11] (model 2) and rejected since it did not match the distribution of distances from EXAFS. On the (1 0 0) face, we have optimised the geometry under constraint to maintain the angles of the tetrahedral Table 4 for the adsorption of complexes on the 1 1 0 face Distances (A) (see labels in Fig. 5) TiCl2 (A) TiCl1 TiCl2 TiCllattice MgCl1
TiCl2 (L)
2.45 2.41 2.26 2.54±2.56 2.43 2.35 2.48
TiCl3 (D3h )
TiCl4 (T)
TiCl4 (O)
2.42±2.43 2.22 2.46 2.41±2.42
2.20 2.19 ± 3.15±3.20
2.36±2.38 2.20±2.21 2.42±2.44
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environment and obtained a negative heat of adsorption (endothermic). On the (1 1 0) face, we have optimised a precursor state where the distortion was weak the Mg±Cl distances are long, and the heat of adsorption is small, 3.15±3.20 A, 4.6 kcal/mol. This adsorption mode is not very favourable. To approach closer to the surface, TiCl4 has to adapt to the local symmetry of the adsorption site and the cost of distortion reduces the heat of adsorption. From X-ray measurements, TiCl4 is supposed to distort toward an octahedral environment [12], being bound to MgCl2 via a double Cl bridge (a formation of two Ti±Cl bonds). For the adsorption on the 1 0 0 surface, Colbourn et al. [30] have shown that the doubly bound structure (incomplete octahedron with one Ti±Cl bond and one Mg±Cl bond) was not stable while the triply bound species (two Ti±Cl and one Mg±Cl bonds) led to a binding energy of 25.7 kcal/mol. Similarly, Corradini et al. [1] have proposed a ®ve-fold titanium atom (one l3 -Cl, two l2 -Cl and two terminal Cls). From EXAFS results [11], it has been suggested that a distortion to the square planar is produced. In our calculations for the (1 0 0) face when the constraints were released, we have obtained the adsorption mode shown in Fig. 4 where the titanium atom is at the centre of a trigonal bipyramid (the main axis of the bipyramid is parallel to the surface plane) that is close to the model proposed by Corradini. The distortion of TiCl4 is indeed signi®cant. This adsorption mode is similar to those obtained for TiCl2 and TiCl3 ; three bonds are built and the dierence concerns the number of terminal ligands that are not directly involved in the adsorption process. However, despite this resemblance, the adsorption is quasi-athermic since the cost for the distortion is large for the tetracoordinated Ti. The Ti±Cl distance (that involving the l3 -Cl atom coming from compared with the lattice) is very long, 2.84 A, those for the adsorption of TiCl2 and TiCl3 (see Table 3); the increase of the number of ligands induces a repulsion between the chlorine atoms and this reduces the heat of adsorption. On the (1 1 0) face and for a smaller coverage, we obtained a much larger heat of adsorption (Table 2 and Fig. 5). The titanium atom is hexa-
coordinated, in a nearly octahedral environment as also proposed by Jones and Oldman [12] (except that two Cl ligands from TiCl4 also bind to Mg) and by Corradini; we will later on refer to this model as model O. It is bound to two Cl from the lattice (l3 -Cl) that belongs to the same (1 1 0) layer; two Cls from TiCl4 bind to the Mg atoms (l2 -Cl) while the two others remain in terminal position. We conclude that addition of TiCl4 is exothermic only when the titanium atom has an octahedral environment as suggested by Colburn [30]. The formation of a ®ve-coordinated titanium complex leading to an octahedral environment with a vacancy [35] is less favourable since it builds only one Ti±Cl bond instead of two. From Table 2, it seems that TiCl4 can only be easily adsorbed on the (1 1 0) face of MgCl2 . 4.4. The adsorption of (TiCl2 )2 and Ti2 Cl3 CH3 First, we have searched for an adsorption mode on the 1 0 0 surface resulting from the formation of three bonds, two Ti±Cl bonds and one Mg±Cl bond (connecting the magnesium atom from the surface to the bridging atom of the dimer). MgCl2 was not relaxed in this preliminary study. Such systems remain in high spin states (quintet). The heat of adsorption is 14.6 kcal/mol. The coupling of the adsorbed TiCl2 species on the 1 0 0 surface represents a gain of 16.3 kcal/mol, indicating that the monomeric complexes should not remain separate. The substitution of the other bridging ligand of the dimer by a methyl group leads to the adsorbed Ti2 Cl3 CH3 complex. The methyl group remains bridging as found in Ref. [18]. The heats of adsorption for these two complexes are the same (13.1 kcal/mol for the later). Thus, the substitution by CH3 has little eect on the bonding in agreement with Lin and Catlow [20]. Next, we have moved the terminal Cl atoms to form two more Mg±Cl bonds, the adsorption mode involving ®ve bonds (see Fig. 6, right hand side) and we allowed the relaxation of the slab. After a second trial, we obtained the best mode, the heat of adsorption raises to 45.1 kcal/mol (Table 5). The ®ve atoms of the dimer that bind to MgCl2 are coplanar and form a W frame; the last one is out of the plane. Contrary to the impression
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245
Fig. 6. The (1 0 0) face with dimeric complexes. Above three structures for (TiCl2 )2 ; below (TiCl3 )2 and (TiCl4 )2 .
from Fig. 6, the Ti atoms and the Cl atoms bind to atoms that pertains to dierent MgCl2 frameworks. This is apparent in Figs. 7 and 8. In the ®rst optimisation process, only one new bond was made (see Fig. 6, middle); the heat of adsorption is slightly inferior, 43.0 kcal/mol. On the (1 1 0) surface, we have searched for an adsorption structure involving the formation of four bonds, two Ti±Cl bonds and three Mg±Cl bonds (modes O in Fig. 9). Starting by mode O1 , the optimisation led to the mode O2 where Ti2 is three coordinated. This mode involves the same number of bonds than O1 ; indeed, with respect to O1 , for Ti2 the coordination increases from 2 to 3 while, for Ti1 , it decreases from 6 to 5. This represents a better balance between the two titanium atoms. The heat of adsorption is 57 kcal/mol. Thus, it is concluded that, despite the good ®t between Table 5 Heat of adsorption in kcal/mol for the best mode of the TiCln dimeric complexes 100 (TiCl2 2 (TiCl3 2 (TiCl4 2
110
dimer
mono
dimer
mono
45.1 22.8 17.2
2.5 17.8 endo
57.0 59.7a decomposition
23.3 35.2 69.9
For an indicative comparison, the heat of adsorption of two monomeric species plus that for the dissociation of the dimers is given on the even columns. a In the case of (TiCl3 )2 the best structure on the 1 1 0 surface is not a dimer but an extended polymer.
Fig. 7. A perspective view of the (1 0 0) face showing the connections of the (TiCl2 )2 to MgCl2 . In Fig. 6 (above the right hand side) the atoms labelled 1 (in front) and 2 (behind) are superposed. The Ti from the dimer are bound to the chlorine atoms 1 whereas the Cls are bound to the magnesium atoms 2. A top view is displayed in Fig. 8.
the dimer and the (1 0 0) surface, the (1 1 0) surface is more reactive than the (1 0 0) face. 4.5. The adsorption of (TiCl3 )2 and (TiCl3 )n The adsorption modes on the (1 1 0) surface are displayed in Fig. 9. We started from the best geometry for (TiCl3 )2 from Ref. [18], ClTi(l2 -Cl)3 TiCl2 with three bridging Cls, and approached the dimer with the Ti±Ti axis normal to the surface, the TiCl2 edge being oriented toward the surface magnesium site. The binding is an extension of the mode T (as de®ned in Section 4.3) which was slightly endothermic for TiCl4 . Let us however note that the
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Fig. 8. A top view of the (1 0 0) face showing the connections of the (TiCl2 )2 to MgCl2 . The chlorine bridging atom that is not bound to Mg does not belong to the plane that contains all the other atoms from the dimer. This adsorption mode, though with some similarities with that proposed by Lin and Catlow presents a dierent topology.
resemblance is geometrical and not electronic; in the present case, the titanium atom is a Ti(III) which is supposed to be more reactive than a Ti(IV). The optimised Mg±Cl bond distances are vs. 3.15±3.20 shorter than for TiCl4 (2.59±2.63 A A) and the adsorption energy is exothermic by
8.2 kcal/mol. The ClTi(l2 -Cl)2 (l2 -CH3 )TiCl2 complex behaves similarly with a heat of adsorption in the same range, 11.9 kcal/mol. Since the dimeric complexes optimised with the VASP code have two bridging ligands (Section 4), the structure of adsorption of the Cl2 Ti(l2 -Cl)2 TiCl2 isomer with two bridging Cl atoms is also a little better than that with three bridging Cls. Next, we investigated another perpendicular binding, connecting the cluster to the surface with the mode O (see Fig. 9) that allows the formation of four bonds. This is a better adsorption mode; the heat of adsorption is 48.8 kcal/mol. No model for an epitaxial adsorption parallel to the surface have been proposed to our knowledge. Using a double unit cell for the a-MgCl2 phase, we optimised a structure (mode F from Figs. 9 and 10) for which we obtained the largest heat of adsorption, 59.7 kcal/mol. This structure is an extended one-dimensional periodic structure and Fig. 9 only shows the pro®le of one polymer. TiCl3 growth leads to solids an not to dimers; the epitaxy as shown in Fig. 10 is very favourable. By analogy, it is not surprising to ®nd a periodic structure at high coverage. Although the structure that we have
Fig. 9. The adsorption on (1 1 0) surface. Top, left hand side: Of (TiCl3 )n polymer. Top, right hand side: Of the (TiCl2 )2 dimeric complex (model O). Bottom: Of the (TiCl3 )2 dimeric complexes.
C. Martinsky et al. / Surface Science 490 (2001) 237±250
Fig. 10. Top view of the adsorption of (TiCl3 )n on the 1 1 0 surface of the a-MgCl2 crystal with mode F. The black circles are Ti atoms and the white circles are Cl atoms.
calculated is ferromagnetic, since a part of TiCl3 is silent for the EPR signal, we believe that the system of lowest energy should be antiferromagnetic. For the adsorption on the 1 0 0 surface, Corradini proposed a model where the Ti±Ti axis is parallel to the surface plane; thus, ®ve bonds can be formed (two Ti±Cl and three Mg±Cl) (see Fig. 5). According to the charges calculated on cluster models [37], this dimer on the (1 0 0) face should be more active than that on the (1 1 0) face: the titanium atoms are more electrophilic (sponge eect of the support). We have found a heat of adsorption of only 22.8 kcal/mol for the 1 0 0 face (Table 5). 4.6. The adsorption of (TiCl4 )2 The dierent models for the adsorption are a parallel mode on the 1 0 0 face (Fig. 9) and a per-
247
pendicular mode for the 1 1 0 face. For the former, ®ve bonds are made (three Mg±Cl and two TiCl) as shown in Fig. 6; this structure matches the EXAFS data [11] assuming an asymmetry: Cl1 and Cl3 are not equally bound to the titanium atoms but each one is closer to one titanium centre. We have found a slight asymmetry which is not larger than those for the other dimer structures and comparable with that of the dimer in the gas is close to that phase. The Ti±Ti distance, 3.90 A, obtained by Potapov [11]. When adsorbed, this remain octahedral and there is no cost for such distortion as in the adsorption of the monomeric complex. The heat of adsorption is 11.3 eV without relaxation and 17.2 eV when relaxation is allowed. An ELF analysis of (TiCl4 )2 in the geometry of the adsorption [38] con®rms the octahedral environment around the titanium centres. For the (1 1 0) surface, the adsorption mode that we have investigated is an extension of the model O by adding two Cl ligands to the atom Ti2 from (TiCl3 )2 (see Fig. 9). It led to a decomposition of the dimer in two fragments, a TiCl3 complex adsorbed on the surface and a TiCl5 that is desorbed. Since TiCl5 easily decomposes to give TiCl4 1=2Cl2 , this process could generate reduced titanium atom at the surface. In any cases, on the (1 1 0) surface, the cleavage of the dimer leading to two adsorbed TiCl4 monomers is thermodynamically the most favourable result (exothermic by 69.9 kcal/mol). 4.7. Interatomic distances From Fourier transformed EXAFS data [11], four dierent interatomic distances emerge. Without any phase correction, they correspond to 1.7, After correction, the set of 2.5, 2.9 and 3.5 A. ``experimental distances'' are, 2.1, 3.09, 3.5 and 4 The best match for these distances was obtained A. for (TiCl4 )2 /1 0 0 indicating that this species is the most abundant on the support. Our results for the various titanium chlorides are fully optimised and justify several proposed topologies. Some of the assumptions on the numeric values used in Ref. [11] have nevertheless to assumed for all the be re®ned. The value of 2.1 A
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C. Martinsky et al. / Surface Science 490 (2001) 237±250
Ti±Cl distances from the ®rst coordination sphere is too short especially when Cl is bridging l2 -Cl. Terminal Cls and bridging l2 -Cl should be resolved into two sets of distances, a ®rst range of for the terminal bonds (shorter for the 2.18±2.27 A saturated monomeric species as already noticed [19]) and a second one for the bridging l2 -Cls at (Table 6). The value assumed for 2.51±2.59 A is close to our result; let the bridging l3 -Cl, 2.56 A, us note that it could perhaps not be easily distinguished from the bridging l2 -Cl values. The Ti±Cl involving the Cl from the lattice are slightly longer, The Mg±Cl distance, with the ex2.53±2.82 A. ception of TiCl4 (T) with a very long distance, close to the value remain in the range 2.55±2.66 A 2.56 from Ref. [11]. The Ti±Mg distances that we have obtained (see Table 7) vary from 3.38 to 3.99 they are often longer than published in Ref. A; [11]. As has been noticed, the dimers do not reach perfect symmetry.
Table 6 for the adsorption of dimeric complexes (see laDistances (A) bels in Fig. 6)
TiCl1 TiCl2 TiCl3 TiCl4;6 TiCl5 TiCllattice MgCl
TiCl2 2 / 100
TiCl2 2 / 100
TiCl3 2n / 110
TiCl4 2 / 100
2.41 2.37±2.39 2.43±2.44 ±
2.38 2.32±2.34 2.43±2.44 ±
2.58±2.59 2.27 2.45±2.46 2.18±2.19
2.40±2.41 2.53± 2.56±2.66
2.57±2.62 2.70± 2.69±2.86
2.39 2.51±2.53 2.38 2.20 2.43±2.44 2.53±2.54 2.44± 2.49±2.50
2.82 2.64
5. Mg adsorption on the 0 0 0 1 surface of -MgCl2 The lack of reactivity of the 0 0 0 1 surface has been attributed to the fact that metallic centres were not accessible; a possibility to make it reactive would be to add Mg atoms. However, the experimental attempts to ®x Mg atoms on the surface failed. The Mg-containing MgCl2 faces are thermodynamically unstable [39]. We have investigated the addition of a single atom on the slab de®ned in Section 3. When optimised, the mag in the middle of nesium atom is located at 5.5 A the space between successive slabs and the interaction is repulsive. It is similar for molecular calculations, Mg does not bind to a MgCl2 molecule. This is because the magnesium atom has a 3s2 con®guration and is poorly reactive unless being oxidised. This is similar to Be2 whose weak binding results from hybridisation, the dimer being sensitive to correlation eects and basis-set size [40]. Metallic Mg is eective in reducing the TiCl4 complex [13]. Stable ®lms could be obtained by TiCl4 and Mg codeposition on MgCl2 [39]. Contrary to MgCl2 that cannot be reduced, TiCl4 can be converted into TiCl2 allowing the oxidation of Mg. However, this conversion is not thermodynamically favourable if the interaction between MgCl2 and TiCl2 is not involved since the Ti±Cl bonds are stronger than the Mg±Cl bonds. Mg TiCl4 ! MgCl2 TiCl2 DH 6:8 kcal=mol Mg 2TiCl4 ! MgCl2 2TiCl3 DH 10:2 kcal=mol
Table 7 ®rst lines: our results; second lines Ref. Ti±Mg distances (A) [11] TiCl2 /1 0 0 TiCl3 /1 0 0 TiCl4 /1 0 0 TiCl3 /1 1 0 (B) TiCl2 /1 1 0 (L) TiCl3 /1 1 0 (C) TiCl4 /1 0 0 (T) TiCl4 /1 1 0 (O) (TiCl4 )2 /1 0 0 (C)
3.38 3.40±3.44 3.87±3.90 3.72 3.58 3.62±3.98 3.64 3.86 3.79±3.91
3.22±3.63
If this interaction is taken into account the reaction becomes favourable because the formation of bimetallic complexes with MgCl2 is strongly exothermic and the reduction of the titanium atom occurs without breaking bonds [18]. Mg TiCl4 ! ClMg l2
2.89±3.12±3.63 3.63 3.56±4.10
DH
Cl3 Ti
50:3 kcal=mol
The bimetallic complex is in a triplet state.
C. Martinsky et al. / Surface Science 490 (2001) 237±250
6. Conclusions Results from periodic calculations on the adsorption of TiCln complexes and related bimetallic complexes on MgCl2 essentially validate the structures already found by means of molecular calculations [18,19,35] or postulated as models inspired by experiments [1,11]. This study also propose new adsorption modes: the extended (TiCl3 )2n structure and the dimer O for (TiCl2 )2 on the 1 1 0 surface. Table 5 summarises our results for the adsorption of monomeric and dimeric species on the two most reactive surfaces. All the values refer to the dimer in the gas phase and should then be comparable. Note however that the adsorption energies for each system have been calculated independently at dierent coverage according to the best aordable model for each case; they could be slightly dierent if recalculated at the same coverage within the same model. Trends nevertheless emerge. The reduced forms, TiCl2 and TiCl3 , are adsorbed as dimers while (TiCl4 )2 decomposes in monomers. TiCl4 is preferably adsorbed on the (1 1 0) face where the Ti atom is hexacoordinated (model O). Both Ti±Cl and Mg±Cl bonds contribute to the adsorption; the best adsorption mode correspond to the maximum of bonds that can be formed. Dimers are preferentially adsorbed on the (1 1 0) face. The Ti atoms from (TiCl2 )2 and one of them from (TiCl3 )2n are pentavalent; this is a good starting point to have a high stereospeci®city. The adsorption mode O for (TiCl3 )2 on (1 1 0) is also favourable but less than with the ¯at mode, F; in this mode, the closest Ti atom to the surface, Ti1 , is hexacoordinated allowing a strong binding, while the other Ti atom, Ti2 , is only tetravalent which may decrease the stereospeci®city. On the tests that we have done, the alkyl group does not modify the adsorption modes. Finally, we should remark that this study describes the most stable species and we are conscious that the most abundant species may not be the most reactive. Nevertheless, the search for the catalyst structure remains a necessary step for the search of the active sites. The hexagonal surface of MgCl2 is not reactive and the deposition of Mg atoms could not activate the surface since MgCl2 is not reducible; on the
249
other hand, the addition of metallic magnesium can reduce TiCl4 species.
Acknowledgements This work has been accomplished in the framework of the GDR ``Dynamique Moleculaire Quantique Appliquee a la catalyse''; the ®nancial support of the French Ministry of Education, Technology and Research, the Spanish CICyt PB98-1216-CO2-02 and partially the Catalan 1999SCR00182 projects are gratefully acknowledged. C. Martinsky acknowledges the ERB FMGE CT95 0062 European TMR program held in CESCA/CEPBA supercomputer centres for supporting his stay in Tarragona. We also thank CCR and CNRS-IDRIS for computing facilities. C. Minot is grateful to G. Somorjai, M. Van Hove, J. Roberts, E. Magni and A. Markovits for stimulating discussions.
References [1] P. Corradini, V. Busico, G. Guerra, in: W. Kaminsky, H. Sinn (Eds.), Transition Metals and Organometallics as Catalysts for Ole®n Polymerization, Springer, Berlin, 1988, p. 337. [2] H. Fuhrmann, W. Herrmann, Macromol. Chem. Phys. 195 (1994) 3509. [3] N. Kashiwa, J. Yoshitake, Makromol. Chem. 185 (1984) 1133. [4] J.C.W. Chien, J.C. Wu, C.I. Kuo, J. Polym. Sci. 20 (1982) 2019. [5] P. Brant, A.N. Speca, Macromolecules 20 (1986) 2740. [6] G.D. Butakov, V.S. Goncharov, V.A. Zakharov, React. Kinet. Catal. Lett. 9 (1995) 1751. [7] H. Mori, K. Hasebe, M. Terano, J. Mol. Catal. A: Chem. 140 (1999) 165. [8] P.G. Gassman, M.R. Callstrom, J. Am. Chem. Soc. 109 (1947) 7875. [9] M. Faruta, J. Polym. Sci: Polym. Phys. Ed. 19 (1981) 135. [10] J.G. Roberts, M. Gierer, D.H. Fairbrother, M.A. VanHove, G.A. Somorjai, Surf. Sci. 399 (1998) 123. [11] A.G. Potapov, V.V. Kriventsov, D.I. Kochubey, G.D. Bukatov, V.A. Zakharov, Macromol. Chem. Phys. 198 (1997) 3477. [12] P.J.V. Jones, R.J. Oldman, in: W. Kaminsky, H. Sinn (Eds.), Transition Metals and Organometallics as Catalysts for Ole®n Polymerization, Springer, Berlin, 1988, p. 223.
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C. Martinsky et al. / Surface Science 490 (2001) 237±250 S.H. Kim, G.A. Somorjai, J. Phys. Chem. 104 (2000) 5519. J.C.W. Chien, J.C. Wu, J. Polym. Sci. 20 (1982) 2461. J.C.W. Chien, J.C. Wu, J. Polym. Sci. 20 (1982) 2445. J.C.W. Chien, P.L. Bres, J. Polym. Sci.: Part A 24 (1986) 2483. J.C.W. Chien, J.C. Wu, J. Polym. Sci.: Part A: Polym. Chem. 27 (1989) 897. C. Martinsky, C. Minot, Surf. Sci. 467 (2000) 152. C. Martinsky, C. Minot, New Trends in Quantum Systems in Chemistry and Physics, Progress in Theoretical Chemistry and Physics, QSCP, B 2, Kluwer, Dordrecht, 2001, p. 269. J.S. Lin, C.R.A. Catlow, J. Catal. 157 (1995) 145. E. Magni, G.A. Somorjai, Appl. Surf. Sci. 89 (1995) 187. M. Boero, M. Parinello, S. H uer, H. Weiss, J. Am. Chem. Soc. 122 (2000) 501. G. Kresse, J. Hafner, Phys. Rev. B 47 (1993) 558. G. Kresse, J. Hafner, Phys. Rev. B 48 (1993) 13115. G. Kresse, J. Hafner, Phys. Rev. B 49 (1994) 14251. J.P. Perdew, Y. Wang, Phys. Rev. B 45 (1992) 13244. J.P. Perdew, J.A. Chevary, S.H. Vosko, K.A. Jackson, M.R. Pederson, D.J. Singh, C. Fiolhais, Phys. Rev. B 46 (1992) 6671. D. Vanderbilt, Phys. Rev. B 41 (1990) 7892. G. Kresse, J. Hafner, J. Phys. Condens. Matter 6 (1994) 8245. E.A. Colbourn, P.A. Cox, B. Carruthers, P.J.V. Jones, J. Mater. Chem. 4 (1994) 805.
[31] J. Xu, L. Feng, S. Yang, X. Kong, Macromolecules 30 (1997) 7655. [32] M. Kioka, N. Kashiwa, J. Mol. Catal. 82 (1993) 11. [33] V.K. Gupta, M. Ravindranathan, Polymer 37 (1996) 1399. [34] E. Puhakka, T.T. Pakkanen, T.A. Pakkanen, J. Phys. Chem. A 101 (1997) 6063. [35] E. Puhakka, T.T. Pakkanen, T.A. Pakkanen, Surf. Sci. 334 (1995) 289. [36] M.J. Frisch, G.W. Trucks, H.B. Schlegel, P.M.W. Gill, B.G. Johnson, M.A. Robb, J.R. Cheeseman, T.A. Keith, G.A. Petterson, J.A. Montgomery, K. Raghavachari, M.A. Al-Laham, V.G. Zarzewski, J.V. Ortiz, J.B. Foresman, J. Cioslowski, B.R. Stefanov, A. Nanayakkara, M. Challacombe, C.Y. Peng, P.Y. Ayala, W. Chen, M.W. Wong, J.L. Andres, E.S. Replogle, R. Gomperts, R.L. Martin, D.J. Fox, J.S. Binkley, D.J. Defrees, J. Baker, J.P. Stewart, M. Head-Gordon, C. Gonzales, J.A. Pople G A U S S I A N 9 4 , Revision B.1, Pittsburgh PA., 1995, Gaussian. [37] M. Farina, C. Puppi, J. Mol. Catal. 82 (1993) 3. [38] C. Martinsky, Ph.D., Universite UPMC, Paris VI (2000). [39] E. Magni, G.A. Somorjai, J. Phys. Chem. B 102 (1998) 8788. [40] L. Fusti-Molnar, P.G. Szalay, Chem. Phys. Lett. 258 (1996) 400. [41] R.W.G. Wycko, Crystal Structures, second ed., vol. 1, Wiley, New York, 1982, p. 269.
www.elsevier.com/locate/susc
A theoretical investigation of the binding of TiCln to MgCl2 C. Martinsky a, C. Minot a,*, J.M. Ricart b a
Laboratoire de Chimie Th eorique, UMR 7616 CNRS, Universit e P. et M. Curie, Bo^õte 137 Tour 23-22, 4 Place Jussieu, Paris 75252 Cedex 5, France b Departament de Quimica Fõsica i Inorg anica i Institut d'Estudis Avancßats, Universitat Rovira i Virgili, Pcßa Imperial Tarraco, 1 43005 Tarragona, Spain Received 10 March 2001; accepted for publication 20 June 2001
Abstract The structure of the (0 0 0 1) surface of the a-MgCl2 crystal has been investigated using DFT-GGA periodic calculations. The calculated surface relaxation is in agreement with LEED measurements. Motivated for the use of MgCl2 as support for the Ziegler±Natta reaction, we have studied the adsorption of the catalyst (titanium chlorides as monomers or dimers) on the (1 0 0) and (1 1 0) MgCl2 surfaces. The structures of adsorbed species are close to those previously found on cluster models: bridging chlorine atoms connect the Ti to the Mg atoms and the systems remain in high spin states. The (0 0 0 1) surface is the most stable face of the a-MgCl2 crystal; however it is Cl-terminated and henceforth poorly reactive; it had been suggested to deposit metallic Mg in order to improve its reactivity. Our modelling explains the failure of this tentative; the interaction between the deposited metal and the surface is repulsive and uncharged Mg atom does not bind. Ó 2001 Elsevier Science B.V. All rights reserved. Keywords: Computer simulations; Molecular dynamics; Density functional calculations; Halides; Catalysis; Chemisorption
1. Introduction Magnesium chloride is often used as a catalyst support for the Ziegler±Natta polymerisation of a-ole®ns. Crystallographic faces of the magnesium chlorides dier by the nature of surface ions (Mg2 , Cl or both) and by their coordination: the small particles of titanium chloride bind in dierent ways in¯uencing the stereoselectivity of the polymerisation reaction. The index of isotacticity increases when an appropriate active site is exclusively prepared by the adsorption of the catalyst * Corresponding author. Tel.: +33-1-44272505; fax: +33-144274117. E-mail address: [email protected] (C. Minot).
on a well-de®ned crystallographic surface of the support. The most stable surface with saturated Mg atoms is not reactive since the steric hindrance prevent adsorption. The active sites are then thought to be located on the coordinatively unsaturated lateral faces [1]. However, sites of very low coordination could have the same activity on polymers of dierent topology and be inecient to control the stereospeci®city. The titanium chloride catalyst may coexist on the support with dierent oxidation states. The proportion of Ti4 varies according to experimental conditions [2±4]. It is generally believed that a large amount of Ti4 is associated with a large activity [5] and a poor stereospeci®cy. The stereoactive centres may represent only several percents of Ti in the catalyst [6].
0039-6028/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 9 - 6 0 2 8 ( 0 1 ) 0 1 3 7 3 - 5
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C. Martinsky et al. / Surface Science 490 (2001) 237±250
There is no direct proof of the location and on the nature of the active sites of the Ziegler±Natta catalyst at the atomic level [7]. The geometry of the active sites and their oxidation state are not perfectly known and only few surface determinations have been made [8,9]. The lack of information on the MgCl2 surface structure arises from the diculty in characterising insulators [10] due to their tendency to become charged under irradiation by an electron beam. Some EXAFS [11,12], XPS [13], EPR [4,13±16] and LEED [10] studies however lead to propositions. Ti is adsorbed as monomer or dimer; according to the conditions (the presence of a cocatalyst is necessary for the reaction) and it is partially reduced. The percentage of reduced Ti atoms varies. Some analyses [3] estimate that Ti2 represent 80% of the total titanium. In some EPR experiments [4] Ti2 and Ti3 species represent 8% and 38% of the content, a fraction of which is seen in EPR (that corresponding to monomeric complexes) while the other part, silent to EPR, is attributable to dimers. Superexchange of the Ti3 ions results in antiferromagnetism for the bridged complexes [17]. Calculations indeed always found high spin states [18] for the reduced species. A Cl content of 3.5 per Ti was observed [4], showing that some chlorine has desorbed and that a partial reduction had occurred. In the presence of methylp-toluate, 90% of the Ti4 is reduced [4] producing a multitude of Ti3 species [14]. This Ti3 species is supposed to have D3h symmetry with no other adjacent Ti3 in the vicinity [14]. EXAFS [11,12] agree to a predominant adsorption of TiCl4 with the formation of dimeric complexes; such species could be precursors of nonstereospeci®c sites, the active centres representing only several percents of Ti in the catalyst [6]. In summary, literature refers to many species on the surface, monomers and dimers, in dierent oxidation states. We have recently investigated the bonding and the reactivity of TiCln , TiCln 1 CH3 complexes and related dinuclear complexes [18,19] by means of quantum mechanic calculations using the density functional theory. The coupling of TiCln , (dimerisation, addition to TiCln 1 CH3 and complexation by the magnesium chloride) results from the donation of the electron pairs from the chlorine ligands to the metal atoms leading to bridging
structures (2 or 3 bridging Cls) as proposed from EXAFS [11,12]. The bridging structures arise from the formation of both Ti±Cl and Mg±Cl bonds and not from Ti±Cl bond only as was initially proposed [20]. Moreover, the alkyl groups could also bridge the two metal centres of the dinuclear complexes. In this paper, we present periodic DFT-GGA calculations for the MgCl2 surface, using the Vienna ab intio simulation program (VASP) method, and show that they reproduce the experimental relaxation of the (0 0 1) face (Section 3). Unfortunately, this surface, stable and eectively observed, is poorly reactive. All the surface atoms are chlorine atoms and the Mg atoms remain saturated (hexacoordinated) in the sublayer and poorly accessible. TiCl4 does not chemisorb on this Cl-terminated ®lm in UHV [21]. We therefore turn to other orientations to study the adsorption of small (TiCln )x units. In the Section 6, we will return to the possibility to add extra Mg atoms on the (0 0 0 1) surface to improve its reactivity. In Section 4, we will use a periodic approach to study, on the (1 0 0) and (1 1 0) surfaces, the adsorption of the structures previously obtained by means of cluster models. We show that adsorption of small particles of titanium chlorides always results from the donation of the electron pairs from the chlorine ligands to the metal atoms leading again to bridging structures. In the surfaces that we have considered, the chlorine atoms of the lattice are already bridging; when they bind to the titanium centre and form a new Ti±Cl bond, they become (l3 -Cl). When the chlorine atoms from the TiCln monomers bind to the magnesium centre (formation of a Mg±Cl bond), they become bridging (l2 -Cl). This description is in agreement with the models used for the Ziegler±Natta reaction [22] where the dominant species, TiCl4 or TiCl3 R, is considered. In the cases of dimers, the bridging chlorine atoms become (l3 -Cl). 2. Computational details All the calculations have been performed using the VASP [23±25]. The Kohn±Sham equations are solved with the generalised gradient approximation
C. Martinsky et al. / Surface Science 490 (2001) 237±250
(GGA) proposed by Perdew et al. [26,27]. Ultrasoft pseudopotential have been used [28,29] with the default parameters provided by the program; for the metal atoms we have chosen those which include functions that usually are considered in the core (3p for Ti) and that are supplied by the VASP basis set library. The unit cell is repeated in three directions. For the slabs, we have considered a cell vector perpendicular to the surface plane large enough to leave a signi®cant empty space between We have tested on MgCl2 successive slabs (11 A). and TiCln bulk that four k-points, associated to the in-plane periodicity, were enough to reach a 50 meV precision. For the adsorption of the monomeric species on the (1 0 0) surface, we have considered a three multilayer slab and a double unit cell (six MgCl2 per unit cell). The lowest multilayer was kept ®xed and the other relaxed. For the dimeric species, we have taken a two multilayer slab and a triple unit cell (again six MgCl2 per unit cell), only the upper multilayer being relaxed in this case. For the (1 1 0) surface, we have taken two multilayers and a double unit cell (four MgCl2 per unit cell) for the a and the b phases. The adsorption energies have been de®ned using the expression: Eads E A E MgCl2 E A= MgCl2 where A represents the adsorbate. Positive values correspond to exothermic adsorption.
3. The bulk and the main surface structures of MgCl2 MgCl2 exists as two crystalline forms: the ®rst one is the a-MgCl2 (R3m or P1) with the chloride anions organised in a face-centred cubic arrangement and the Mg cations in the octahedral interstices; the primitive cell is rhombohedric and the conventional cell hexagonal. It is more stable than the b-MgCl2 (Cm) with the chloride anions organised in a hcp arrangement. In the following, we will refer to the hexagonal cells for the two varieties. The two structures dier by the stacking of hexagonal layers: AbC BcA CaB. . . or AbC AbC AbC. . . for the a-MgCl2 and b-MgCl2 respectively. The (0 0 0 1) slabs are very stable. The building
239
Table 1 The calculated lattice parameters of the crystal structures compared with the experimental values [41] a-MgCl2 (calculated) a-MgCl2 (experimental) b-MgCl2 (calculated) b-MgCl2 (experimental)
a
c
u
3.634
17.755
0.257
3.59
17.59
0.256
3.700
5.873
0.231
3.66
5.80
0.240
E (eV) 10.823
10.799
The calculated energies for the optimised structures are given in eV.
unit, AbC, is made of three layers, a sandwich of two layers of Cl with a layer of Mg in the middle. The stacking of these units is made by van der Waals bonds and the cleavage between two units does not break any chemical bond. The 0 0 0 1 layers containing the Cl atoms are not equally spaced; the spacing is slightly shorter within the three layers than between them. 1 Calculated structural parameters and the cohesive energy are presented in Table 1. The a-phase is slightly more stable than the b-phase. Indeed, in this stacking, the closest Cl atoms from the next three layer are right above and below the magnesium atoms These atoms are labelled by the (dMg±Cl 4:48 A). same letter (underlined) in the sequence AbC BcA CaB. For a-MgCl2 , a clean slab was prepared by deposition on palladium [10] and the relaxation was studied by dynamical LEED. It was found that the epitaxy imposes a slight increase of the lattice parameter (3%) for the 0 0 0 1 surface. In the obtained model, we ®xed the cell vector to 3.635 A in the optimisation of the bulk; this represents a small increase relative to the experimental parameter of the bulk that corresponds to the epitaxy. The optimisation of a nine-layer slab reproduces the experimental relaxation. The spacing between the top six layers have been varied and that of the three lowest one have been kept ®xed. The spacing between the two Cl layers within the three-layer 1 1 2uc=3 and 2uc vs. 2uc=3 and 1 2uc for the aMgCl2 for the b-MgCl2 respectively (u from Table 1).
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Fig. 1. The 1 0 0 surface of the b-MgCl2 crystal.
the unit (®rst and second ones) are 2.72±2.74 A, exact values obtained from LEED [10]. The spacing between the two adjacent Cl layers (between vs. 3.13 A. the two ®rst three-layer units) is 3.15 A Let us note, however, that in spite of the excellent agreement for the upper layer spacing, we do not obtain pronounced variations relative to the bulk (expansion of the MgCl interlayer distance and contraction of the ClCl interlayer distance) if we
refer to the optimised values obtained for the aMgCl2 bulk (Table 1). The other cleavages lead to unsaturated Mg atoms. In b-MgCl2 , the Mg atoms at the (1 0 0) surface are pentacoordinated (Fig. 1). In the aMgCl2 species, the net cleavage leaves Mg atoms with dierent coordination (3, 5 and 6) but a reconstruction [20,30] leads again to pentacoordination (Fig. 2). This reconstruction is correctly reproduced by the slab optimisation. Other faces also lead to the coordination 5: the (1 0 4) and (1 0 1) surfaces that do not reconstruct [30]; however, since information on the their reactivity is missing, we have considered the (1 0 0) surface to study the reactivity on a pentacoordinated Mg atom. The (1 1 0) surface is promising for the potential reactivity since the coordination of the Mg atoms at the surface is lower (4 only); let us note however, that this goes along with a decrease of stereospeci®city due to the presence of two vacancies [31]; the stereospeci®city could be restored at the expenses of the reactivity by a poisoning eect when one of the vacancies is occupied by a ligand (a Lewis base as Ph2 Si(OMe)2 [32,33]). The adsorption sites for the a and b-MgCl2 are very similar, diering only by the repetition mode (Fig. 3). Thus, we have chosen the a phase to study the adsorption of the titanium chlorides thereon. There are some studies [34] on the adsorption of molecules on MgCl2 . Alcohols and esters form the most stable complexes on the (1 0 1) surfaces and it
Fig. 2. The 1 0 0 surface of the a-MgCl2 crystal after reconstruction.
C. Martinsky et al. / Surface Science 490 (2001) 237±250
241
Fig. 3. (a) The top view of the (1 1 0) surface for the b-MgCl2 crystal. Atoms from p the surface layer are labelled by 0 and atoms from the ®rst sublayer are labelled by 1. The unit cell is shown; the cell vectors are a 3 and c. (b) The top view of the (1 1 0) surface for the a-MgCl2 crystal. Atoms from the surface layer are labelled by 0 and atomsfrom the by 1. The active sites are 1=2®rst sublayer are labelled p 1=2 2 2 . 2a if c a 83 very similar, however the unit cells dier. The cell vectors are, a 3 and 4a3 c9
has been shown that the binding bene®ts from Hbonding. Ketones are preferably coordinated to the (1 1 0) surface. For TiCln complexes, the common features of b-TiCl3 and MgCl2 suggest an easy interaction with a titanium in an octahedral environment; this has been proposed for a TiCl4 ± MgCl2 interaction from a cluster model approach [35]. 4. The adsorption of TiCln on MgCl2 on the (1 0 0) and (1 1 0) surfaces In this section, we present the adsorption of titanium chlorides (monomers, dimers and some methyl derivatives) on the (1 0 0) and (1 1 0) surfaces of MgCl2 . Clusters for the reference energies have been or more with the recalculated in boxes of 10 A geometries previously optimised [18,19] with the G A U S S I A N program [36] and reasonable basis sets
and pseudopotentials, using the Perdew±Wang 1991 density functional. The present structures of the monomeric TiCln complexes are close to those obtained with the G A U S S I A N program. TiCl2 is TiCl3 has D3h symmetry linear (dTi±Cl 2:21 A), (dTi±Cl 2:24 A) and TiCl4 is tetrahedral (dTi±Cl For the dimeric complexes, the best 2:19 A). structures obtained using the VASP program have two bridging chlorine atoms (l2 -Cl) instead of three. For (TiCl2 )2 and (TiCl3 )2 the structures ClTi(l2 -Cl)2 TiCl and Cl2 Ti(l2 -Cl)2 TiCl2 are lower in energy than the structures ClTi(l2 -Cl)3 TiCl and ClTi(l2 -Cl)3 TiCl2 by 4.4 and 5.9 kcal/mol respectively; they were higher by 15.9 kcal/mol and 3.1 kcal/mol using G A U S S I A N . The (TiCl4 )2 best structure obtained with the VASP code has also two bridging chlorine atoms (l2 -Cl); it is more stable by two kcal/mol than that with three asymmetrically bridging chlorine atoms described in Ref. [18]. The formation energy of the (TiCln )2 dimer decreases with n; these values calculated by VASP
242
C. Martinsky et al. / Surface Science 490 (2001) 237±250
are smaller than those from Ref. [18] and decrease more rapidly (52.5, 28.8 and 7.9 kcal/mol for n 2, 3 and 4 respectively). 4.1. The adsorption of TiCl2 The addition of TiCl2 to a MgCl2 molecule (triplet state) builds three bonds: two Mg±Cl bonds and one Ti±Cl bond resulting in a Ti(l2 Cl)3 MgCl structure with the terminal ligand bound to the magnesium atom and not to the titanium atom; the Mg±Cl bond strength is larger than the Ti±Cl bond one [18]. The addition of TiCl2 on the (1 0 0) surface of b-MgCl2 also introduces three bonds: two Ti±Cl (found asymmetrical ± see the distances in Table 3) and one Mg±Cl; the titanium
atom becomes threefold coordinated, bound to one l3 -Cl and to two l2 -Cls (see Fig. 4) and is deprived of terminal ligand. The adsorption energy, 27.5 kcal/mol, is small compared with the interaction energy of the molecular system, 57.9 kcal/mol because of the constraint for the chlorine atoms that are also bound to the lattice. Another adsorption mode, with two new bonds only (one chlorine atom remaining in terminal position) is slightly above in energy (2.1 kcal/mol). The addition of TiCl2 to a-MgCl2 (1 1 0) results from the formation of four bonds (two Ti± Cl and two Mg±Cl; see mode L in Fig. 5). The binding energy is larger (Table 2). Another mode (mode A) with the formation of three bonds only is less favourable but with an adsorption energy
Fig. 4. The (1 0 0) face with a TiCl2 , a TiCl3 and a TiCl4 adsorbed. The binding introduces 2 Mg±Cl (the chlorine atoms from the complex become l2 ) and one Ti±Cl bond (the chlorine atom from the lattice becomes l3 ).
Fig. 5. The (1 1 0) face with adsorbed TiCl2 (left, above and below) TiCl3 (middle and right, above) and TiCl4 (middle and right, below) species.
C. Martinsky et al. / Surface Science 490 (2001) 237±250
(Eads 37.9 kcal/mol) larger than that on the 100 face. 4.2. The adsorption of TiCl3 and TiCl2 CH3 The Ziegler±Natta reaction is a polymerisation reaction; an alkyl ligand of increasing size is bound to the metal. The propagation steps adds a C2 unit to its length. For simplicity, we have modelled, in addition to pure chlorides, the alkylated species by methyl species. According to Corradini [1], TiCl3 complexes are adsorbed to form a fourfold coordinated nonstereospeci®c Ti centre on the 1 0 0 surface and a ®vefold coordinated stereospeci®c Ti centre on the 1 1 0 surface. On the (1 0 0) surface, we indeed obtain a fourfold coordination (one (l3 -Cl), two (l2 -Cl) and a terminal Cl; see Fig. 4). The adsorption mode is identical to that of TiCl2 except that there is an extra ligand (the terminal ligand) that is inactive relative to the adsorption; the same bonds are formed. The heat of adsorption and the distances are thus similar to that of TiCl2 (Tables 2 and 3). Next, we have replaced the terminal Cl ligand by a methyl group. The heat of adsorption is now 24.7 kcal/mol. Afterwards, we have replaced one of the (l2 -Cl) by a methyl group and obtained another isomer that is very close in energy (2.7 Table 2 Heat of adsorption in kcal/mol for the best mode of the TiCln monomeric complexes TiCl2 TiCl3 TiCl4 a
100
110
MgCl2 moleculea
27.5 23.3 3
46.1 32 31 (h 1=4)
57.9 62.7 44.4
From Ref. [18]
Table 3 for the adsorption of complexes on the 1 0 0 face Distances (A) (see labels in Fig. 4) TiCl1 TiCl2 TiCllattice MgCl1
TiCl2
TiCl3
TiCl4
2.30±2.31 ± 2.40 2.54±2.64
2.30±2.31 2.20 2.51 2.55±2.56
2.27 2.17 2.84 2.66±2.70
243
kcal/mol higher in energy). The methyl group can easily switch to the bridging position with the chlorine group. Thus, TiCl2 CH3 complexes behave similarly to TiCl3 complexes. On the (1 1 0) surface, we have optimised two adsorption modes, B and C (see Fig. 5). The best (mode B) is that proposed by Corradini where four bonds are formed (two Ti±Cl and two Mg±Cl). The Ti centre is ®ve-fold coordinated with a distribution: two l3 -Cl, two l2 -Cl and one terminal Cl. The heat of adsorption is 32 kcal/mol. In the mode C, three bonds are formed (two Ti± Cl and one Mg±Cl) and the Ti centre is also ®vefold coordinated with a dierent distribution: two l3 -Cl, one l2 -Cl and two terminal Cls. The heat of adsorption is 24.5 kcal/mol. The substitution of the terminal Cl by a methyl group leads to a structure with a heat of adsorption of 24.7 kcal/mol (on the (1 0 0) face). The TiCl3 adsorption on the MgCl2 surface appears to be similar to that for TiCl2 ; This fact was already found for the coupling with a MgCl2 molecule [18] (Table 4). 4.3. The adsorption of TiCl4 The TiCl4 is a closed shell molecule with a tetrahedral geometry; the distortion to a square planar geometry is expensive in energy (55.0 kcal/ mol). We ®rst searched for a tetrahedral precursor state (here referred as mode T) where the titanium atom remains tetravalent as proposed by Lin [20]. This model was considered by Potapov [11] (model 2) and rejected since it did not match the distribution of distances from EXAFS. On the (1 0 0) face, we have optimised the geometry under constraint to maintain the angles of the tetrahedral Table 4 for the adsorption of complexes on the 1 1 0 face Distances (A) (see labels in Fig. 5) TiCl2 (A) TiCl1 TiCl2 TiCllattice MgCl1
TiCl2 (L)
2.45 2.41 2.26 2.54±2.56 2.43 2.35 2.48
TiCl3 (D3h )
TiCl4 (T)
TiCl4 (O)
2.42±2.43 2.22 2.46 2.41±2.42
2.20 2.19 ± 3.15±3.20
2.36±2.38 2.20±2.21 2.42±2.44
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environment and obtained a negative heat of adsorption (endothermic). On the (1 1 0) face, we have optimised a precursor state where the distortion was weak the Mg±Cl distances are long, and the heat of adsorption is small, 3.15±3.20 A, 4.6 kcal/mol. This adsorption mode is not very favourable. To approach closer to the surface, TiCl4 has to adapt to the local symmetry of the adsorption site and the cost of distortion reduces the heat of adsorption. From X-ray measurements, TiCl4 is supposed to distort toward an octahedral environment [12], being bound to MgCl2 via a double Cl bridge (a formation of two Ti±Cl bonds). For the adsorption on the 1 0 0 surface, Colbourn et al. [30] have shown that the doubly bound structure (incomplete octahedron with one Ti±Cl bond and one Mg±Cl bond) was not stable while the triply bound species (two Ti±Cl and one Mg±Cl bonds) led to a binding energy of 25.7 kcal/mol. Similarly, Corradini et al. [1] have proposed a ®ve-fold titanium atom (one l3 -Cl, two l2 -Cl and two terminal Cls). From EXAFS results [11], it has been suggested that a distortion to the square planar is produced. In our calculations for the (1 0 0) face when the constraints were released, we have obtained the adsorption mode shown in Fig. 4 where the titanium atom is at the centre of a trigonal bipyramid (the main axis of the bipyramid is parallel to the surface plane) that is close to the model proposed by Corradini. The distortion of TiCl4 is indeed signi®cant. This adsorption mode is similar to those obtained for TiCl2 and TiCl3 ; three bonds are built and the dierence concerns the number of terminal ligands that are not directly involved in the adsorption process. However, despite this resemblance, the adsorption is quasi-athermic since the cost for the distortion is large for the tetracoordinated Ti. The Ti±Cl distance (that involving the l3 -Cl atom coming from compared with the lattice) is very long, 2.84 A, those for the adsorption of TiCl2 and TiCl3 (see Table 3); the increase of the number of ligands induces a repulsion between the chlorine atoms and this reduces the heat of adsorption. On the (1 1 0) face and for a smaller coverage, we obtained a much larger heat of adsorption (Table 2 and Fig. 5). The titanium atom is hexa-
coordinated, in a nearly octahedral environment as also proposed by Jones and Oldman [12] (except that two Cl ligands from TiCl4 also bind to Mg) and by Corradini; we will later on refer to this model as model O. It is bound to two Cl from the lattice (l3 -Cl) that belongs to the same (1 1 0) layer; two Cls from TiCl4 bind to the Mg atoms (l2 -Cl) while the two others remain in terminal position. We conclude that addition of TiCl4 is exothermic only when the titanium atom has an octahedral environment as suggested by Colburn [30]. The formation of a ®ve-coordinated titanium complex leading to an octahedral environment with a vacancy [35] is less favourable since it builds only one Ti±Cl bond instead of two. From Table 2, it seems that TiCl4 can only be easily adsorbed on the (1 1 0) face of MgCl2 . 4.4. The adsorption of (TiCl2 )2 and Ti2 Cl3 CH3 First, we have searched for an adsorption mode on the 1 0 0 surface resulting from the formation of three bonds, two Ti±Cl bonds and one Mg±Cl bond (connecting the magnesium atom from the surface to the bridging atom of the dimer). MgCl2 was not relaxed in this preliminary study. Such systems remain in high spin states (quintet). The heat of adsorption is 14.6 kcal/mol. The coupling of the adsorbed TiCl2 species on the 1 0 0 surface represents a gain of 16.3 kcal/mol, indicating that the monomeric complexes should not remain separate. The substitution of the other bridging ligand of the dimer by a methyl group leads to the adsorbed Ti2 Cl3 CH3 complex. The methyl group remains bridging as found in Ref. [18]. The heats of adsorption for these two complexes are the same (13.1 kcal/mol for the later). Thus, the substitution by CH3 has little eect on the bonding in agreement with Lin and Catlow [20]. Next, we have moved the terminal Cl atoms to form two more Mg±Cl bonds, the adsorption mode involving ®ve bonds (see Fig. 6, right hand side) and we allowed the relaxation of the slab. After a second trial, we obtained the best mode, the heat of adsorption raises to 45.1 kcal/mol (Table 5). The ®ve atoms of the dimer that bind to MgCl2 are coplanar and form a W frame; the last one is out of the plane. Contrary to the impression
C. Martinsky et al. / Surface Science 490 (2001) 237±250
245
Fig. 6. The (1 0 0) face with dimeric complexes. Above three structures for (TiCl2 )2 ; below (TiCl3 )2 and (TiCl4 )2 .
from Fig. 6, the Ti atoms and the Cl atoms bind to atoms that pertains to dierent MgCl2 frameworks. This is apparent in Figs. 7 and 8. In the ®rst optimisation process, only one new bond was made (see Fig. 6, middle); the heat of adsorption is slightly inferior, 43.0 kcal/mol. On the (1 1 0) surface, we have searched for an adsorption structure involving the formation of four bonds, two Ti±Cl bonds and three Mg±Cl bonds (modes O in Fig. 9). Starting by mode O1 , the optimisation led to the mode O2 where Ti2 is three coordinated. This mode involves the same number of bonds than O1 ; indeed, with respect to O1 , for Ti2 the coordination increases from 2 to 3 while, for Ti1 , it decreases from 6 to 5. This represents a better balance between the two titanium atoms. The heat of adsorption is 57 kcal/mol. Thus, it is concluded that, despite the good ®t between Table 5 Heat of adsorption in kcal/mol for the best mode of the TiCln dimeric complexes 100 (TiCl2 2 (TiCl3 2 (TiCl4 2
110
dimer
mono
dimer
mono
45.1 22.8 17.2
2.5 17.8 endo
57.0 59.7a decomposition
23.3 35.2 69.9
For an indicative comparison, the heat of adsorption of two monomeric species plus that for the dissociation of the dimers is given on the even columns. a In the case of (TiCl3 )2 the best structure on the 1 1 0 surface is not a dimer but an extended polymer.
Fig. 7. A perspective view of the (1 0 0) face showing the connections of the (TiCl2 )2 to MgCl2 . In Fig. 6 (above the right hand side) the atoms labelled 1 (in front) and 2 (behind) are superposed. The Ti from the dimer are bound to the chlorine atoms 1 whereas the Cls are bound to the magnesium atoms 2. A top view is displayed in Fig. 8.
the dimer and the (1 0 0) surface, the (1 1 0) surface is more reactive than the (1 0 0) face. 4.5. The adsorption of (TiCl3 )2 and (TiCl3 )n The adsorption modes on the (1 1 0) surface are displayed in Fig. 9. We started from the best geometry for (TiCl3 )2 from Ref. [18], ClTi(l2 -Cl)3 TiCl2 with three bridging Cls, and approached the dimer with the Ti±Ti axis normal to the surface, the TiCl2 edge being oriented toward the surface magnesium site. The binding is an extension of the mode T (as de®ned in Section 4.3) which was slightly endothermic for TiCl4 . Let us however note that the
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C. Martinsky et al. / Surface Science 490 (2001) 237±250
Fig. 8. A top view of the (1 0 0) face showing the connections of the (TiCl2 )2 to MgCl2 . The chlorine bridging atom that is not bound to Mg does not belong to the plane that contains all the other atoms from the dimer. This adsorption mode, though with some similarities with that proposed by Lin and Catlow presents a dierent topology.
resemblance is geometrical and not electronic; in the present case, the titanium atom is a Ti(III) which is supposed to be more reactive than a Ti(IV). The optimised Mg±Cl bond distances are vs. 3.15±3.20 shorter than for TiCl4 (2.59±2.63 A A) and the adsorption energy is exothermic by
8.2 kcal/mol. The ClTi(l2 -Cl)2 (l2 -CH3 )TiCl2 complex behaves similarly with a heat of adsorption in the same range, 11.9 kcal/mol. Since the dimeric complexes optimised with the VASP code have two bridging ligands (Section 4), the structure of adsorption of the Cl2 Ti(l2 -Cl)2 TiCl2 isomer with two bridging Cl atoms is also a little better than that with three bridging Cls. Next, we investigated another perpendicular binding, connecting the cluster to the surface with the mode O (see Fig. 9) that allows the formation of four bonds. This is a better adsorption mode; the heat of adsorption is 48.8 kcal/mol. No model for an epitaxial adsorption parallel to the surface have been proposed to our knowledge. Using a double unit cell for the a-MgCl2 phase, we optimised a structure (mode F from Figs. 9 and 10) for which we obtained the largest heat of adsorption, 59.7 kcal/mol. This structure is an extended one-dimensional periodic structure and Fig. 9 only shows the pro®le of one polymer. TiCl3 growth leads to solids an not to dimers; the epitaxy as shown in Fig. 10 is very favourable. By analogy, it is not surprising to ®nd a periodic structure at high coverage. Although the structure that we have
Fig. 9. The adsorption on (1 1 0) surface. Top, left hand side: Of (TiCl3 )n polymer. Top, right hand side: Of the (TiCl2 )2 dimeric complex (model O). Bottom: Of the (TiCl3 )2 dimeric complexes.
C. Martinsky et al. / Surface Science 490 (2001) 237±250
Fig. 10. Top view of the adsorption of (TiCl3 )n on the 1 1 0 surface of the a-MgCl2 crystal with mode F. The black circles are Ti atoms and the white circles are Cl atoms.
calculated is ferromagnetic, since a part of TiCl3 is silent for the EPR signal, we believe that the system of lowest energy should be antiferromagnetic. For the adsorption on the 1 0 0 surface, Corradini proposed a model where the Ti±Ti axis is parallel to the surface plane; thus, ®ve bonds can be formed (two Ti±Cl and three Mg±Cl) (see Fig. 5). According to the charges calculated on cluster models [37], this dimer on the (1 0 0) face should be more active than that on the (1 1 0) face: the titanium atoms are more electrophilic (sponge eect of the support). We have found a heat of adsorption of only 22.8 kcal/mol for the 1 0 0 face (Table 5). 4.6. The adsorption of (TiCl4 )2 The dierent models for the adsorption are a parallel mode on the 1 0 0 face (Fig. 9) and a per-
247
pendicular mode for the 1 1 0 face. For the former, ®ve bonds are made (three Mg±Cl and two TiCl) as shown in Fig. 6; this structure matches the EXAFS data [11] assuming an asymmetry: Cl1 and Cl3 are not equally bound to the titanium atoms but each one is closer to one titanium centre. We have found a slight asymmetry which is not larger than those for the other dimer structures and comparable with that of the dimer in the gas is close to that phase. The Ti±Ti distance, 3.90 A, obtained by Potapov [11]. When adsorbed, this remain octahedral and there is no cost for such distortion as in the adsorption of the monomeric complex. The heat of adsorption is 11.3 eV without relaxation and 17.2 eV when relaxation is allowed. An ELF analysis of (TiCl4 )2 in the geometry of the adsorption [38] con®rms the octahedral environment around the titanium centres. For the (1 1 0) surface, the adsorption mode that we have investigated is an extension of the model O by adding two Cl ligands to the atom Ti2 from (TiCl3 )2 (see Fig. 9). It led to a decomposition of the dimer in two fragments, a TiCl3 complex adsorbed on the surface and a TiCl5 that is desorbed. Since TiCl5 easily decomposes to give TiCl4 1=2Cl2 , this process could generate reduced titanium atom at the surface. In any cases, on the (1 1 0) surface, the cleavage of the dimer leading to two adsorbed TiCl4 monomers is thermodynamically the most favourable result (exothermic by 69.9 kcal/mol). 4.7. Interatomic distances From Fourier transformed EXAFS data [11], four dierent interatomic distances emerge. Without any phase correction, they correspond to 1.7, After correction, the set of 2.5, 2.9 and 3.5 A. ``experimental distances'' are, 2.1, 3.09, 3.5 and 4 The best match for these distances was obtained A. for (TiCl4 )2 /1 0 0 indicating that this species is the most abundant on the support. Our results for the various titanium chlorides are fully optimised and justify several proposed topologies. Some of the assumptions on the numeric values used in Ref. [11] have nevertheless to assumed for all the be re®ned. The value of 2.1 A
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C. Martinsky et al. / Surface Science 490 (2001) 237±250
Ti±Cl distances from the ®rst coordination sphere is too short especially when Cl is bridging l2 -Cl. Terminal Cls and bridging l2 -Cl should be resolved into two sets of distances, a ®rst range of for the terminal bonds (shorter for the 2.18±2.27 A saturated monomeric species as already noticed [19]) and a second one for the bridging l2 -Cls at (Table 6). The value assumed for 2.51±2.59 A is close to our result; let the bridging l3 -Cl, 2.56 A, us note that it could perhaps not be easily distinguished from the bridging l2 -Cl values. The Ti±Cl involving the Cl from the lattice are slightly longer, The Mg±Cl distance, with the ex2.53±2.82 A. ception of TiCl4 (T) with a very long distance, close to the value remain in the range 2.55±2.66 A 2.56 from Ref. [11]. The Ti±Mg distances that we have obtained (see Table 7) vary from 3.38 to 3.99 they are often longer than published in Ref. A; [11]. As has been noticed, the dimers do not reach perfect symmetry.
Table 6 for the adsorption of dimeric complexes (see laDistances (A) bels in Fig. 6)
TiCl1 TiCl2 TiCl3 TiCl4;6 TiCl5 TiCllattice MgCl
TiCl2 2 / 100
TiCl2 2 / 100
TiCl3 2n / 110
TiCl4 2 / 100
2.41 2.37±2.39 2.43±2.44 ±
2.38 2.32±2.34 2.43±2.44 ±
2.58±2.59 2.27 2.45±2.46 2.18±2.19
2.40±2.41 2.53± 2.56±2.66
2.57±2.62 2.70± 2.69±2.86
2.39 2.51±2.53 2.38 2.20 2.43±2.44 2.53±2.54 2.44± 2.49±2.50
2.82 2.64
5. Mg adsorption on the 0 0 0 1 surface of -MgCl2 The lack of reactivity of the 0 0 0 1 surface has been attributed to the fact that metallic centres were not accessible; a possibility to make it reactive would be to add Mg atoms. However, the experimental attempts to ®x Mg atoms on the surface failed. The Mg-containing MgCl2 faces are thermodynamically unstable [39]. We have investigated the addition of a single atom on the slab de®ned in Section 3. When optimised, the mag in the middle of nesium atom is located at 5.5 A the space between successive slabs and the interaction is repulsive. It is similar for molecular calculations, Mg does not bind to a MgCl2 molecule. This is because the magnesium atom has a 3s2 con®guration and is poorly reactive unless being oxidised. This is similar to Be2 whose weak binding results from hybridisation, the dimer being sensitive to correlation eects and basis-set size [40]. Metallic Mg is eective in reducing the TiCl4 complex [13]. Stable ®lms could be obtained by TiCl4 and Mg codeposition on MgCl2 [39]. Contrary to MgCl2 that cannot be reduced, TiCl4 can be converted into TiCl2 allowing the oxidation of Mg. However, this conversion is not thermodynamically favourable if the interaction between MgCl2 and TiCl2 is not involved since the Ti±Cl bonds are stronger than the Mg±Cl bonds. Mg TiCl4 ! MgCl2 TiCl2 DH 6:8 kcal=mol Mg 2TiCl4 ! MgCl2 2TiCl3 DH 10:2 kcal=mol
Table 7 ®rst lines: our results; second lines Ref. Ti±Mg distances (A) [11] TiCl2 /1 0 0 TiCl3 /1 0 0 TiCl4 /1 0 0 TiCl3 /1 1 0 (B) TiCl2 /1 1 0 (L) TiCl3 /1 1 0 (C) TiCl4 /1 0 0 (T) TiCl4 /1 1 0 (O) (TiCl4 )2 /1 0 0 (C)
3.38 3.40±3.44 3.87±3.90 3.72 3.58 3.62±3.98 3.64 3.86 3.79±3.91
3.22±3.63
If this interaction is taken into account the reaction becomes favourable because the formation of bimetallic complexes with MgCl2 is strongly exothermic and the reduction of the titanium atom occurs without breaking bonds [18]. Mg TiCl4 ! ClMg l2
2.89±3.12±3.63 3.63 3.56±4.10
DH
Cl3 Ti
50:3 kcal=mol
The bimetallic complex is in a triplet state.
C. Martinsky et al. / Surface Science 490 (2001) 237±250
6. Conclusions Results from periodic calculations on the adsorption of TiCln complexes and related bimetallic complexes on MgCl2 essentially validate the structures already found by means of molecular calculations [18,19,35] or postulated as models inspired by experiments [1,11]. This study also propose new adsorption modes: the extended (TiCl3 )2n structure and the dimer O for (TiCl2 )2 on the 1 1 0 surface. Table 5 summarises our results for the adsorption of monomeric and dimeric species on the two most reactive surfaces. All the values refer to the dimer in the gas phase and should then be comparable. Note however that the adsorption energies for each system have been calculated independently at dierent coverage according to the best aordable model for each case; they could be slightly dierent if recalculated at the same coverage within the same model. Trends nevertheless emerge. The reduced forms, TiCl2 and TiCl3 , are adsorbed as dimers while (TiCl4 )2 decomposes in monomers. TiCl4 is preferably adsorbed on the (1 1 0) face where the Ti atom is hexacoordinated (model O). Both Ti±Cl and Mg±Cl bonds contribute to the adsorption; the best adsorption mode correspond to the maximum of bonds that can be formed. Dimers are preferentially adsorbed on the (1 1 0) face. The Ti atoms from (TiCl2 )2 and one of them from (TiCl3 )2n are pentavalent; this is a good starting point to have a high stereospeci®city. The adsorption mode O for (TiCl3 )2 on (1 1 0) is also favourable but less than with the ¯at mode, F; in this mode, the closest Ti atom to the surface, Ti1 , is hexacoordinated allowing a strong binding, while the other Ti atom, Ti2 , is only tetravalent which may decrease the stereospeci®city. On the tests that we have done, the alkyl group does not modify the adsorption modes. Finally, we should remark that this study describes the most stable species and we are conscious that the most abundant species may not be the most reactive. Nevertheless, the search for the catalyst structure remains a necessary step for the search of the active sites. The hexagonal surface of MgCl2 is not reactive and the deposition of Mg atoms could not activate the surface since MgCl2 is not reducible; on the
249
other hand, the addition of metallic magnesium can reduce TiCl4 species.
Acknowledgements This work has been accomplished in the framework of the GDR ``Dynamique Moleculaire Quantique Appliquee a la catalyse''; the ®nancial support of the French Ministry of Education, Technology and Research, the Spanish CICyt PB98-1216-CO2-02 and partially the Catalan 1999SCR00182 projects are gratefully acknowledged. C. Martinsky acknowledges the ERB FMGE CT95 0062 European TMR program held in CESCA/CEPBA supercomputer centres for supporting his stay in Tarragona. We also thank CCR and CNRS-IDRIS for computing facilities. C. Minot is grateful to G. Somorjai, M. Van Hove, J. Roberts, E. Magni and A. Markovits for stimulating discussions.
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