On Conformational Flexibility of Half-Titanocene Catalysts with Aryloxy

Organometallics 2010, 29, 5341–5352 DOI: 10.1021/om100453k

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On Conformational Flexibility of Half-Titanocene Catalysts with Aryloxy Ligands for High-Temperature Olefin Polymerization Processes: Static and Dynamic Theoretical Studies† )

Monika Srebro,‡ Łukasz Pie-kos,‡ Tae-Jin Kim,§ Minserk Cheong,^ Myung-Ahn Ok, Sang Ook Kang,*,§ and Artur Michalak*,‡ ‡

)

Department of Theoretical Chemistry, Faculty of Chemistry, Jagiellonian University, R. Ingardena 3, 30-060 Cracow, Poland, §Department of Materials Chemistry, Sejong Campus, Korea University, 208 Seochang, Chochiwon, Chung-nam 339-700, Korea, ^Department of Chemistry and Research Institute for Basic Sciences, Kyung Hee University, Seoul 130-701, Korea, and Institute of Technology, SK Energy, 140-1 Wonchon-dong, Yuseong-gu, Daejeon 305-712, Korea Received May 11, 2010

The static DFT calculations and Car-Parrinello molecular dynamic simulations were performed for a series of half-metallocene ethylene-polymerization catalysts based on Ti(IV) complexes with aryloxy ligands, varied in cyclopentadienide Cp/Cp* and 2,6-di-/2-monosubstituted phenoxy ligand combinations. The results confirm the more pronounced conformational flexibility of the monosubstituted systems, demonstrated by a relatively easy rotation of the aryloxy ligand. In the case of the complex with a 2-phenylphenoxy ligand, a substantial decrease in rotational barrier is observed due to the secondary interactions between the phenyl substituent and the methyl protons of Cp*. In the catalytically active species derived from the corresponding precatalysts, the barrier for the ligand rotation is decreased compared to the precatalysts. For the monosubstituted aryloxy complexes such an easy rotation allows for the transition between the “nonreactive” and “reactive” propagation pathways (anti and syn), which can lead to an increase in their catalytic activity. Introduction Due to a broad spectrum of applications, polyolefins remain one of the fastest-developing branch of the polymer industry with regard to both worldwide production and techniques and catalysts used in the polymerization processes. Since the “metallocene revolution” period,1 both academic and industrial research laboratories have still been searching for new organometallic, post-metallocene complexes2-5 serving as single-site polymerization catalysts. Recently, among other types of complexes, particular attention has been paid to half-metallocenes.5-8 The most well-known examples of such systems are the

Dow constrained geometry catalysts (CGC),9-12 the phenoxyinduced complex of Sumitomo, Phenics catalytic systems,13,14 phosphinimine-based complexes introduced by Stephan,15,16 and aryloxy catalysts with the 2,6-positions of the phenoxy ligand substituted with either alkyl or phenyl groups introduced by Nomura17-19 and Rothwell.20 Recently, a thorough study on five different types of halftitanocenes testing as olefin polymerization catalysts was performed.21 Considered systems varied in cyclopentadienide Cp/Cp* and 2,6-di-/2-monosubstituted phenoxy ligand

Part of the Dietmar Seyferth Festschrift. This paper is dedicated to our mentor, Prof. Dietmar Seyferth, for his passion for Organometallics. *To whom correspondence should be addressed. E-mail: sangok@ korea.ac.kr; [email protected]. (1) Sinn, H.; Kaminsky, W. Adv. Organomet. Chem. 1980, 18, 99. (2) Alt, H. G.; Koppl, A. Chem. Rev. 2000, 100, 1205. (3) Ittel, S. D.; Johnson, L. K.; Brookhart, M. Chem. Rev. 2000, 100, 1169. (4) Gibson, V. C.; Spitzmesser, S. K. Chem. Rev. 2003, 103, 283. (5) Nomura, K.; Liu, J.; Padmanabhan, S.; Kitiyanan, B. J. Mol. Catal. A 2007, 267, 1. (6) Sita, L. R.; Babcock, R. Organometallics 1998, 17, 5228. (7) Zhang, S.; Piers, W. E.; Gao, X.; Parvez, M. J. Am. Chem. Soc. 2000, 122, 5499. (8) (a) Manz, T. A.; Phomphrai, K.; Medvedev, G.; Krishnamurthy, B. B.; Sharma, S.; Hag, J.; Novstrup, K. A.; Thomson, K. T.; Delgass, W. N.; Caruthers, J. M.; Abu-Omar, M. M. J. Am. Chem. Soc. 2007, 129, 3776. (b) Manz, T. A.; Sharma, S.; Phomphrai, K.; Novstrup, K. A.; Fenwick, A. E.; Fanwick, P. E.; Medvedev, G. A.; Abu-Omar, M. M.; Delgass, W. N.; Thomson, K. T.; Caruthers, J. M. Organometallics 2008, 27, 5504. (9) Chen, Y.-X.; Marks, T. J. Organometallics 1997, 16, 3649. (10) Stevens, J. C. Stud. Surf. Sci. Catal. 1994, 89, 277. (11) Stevens, J. C. Stud. Surf. Sci. Catal. 1996, 101, 11.

(12) Stevens, J. C.; Timmers, F. J.; Wilson, D. R.; Schmidt, G. F.; Nickias, P. N.; Rosen, R. K.; Knight, G. W.; Lai, S. Y. EP 90-309496 416815, 19900830, 1991. (13) Hanaoka, H.; Hino, T.; Nabika, M.; Kohno, T.; Yanagi, K.; Oda, Y.; Imai, A.; Mashima, K. J. Organomet. Chem. 2007, 692, 4717. (14) Katayama, H.; Nabika, M.; Imai, A.; Miyashita, A.; Watanabe, T.; Johohji, H.; Oda, Y.; Hanaoka, H. PCT Appl. WO 97-03992, 1997. (15) Stephan, D. W.; Stewart, J. C.; Guerin, F.; Courtenay, S.; Kickham, J.; Hollink, E.; Beddie, C.; Hoskin, A.; Graham, T.; Wei, P.; Spence, R. E. v. H.; Xu, W.; Koch, L.; Gao, X.; Harrison, D. G. Organometallics 2003, 22, 1937. (16) Stephan, D. W.; Stewart, J. C.; Guerin, F.; Spence, R. E. v. H.; Xu, W.; Harrison, D. G. Organometallics 1999, 18, 1116. (17) Nomura, K.; Naga, N.; Miki, M.; Yanagi, K.; Imai, A. Organometallics 1998, 17, 2152. (18) Nomura, K.; Naga, N.; Miki, M.; Yanagi, K. Macromolecules 1998, 31, 7588. (19) Nomura, K.; Tanaka, A.; Katao, S. J. Mol. Catal. A 2006, 254, 197. (20) Phomphrai, K.; Fenwick, A. E.; Sharma, S.; Fanwick, P. E.; Caruthers, J. M.; Delgass, W. N.; Abu-Omar, M. M.; Rothwell, I. P. Organometallics 2006, 25, 214. (21) Kim, T.-J.; Kim, S. K.; Kim, B.-J.; Hahn, J. S.; Ok, M.-A.; Song, J. H.; Shin, D.-H.; Ko, J.; Cheong, M.; Kim, J.; Won, H.; Mitoraj, M.; Srebro, M.; Michalak, A.; Kang, S. O. Macromolecules 2009, 42, 6932.

r 2010 American Chemical Society

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Organometallics, Vol. 29, No. 21, 2010 Scheme 1. Systems Studied in the Present Work

combinations. It was revealed that the Cp*-based complexes with the monosubstituted ortho-position of the phenoxy ligand, Cp*TiCl2(O-2-RC6H4), R = Me, Pri, But, Ph (type 4 in Scheme 1), exhibit enhanced catalytic activity in the high-temperature processes of ethylene polymerization (33.0-39.0 kg/(mmol of Ti 3 h)) compared to those found in the other types (3.6-27.6 kg/(mmol of Ti 3 h)). Among the type 4 catalysts, the phenyl-phenoxy system 18 (39.0 kg/(mmol of Ti 3 h)) is the most active one, surpassing both Cp*/2-alkyl ligand combinations of compounds 15-17 (33.0-36.0 kg/(mmol of Ti 3 h)) as well as the reference catalyst CGC (33.0 kg/(mmol of Ti 3 h)).21 Along with experimental research, a theoretical mechanistic investigation was carried out for selected examples of the phenoxy half-titanocenes, namely, one complex of type 1 (3), two of type 3 (10, 12), four of type 4 (15, 16, 17, 18 in Scheme 1), and the constrained geometry catalyst as a reference.21,22 The main goal of the DFT calculations was to understand the details of the molecular mechanism of the ethylene polymerization process and thus rationalize the differences in the experimental catalytic activity of the particular types of complexes. The most widely accepted mechanism of olefin polymerization reactions catalyzed by organometallic complexes is based on the original Cossee-Arlman idea.23-27 It includes, after the activation of a single-site catalyst, the chain propagation and termination steps. The mechanistic details of these reactions were fairly well established due to the extensive and thorough research carried out by both experimentalists and theoreticians.28 Namely, in the case of early transition-metal-based catalysts, the β-agostic alkyl complex was revealed to be a resting state, which implies two possible complexation modes and thus two main propagation mechanisms, i.e., frontside (FS) and backside (BS) insertion.29,30 They are schematically presented in Scheme 2. The backside complexation of ethylene to a β-agostic alkyl complex (A) leads to a BS π-complex in which the monomer (22) Srebro, M.; Pie-kos, Ł.; Kim, T.-J.; Cheong, M.; Ok, M.-A.; Kang, S. O.; Michalak, A. Macromol. Res. 2010, DOI: 10.1007/s13233010. (23) Cossee, P. Tetrahedron Lett. 1960, 38, 12. (24) Cossee, P. J. Catal. 1964, 3, 80. (25) Arlman, E. J. J. Catal. 1964, 3, 89. (26) Arlman, E. J.; Cossee, P. J. Catal. 1964, 3, 99. (27) Arlman, E. J. J. Catal. 1966, 5, 178. (28) Rappe, A. K.; Skiff, W. M.; Casewit, C. J. Chem. Rev. 2000, 100, 1435, and references therein. (29) Margl, P.; Deng, L.; Ziegler, T. Organometallics 1998, 17, 933. (30) Margl, P.; Deng, L.; Ziegler, T. J. Am. Chem. Soc. 1998b, 120, 5517.

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is located in the position anti to the β-agostic bond. Starting from this structure, a direct migratory insertion of ethylene into the metal-alkyl bond (B) proceeds, and as a result of this BS insertion, a δ-agostic complex is formed. It can easily further rearrange into generally a more stable β-agostic system by a simple rotation of the alkyl chain (C). The frontside insertion pathway starts with the complexation of ethylene to the metal center of the β-agostic alkyl complex in the position syn to the β-agostic bond (D). From a resulting structure, labeled here as a BHT π-complex, the termination of the chain due to a transfer of the polymer β-hydrogen to the approaching monomer (β-hydrogen transfer, BHT (E)) can directly start.31 The FS insertion requires a rearrangement of such a complex into an R-agostic π-complex, a FS π-complex (F). The direct product of the FS insertion (G) is a γ-agostic alkyl complex, which eventually isomerizes to the β-agostic complex (H). Our previous studies21,22 show that the relative polymerization activities of catalysts can be successfully estimated from the results of the theoretical DFT calculations. We have introduced a theoretical activity parameter (v), which, taking into account the existence of possible insertion pathways, corresponds directly to the overall effective propagation rate. The contributions from the particular pathways are calculated using the activation barriers and the populations of the lowest energy ethylene π-complexes of a different type (BS, FS, BHT). This quantity was found to correlate well with the experimental data, confirming the high activity of the Cp*/phenoxy titanium(IV) complexes with a single ortho-substituent on the aryloxy ligand (15-18, type 4).21 It was also revealed previously21,22 that a distinctive feature of type 4 catalysts (15-18) is the energetic preference of the backside insertion pathway. For disubstituted type 1 (3) and type 3 (10, 12) systems, as well as for the CGC catalyst, the frontside insertion contributes predominantly to the catalyst activity, while the BS insertion is almost negligible. It was further found22 that the final preference of the backside or frontside transition state comes as a balance between the electronic preference of the former and the steric preference of the latter. The unique energetic preference of the backside insertion observed for type 4 catalysts appears as a result of the reduced steric congestion in the vicinity of the metal, stemming from the monosubstitution of the phenoxy ligand and its conformational flexibility. Such an openness near the active center of the catalyst is reflected in the enhanced catalytic activity of those systems. Accordingly, the main goal of the present theoretical study is to examine the conformational flexibility of selected examples of the half-titanocenes with the aryloxy ligand by DFT calculations, using both typical static calculations and ab initio molecular dynamics in the Car-Parrinello approach. The comparison of the energy barriers for the rotation of the aryloxy ligand around the Ti-(O)-C axis (i.e., around two “single” bonds, Ti-O and O-C, determining the conformation of the ligand) will be presented for both precatalysts and active species of ethylene π-complexes. For system 18, the secondary interactions between the methyl groups of the Cp* and phenyl substituent at the orthoposition of the phenoxy ligand will also be discussed. (31) Margl, P.; Deng, L.; Ziegler, T. J. Am. Chem. Soc. 1999a, 121, 154.

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Scheme 2. Ethylene Polymerization Mechanism

Computational Details The systems discussed in the present work are presented in Scheme 1. They include one complex of type 1 (3), two of type 3 (10, 12), as well as four of type 4 (15, 16, 17, 18). To avoid confusion, we use here the same labeling scheme as before.21,22 DFT calculations based on the Becke88 exchange32 and Perdew86 correlation33,34 functional (BP86) were performed using the Amsterdam Density Functional (ADF) program, versions 2004.01, 2006.01, and 2007.01.35-39 A standard double-ζ STO basis included in the ADF package with one set of polarization functions was applied for H, C, O, Si, and Cl atoms, while a standard triple-ζ basis set was employed for Ti atom. The 1s electrons of C, N, and O as well as the 1s-2p electrons of Ti, Si, and Cl were treated as frozen core. Auxiliary s, p, d, f, and g STO functions, centered on all nuclei, were used to fit the electron density and obtain accurate Coulomb and exchange potentials in each SCF cycle. In the geometry optimization the following convergence criteria were applied: -0.001 au and 0.001 au/A˚ for changes in the energy and energy gradients, as well as 0.003 A˚ and 0.5 for changes in bond lengths and bond and dihedral angles, respectively. The 1H NMR chemical shifts with respect to the calculated isotropic shielding value of tetramethylsilane (TMS) (31.57 ppm) were obtained using the Schreckenbach and Ziegler approach implemented in the NMR program40-44 of the ADF 2006.01 and 2007.01 packages. (32) Becke, A. Phys. Rev. A 1988, 38, 3098. (33) Perdew, J. P. Phys. Rev. B 1986, 33, 8822. (34) Perdew, J. P. Phys. Rev. B 1986, 34, 7406. (35) teVelde, G.; Bickelhaupt, F. M.; Baerends, E. J.; Fonseca Guerra, C.; van Gisbergen, S. J. A.; Snijders, J. G.; Ziegler, T. J. Comput. Chem. 2001, 22, 931, and references therein. (36) Baerends, E. J.; Ellis, D. E.; Ros, P. Chem. Phys. 1973, 2, 41. (37) Baerends, E. J.; Ros, P. Chem. Phys. 1973, 2, 52. (38) te Velde, G.; Baerends, E. J. J. Comput. Phys. 1992, 99, 84. (39) Fonseca Guerra, C. G.; Visser, O.; Snijders, J. G.; te Velde, G.; Baerends, E. J. In Methods and Techniques in Computational Chemistry, METECC-95; Clementi, E., Corongiu, G., Eds.; STEF: Cagliari, Italy, 1995; p 303. (40) Schreckenbach, G.; Ziegler, T. J. Phys. Chem. 1995, 99, 606. (41) Schreckenbach, G.; Ziegler, T. Int. J. Quantum Chem. 1996, 60, 753. (42) Schreckenbach, G.; Ziegler, T. Int. J. Quantum Chem. 1997, 61, 899. (43) Wolff, S. K.; Ziegler, T. J. Chem. Phys. 1998, 109, 895. (44) Wolff, S. K.; Ziegler, T.; van Lenthe, E.; Baerends, E. J. J. Chem. Phys. 1999, 110, 7689.

Scheme 3. Dihedral Angles Cp*(cent)-Ti-C(ipso)-C(R) and C(Cp*)-Cp*(cent)-Ti-Cl Describing the Rotation of the Aryloxy Ligand (a) and the Cp* Ring (b), Respectivelya

a

The phenyl-phenoxy precatalyst, 18 (R = Ph), was used here as an example.

The static energy barriers for the rotation of the aryloxy ligand around the Ti-(O)-C axis (i.e., around two “single” bonds, Ti-O and O-C, determining the conformation of the ligand) were determined for all the aryloxy precatalysts studied here (3, 10, 12, 15-18). For the active species, i.e., the BS, FS, and BHT ethylene π-complexes, the ligand rotation in one type 3 (12) and two type 4 (16, 18) systems was investigated. The corresponding energy profiles were obtained from a series of constrained optimizations with a frozen dihedral angle of Cp*(cent)-Ti-C(ipso)-C(R) according to the panel a of Scheme 3. It is important to point out here that due to the fact that the Ti-O-C angle is nearly linear, neither the Ti-O nor O-C bond can be used in the constraint in the calculations of the rotation profiles. Similarly, for the precatalyst 18 we determined the energy profile for the rotation of the Cp* ring between two equivalent positions described by the dihedral angle C(Cp*)-Cp*(cent)-Ti-Cl as presented in panel b of Scheme 3. Molecular dynamics simulations for complexes (precatalyst and active forms) 18 and 16 were carried out at the CarParrinello ab initio level, as implemented in the CPMD software package.45 CPMD simulations were performed with a plane wave basis set and the cutoff energy of 80 Ry, within a cubic cell, 16 A˚ in length. For a description of the inner electrons, the Goedecker-type (45) CPMD, Copyright IBM Corp. 1990-2006, Copyright MPI f€ur Festk€orperforschung Stuttgart 1997-2001.

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pseudopotentials were used.46 Valence electrons were treated explicitly within the DFT formalism. For consistency with the static DFT calculations the same Becke-Perdew exchange-correlation functional32-34 was used here. The simulation length was ca. 60 ps (corresponding to 600 000 time steps) for the active form species and ca. 20 ps (corresponding to 200 000 time steps) for precatalyst forms with a time step length of 4.134 au (0.1 fs). A temperature of 413 K was controlled via a Nose-Hoover chain thermostat. It is important to point out that the simulations were performed without a separate thermal equilibration stage. However, since the unconstrained MD simulations were started from optimized structures and we are not calculating any averaged quantities, there is no need to run a simulation in distinct stages. The conformational transitions we are describing do not happen earlier than 10 ps (i.e., after at least 100 000 time steps). Thus, the first several picoseconds can be formally considered as an equilibration stage.

Results and Discussion The revolving nature of the phenyl-phenoxy ligand around the Ti-O-C axis in the system 18 responsible for its conformational flexibility was demonstrated previously21,47 by both experimental and theoretical studies. Namely, the rapid rotation of the phenyl-phenoxy ligand at room temperature was identified by the variable-temperature 1H NMR spectra and further confirmed by the NOESY correlation peaks between the methyl protons of Cp* and protons of the ancillary phenylphenoxy ligand in compound 18. Energy barriers of 4.3 and 1.4 kcal/mol estimated from the DFT studies for the precatalyst and corresponding ethylene BS π-complex, respectively, also demonstrated that such a rotation is feasible. It was further confirmed by the results of the molecular dynamics (MD) simulations at both the semiempirical (Born-Oppenheimer MD) and DFT level (Car-Parrinello MD). Since this conformational flexibility, resulting in a lack of steric congestion near the metal center, i.e., active site of the catalyst, is directly responsible for the enhanced catalytic activity of type 4 systems, it seems to be instructive to examine the rotation of the aryloxy ligand for all the other catalysts studied in our mechanistic investigations. Static DFT Calculations for the Precatalysts. We will start the discussion with rotational barriers for the considered precatalysts obtained from the static DFT calculations. The general representation of rotation of an aryloxy ligand around the Ti-O-C axis starting from its minimum energy position in a structure i of a precatalyst, ΔE(i) = 0, to the equivalent position in a structure iii, a mirror image of i, ΔE(i) = ΔE(iii), for a Cp*-based complex is presented in the top part of Figure 1. The bottom part of this figure shows three selected examples of the energy profiles for such a rotation calculated for the systems 12 of type 3 (panel a) and 16 (panel b) and 18 (panel c) of type 4. The corresponding rotational energies determined for all the complexes are collected in Table 1. According to the scheme of the rotation shown in the top part of Figure 1, it should be pointed out that for the catalysts of type 4, i.e., with monosubstituted phenoxide, R = Me, Pri, But, Ph, R0 = H, the rotation of the aryloxy ligand may proceed in two ways due to asymmetry, namely, with passing (46) Hartwigsen, C.; Goedecker, S.; Hutter, J. K. Phys. Rev. B 1998, 58, 3641. (47) Kim, T.-J.; Kim, S.-K.; Kim, B.-J.; Son, H.-J.; Hahn, J. S.; Cheong, M.; Mitoraj, M.; Srebro, M.; Pie-kos, Ł.; Michalak, A.; Kang, S. O. Chem.;Eur. J. 2010, 16, 5630.

Figure 1. Schematic representation of the rotation of the aryloxy ligand around the Ti-O-C bonds (top) together with the energy profiles for such a rotation for the precatalyst 12 (bottom, a), 16 (bottom, b), and 18 (bottom, c). The δ values correspond to the 1H NMR chemical shifts of the Cp* methyl protons from the DFT calculations.

the barriers of ΔE(ii) and ΔE(iv), corresponding to the geometry in which the substituent R on the aryloxy ligand is located on the opposite side of the Cp* ring: a structure ii and, close to it, a structure iv. We will refer to these two situations as a “bottom” and “top” rotation. In the case of the disubstituted type 1 and type 3 systems, due to symmetry of the rotating aryloxy ligand, there is no difference between structures ii and iv. Consequently, the full rotation is characterized by only one energy barrier, ΔE(ii) = ΔE(iv). Let us discuss first the energy profiles of the aryloxy ligand rotation obtained for the corresponding precatalysts 12, 16,

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Table 1. Energy Barriers (in kcal/mol) of the Rotation of the Aryloxy Ligand around the Ti-O-C Bonds for the Studied Precatalysts: One Complex of Type 1 (3), Two of Type 3 (10, 12), and Four of Type 4 (15, 16, 17, 18) rotational barrierb ΔE(ii)

a

complex 3 10 12 15 16 17 18

Cp, R = R0 = (i-Pr)2 Cp*, R = R0 = H Cp*, R = R0 = (i-Pr)2 Cp*, R = Me, R0 = H Cp*, R = i-Pr, R0 = H Cp*, R = t-Bu, R0 = H Cp*, R = Ph, R0 = H

a See Scheme 1 and Figure 1 minimum energy structure i.

b

ΔE(iv) 4.64 2.75 7.08

2.71 3.30 4.49 6.57

3.59 4.02 5.73 4.32

Relative to the precatalyst of the

and 18, presented in panels a, b, and c of Figure 1, respectively. It is clearly seen that both rotational barriers calculated for the monosubstituted phenoxy systems of type 4, 16 (“bottom”: ΔE(ii) = 3.3 kcal/mol, “top”: ΔE(iv) = 4.0 kcal/mol) and 18 (“bottom”: ΔE(ii) = 6.6 kcal/mol, “top”: ΔE(iv) = 4.3 kcal/ mol), are substantially lower than that calculated for the di-Prisubstituted phenoxy compound of type 3, 12 (7.1 kcal/mol). Accordingly, the complex with only one substituent on the aryloxy ligand reveals more pronounced conformational flexibility compared to the more crowded system with two such substituents. Analyzing the data collected in Table 1, it is seen that di-Prisubstituted phenoxy precatalyst of type 3, 12, demonstrates the highest energy barrier for the rotation of the aryloxy ligand around the Ti-O-C axis from among all the complexes studied. Lower values of the rotational barrier come as a result of a lower steric congestion of the ancillary ligands stemming from (i) no substitution of the cyclopentadienyl ring, i.e., the presence of the Cp instead of Cp* ligand, in the case of system 3 (ΔE = 4.6 kcal/mol), (ii) no substitution of the phenoxy ligand, i.e., the presence of the aryloxy substituent R = R0 = H in the case of 10 (ΔE = 2.6 kcal/mol), and finally (iii) an aforementioned monosubstitution of the phenoxy ligand in the case of 15-18 (ΔE = 2.7-4.5 kcal/mol). Comparing the different precatalysts of type 4, it can be noticed that the energetic cost of the monosubstituted phenoxy ligand rotation increases with the size of the substituent of the phenoxide, i.e., But > Pri > Me. The corresponding ΔE(ii) (“bottom”) and ΔE(iv) (“top”) are 4.5 > 3.3 > 2.7 kcal/mol and 5.7 > 4.0 > 3.6 kcal/mol, respectively. The system 18 comprising the bulky phenyl-phenoxy ligand, however, is exceptional. From among type 4 complexes, it demonstrates simultaneously the highest “bottom” rotational barrier of 6.6 kcal/mol and the “top” ΔE(iv) value of 4.3 kcal/mol, lower than that obtained for the system with the tert-butyl substituent, 17. Furthermore, it is worth emphasizing that for all type 4 catalysts with the exception of 18, the “bottom” rotation is favored. The reason is the increased steric repulsion between the substituent on the aryloxy ligand and the methyl groups on the cyclopentadienyl ring in the case of the “top” rotation, resulting in a higher energy barrier, ΔE(iv) > ΔE(ii), namely, 3.6-5.7 > 2.7-4.5 kcal/mol. For 18, however, the “top” rotation path is preferred, by 2.3 kcal/mol. This is due to the secondary interactions between the phenyl substituent and methyl protons of Cp* (Ph--H) identified on the basis of the molecular structure of 18 obtained from the DFT geometry optimization and further confirmed by detailed theoretical and experimental 1H NMR studies.21,47 They are responsible

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for the stabilization of the transition state of the “top” rotation and, thus, the decrease in the ΔE(iv) value: ΔE(iv) < ΔE(ii). Such an inversion of the preferred rotation barrier, “bottom” vs “top”, is clearly visible from the energy profiles of the aryloxy ligand rotation for 16 and 18 presented in panels b and c of Figure 1, respectively. As already mentioned in our previous study,21,47 these secondary interactions can be easily disclosed by a 1H NMR study since they are reflected in an upfield shift of the proton chemical shifts of the Cp* methyl protons. Thus, in order to demonstrate the presence of such interactions we calculated average 1H NMR chemical shifts for the methyl protons of Cp* for systems 12, 16, and 18 in the geometry of structures i, ii, and iv. The corresponding values of δ are presented in Figure 1. In the case of the complexes 12 and 16 the calculated average values of δ are quite similar and increase slightly for the transition states of the rotation, from 2.0 (2.1) to 2.2 (2.2) for 12 (16). Since such values of δ are in the range of the free Cp* anion (δ 2.2), it can be concluded that the isopropyl substituent on the aryloxy ligand does not interact with the Cp* ring. On the contrary, the system 18 in the minimum energy geometries of i demonstrates a significantly lower value of δ 1.7 compared to nonbound Cp*, which confirmed the presence of the secondary interactions between the Cp* methyl protons and phenyl π-electron system (Ph--H). These interactions disappear during the “bottom” rotation (δ 2.2), but clearly remain preserved (δ 1.8) in the transition states of the “top” rotation, which confirms their stabilizing role in the case of the phenyl-phenoxy system. In order to estimate the energy of the Ph--H secondary interactions for the precatalyst 18 in its optimal geometry of i, we calculated the energy profile for the rotation of the Cp* ring between two equivalent positions. The 1H NMR chemical shifts for selected methyl protons in the vicinity of the phenyl ring were also determined. The results are shown in Figure 2. It is seen from the energy profile presented in the panel a of Figure 2 that the energetic cost of the Cp* rotation is very low, only 1.0 kcal/mol. However, it should be emphasized that the weak secondary interactions are present for all the structures occurring along the rotation path. The chemical shift plot in panel b of Figure 2 clearly shows that while a distance between the phenyl substituent and a proton increases during the rotation, leading to the weakening of the secondary interactions, another proton approaches phenyl, strengthening them. This is very nicely reflected by the changes of the chemical shifts for selected methyl hydrogen atoms in the vicinity of the phenyl ring, i.e., H1, H2, and H3. As can be noticed from the plot of Figure 2, the 1H NMR chemical shift value calculated for the proton that at first directly interacts with the phenyl substituent, i.e., H1 (blue squares), after its initial decrease, increases further slowly from ca. δ 0.0 to ca. δ 1.5 during the Cp* ring rotation. While H1 is leaving the vicinity of the phenyl ring, another proton, H2 (green triangles), is approaching it. It is accompanied by the decrease in its chemical shift from ca. δ 1.7 to ca. δ 0.0 for the maximum Ph--H interaction reached for the angle C(Cp*)-Cp*(cent)-Ti-Cl of ca. 215. The further rotation leads to the increase in the distance between the phenyl substituent and the proton H2 and weakening of the secondary interactions. Consequently, the corresponding δ value increases to ca. 1.5. In place of the receding H2, however, the next proton is appearing, H3 (red dots), strengthening the

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Figure 2. Calculated energy profile for the rotation of the Cp* ring between two equivalent positions for the precatalyst 18 (a) and the changes in the chemical shifts of the Cp* methyl protons due to the rotation (b).

secondary interactions with Ph. This is clearly reflected in its chemical shift value, decreasing from ca. δ 2.6 to ca. δ 0.4 during the rotation. Thus, an increase in the value δ recorded for an outgoing proton is strictly correlated with a decrease in the corresponding value for an incoming proton. Consequently, the average value of chemical shifts for all the Cp* protons remains almost intact, ∼δ 1.7. Therefore, although such Ph--H interactions are too weak to prevent the Cp* ring rotation, they are crucial for the increase in the conformational flexibility of the phenylphenoxy system 18 due to their dynamic nature. Finally, it is important to comment on the nature of the weak Ph--H interactions, as it is well known that DFT is unable to correctly describe weak dispersive interactions. However, the Ph--H interaction discussed here does not come solely from a dispersion. A large part of this weak interaction comes from electrostatics (a proton placed in the negative electrostatic potential of the phenyl π-electron system), as well as a charge transfer (see Appendix). A “model system” for this interaction; methane interacting with benzene;was studied in the literature.48 A CCSD(T)/aug(d,p)-6-311G** estimate of the interac(48) Tsuzuki, T.; Honda, K.; Uchimaru, T.; Mikami, M.; Tanabe, K. J. Am. Chem. Soc. 2000, 122, 3746.

tion energy for this system is -1.23 kcal/mol.48 Our DFT estimate for the same system is -1.01 kcal/mol (see Appendix). An error of 0.22 kcal/mol will certainly not change the qualitative picture emerging from our calculations. This is true in particular for the preference of “on top” rotation for 18, since the DFT value is slightly underestimated. Taking dispersion correctly into account would further enhance this preference. CPMD Simulations for the Precatalysts. Conformational flexibility of the investigated systems at nonzero temperature was further confirmed by the molecular dynamics simulations, performed at a temperature of 413 K, corresponding to a desired working temperature of the investigated catalysts. It is important to point out that MD simulation at elevated temperature includes in a natural way the entropic effects not taken into account in the static calculations (corresponding to T = 0 K). CPMD simulations for the precatalysts 16 and 18 both demonstrate numerous conformational transitions, involving rotation of the phenoxy ligand around the Ti-O-C axis. Temporal evolution of the dihedral angle describing this rotation is depicted in Figure 3, for both precatalysts (16 and 18). In Figure 3, the “bottom” rotation is indicated by passing the dihedral angle value of 180 (modulo 360), denoted by the horizontal red line. Correspondingly, the “top” rotation occurs when passing the 0 (modulo 360) level, indicated by the horizontal green line.

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Figure 3. Changes in the dihedral angle describing the rotation around the Ti-O-C axis of the aryloxy ligand along the molecular dynamics trajectory for the precatalyst species 16 and 18 (a and b, respectively). Passing 180 or -180 levels (indicated by a red line) corresponds to the “bottom” rotation, while passing 0 or -360 levels (indicated by a green line) corresponds to the “top” rotation. Panels c and d show snapshots of trajectories for the precatalysts 16 and 18, respectively; vertical blue lines indicate the time interval during which the snapshots were taken.

Conformational transitions observed in the CPMD trajectories confirm flexibility of the studied systems, giving the overall picture that is fully consistent with the results of static DFT calculations. For the precatalyst 16 the total number of rotations observed along the CPMD trajectory is seven, of which six correspond to the “bottom” and one to the “top” rotation. For precatalyst 18 the total number of rotations is three (one “bottom” and two “top”). Thus, for both systems, the number of “top” and “bottom” rotations observed along the corresponding CPMD trajectories stays in qualitative agreement with the barriers obtained from static calculations (cf. Table 1). It is also worth emphasizing that the CPMD simulation performed for 18 clearly indicates that the stable, equilibrium structures occurring between the ligand rotations are stabilized by the secondary interactions between the phenyl ring and the hydrogen atoms on the Cp*-methyls. Furthermore, such interactions facilitate the “top” rotation of the aryloxy ligand. Both of these effects are seen in the snapshots from the trajectory shown in panel d of Figure 3. The results of the CPMD simulations for both investigated precatalysts also show a relatively easy (and, hence, frequently occurring) rotation of the Cp* ligand. Temporal evolution of the dihedral angle describing such a rotation is

shown in Figure 4. One full (360) rotation of the Cp* ligand corresponds to five transitions, each resulting in a symmetrically equivalent position. In the presented case of the precatalyst 18, the Cp* ligand never stays in one minimum for longer than 5 ps. Static DFT Calculations for the Active Species. Let us discuss now the conformational flexibility of the catalyst active species, i.e., ethylene π-complexes of the BHT, BS, and FS type. Here, only three compounds were studied, namely, one complex of type 3, 12, and two of type 4, 16 and 18. In the case of the systems with the single ortho-substituted aryloxy ligand, due to asymmetry, the number of possible ethylene π-complexation modes is doubled in comparison with the disubstituted aryloxy symmetric catalysts. Thus, as presented in Scheme 4, six main structures of the π-complexes can be distinguished for the type 4 systems, two of the BS, two of the FS, and two of the BHT type, each of them with ethylene located in the position either syn or anti to the aryloxy substituent R. Consequently, in such a case, the syn and anti BS and FS insertion as well as BHT termination pathways should be considered. Nevertheless, we have already demonstrated in our previous studies21,22 that the contributions of the particular anti, frontside and backside, insertion pathways to the catalyst activity are generally

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Figure 4. Changes in the dihedral angle describing the rotation of the Cp* ligand along the molecular dynamics trajectory for the precatalyst 18. Every difference of levels of 72 (360/5; indicated by red lines) corresponds to the rotation into a symmetrically equivalent position of the Cp* ligand. Panels c and d show snapshots of trajectory; vertical blue lines indicate time interval from which the snapshots were taken. For clarity, to indicate the Cp* ligand rotation, one of its methyl carbon atoms is indicated in violet. Scheme 4. Insertion and Termination syn and anti Pathways for the Systems of Type 4 As a Result of the Aryloxy Ligand Asymmetry Together with Possible Transitions between Them Stemming from the Rotations of the Aryloxy and/or Alkyl Ligand

smaller compared to the contributions of the corresponding syn pathways. Thus, the syn insertion pathways were found to be energetically preferred (“reactive”), while the anti pathways were found to be energetically disfavored (“nonreactive”).21,22 In this context, the possibility of the switch between the particular pathways seems to be especially important. According to Scheme 4, the transition between the ethylene π-complexes of a different type can be realized by (i) the rotation of the alkyl ligand, BS T FS T BHT, and (ii) the

rotation of the aryloxy ligand: syn T anti. Thus, the conformational flexibility of the ethylene π-complexes stemming from the revolving nature of the aryloxy ligand determines the transition between the reactive and nonreactive propagation pathways, and consequently it can further increase the catalytic activity of the type 4 systems. The general representation of a rotation of an aryloxy ligand around the Ti-O-C axis starting from its minimum energy position in a structure i of an active species, ethylene π-complex, ΔE(i) = 0, to the corresponding position in a structure iii is presented in the top part of Figure 5. In the bottom part of this figure three selected examples of the energy profiles for such a rotation determined for the BS π-complexes of 12, 16, and 18 are presented (panels a, b, and c, respectively). The corresponding rotational energies for all the active species of the considered catalysts are collected in Table 2. It should be pointed out that in the case of the symmetric disubstituted systems, such as the catalyst 12, R = R0 = i-Pr, the structures i and iii are indistinctive, and the transition between them proceeds as the rotation of the aryloxy ligand around the Ti-O-C bonds characterized by the energy barrier of ΔE(ii) = ΔE(iv). For the asymmetric monosubstituted systems, such as the catalysts 16 and 18, R = i-Pr and Ph, respectively, R0 = H, in turn, the structures i and iii correspond to the anti and syn ethylene π-complexes with the monomer located in the position respectively anti and syn to the aryloxy substituent R. According to the scheme shown in the top part of Figure 5, the transition between this anti and syn π-complex may proceed in two ways, via the “bottom” or “top” rotation characterized by the barriers of ΔE(ii) and ΔE(iv) by analogy with the precatalyst case. Comparing the energy profiles for the rotation of the aryloxy ligand around the Ti-O-C bonds for the BS π-complexes of 12 (type 3) and 16 and 18 (type 4) shown in the bottom part of Figure 3, it can be concluded that, similarly to the precatalysts, also the active species of the type 4 catalysts reveal more pronounced conformational flexibility compared to the type 3 system. The corresponding rotational barriers are 3.3 kcal/mol for 12, 1.2 kcal/mol

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Table 2. Energy Barriers (in kcal/mol) of the Rotation of the Aryloxy Ligand around the Ti-O-C Bonds for the Active Species, Ethylene π-Complexes of the Selected Catalysts 12 (Type 3) and 16 and 18 (Type 4) rotational barrierb ΔE(ii)

a

complex 12

Cp*, R = R0 = (i-Pr)2

16

Cp*, R = i-Pr, R0 = H

18

Cp*, R = Ph, R0 = H

BS FS BHT BS FS BHT BS FS BHT

ΔE(iv)

ΔE(iii)b

1.91 5.06 3.12 2.56 5.69 2.49

0.00 0.00 0.00 -1.31 0.45 0.56 -2.31 -0.43 -1.49

3.31 8.25 4.04 1.16 4.59 2.21 1.35 4.33 0.51

a See Scheme 1, Scheme 3, and Figure 3. b Relative to the ethylene π-complex of the minimum energy structure i.

Figure 5. Schematic representation of the rotation of the aryloxy ligand around the Ti-O-C bonds (top) together with the energy profiles for such a rotation for the BS π-complexes of 12 (bottom, a), 16 (bottom, b), and 18 (bottom, c).

(“bottom”) and 1.9 kcal/mol (“top”) for 16, and 1.4 kcal/mol (“bottom”) and 2.6 kcal/mol (“top”) for 18. Consequently, the low rotational barriers determined from the static DFT calculations in the case of both type 4 catalysts, 16 and 18, confirm the possibility of the easy transition between the BS anti and the energetically preferred syn π-complex/pathway. Thus, the rotation of the phenoxy ligand around the Ti-O-C axis indeed allows for the switch between the nonreactive and reactive propagation pathway, contributing further to the increase in the catalytic activity of the type 4 catalysts. Let us analyze now the rotational barriers determined for all the active species, i.e., the lowest energy BS, FS, and BHT

π-complexes of the catalysts considered. Three main conclusions can be drawn from the data of Table 2. First, the rotational barriers determined for all the π-complexes of the systems 16 and 18 are always substantially lower compared to the corresponding values calculated for the catalyst 12. The corresponding energy barriers obtained for the complexes of 12, 16, and 18 are 3.3 vs 1.2 vs 1.4 kcal/mol for the BS, 8.3 vs 4.6 vs 4.3 kcal/mol for the FS, and 4.0 vs 2.2 vs 0.5 kcal/mol for the BHT ethylene π-complexes. It is also clearly seen from the data that the rotation of the aryloxy ligand around the Ti-O-C axis proceeds much easier in the π-complexes with the β-agostic interaction, i.e., the BS and BHT systems. For the FS active species, the highest rotational barriers were determined in all cases. Accordingly, the presence of the β-agostic bond implies the weakening of the Ti-O bond as a consequence of the lowering of the electron density on the metal, as indicated by the calculated Hirshfeld charges (see Supporting Information). Second, analyzing the results obtained for the type 4 π-complexes, in all cases the “bottom” rotation pathway is preferred, namely, ΔE(iv) >ΔE(ii). The corresponding ΔE(iv) and ΔE(ii) values determined for 16 (18) vary between 1.2-4.6 (0.5-4.3) and 1.9-5.1 (2.5-5.7) kcal/mol, respectively. Such an inversion of the favored rotation pathway compared to the precatalyst observed for the system 18 can also be explained on the basis of the secondary interactions Ph--H. Namely, in the π-complex geometries, such interactions are possible not only between the phenyl substituent and the Cp*-protons but also between the phenyl and the hydrogen atoms of the alkyl (the polymer chain) or ethylene. Stabilizing the transition state of the rotation, they are also responsible for the substantial lowering of the barriers in the case of the active species of 18 to the level or even below the level of values determined for the corresponding π-complexes of 16. Finally, comparing the energy barriers calculated for the aryloxy ligand rotation in the cationic active forms and the corresponding precatalysts, it is also worth emphasizing that for all the ethylene π-complexes with the β-agostic-bound propyl, the rotation proceeds much easier than for the precursors. The rotational barriers for the BS and BHT π-complexes vs precatalyst are 3.3 and 4.0 vs 7.1 kcal/mol for 12, 1.2 and 2.2 vs 3.3 kcal/mol for 16, and 1.4 and 0.5 vs 4.3 kcal/mol for 18. On the contrary, the energetic cost of the rotation for the FS π-complexes is generally higher: 8.3, 4.6, and 4.3 kcal/mol for 12, 16, and 18, respectively.

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Figure 6. Changes in the dihedral angle describing the rotation around the Ti-O-C axis of the aryloxy ligand along the molecular dynamics trajectory for the active species, ethylene π-complexes of 16 and 18 (a and b, respectively). Passing 180 or -180 levels (indicated by red line) corresponds to the “bottom” rotation. Panels c and d show snapshots of trajectories for the ethylene π-complexes of 16 and 18, respectively; vertical blue lines indicate time interval during which the snapshots were taken.

CPMD Simulations for the Active Species. The overall conclusions obtained from static DFT calculations are further supported by the results of molecular dynamic simulations for active species, ethylene π-complexes of 16 and 18. Before discussing the example results, it should be pointed out that in the case of the active species the analyzed time of the simulation was shorter (20-25 ps) than for the corresponding precatalysts (60 ps). This was due to the spontaneously occurring ethylene insertion reactions, starting from the analyzed π-complexes. In Figure 6 we present the evolution of the dihedral angle describing rotation of the phenoxy ligand around the Ti-O-C axis along the dynamical trajectory. For the system 16 one “bottom” and for the system 18 two “bottom” rotations are observed. In the case of the active species, no spontaneous “top” rotations are observed for the active species. However, the observed preference of the “bottom” rotation stays in general agreement with rotational barriers obtained from the static calculations (cf. Table 2). As in the case of the precatalysts, the results of the CPMD simulation performed for the π-complex derived from 18 show that the stable, equilibrium structures occurring between the ligand rotations are stabilized by the secondary interactions. However, in the case of the active species such interactions involve not only the hydrogen atoms on the Cp*-methyls but as well those on the alkyl chain, facilitating the “bottom” rotation in this case. The presence of such secondary interactions is clearly seen in the snapshots from the trajectory shown in panel d of Figure 6.

Concluding Remarks The results of the static and dynamic DFT calculations presented here confirm the more pronounced conformational flexibility of the monosubstituted systems of type 4 compared to the precatalyst 12 that exhibits substantial steric congestion imposed by the ancillary ligand combination of Cp*/(O-2,4-(i-Pr)2C6H3). Particularly, in the case of the precatalyst 18, with a rather bulky phenyl-phenoxy ligand, the decrease in the “top” rotational barrier is observed due to the secondary interactions between the phenyl substituent and the methyl protons of Cp*. This leads to the energetic preference of the corresponding “top” over “bottom” rotation, favored in turn for the alkyl-substituted complexes 15-17. Using the calculated 1H NMR chemical shifts of the Cp* methyl protons, the Ph--H secondary interactions for the systems comprising the phenyl substituents on the aryloxy ligand observed in the molecular structures of the intermediate species of 18 were further confirmed. It was shown that such interactions are too weak to prevent the Cp* ring rotation. Nevertheless, their dynamic nature, demonstrated here, is crucial for the rotation of the phenyl-phenoxy ligand at finite temperature. The results obtained for the rotation of the phenoxy ligand around the Ti-O-C axis in the active species, i.e., ethylene π-complexes, show that in such cases the rotation can proceed even easier than in the corresponding precatalysts. Especially, the ethylene systems with β-agostic propyl reveal more pronounced conformational flexibility. It seems to be

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Table Al. Methane-Benzene Bond-Energy Components (in kcal/mol) for the Considered Methane-Phenyl Complexes According to the Ziegler-Rauk Energy Decomposition Schemea component

complex 1b

complex 2b

ΔEelstat ΔEPauli ΔEorb ΔEtot ΔEtot CCSD(T)/aug(d,p)-6-311G**c

-1.25 1.74 -1.41 -0.92

-1.53 2.14 -1.63 -1.01 -1.23

ΔEtot = ΔEelstat þ ΔEPauli þ ΔEorb. See Figure ref 48. a

Figure A1. Methane-benzene complexes studied (a) together with the dominating contribution to the deformational density, ΔF, according to the ETS-NOCV analysis (b).

particularly important for the type 4 catalysts, since such an easy rotation allows for the easy transition between the anti and syn, i.e., nonreactive and reactive, propagation pathways,21,22 which can lead to an increase in the catalytic activity of such systems. A significant decrease in the rotational barriers observed for the π-complexes of 18 also comes from the secondary interactions Ph--H, possible here not only between the phenyl substituent and the Cp*-protons but also between the phenyl and the hydrogen atoms of the alkyl or ethylene.

Appendix In order to understand the nature of the weak interaction between the Cp* protons and the phenyl on the aryloxy ligand, Ph--H, discussed in the present article, we performed the Ziegler-Rauk bond-energy decomposition analysis (extended transition state, ETS)49-51 and the analysis of natural orbitals for chemical valence (NOCV)52-54 within the combined ETSNOCV scheme54 implemented in the ADF 2009.01 program for two methane---benzene complexes, 1 and 2 (Figure A1). The structure 1 of the CH4---C6H6 complex was constructed from the precatalyst 18, from which the interacting Cp*-methyl and phenyl groups were cut out and saturated with two hydrogens atoms (see Figure A1, panel a). The geometry 2 of the CH4---C6H6 complex was based on ref 48; in this structure one of the hydrogen atoms is placed symmetrically above the middle of benzene ring at a distance of 3.8 A˚. In the Ziegler-Rauk ETS energy decomposition scheme49-51 the total bonding energy ΔEtot between interacting fragments (in the geometries as in the complex) is divided into three components:

ΔEtot ¼ ΔEelstat þ ΔEPauli þ ΔEorb

ð1Þ

(49) Ziegler, T.; Rauk, A. Theor. Chim. Acta 1978, 46, 1. (50) Ziegler, T.; Rauk, A. Inorg. Chem. 1979, 18, 1558. (51) Ziegler, T.; Rauk, A. Inorg. Chem. 1979, 18, 1755. (52) Mitoraj, M.; Michalak, A. J. Mol. Model. 2007, 13, 347. (53) Michalak, A.; Mitoraj, M.; Ziegler, T. J. Phys. Chem. 2008, 112, 1933. (54) Mitoraj, M.; Michalak, A.; Ziegler, T. J. Chem. Theory Comput. 2009, 5, 962.

b

A1 c

. According to

The first term, ΔEelstat, corresponds to the classical electrostatic interaction between the promoted fragments as they are brought to their positions in the final complex. The second term, ΔEPauli, accounts for the repulsive Pauli interaction between occupied orbitals on the two fragments in the combined molecule. Finally, the last stabilizing term, ΔEorb, represents the interactions between the occupied molecular orbitals of one fragment and the unoccupied molecular orbitals of the other fragment as well as mixing of occupied and virtual orbitals within the same fragment (inner-fragment polarization). Natural orbitals for chemical valence have been defined53,54 as eigenvectors of the deformation density matrix. It was shown that the natural orbitals for chemical valence pairs (ψ-k, ψk) decompose the differential density ΔF into NOCV contributions (ΔFk):

ΔFðrÞ ¼

M=2 X k¼1

vk ½ - ψ2- k ðrÞ þ ψ2k ðrÞ ¼

M=2 X

ΔFk ðrÞ ð2Þ

k¼1

where νk and M stand for the NOCV eigenvalues and the number of basis functions, respectively. In the combined ETS-NOCV scheme54 the orbital interaction term (ΔEorb) is expressed in terms of the NOCV eigenvalues (vk) as

ΔEorb ¼

X k

ΔEorb ðkÞ ¼

M=2 X k¼1

TS vk ½ - F TS - k, - k þ Fk, k ð3Þ

where FTS i,i are diagonal Kohn-Sham matrix elements defined over NOCV with respect to the transition state (TS) density (at the midpoint between density of the molecule and the sum of fragment densities). The above components ΔEorb(k) provide the energetic estimation of the charge-flow channel ΔFk. The ETS bond-energy contributions are collected in Table Al. The results show that in both complexes 1 and 2 the electrostatic component, ΔEelstat, is relatively large, -1.3 and -1.5 kcal/mol, respectively. It comes mostly from the interaction of the proton placed in the vicinity of the minimum of the benzene electrostatic potential. This term is counterbalanced by the Pauli term, ΔEPauli, 1.7 and 2.1 kcal/ mol for 1 and 2, respectively. Finally, the stabilization from the orbital interaction term, ΔEorb, corresponding to the charge transfer between the subsystems is also relatively large: -1.4 and -1.6 kcal/mol for 1 and 2, respectively. The dominating NOCV charge transfer channel (i.e., NOCV contribution to the deformation density) is shown in part b of Figure A1; this contribution accounts for -1.1 and -1.3 kcal/mol, respectively. The sum of all these contributions, the total interaction energy, ΔEtot, is -0.9 and -1.0 kcal/mol for 1 and 2, respectively. It is worth pointing out that the total interaction energy for 2, -1.0 kcal mol, compares quite well

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with the CCSD(T)/aug(d,p)-6-311G** value of -1.2 kcal/ mol calculated by Tsuzuki et al.48 It may be concluded that the dispersive part of the interaction that is not covered by DFT introduces a relatively small error of 0.2 kcal/mol for 2. Thus, since the methane-benzene interaction energies in 1 and 2 differ only by 0.1 kcal/mol, the corresponding error in the description of the Ph--H interaction in the precatalyst 18 should be comparable as well.

Poland (N N204 227534) and the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science, and Technology (No. 2010-0018456).

Acknowledgment. This work was supported by a research grant from the Ministry of Science and Higher Education in

Supporting Information Available: This material is available free of charge via the Internet at http://pubs.acs.org.

Note Added after ASAP Publication. This paper was published on the Web on Oct 1, 2010, with an omission in ref 8. The corrected version was reposted on Nov 1, 2010.

On Conformational Flexibility of Half-Titanocene Catalysts with Aryloxy

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