Key Interactions in Heterogeneous Ziegler−Natta Catalytic Systems

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J. Phys. Chem. C 2007, 111, 4412-4419

Key Interactions in Heterogeneous Ziegler-Natta Catalytic Systems: Structure and Energetics of TiCl4-Lewis Base Complexes Luigi Cavallo,*,† Silvia Del Piero,‡ Jean-Marie Duce´ re´ ,† Rosalisa Fedele,‡ Andrea Melchior,‡ Giampiero Morini,§ Fabrizio Piemontesi,§ and Marilena Tolazzi*,‡ Dipartimento di Chimica, UniVersity of Salerno, V. Ponte don Melillo, Fisciano (SA), I-84084, Italy, Dipartimento di Scienze e Tecnologie Chimiche, UniVersity of Udine, V. del Cotonificio 108, Udine, I-33100, Italy, and Basell Poliolefine Italia, Centro Ricerche G. Natta, p. Donegani 12, Ferrara, I-44100, Italy ReceiVed: NoVember 24, 2006; In Final Form: January 10, 2007

Extensive calorimetric investigations on the interaction of TiCl4 with some Lewis bases are presented. Some of the bases were chosen for their industrial relevance in heterogeneous Ziegler-Natta polymerization of propene (ethyl benzoate, L2, diisobutyl phthalate, L3, (2R,3S)-diethyl 2,3-diisopropylsuccinate, L6, (2S,3S)diethyl 2,3-diisopropylsuccinate, L7, and 9,9-bis(methoxymethyl)-9H-fluorene, L13) while other bases were chosen as probe molecules to explore the electronic and steric effects on the complexation energy (ethyl acetate, L1, diethyl phthalate, L4, diethyl succinate, L5, tetrahydrofuran, L8, dimethoxyethane, L9, dimethoxypropane, L10, dimethoxybutane, L11, and 3,3-bis(methoxymethyl)-2,6-dimethylheptane, L12). 1,1,2,2,-Tetrachloroethane was selected as the solvent for its low donating properties, which allows the focus to be on the metal-donor interaction. The calorimetric data are discussed and compared with the efficiency of the derived catalysts. Further understanding is obtained by comparison of the experimental results with theoretical calculations based on density functional theory (DFT). The performance of different computational approaches was validated by comparison of the calculated and experimental complexation energies.

Introduction Supported MgCl2/TiCl4 Ziegler-Natta catalysts of the latest generations allow for the morphological control of the polymer particles and require low amounts of titanium and aluminum compounds, ensuring at the same time an easy control of the polymerization. Unfortunately, they are multisite catalysts, which makes their design extremely complicated. Nevertheless, the catalytic systems currently used have reached amazing performances, which allows for the design of versatile, clean, and economical industrial processes.1 The presence of Lewis bases is essential to improve the stereoselectivity in polypropene synthesis using supported MgCl2/TiCl4 Ziegler-Natta catalysts: they can be added in catalyst preparation (internal donors) or during polymerization (external donors). With the internal-external donors pair, it is possible to modulate the performance of the catalyst (activity, stereoselectivity) and to fine-tune the characteristics of the resulting polymer (molecular mass, molecular mass distribution, microtacticity, intra- and inter-comonomer distribution). Among the internal bases, ethylbenzoate2 and phthalic esters3 are always used in combination with an external donor and are the systems most widely studied in literature. 4 Subsequent studies led to the discovery of new Lewis bases, 1,3-diethers, that result in stereoselective catalytic systems when used in the absence of external bases.5 Recently, a new class of donors has been proposed,6 2,3-disubstitued succinates, which allows for the * To whom correspondence should be [email protected] and [email protected]. † University of Salerno. ‡ University of Udine. § Basell Poliolefine Italia.

addressed.

E-mails:

synthesis of highly stereoregular polymers with quite broad molecular mass distributions. The balance between MgCl2-TiCl4, MgCl2-Lewis base, and TiCl4-Lewis base interactions can affect both the composition and the performance of the catalyst: several efforts have been attempted to characterize them. For instance, the MgCl2-TiCl4 system has been investigated by several authors. Observations of MgCl2 microcrystals by optical microscopy7 and by HRTEM8 confirmed the copresence of (100) and (110) lateral cuts.9 Raman spectra of comilled MgCl2-TiCl4 samples suggested the formation of stable complexes of TiCl4 only on the (110) side surface.10 In line with these results, theoretical studies indicated that TiCl4 adsorbs on both the (100) and (110) cuts of MgCl2. However, while interaction between TiCl4 and the (110) lateral cut is rather strong, these studies suggested that interaction between TiCl4 and the (100) cut of MgCl2 is extremely weak11 and that TiCl4 desorption is very likely to occur.11a,b The MgCl2-Lewis base interaction (1,3-diethers in particular) has also been investigated. Although a semiempirical approach was used, it was concluded that 1,3-diethers coordinate strongly to both the (100) and (110) MgCl2 lateral cuts, even if coordination on the (110) cut and is preferred.12 Models able to explain the effect of the Lewis bases on the stereospecificity of propene polymerization have also been proposed.11,13 These models range from a “simple” poisoning of aspecific sites13a to direct chemical and sterical modification of the surroundings of isospecific sites with a direct control on monomer insertion.11a,13e,f However, the exact mechanism through which Lewis bases operate and the details of the various key equilibria present in Ziegler-Natta catalytic systems are still unclear. For this reason, in the wake of the basic studies concerned with the MgCl2TiCl4 and MgCl2-Lewis base interaction, we focus here on the

10.1021/jp0678204 CCC: $37.00 © 2007 American Chemical Society Published on Web 02/27/2007

Heterogeneous Ziegler-Natta Catalytic Systems interaction of TiCl4 with some Lewis bases, which represent examples of industrial relevant donors such as ethyl benzoate (L2), diisobutyl phthalate (L3), (2R,3S)-diethyl 2,3-diisopropylsuccinate (L6), (2S,3S)-diethyl 2,3-diisopropylsuccinate (L7), and 9,9-bis(methoxymethyl)-9H-fluorene (L13). Other donors, such as ethyl acetate (L1), diethyl phthalate (L4), diethyl succinate (L5), tetrahydrofuran (L8), dimethoxyethane (L9), dimethoxypropane (L10), dimethoxybutane (L11), and 3,3-bis(methoxymethyl)-2,6-dimethylheptane (L12), have been investigated in order to understand the influence of (i) different substituent groups, (ii) ring sizes, (iii) steric effects, and (iv) isomerism on the energetics of the complexation reaction. Thanks to the absence of the MgCl2 support, whose presence inevitably introduces enormous complications due to its heterogeneous nature, the simple TiCl4-Lewis base systems will allow the characterization of systems with a well-defined chemistry. To this end, a combined experimental and theoretical approach has been used. On the experimental side, the enthalpy functions associated with the reaction between TiCl4 and the ligands have been obtained by calorimetric titration in solution. Whenever possible, the stability constants for complex formation, βj, were obtained from minimization of the calorimetric data. FT-IR spectra were recorded to gain information on the bonding mode in solution. 1,1,2,2,-Tetrachloroethane (TCE) was chosen as the solvent for its low donating properties,14 which allows the focus to be on the metal-donor interaction and since it provides good solubility for all the compounds considered. On the theoretical side, some of the most popular computational approaches have been tested. In addition to insights on the energetics and structure of the TiCl4-Lewis base complexes, a critical comparison between the experimental and the theoretical results offers the invaluable opportunity to test which computational approach performs better in describing this kind of system. This aspect is quite important considering that computational chemistry has been and will be used extensively to describe systems whose characterization presents formidable challenges. Experimental Methods General Remarks. TiCl4 strongly fumes in moist air and is hydrolyzed by water. Extreme care was taken to obtain and maintain the lowest content of water in the systems by working under an inert atmosphere in a glovebox. The solvent was dried and stored over 4 Å molecular sieves. All the experiments were carried out at 25 °C. Chemicals. Ligand solutions were supplied by Basell, Centro Ricerche G. Natta, Ferrara, Italy. Their purities (>99%) were checked by GC mass spectrometry and 1H NMR measurements. TiCl4 dilute solutions were prepared from Aldrich ReagentPlus, 99.9%, using anhydrous TCE (Fluka, purum of >98%). All standard solutions were prepared and stored in a MB Braun 150 glovebox under a controlled atmosphere containing less than 1 ppm of water. The water content in the solutions, typically 5-7 ppm, was determined by a Metrohm 684 KF coulometer. Titration Calorimetry. To measure the heats of reaction, a Tronac model 87-558 precision calorimeter equipped with a 25 mL titration vessel was employed. The cover of the titration vessel and its connection to the calorimeter were modified to ensure that the reactions proceeded in an inert atmosphere. Both the vessel and the piston burette were filled and joined together inside the glovebox, taken out, and connected to the calorimeter for measurements. Periodic checks of the accuracy and reproducibility of the apparatus were performed to determine an average heat of neutralization of tris(hydroxymethyl)methy-

J. Phys. Chem. C, Vol. 111, No. 11, 2007 4413 lamine (THAM) with 0.1 mol‚dm-3 HCl. The experimental value of the heat of neutralization of THAM was found to be ∆H° ) -47.59 kJ‚mol-1, in good agreement with the accepted value of -47.53 ( 0.13 kJ‚mol-1.15 The calorimetric titrations were performed at 298.00 ( 0.02 K by adding at a constant rate known volumes of ligand solutions (200 < C°L < 400 mmol‚dm-3) with a burette to 20 mL of TiCl4 solution (5.0 < C°TiCl4 < 20.0 mmol‚dm-3) in the reaction vessel. To achieve better statistics in the calculation of the thermodynamic data, three to four titration runs with different initial metal concentrations, C°TiCl4, were performed for each system. For each titration run, n experimental values of the total heat produced in the reaction vessel, Qex,j, j ) 1-n, were calculated as a function of the added titrant. The Qex,j values were corrected only for the heat of dilution of the titrant, Qdil,j, which was determined separately. The net reaction heat at the jth point, Qr,j, was obtained as Qr,j ) Qex,j - Qdil,j. The total heat per mole of metal ion, ∆hv, was calculated as ∆hv ) Qr,j/nM, where nM is the number of moles of metal in the calorimeter vessel.16 When only mononuclear metal-ligand complexes are formed, the mathematical relationship between the experimental data, the thermodynamic parameters, and ∆hv is given in eq 1: n

∆hv )

∑ p)1

m

qp

CTiCl4Vp

)

βj[L]jp∆H°βj ∑ j)1 m

1+

(1)

βj[L]jp ∑ j)1

where n is the number of experimental measurements, qp is the pth experimental heat change, CTiCl4 is the metal concentration, Vp is the volume of the test solution, m the maximum number of ligands bound to the metal ion in the complexes MLj, βj and ∆H°βj are the thermodynamic parameters for the formation of the jth complex, and [L]p is the concentration of the free donor at the pth point. From eq 1 it is clear that the value of ∆hv at CL/CTiCl4 ) j corresponds to ∆H°βj, if the βj value is large enough. The constants and enthalpy changes of the identified complexes were calculated with the Hyp∆H software.17 FT-IR Spectroscopy. The FT-IR spectra were recorded covering the wavenumber range of 800-4000 cm-1 under dryair purge at 25 ( 1 °C on a Bruker Vector 22 FT-IR spectrometer with a 2 cm-1 resolution and 256 scans. A cell with BaF2 windows (thickness of 25 µm) was used. The cell was filled with the sample solutions in the glovebox. The spectrum of TCE was kept as background. DFT Calculations. The calculations were performed with the TURBOMOLE 5.8 package.18 The GGA functional of Perdew, Burke, and Ernzerhof (PBE) was applied.19 The triple-ζ basis set augmented with two polarization shells on each atom and augmented with a s-function on C and O and a d-function on Ti, referred to as def2-TZVPP in TURBOMOLE, was used.20 To speed up the calculations the RI-J approximations were adopted.21 The auxiliary basis set corresponding to def2-TZVPP was used. Solvation in TCE was modeled using Klamt’s conductor-like solvation model (COSMO)22 with a dielectric constant of 8.42 and a solvent radius of 2.79 Å. The cavity was defined using Klamt’s optimized radii for H, C, O, and Cl and a value of 2.223 for Ti. As TCE is a low polarity solvent, nonelectrostatic cavitation, dispersion, and repulsion terms are expected to play a non-negligible role. To evaluate these terms, the Gaussian 03 program was run. Finally, all the binding energies were corrected of the basis set superposition error

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TABLE 1: Overall Stability Constants and Corresponding Thermodynamic Parameters for Formation of TiCl4-Ligand Complexes (T ) 298 K)b

a

Overall formation constants for equilibrium 2. b The error limits represent 3σ.

(BSSE) using Boys and Bernardi’s counterpoise method.23 Test calculations were done using the hybrid B3LYP functional24 and the hybrid version of the TPSS meta-GGA functional (TPSSh)25 in combination with the def2-TZVPP basis set and with the second-order Møller-Plesset perturbation method26 in combination with the quadruple-ζ QZVPP basis set,27 since postHartree-Fock methods are more sensitive to the basis set size than DFT ones. The geometries were the ones optimized at the PBE/def2-TZVPP level and were not further reoptimized. The BSSE for B3LYP and TPSSh were assumed to be the same as the PBE ones, as the differences are expected to be small (within 1-2 kJ‚mol-1), while the BSSE of the MP2 calculations was explicitly calculated. Again, solvent effects were introduced using COSMO, and in the case of the MP2 calculations, COSMO was only introduced at the Hartree-Fock level, the perturbation step using the solvated HF orbitals.28 Finally, in the case of the 2,3 i-Pr substituted succinates L6 and L7, calculations were performed on the simpler 2,3 Me substituted

succinates L6a and L7a to avoid the complications of local minima associated with different conformations of the i-Pr groups. Results and Discussion Calorimetry. The enthalpy and, when possible, entropy and stability constants of complexation were calculated from the reaction heats of the TiCl4-donor interaction. The results are summarized in Table 1. Several combinations of species with different stoichiometries were considered to model these systems. The best results from the data refinements were obtained when only two mononuclear complexes, 1:1 and in some cases 1:2, were taken into account. As representative examples, in Figures 1 and 2 we report some of the experimental thermograms (for esters and ethers, respectively) as ∆hv vs the ligand to metal ratio, Rc ) CL/CTiCl4. The slope change at Rc ) 1 for the TiCl4-L1 system (see Figure 1) indicates formation

Heterogeneous Ziegler-Natta Catalytic Systems

J. Phys. Chem. C, Vol. 111, No. 11, 2007 4415 The overall complexation reactions taken into account are represented by equilibrium 2:

TiCl4 + jL h TiCl4(L)j

Figure 1. Total molar enthalpy changes per mole of TiCl4, ∆hV, as a function of the ligand to metal ratio Rc ) CL/CTiCl4: (a) TiCl4-L1 system, (O) C°TiCl4 ) 19 mmol‚dm-3, (b) C°TiCl4 ) 5 mmol‚dm-3; (b) TiCl4-L2 system, (]) C°TiCl4) 19 mmol‚dm-3, ([) C°TiCl4 ) 5 mmol‚dm-3; (c) TiCl4-L3 system, (9) C°TiCl4 ) 19 mmol‚dm-3; (d) TiCl4-L4 system, (3) C°TiCl4 ) 19 mmol‚dm-3.

Figure 2. Total molar enthalpy changes per mole of TiCl4, ∆hv, as a function of the ligand to metal ratio Rc ) CL/CTiCl4: (a) TiCl4-L8 system, C°TiCl4 ) 19 mmol‚dm-3 (0) and C°TiCl4 ) 5 mmol‚dm-3 (9); (b) TiCl4-L9 system (O); (c) TiCl4-L10 system (4); (d) TiCl4-L11 system (×) all with C°TiCl4 ) 19 mmol‚dm-3.

of a first complex of high stability, whereas separation of the plots at Rc > 1, corresponding to different C°TiCl4 indicates formation of additional species of lower stability. In the case of the TiCl4-L2 system, the shape of the curves clearly suggests formation of weak complexes (see Figure 1). In these cases both the formation constants and the enthalpy of complexation can be evaluated.29 For the TiCl4-L3 and TiCl4-L4 systems, ∆hv increases linearly up to Rc ) 1 (see Figure 1). This suggests formation of a strong 1:1 complex. For Rc > 1, no heat is evolved, proving that no other species are formed beyond the 1:1 complex. In this case, it is not possible to calculate the formation constants of the TiCl4-L3 and TiCl4-L4 complexes. Nevertheless, the enthalpy of complexation can be accurately determined and the lower limit of K1 can be estimated to be g105.5. The thermograms relative to the succinates are very similar, also in shape, to those for phthalates and therefore not reported here. Moving to ethers, the curvature at Rc > 1 in the plot of the TiCl4-L8 system (see Figure 2) suggests formation of further complexes beyond the 1:1 complex. This is not true for the other reported ethers. The qualitative behavior of the TiCl4-L12 and TiCl4-L13 systems (not plotted here) is very similar to that of TiCl4-L10. The best fitting curves of the calorimetric titrations were calculated from βj and ∆H°βj in Table 1 and reported as full lines in Figures 1 and 2. The fit between the experimental and the calculated data is good for all the systems considered.

j ) 1-2

(2)

A common thermodynamic feature of all systems emerges from the analysis of Figures 1 and 2 and from the results reported in Table 1. The complexation of TiCl4 with the ligands is always strongly exothermic, while the entropy term, when known, is negative and opposes complex formation. The negative enthalpy values found here are typical of reactions involving complexation in aprotic solvents,30 which indicate formation of strong coordinative bonds with a marked covalent character and weak solvation of the species implied in complex formation.31 TiCl4-Esters Systems. Two successive mononuclear complexes are formed by L1 and L2. Both the X-ray structures of (TiCl4‚CH3COOC2H5)2 (dimer) and TiCl4‚2PhCOOEt (monomer) display octahedral coordination around the Ti center, with the esters coordinated to the Ti via the carbonyl oxygen atoms.32 Considering that in the two X-ray structures the esters are cis coordinated and that a cis geometry is also favored by the DFT calculations reported in Table 4, it is reasonable to conclude that the esters are also cis coordinated in solution. The calorimetric data reported in Table 1 show that L1 interacts more strongly than L2 with the metal center, being that the enthalpy term is much more favorable and the entropy term is more unfavorable, due to the different group in position 2 to the ester function:33 it should be expected that the phenyl ring exerts +I and -R effects on the adjacent O-CdO group, thus decreasing the donor ability of the ligand. In addition, the steric hindrance of the phenyl ring should also contribute to lower the enthalpy gain. Furthermore, it can be noted that when more than one complex is formed, the increased stepwise entropy suggests that desolvation occurs predominantly in the first complexation step. The data for L3 and L4 indicate that both ligands act as bidentate via the two carbonyl groups, leading to an octahedrally coordinated Ti atom. This is suggested by the much higher stability and exothermicity and by the very unfavorable entropy term with respect to the first complex formed by the L1 and L2 monoesters. Further support is provided by the FT-IR data. The band at about 1720 cm-1, associated with the stretching of the CdO group in free L3 and L4, is red-shifted to 1658 and 1657 cm-1 when the ligand is bound to the titanium atom: at Rc ) CL3(or CL4)/CTiCl4 ) 0.88, the band of the free ligand disappears for both the L3 and the L4 systems, confirming that in solution complexation is achieved by chelation. The solution structure of the TiCl4-L3 and TiCl4-L4 complexes appears to be very similar to the structure of [o-C6H4(COO-i-Bu)2TiCl4]‚CH2Cl2 in the solid state.34 The +I effect exerted by the isobutyl groups in L3 as compared with the ethyl groups in L4 seems to favor only slightly the formation of the TiCl4-L3 complex, being that this effect is compensated by the higher steric hindrance of the isobutyl group. The data in Table 1 also show that for the TiCl4-succinate complexes, coordination in solution is realized with both carbonyl oxygens. Comparison of the L5, L6, and L7-based complexes allows insight into the role played by the isopropyl substituents and by the different stereoisomerism of the complexation mechanism. Coordination of the L7 rac-isomer on the Ti atom is favored relative to coordination of the L6 mesoisomer. This difference can be easily rationalized considering the DFT optimized structures reported in Figure 3. Chelation of the L6 meso-isomer results in very short distances and hence

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Figure 3. Selected geometries of TiCl4-ligand complexes calculated at the PBE/def2-TZVPP level.

increased steric repulsion between the isopropyl substituents. Differently, in the complex with the L7 rac-isomer, the two isopropyl groups are more distant, which results in a decreased steric repulsion. At this point, the higher stability constant associated with complexation of L7 relative to the unsubstituted L5 succinate can be easily ascribed to the +I effect of the isopropyl groups in L7. In Table 2 the enthalpy of complexation of the L3-L7 esters, together with some parameters used to assess the efficiency of polymerization when the L3-L7 esters are used as internal donors, are reported. These parameters are productivity and xylene-insoluble polymer fraction (XI) at 25 °C, which is a measure of the amount of isotactic polypropene produced. Although the complexation enthalpies span the small range of about 6 kJ‚mol-1 only, a clear trend emerges. The higher the ∆H°βj is, the higher the productivity and XI are: this correlation between catalyst efficiency and enthalpy of complexation indicates that higher affinities of the donors for TiCl4 should be taken as a requirement to build an effective ZieglerNatta supported catalyst. Additionally, higher affinity for TiCl4 could translate into a better interaction with the MgCl2 surface and, consequently, to a higher stabilization of lateral cuts of MgCl2 catalyst crystallites. Therefore, donors with more favorable complexation enthalpies are expected to increase the MgCl2 specific surface, thus increasing the number of titanium active sites and the catalyst productivity.35 On the other hand, the explanation of the parallel increase of catalyst isospecificity

TABLE 2: Enthalpy Values, -∆H°βj from Table 1, for Formation of TiCl4-Ester Complexes, Productivities, and XI (Liquid Monomer Polymerization, 70 °C, Silane as External Donor)

(increase of XI content) is more difficult as complex equilibria involving the external donor contribute to the catalyst isospecificity, and not surprisingly, contrasting hypotheses have been proposed to rationalize the role of the donors.36 Considering the donor-TiCl4 interaction only, our results would be consistent with the proposal that an internal donor enhances stereospeci-

Heterogeneous Ziegler-Natta Catalytic Systems ficity due to its coordination on a vacancy of the Ti active species.37 Alternatively, a better interaction between the internal donor and the MgCl2 surface could result in the formation of a greater number of Mg sites able to also bond to the external donor. Thus, the internal donor extracted by the Al-alkyl cocatalyst can be efficiently substituted by the external donor. TiCl4-Ether Systems. Coordination of two L8 molecules is highly exothermic, which is reasonable considering that the small L8 molecule can easily approach the metal center. The addition of a second donor molecule can be achieved without energy losses due to conformational rearrangement. As already observed for L1 and L2, also in this case the desolvation occurs mainly at the first step of complexation. Formation of a TiCl4(L8)2 complex in solution is consistent with the solid-state structure of [TiCl4(THF)2] crystals obtained by dropwise addition of THF to a TiCl4 solution.38 Comparison of the data for both complexation steps of L8 with those of monoesters clearly shows that the ether oxygen is a much better σ donor than the ester one. The data reported for complexation of the L9-L13 diethers, as compared with those for complexation of the L8 monoether, clearly indicate a chelating behavior for all the diethers. The size of the chelating ring plays an important role in controlling the affinity for the metal atom.39 The five-membered ring, formed upon complexation of L9, is less destabilized (with respect to L10 and L11) by steric repulsions with the bulky Cl atoms. As previously discussed, the smaller the ligand is the easier are the approach and coordination to the metal. Unfortunately, the lack of entropy data for L9 and L10 does not allow for a detailed comparison among these systems. The L10, L12, and L13 1,3-diethers form a six-membered ring upon chelation to Ti but bear different substituents in position 2. The influence of the substituents can be rationalized as follows: (i) The alkyl groups of L12 can sterically destabilize the complex but can also be responsible for a stabilizing +I effect. Complexation of L12 is favored relative to complexation of the unsubstituted L10 diether; therefore, the stabilizing electronic effect prevails., (ii) On the contrary, the aromatic substituent in L13 seems to exert a destabilizing influence. The structure rigidity and hindrance are likely responsible for the lower enthalpic contribution to complex formation. The higher affinity of L12 compared to L10 for TiCl4 can be again related to a higher affinity of L12 relative to L10 for MgCl2 also. This hypothesis is supported by semiempirical AM1 calculations, which indicated that coordination of L12 to the (110) lateral cut of MgCl2 is favored relative to coordination of L10.12 In that study, the increased bulkiness of the substituents on the 2 position of 1,3-diethers was shown to correspond to an increased preference for adsorption on the (110) rather than on the (100) lateral cut of MgCl2. It was then hypothesized that the high XI experimentally determined for 1,3-diethers with bulky substituents could be related to a selective coordination of these bulky diethers on the (110) lateral cut (poisoning effect).12 However, there is a growing body of experimental facts indicating that the donors can influence the stereoselectivity by direct interactions with the active Ti species and that, usually, bulkier donors result in higher stereospecificity. This also holds for substituted external donors such as alkoxysilanes.40 DFT Calculations. In order to gain additional insight on the structure of the complexes and to possibly validate a computational method that would allow predictions to be done for this class of compounds, density functional theory calculations were performed on complexes of TiCl4 with ligands representative of each category: L1, L4, L5, L8, and L9. In addition,

J. Phys. Chem. C, Vol. 111, No. 11, 2007 4417 TABLE 3: Experimental Enthalpy Values, -∆H°βj from Table 1, for Formation of TiCl4-Ligand Complexes and DFT Binding Energies, -∆EPBE, at the PBE/def2-TZVPP Level

The experimental -∆H°βj is for the i-Pr substituted L6 donor. b The experimental -∆H°βj is for the i-Pr substituted L7 donor.

a

calculations were also extended to the complexes formed with L6a, L7a, L10, and L11 to check if the experimentally observed small binding energy difference and the small dependence of the binding energy with the length of the chain were reproducible (Table 3). The crystal structures of complexes of TiCl4 with various diesters including the diethylorthophthalate (L4) and the cis1,2-diisobutylcyclohexanoate, similar to L5, L6(L6a), and L7 (L7a), have been reported.41 For the phthalate, a Ti-O bond length of 2.068 Å was reported that is slightly shorter than the value calculated here of 2.147 Å. In the case of the diisobutylcyclohexanoate, the experimental X-ray Ti-O distance is 2.094 Å, while values of 2.147 Å for L7a and of 2.159 Å for L5 are found here. Again the calculated bond lengths are slightly overestimated. The crystal structures of the cis and the trans isomers of the THF (L8) complexes have also been reported.38 The experimental Ti-O distances are 2.117 and 2.050 Å for the cis and the trans, respectively, while the calculated are 2.183 and 2.088 Å, still slightly longer than the crystallographic data. From these comparisons it can be concluded that the PBE/def2-TZVPP method consistently overestimates the Ti-O bond length by an amount of 0.05-0.10 Å, for both sp2 and sp3 hybridizations of the coordinating oxygen atom. As far as the energetics of complex formation is concerned, the calculated binding energies reported in Table 4 are systematically much lower than the experimental ∆H°βj. This behavior had already been observed in the case of complexes of TiCl4

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TABLE 4: Experimental Enthalpy Values, -∆H°βj from Table 1, for Formation of TiCl4-Ligand Complexes and Quantum Mechanics Binding Energies at the PBE/def2-TZVPP, B3LYP/def2-TZVPP, TPSSh/def2-TZVPP, and MP2/QZVPP Levels

with ammonia42 for which it had been found that the hybrid functional B3LYP used with the 6-311+G(3df,2p) basis set, which is similar to the def2-TZVPP in term of quality, led to a significant underestimation of the binding energy with respect to the high level G2 method by an amount of approximately 30 kJ‚mol-1. Despite this disappointing result, the very systematic failure of PBE, both in direction and in magnitude, is rather encouraging. In fact, while the absolute stability of the complexes is underestimated, the relative stability between the different complexes is rather well reproduced. Indeed, deviation of the calculated binding energies from the experimental ∆H°βj falls between 41 and 48 kJ‚mol-1. Such a narrow distribution, 7 kJ‚mol-1, suggests that artificially shifting the calculated values by approximately 45 kJ‚mol-1 would allow for the experimental data to be reproduced. However, while just shifting the calculated values provides good results, a more accurate, yet tractable, calculation method would be by far more satisfying. To this end, other methods were tested to calculate the energy of the complexes of TiCl4 with L4, L5, L9, and L10. These calculations were done using the popular hybrid B3LYP functional and the hybrid version of the TPSS meta-GGA functional (TPSSh) in combination with the def2-TZVPP basis set and with the second-order Møller-Plesset perturbation method (MP2) in combination with the quadruple-ζ QZVPP basis set. The results of these calculations are displayed in Table 4. As can be seen, the B3LYP functional does not provide any improvement of the PBE results, leading to an even stronger underestimation of the binding energy by an amount of 8-15 kJ‚mol-1 with respect to PBE values, that are still too low by 41-48 kJ‚mol-1. The other tested functional, TPSSh, gives an increase of the calculated values of 11-15 kJ‚mol-1, which is better but still far from being satisfying. The results obtained at the MP2 level are more ambiguous. On one hand, the calculated MP2 interaction energies for the two diethers are in excellent agreement with the experimental ∆H°βj values. On the other hand, the experimental ∆H°βj values are still underestimated by 17 and 20 kJ‚mol-1 for the complexes L4 and L5, respectively. While the MP2 values are in better agreement with the experimental values than the PBE (or other functionals) ones, this lack of consistency limits the prediction capabilities of the method. It appears that formation energies of TiCl4-donor complexes are very difficult to model. Indeed, three different density functionals and the MP2 method severely underestimate them. Considering the similar conclusion previously reported for TiCl4-ammonia complexes,42 it is very likely that the TiCl4 adsorption energies on MgCl2 previously reported are severely

underestimated as well. This is particularly relevant since on the basis of calculated MgCl2-TiCl4 interaction energies it was suggested that TiCl4 does not adsorb on the (100) MgCl2 lateral cut, and thus active Ti species should probably be located on the (110) MgCl2 lateral cut.11a,b In light of the results presented here this conclusion needs to be reconsidered. Finally, since DFT errors appear to be very systematic in the case of octahedral Ti-donor complexes, relative binding energies can be calculated with reasonable accuracy, while a shifting of the calculated DFT formation energy could be a practical solution if absolute binding energy of other donors is to be predicted. As this result stands for the PBE functional and for the computationally more demanding B3LYP and TPSSh functionals, the PBE functional should be considered as the method of choice. Conclusions These data represent the first quantitative evaluation of thermodynamic functions, derived from calorimetric experimental data, for the complexation of TiCl4 with ligands used as donors in heterogeneous supported Ziegler-Natta catalytic systems. The results indicated that in all cases the stable structure in solution is represented by an octahedral Ti atom with two oxygen atoms coordinated. In the case of the bidentate ligands, coordination always occurs by chelation of the donor. The thermodynamic parameters associated with formation of the TiCl4-donor complexes show that (1) the ether oxygen atom is a much better σ-donor than the ester oxygen atom, (2) the substituents produce significant stabilizing (L12, L6, L7) or destabilizing (L13) effects on the TiCl4-donor complexes with respect to the unsubstituted ones (L11, L5), (3) an increase of the ring size on chelation matches a decrease in the enthalpy of complex formation, and (4) different isomerism can lead to different spatial arrangements of the substituents that result in higher (L7) or lower (L6) affinity for the metal center. Correlation between catalyst efficiency and higher enthalpy terms was found and suggests that a somewhat higher affinity for TiCl4 should be a basic requirement of a well performing donor. This hypothesis deserves further detailed investigations. The choice of TiCl4 as the probe molecule to understand the interaction between donors and the catalyst surface could be a viable approach to test new donors. The DFT calculations provided geometric information on the formed complexes and in some cases were useful to rationalize the relationship between structure and energetics of complex formation. However, while the relative binding energies of

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