Theoretical Study on Ethylene Polymerization Catalyzed by Half-Titanocenes Bearing Different Ancillary Groups

: Half-titanocenes are well known to show high activity for ethylene polymerization and good capability for copolymerization of ethylene with other oleﬁns, and the ancillary ligands can crucially affect the catalytic performance. In this paper, the mechanisms of ethylene polymerization catalyzed by three half-metallocenes, ( η 5 -C 5 Me 5 )TiCl 2 (O-2,6-i Pr 2 C 6 H 3 ) ( 1 ), ( η 5 -C 5 Me 5 )TiCl 2 (N=C t Bu 2 ) ( 2 ) and [Me 2 Si( η 5 -C 5 Me 4 )(N t Bu)]TiCl 2 ( 3 ), have been investigated by density functional theory (DFT) method. At the initiation stage, a higher free energy barrier was determined for complex 1 , probably due to the presence of electronegative O atom in phenoxy ligand. At the propagation stage, front-side insertion of the second ethylene is kinetically more favorable than back-side insertion for complexes 1 and 2 , while both side insertion orientations are comparable for complex 3 . The energy decomposition showed that the bridged cyclopentadienyl amide ligand could enhance the rigidity of the active species as suggested by the lowest deformation energy derived from 3 . At the chain termination stage, β - H transfer was calculated to be a dominant chain termination route over β -H elimination, presumably owing to the thermodynamic perspective.


Introduction
Since the discovery of Ziegler-Natta and Phillips catalysts in 1950s, polyolefins, mainly consisting of polyethylene (PE) and polypropylene (PP), have become the largest class of commercial thermoplastics, making the polyolefin industry a multibillion-dollar business [1].Although the industrial application predominantly employs heterogeneous transition metal catalysts, a large number of homogeneous catalysts have been developed for olefin polymerization in both industry and academia [2][3][4].Well-defined molecular catalysts can precisely control the catalytic activity as well as modify the molecular weight, molecular weight distribution, comonomer incorporation, and the microstructure of the polyolefin by tailoring the coordination environment of the metal center [5,6].The modification of ligand generally gives clear feedback to the catalytic performance of the transition metal catalysts.Moreover, it is beneficial to investigate the polymerization mechanism thanks to their well-defined molecular structures and homogeneous reaction conditions [7,8].
Computational chemistry has been considered as a reliable tool to elucidate the mechanism of coordination polymerization recently, promoting the development of transition metal catalysts [23][24][25][26][27][28].The mechanism of ethylene polymerization catalyzed by the nonbridged zirconocenes was systematically studied by Cundari et al.It was shown that the substituents of cyclopentadienyl or indenyl affected the kinetics and thermodynamics of reaction more significantly than the types of cyclopentadienyl ligand attached to Zr, and the substituent effects were greater than those arising from the central metal [18].Moreover, the stronger the metal-counteranion interaction could induce the harder displacement of the counteranion by ethylene, that formed the π-complexes for chain growth [29].By DFT study, it was found that the activation effect of metal chlorides (MgCl 2 , LiCl, ZnCl 2 , CaCl 2 ) on post-titanocene complexes for ethylene polymerization was mainly caused by the secondary complexation reaction between post-titanocene and metal chloride [30].Marks et al. communicated the preliminary results of the ab initio computational investigation on Me 2 Si-bridged Cp/amido systems and found that counteranion and solvation effects were substantial [31,32].They also found that the ion pair Ti•••H 3 CB interaction was predominantly electrostatic in character [32].Recently, we have been focusing on the experimental and theoretical studies on the coordination polymerization of olefins or conjugated dienes by early transition metal complexes [33][34][35][36][37], especially the theoretical study on mechanism of the non-bridged half-titanocene systems for polymerization of 1,7-octadiene and copolymerization of ethylene and styrene [36,37].The ancillary ligand is a key factor in determining the selectivity; on the other hand, the chain-end of polymer can also affect the insertion.
In the present study, we focused on the reactivity of the half-titanocene-catalyzed ethylene polymerization to get insights into the roles of different ancillary groups.Thus, we report the study on the mechanisms of ethylene polymerization catalyzed by three halftitanocenes bearing different ancillary groups by DFT method.In addition, we investigated the influence of steric hindrance and electronic effect of the ancillary groups on the catalytic activity of ethylene polymerization during initiation and propagation stage that was discussed in the latter sections.Moreover, β-H transfer and the β-H elimination pathway in the termination stage were also investigated.

The Chain Initiation
The complexes (η 5 -C 5 Me 5 )TiCl 2 (O-2,6-i Pr 2 C 6 H 3 ) (1), (η 5 -C 5 Me 5 )TiCl 2 (N=C t Bu 2 ) (2) and [Me 2 Si(η 5 -C 5 Me 4 )(N t Bu)]TiCl 2 (3) could be considered to generate the alkyl titanium cations [Cp*Ti(O-2,6-i Pr 2 C 6 H 3 )CH 3 ] + (1A), [Cp*Ti(N=C t Bu 2 )CH 3 ] + (2A) and [(Me 2 Si(Me 4 Cp) (N t Bu)TiCH 3 ] + (3A), respectively, which served as the initial active species in the present computational study (Figure 1).For the process of ethylene insertion, the modified Cossee-Arlman mechanism was employed for the three active species with d 0 -metal Ti 4+ [38,39], consisting of three main steps (Figure 2): (1) the ethylene coordinates to the vacant site of active species (A) to generate an ethylene π-complexes (B); (2) the coordinated ethylene inserts into the Ti-C(sp 3 ) bond through a four-center transition state TS (B-C) and alkyl migration, resulting in the intermediate C with a γ-agostic bond; (3) and the intermediate C isomerizes to form the more stable complex D with a β-agostic bond.According to the proposed mechanism of initiation stage, the potential energy profiles were calculated and shown in Figure 3.With the coordination of ethylene to 1A, 2A, and 3A, the corresponding π-complexes 1B, 2B, and 3B were generated along with releasing energies of 9.9, 6.2, and 8.1 kcal/mol, respectively.Through the four-center transition states 1TS (B-C) , 2TS (B-C) , and 3TS (B-C) , the respective free energy barriers of 12.0, 10.3, and 9.2 kcal/mol had to be overcome for insertion of ethylene into 1A, 2A, and 3A.The ethylene insertion pathway into the Ti−methyl bond of the {[H 2 Si(C 5 H 4 )( t BuN)]TiCH 3 } + {H 3 CB(C 6 F 5 ) 3 } − ion pair was also investigated by Marks et al. [40].The computed results show an ethylene activation/insertion distal to the H 3 CB(C 6 F 5 ) 3 − group in benzene is reported to be 8.0 kcal/mol, in agreement with the present DFT result for 3TS (B-C) in toluene of 8.1 kcal/mol.Then, the ethylene inserted intermediates 1C, 2C, and 3C with γ-agostic bonds and the isomerized products 1D, 2D, and 3D with β-agostic bonds were obtained exothermically (15.3-19.9kcal/mol).It is shown that the first ethylene can be initiated successfully by the above-mentioned three model active species (1A, 2A, and 3A) as suggested by the moderate free energy barriers and the exergonic processes.Moreover, the initiation process of 1A was kinetically less favorable among the three complexes given the highest free energy barrier.
It is known that the insertion of an alkene or alkyne molecule into a metal-C(sp 3 ) bond mainly involves an orbital interaction of the occupied metal-C(sp 3 ) bonding orbital with an unoccupied π* orbital of the alkene or alkyne, implying a nucleophilic attack of the Ti-C(sp 3 ) bond towards one of the alkene or alkyne carbons [41].In other words, the incoming coordinated ethylene can be considered as an electrophile to interact with the Ti-C(sp 3 ) bond under this condition.The natural bond orbital (NBO) analysis was conducted in order to further explore the reason for different free energy barriers.The natural atomic charges of the sp 3 carbon bonded to Ti 4+ were calculated to be −0.95,−0.99, and −1.00 in 1B, 2B, and 3B, respectively, suggesting that the C(sp 3 ) atom was more electron deficient in 1B than those in 2B and 3B.Therefore, the ethylene insertion transition state 1TS (B-C) is electronically unfavorable than 2TS (B-C) and 3TS (B-C) owing to the electron withdrawing property of the electronegative O atom in the phenoxy ligand in 1B.Furthermore, the HOMO and LUMO orbitals of the ethylene coordinated intermediates 1B, 2B, and 3B are shown in Figure 4.The important HOMO orbitals at 1B, 2B, and 3B corresponded to the σ bonding orbital of the Ti-C(sp 3 ) bond, which was the bonding interaction between Ti 3d z 2 and carbon 2p z orbitals.(Some occupied HOMOs of 1B, 2B and 3B were shown in Figure S1 in supporting information).On the other hand, the LUMO orbitals corresponded to the π* orbitals of the ethylene molecule.Similar bonding interactions were described in a previous report [42].The energy gap between important HOMO and LUMO orbitals in 1B was observed to be 4.78 eV (Figure 4a), which was higher than that in 2B of 4.58 eV (Figure 4b) and 3B of 4.55 eV (Figure 4c).These results indicate that the interaction between the ethylene and Ti center in 1B is the weakest.To better evaluate the different steric properties of the ancillary groups in three active species (1A, 2A, and 3A), the steric maps (contours) calculated from optimized structures of active species were compared and the buried volume %V Bur was also calculated (Figure 5) [43].The %V Bur of 1A is calculated to be 70.9 and the largest among three catalysts.The strong steric repulsions in active specie 1A could account for the high free energy barrier in the initiation process of 1A.Additionally, the similar two ketimide is accompanied by a slight increase of the overall steric pressure of the ancillary ligand from %V Bur = 64.4 for non-bridged structure in 2A to %V Bur = 66.4 for bridged CGC structure in 3A.It is indicated the slightly larger steric repulsions, apparently attributed to the more rigid bridged cyclopentadienyl amide ligand of 3A.
Figure 5. Topographic steric maps and the buried volume %V Bur of three active species 1A, 2A, and 3A.The maps were obtained starting from the minimum energy structures of complexes optimized by DFT calculations.

The Chain Propagation
In contrast to the initiation process, during chain propagation stage, the second ethylene molecule will coordinate and insert into the new active species D from two different directions, i.e., the front-side and back-side.The two directions are oriented according to the relative orientation of the incoming ethylene and the agostic interaction in D (Figure 6).Then, the insertion of the second ethylene will be achieved through the four-center transition states to obtain the complexes F-fsi and F-bsi derived respectively from front-side and back-side insertions (Figure 7).After that, the polymer chain can be generated via a similar continuous insertion process.
The free energy profiles in chain propagation process were calculated and shown in Figure 8.After initiation by 1D, the front-side insertion was kinetically more favorable than the back-side insertion in the propagation process of complex 1 (6.8 kcal/mol for front-side insertion and 11.3 kcal/mol for back-side insertion).Similarly, it was also kinetically more favorable for the front-side insertion in the propagation process of complex 2. On the other hand, the free energy barrier of front-side insertion (7.4 kcal/mol) was close to that of back-side insertion (7.9 kcal/mol) in the propagation process of complex 3, suggesting that the tendencies for both side insertion directions are comparable.According to the free energy profiles (Figures 3 and 8), the insertion and chain propagation of ethylene processes were exergonic, indicating that these two processes are thermodynamically favorable for all the complexes.The rate determination step in ethylene polymerization by complexes 1-3 was the insertion of ethylene to the initial active species A, having respective activation energies in initiation stage of 12.0, 10.3, and 9.2 kcal/mol for complexes 1, 2, and 3.It is noted that the order of activation energy is in correspondence with the polymerization activity observed in the experimental findings [21,22].
In order to further investigate the insertion modes and stability of transition states in the propagation stage, the energy decomposition of transition states was carried out [44].The transition states could be considered to consist of two fragments: the active species moiety (I) and the ethylene moiety (II).The single-point energy was calculated to evaluate the energy of transition state, fragments I and II, and their relationship could be evaluated according to the relation: ∆E TS = ∆E int + ∆E def (I) + ∆E def (II).In this expression, ∆E TS represents the single-point energy of transition state.∆E int represents the interaction energy, which is estimated by the single-point energy of corresponding fragments and the energy of transition state.∆E def (I) and ∆E def (II) represent the deformation energies of the two fragments, which are estimated by the differences between the single-point energies of corresponding fragments and their energies in the optimized geometries.
The results of decomposition energy were calculated and shown in Table 1.∆E int in front-side insertions were found to be −37.0kcal/mol for 1TS (E-F) -fsi, −36.0 kcal/mol for 2TS (E-F) -fsi, and −36.3 kcal/mol for 3TS (E-F) -fsi, which were higher than the ∆E int in the corresponding back-side insertions (−40.3 kcal/mol for 1TS (E-F) -bsi, −37.5 kcal/mol for 2TS (E-F) -bsi and −42.7 kcal/mol for 3TS (E-F) -bsi).These results indicate that the interactions between active species and ethylene in back-side insertions are stronger than that in front-side insertions.The deformation energies of active species moiety (∆E def (I)) for 3TS were 18.5 kcal/mol in front-side insertion and 16.4 kcal/mol in back-side insertion, which were lower than the ∆E def (I) energies of 1TS and 2TS in two different directions (Table 1, entries 1-4).It is suggested that the intermediates and transition states derived from 3 are more rigid, apparently attributed to the bridged cyclopentadienyl amide ligand.Moreover, the deformation energies of ethylene ∆E def (II) in front-side insertions were 27.3 kcal/mol for 1TS (E-F) -fsi, 29.6 kcal/mol for 2TS (E-F) -fsi, and 26.5 kcal/mol for 3TS (E-F) -fsi, which were all lower than those in back-side insertions (32.5 kcal/mol for 1TS (E-F) -bsi, 34.6 kcal/mol for 2TS (E-F) -bsi, and 32.1 kcal/mol for 3TS (E-F) -bsi).This is probably caused by the steric hindrance of the alkyl bonded to the central Ti.

The Chain Termination
The molecular weight of polymer material is a vital factor in determining its performance and application.It is therefore of importance to study the chain termination mechanism in order to optimize the catalyst's structure in controlling the molecular weights.Two routes can be considered in the chain termination process derived from complex D with a β-H agostic interaction (Figure 9) [45,46].In one route, a direct β-H elimination occurs to generate a hydride complex (H-E) coordinated with one olefin molecule.In another route, a β-H transfer to ethylene occurs following the coordination of another ethylene to generate a new alkyl complex H-T.
The free energy profiles for two chain termination routes were calculated and shown in Figure 10.The β-H eliminations were all kinetically comparable for complexes 1, 2 and 3, as shown in the similar free energy barriers in the range of 15.1 to 15.7 kcal/mol.The β-H eliminations were all endergonic processes for complexes 1, 2, and 3, indicating that they are thermodynamically unfavorable.Conversely, the β-H transfer could be considered to be a dominant chain termination route as suggested by the exergonic processes with 3.5, 1.5 and 6.8 kcal/mol for complexes 1, 2, and 3, respectively.The free energy barrier of β-H transfer for complex 1 was higher than those for complexes 2 and 3, which might account for the higher molecular weight of polyethylene obtained by using complex 1.According to the calculated free energy profiles (Figures 8 and 10), the free energy barriers of β-H transfer were higher than those of chain propagation regardless of the front-side or back-side insertion.The kinetic results indicate the catalytic systems are favorable to produce the polyethylene with high molecular weights.

Computational Details
Full geometry optimizations have been performed at the Becke3LYP (B3LYP) function of the density functional theory [47].The effective core potentials (ECPs) of Hay and Wadt with a double-ζ valence basis set (LanL2DZ) [48] were used for Ti atom and a 6-31G** basis set was used for all other atoms.Frequency calculations were carried out to confirm the characteristics of all of the optimized structures as minima or transition states.Intrinsic reaction coordinate (IRC) calculations were performed on the transition states in order to confirm the expected reactants and products [49].To obtain the relative Gibbs free energy in solution, single-point energy calculations were carried out using M06-2X functional [50] together with the polarized continuum model (PCM) [51] for considering the toluene solvation effect.The Stuttgart/Dresden effective core potential (ECP) basis set was used for Ti atom, and the larger basis set 6-311G** was used for all the other atoms.All of the DFT calculations were performed with the Gaussian 09 program [52].

Figure 2 .
Figure 2. The proposed initiation process of ethylene polymerization initiated by half-titanocenes.

Figure 3 .
Figure 3.The calculated free energy profiles (energy in kcal/mol) for initiation stage of ethylene polymerization catalyzed by half-titanocenes.

Figure 6 .
Figure 6.Optimized structures (distances in Å) of 1D, 2D, and 3D.Hydrogen atoms of the Cp* ligand and ancillary ligand have been omitted for clarity.

Figure 7 .
Figure 7.The proposed propagation process of ethylene polymerization catalyzed by half-titanocenes.

Figure 8 .
Figure 8.The calculated free energy profiles (energy in kcal/mol) for propagation stage of ethylene polymerization catalyzed by half-titanocenes.

Figure 9 .
Figure 9.The proposed termination process of ethylene polymerization catalyzed by half-titanocenes.

Figure 10 .
Figure 10.The calculated free energy profiles (energy in kcal/mol) for β-H elimination and β-H transfer in the termination stage of ethylene polymerization catalyzed by half-titanocenes.

Table 1 .
The energy decomposition (kcal/mol) of six ethylene insertion transition states in chain propagation stage.