DFT Studies on Styrene Polymerization Catalyzed by Cationic Rare

Sep 8, 2016 - The mechanism of styrene polymerization catalyzed by five analogous cationic rare-earth-metal complexes [(RCH2–Py)Y(CH2SiMe3)]+ (R ...
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DFT Studies on Styrene Polymerization Catalyzed by Cationic RareEarth-Metal Complexes: Origin of Ligand-Dependent Activities Xingbao Wang,† Fei Lin,‡ Jingping Qu,† Zhaomin Hou,†,§ and Yi Luo*,† †

State Key Laboratory of Fine Chemicals, School of Pharmaceutical Science and Technology, Dalian University of Technology, Dalian 116024, China ‡ State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, China § Organometallic Chemistry Laboratory and RIKEN Center for Sustainable Resource Science, RIKEN, Wako, Saitama 351-0198, Japan S Supporting Information *

ABSTRACT: The mechanism of styrene polymerization catalyzed by five analogous cationic rare-earth-metal complexes [(RCH2−Py)Y(CH2SiMe3)]+ (R = C5Me4 (Cp′), 1+; R = C9H6 (Ind), 2+; R = C13H8 (Flu), 3+), [(Flu−Py)Y(CH2SiMe3)]+ (4+), and [(Flu−CH2CH2−NHC)Y(CH2SiMe3)]+ (5+) has been studied through DFT calculations. Having achieved an agreement between theory and experiment in the activity discrepancy and selectivity, it is found that styrene polymerization kinetically prefers 2,1-insertion to 1,2-insertion. The free energy profiles for the insertion of a second monomer molecule have been computed for both migratory and stationary insertion manners, and the former resulting in a syndiotactic enchainment indicates obvious kinetic preference. The current results suggest that the coordination of styrene to the active metal center could play an important role in the observed activity difference. Interestingly, the charge on central metal of the cationic species accounts for the activities of 1+, 2+, and 3+: the higher the charge on the central metal, the higher the activity. The coordination of a THF molecule to the central metal and more difficult generation of the active species could be responsible for the low activity of 4+. For species 5+, the resulting product of the first styrene insertion is quite stable, and the ancillary ligand and styryl group hamper the insertion of the incoming styrene molecule. This could be responsible for the absolute inertness of 5+ toward styrene polymerization. The calculated results also suggest that a longer alkyl chain of the side arm of the ancillary ligand could deter monomer coordination and thus decrease the polymerization activity.

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INTRODUCTION Syndiotactic polystyrene (sPS) has become a very important engineering plastic because of its high melting point (Tm = 270 °C), rapid crystallization ability, low dielectric constant, and excellent resistance to heat and chemicals.1−8 This inexpensive polymer is an attractive material for a large number of industrial applications because of its unique combination of valuable properties.4,9−11 In 1986, sPS was discovered first by Ishihara at Idemitsu by using unlinked half-sandwich titanium catalysts.8 After that, a large number of titanium analogues generally formulated as [LTiX3] have been extensively investigated, where L could be any of cyclopentadienyl-related ligands and X is a halogen or alkoxyl group.2 Among the reported catalysts, only a few examples have appeared to be significantly active for styrene syndiotactic polymerization. Recently, rare-earth-based catalysts with very high activity and syndiospecificity have received academic and industrial attention. In 2004, Carpentier and co-workers disclosed a new class of neutral allylic organolanthanide derivatives that displayed high activity to provide perfect sPS.12 Hou et al. separately reported mono© XXXX American Chemical Society

(cyclopentadienyl) rare-earth-metal bis(alkyl) complexes serving as excellent precursors for syndioselective styrene (co)polymerization.13 After that, other derivatives supported by the substituted cyclopentadienyl (Cp′) and indenyl (Ind) ligands have been reported as efficient catalysts for the syndiospecific styrene polymerization.14−18 Recently, some of us developed a series of rare-earth-metal complexes bearing N-type functionalized Cp′, Ind, and fluorenyl (Flu) ligands for styrene polymerization (Figure 1).2,15,19 A series of rare-earth-metal complexes ([(RCH2− Py)Y(CH2SiMe3)2(THF)]) bearing the pyridyl (Py)-methylene-functionalized Cp′/Ind/Flu ligands were synthesized (1/2/ 3), in which all the CGC ligands adopt a η5/κ1 binding mode.2 These complexes in combination with [Ph3C][B(C6F5)4] and AliBu3 showed different performances toward styrene polymerization, although they have a similar ancillary ligand. The complexes 1 and 2 showed low activity to afford syndiotactic Received: July 12, 2016

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DOI: 10.1021/acs.organomet.6b00558 Organometallics XXXX, XXX, XXX−XXX

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od.28 These computations were mainly intended to investigate the intrinsic role of the chiral orientation of the growing polymeric chain on the regio- (2,1- vs 1,2-insertions) and stereo- (syndiotactic vs isotactic) selectivities. However, to the best of our knowledge, there are few systematic theoretical studies on the origin of ligand-induced catalytic performance for styrene polymerization.22,33,34 The aim of the present contribution on styrene polymerization initiated by the five complexes 1−5 was to explore the molecular origin of their activity discrepancy. We employed the complexes 1, 2, and 3, which have the same side arm moiety, to explore the effect of electron donating of the aromatic ligands during styrene polymerization. The complexes 3, 4, and 5 were employed to explore the effect of the side arm groups of the cyclopentadienyl on the observed catalytic performance for styrene polymerization. In order to exclude the influence of different metal centers, the yttrium metal was considered in all cases.

Figure 1. Rare-earth-metal alkyl complexes 1−5.

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enriched polystyrene. However, complex 3 showed unprecedented high activity (1.56 × 107 g/(molLn·h)) and excellent syndioselectivity (rrrr > 99%). The pyridyl-functionalized Flu Y complex, [(Flu−Py)Y(CH2SiMe3)2(THF)] (4),19 was also designed and synthesized. The X-ray structure of this complex indicated that the Flu moieties were bound to the central metal atoms in an asymmetric η3-allyl fashion rather than a typical symmetric η5 mode. By adding 1 equiv of [Ph3C][B(C6F5)4] and 10 equiv of AliBu3 to the THF-solvated precursor 4, styrene was successfully polymerized in a much lower activity to afford syndiotactic-enriched PS (rrrr = 81−85%). An ethenylbridged carbene modified Flu rare-earth-metal complex ([(Flu−CH2CH2−NHC)Y(CH2SiMe3)2], 5) was also used in an attempt to polymerize styrene. The results showed that 5 was absolutely inert toward styrene polymerization,2 although this complex exhibited high activity, high 3,4-regioselectivity, and the unprecedented livingness for the polymerization of isoprene and (E)-1-(4-methylphenyl)-1,3-butadiene.20,21 As shown above, an intriguing feature of these systems is the strong dependence of catalytic performance on the nature of ligands and the side arm groups on the cyclopentadienyl. Therefore, clarification of the origin of such ligand-dependent polymerization performance is crucial for the design of polymerization catalysts.22 Numerous computational studies have been successfully conducted to investigate the mechanism of styrene polymerizations catalyzed by early transition and rare-earth-metal complexes.9,10,23−32 These theoretical results have effectively promoted the design and development of a homogeneous metal catalyst. For example, the origin of regioselectivity and stereoselectivity of styrene polymerization with a Cp-based ansa-metallocene catalyst SiH2Cp2Ti+−CH3 was computationally investigated by Jo and co-workers.24,25 Caporaso et al. reported a combined experimental and theoretical study on styrene polymerization to clarify the regio- and stereocontrol mechanism operating with a C 6 F 5 -substituted bis(phenoxyimine) titanium dichloride complex.29 Maron and co-workers employed theoretical methods (DFT) to investigate the syndiospecificity of the styrene polymerization catalyzed by single-site allyl ansa-lanthanidocenes {(C 5 H 4 )CMe 2 -(9C13H8)}Ln(C3H5).9,10 In their studies, the factors governing the formation of syndiotactic polystyrene were investigated. Recently, our group computationally studied the copolymerization of styrene and ethylene by the cationic half-sandwich scandium alkyl species (η5-C5Me5)Sc(CH2SiMe3)+ by using the quantum mechanics/molecular mechanics (QM/MM) meth-

COMPUTATIONAL DETAILS

All calculations were performed with the Gaussian 09 program.35 The B3PW91 hybrid exchange−correlation functional was utilized for geometry optimization and frequency calculations.36−38 The 6-31G* basis set was used for H, C, N, and O atoms, and the Si and Y atoms were treated by the Stuttgart/Dresden effective core potential (ECP) and the associated basis sets.39,40 One d-polarization function (exponent of 0.284) was augmented for the basis set of the Si atom. Geometries of all species were fully optimized without symmetry constraints. As shown in previous studies, such functional and basis sets have been fully tested and proved to be reliable.9,10,28,41−44 The transition states were ascertained by a single imaginary frequency for the correct mode. The intrinsic reaction coordinate (IRC) following was conducted for the transition states to verify that they connect two corresponding minima. The minima on the reaction energy profiles were verified to have all real frequencies only. The solvation effects were considered through single-point calculations with the PCM45 solvation model. These single-point calculations are based on the optimized structures, and the basis sets are the same as that for geometry optimizations. Toluene (ε = 2.37) was employed as a solvent in the PCM calculations. The Multiwfn 3.3 program46 was used to calculate the Hirshfeld47 charge using the checkpoint file obtained from the Gaussian calculations. Computed structures are illustrated with CYLView.48 In order to ensure the validity of the theoretical method used to compute energy profiles, the optimized structures of the metal complexes (1, 2, 3, and 4) have been compared with available solidstate structures from X-ray diffraction studies.2,19 The selected geometrical parameters are summarized in Table S1 in the Supporting Information (SI), which shows a good agreement between experimental and calculated ones. In order to compare different methodologies, the energy barrier for styrene polymerization by scandium species ([(Flu−CH2−Py)Sc− (C17H19)]+) analogous to 3+ was calculated by using the B3PW91, B3PW91-D3,49 M06,50 and MPW1K51 functionals on the basis of optimized structures (see Table S2 and Figure S1). The analogous scandium system was considered here since it has available experimental data.52 With the MPW1K functional, the calculated energy barrier (ΔG⧧ = 21.8 kcal/mol and ΔH⧧ = 9.9 kcal/mol) for the scandium system is in good agreement with the experimental data (ΔG⧧expt = 21.3 kcal/mol and ΔH⧧expt = 9.7 kcal/mol).52 Therefore, in this study, single-point energies were calculated using the MPW1K functional, and the energy profiles were constructed at the MPW1K(PCM)//B3PW91 level.

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RESULTS AND DISCUSSION The optimized bare cationic species (1+, 2+, 3+, 4+, and 5+ in Figure 2) were used for modeling the initial active species in the present study. It is noteworthy that, in the case of cationic B

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1,2- (primary) and 2,1-(secondary) insertions), two enantiofaces (re and si) of styrene have been considered. It is worth noting that we are not suggesting absolute enantioface selectivity in the styrene insertion, but rather relative enantioface selectivity to form syndiotactic polystyrene. Styrene Polymerization Catalyzed by [(RCH2−Py)Y(CH2SiMe3)]+ (1+, 2+, and 3+). Insertion Reaction of the First Styrene Molecule. The insertion of the first styrene monomer into the Y−CH2SiMe3 bond of cationic species [(RCH2− Py)Y(CH2SiMe3)]+ was calculated. The computed energy profiles are shown in Figure 3. As shown in this figure, the 2,1-insertion reaction is more kinetically and thermodynamically favorable than 1,2-insertion. The 1,2-insertion process has a higher free energy barrier by more than 5 kcal/mol and is less exergonic by more than 13 kcal/mol in comparison with the 2,1-insertion. This result is consistent with that reported for styrene insertion into the cationic scandium alkyl species (η5C5Me5)Sc(CH2SiMe3)+.28 It is also in line with the previous results for styrene polymerization catalyzed by singlecomponent ansa-lanthanidocenes.9,55 In the present study, the 2,1-re mode is computed to be more favorable than the 2,1-si mode. This could be ascribed to the strong steric repulsion between the phenyl ring of styrene and the bulky ancillary ligands (Cp′, Ind, and Flu) (see the transition structures in Figure S2). In the 2,1-si insertion modes, the phenyl ring points toward the R ligands and thus causes repulsion, which could account for the instability of the given insertion transition state. Overall, the 2,1-re insertion reactions are found to be the most favorable. We focus now exclusively on the most favorable 2,1-re insertion pathway. The reactions start with a styrene π-adduct (see structure in Figure 4). This coordination of styrene monomer is calculated to be thermoneutral. This can be attributed to the loss of entropy by coordination.28,56 It is noted that the coordination process is exothermic (see ΔH in Table S3 in the SI). Therefore, the coordination is predicted to be thermodynamically favorable. The interaction between styrene and cationic species is essentially electrostatic in nature.9 This is suggested by the geometries of these adducts (A12,1‑re, Figure 4). The CC double bond of styrene is elongated by just 0.01 Å with respect to free styrene, and the distance between the C atoms of the double bond and the metal center is rather long (2.82−3.09 Å). In the transition structures, the double bond of the incoming styrene is significantly activated (1.40−1.41 Å vs 1.34 Å in free styrene) and the new bond between Y−Cα is almost formed (2.43−2.48 Å). In the final products (P12,1‑re, Figure 4), the new C−C bond is now fully formed. These

Figure 2. Optimized cationic species showing a significant interaction between the Y atom and a methyl carbon atom of the SiMe3 group, as manifested by the short Y···Cγ contact (2.64−2.68 Å) and elongated Si−Cγ bond length (1.99−2.00 Å) in comparison with the normal Si− C bond length of 1.89 Å.

species 4+, the ligand binds to the central metal atom in an η5cyclopentadienyl/κ1 mode rather than an η3-allyl/κ1 one shown in the corresponding neutral complex.19 It was previously supposed that AliBu3 functions to remove the THF molecule and the Y−Al heterobiometallic species is unlikely to work in such systems.52,53 The bimetallic species is therefore not considered for polymerization in the current study. It was reported that the THF tends to move away from the metal center during chain propagation and thus has no effect on the stereoselectivity.53,54 As shown in the previous study,9 four different possible modes were considered for styrene insertion in the chain initiation step (Chart 1). For each kind of insertion (namely, Chart 1. Various Styrene Insertion Modes

Figure 3. Computed energy profiles (free energy in kcal/mol) for the first styrene insertion into the Y−C bond of the cationic species [(RCH2− Py)Y(CH2SiMe3)]+ (1+, 2+, and 3+). The energy of each structure is relative to the energy sum of the isolated free reactants, i.e., the cationic active species and styrene monomer. C

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Figure 4. Optimized structures and relative energies of the stationary points involved in the 2,1-re insertion of styrene into the Y−CH2SiMe3 bond of [(RCH2−Py)Y(CH2SiMe3)]+. Energies are relative to corresponding cationic species (1+, 2+, or 3+) and monomer. All hydrogen atoms are omitted for clarity.

Figure 5. Computed energy profiles (free energy in kcal/mol) and transition structures (distances in Å) for the frontside “migratory” (bottom) and backside “stationary” (top) insertions of the second monomer into P12,1‑re. Energies are relative to corresponding P12,1‑re and the monomer. All of the hydrogen atoms are omitted for clarity. The SiMe3 group is replaced by a purple ball.

calculated. For the insertion of the second styrene molecule, the frontside “migratory” vs backside “stationary” insertion fashions10 (Figures S3 and S4) were considered, and only the most favorable insertion was calculated (see Figure 5 and Table S4). During the “migratory” insertion, one computationally switches the coordination sites of the migratory growing polystyryl chain and of the incoming monomer at each insertion step, and the “stationary” insertion with a stationary polystyryl chain corresponds to the coordination of the incoming styrene monomer onto the same coordination site as for the first insertion. As shown in Figure 5, the calculation results reveal an obvious kinetic preference for frontside migratory insertion, resulting in a syndiotactic enchainment of the monomer units. The backside insertion resulting in an

insertion reactions are computed to be exergonic by more than 10 kcal/mol. The calculated results reveal that the complexation energy (0.0−0.8 kcal/mol) and energy barrier height (14.1−14.7 kcal/ mol) for the insertion of the first monomer have no significant discrepancy among the systems of 1+, 2+, and 3+ (Figure 3). This result indicates that the insertion of the first monomer into the Y−C σ-bond of 1+, 2+, and 3+ does not correlate with the observed difference in the activity toward styrene polymerization catalyzed by cationic species 1+, 2+, and 3+. Insertion Reactions of the Second and Third Monomers. To investigate the origin of the observed activity discrepancy and the stereoselectivity during the chain propagation, the continuous insertion of the second styrene to P12,1‑re has been D

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Figure 6. Computed energy profiles (free energy in kcal/mol) and transition structures (distances in Å) for insertions of the third monomer into P2migratory. Energies are relative to corresponding P2migratory and the monomer. All the hydrogen atoms are omitted for clarity. The SiMe3 group is replaced by a purple ball.

complexation energy is capable of accounting for the experimental observations. The insertion of styrene into the P23‑migratory is computed to be a feasible process, as indicated by the ΔH⧧ of 9.3 kcal/mol and ΔG⧧ of 22.9 kcal/mol. Overall, the calculation results suggest that the activity discrepancy of the three systems is reflected at the chain propagation rather than chain initiation stage. As aforementioned, the coordination of styrene to the metal center during the chain propagation could account for the observed activity difference of the three precursors, and such a coordination is essentially electrostatic in nature. Considering this, the Mulliken57 and Hirshfeld charges of the central metal (Q) of P2migratory have been analyzed (Table 1). It is found that

isotactic enchainment is at least 16.3 kcal/mol more demanding. This advantage of frontside insertion could be responsible for the observed preference of high syndioselectivity in the experiments. This difference can be explained by analyzing the geometry of the transition states (Figure 5). In the transition states of stationary insertion, because of the steric hindrance around the Y metal, the phenyl group of the newly inserted monomer unit coordinates to the Y metal in a η1fashion rather than a more stable η3-fashion. This haptotropic shift is necessary to allow the stationary insertion of the second incoming styrene unit.10 In contrast, in the transition states of migratory insertion, the phenyl groups retain η3-coordination. The geometric data in Figure 5 suggest that the barrier difference between migratory and stationary insertions could be ascribed to the degree of C2−Cα and C1−Y bond formations in the TS2 species along with the reaction coordinates. That is, the distances of C2···Cα and C1···Y in TS2migratory are much longer than that in TS2stationary, suggesting that the migratory insertion could reach the transition state earlier than the stationary insertion. As shown in Figure 5, the barrier heights for the migratory insertion of the second monomer are 13.1, 14.8, and 13.1 kcal/ mol for the systems 1+, 2+, and 3+, respectively. The adduct 3A2migratory is more stable than 1-A2migratory and 2-A2migratory by 1.0 and 2.2 kcal/mol, respectively. This suggests that the coordination of styrene to the active metal center could play an important role in the observed activity difference among the three systems, as also found in our previous experimental and computational studies.52,54 To further see, from the point of view of theory, whether the cationic species 3+ is more active than 1+ and 2+, the migratory insertions of the third monomer into P2migratory were calculated (see Figure 6 and Table S5). As shown in Figure 6, the coordination free energy of styrene on the metal center of 3P2migratory is 9.3 kcal/mol, which is lower than the cases of 1+ and 2+ by 2.0 and 1.9 kcal/mol, respectively. The free energy barrier for the system 3+ is lower than the cases of 1+ and 2+ by 1.1 and 0.5 kcal/mol. Such complexation energy and energy barrier priorities for the system 3+ were also suggested by the results derived from the MP2 method (see Table S6). Our previous experimental results showed that tiny differences (0.2−0.8 kcal/mol) in energy values could be responsible for the obvious differences in rate constants (1.7 × 10−2 to 12.9 × 10−2 min−1).52 Considering this and the lower activities of 1+ and 2+ compared with 3+, the computed difference in the

Table 1. Mulliken and Hirshfeld Charges on the Central Metal (QM and QH) and LUMO Energy (ELUMO) of P2migratory as Well as Energy Gaps (ΔE)a between the HOMO of Styrene and the LUMO of P2migratory 1-P2migratory 2-P2migratory 3-P2migratory

QM

QH

ELUMO (au)

ΔE (au)

1.124 1.140 1.194

0.447 0.458 0.478

−0.07916 −0.08239 −0.08199

0.14672 0.14349 0.14389

ΔE = ELUMO(active species) − EHOMO(Styrene) (EHOMO(Styrene) = −0.22588 au).

a

the charge on the central metal correlates well with the observed activity difference of the cationic species 1+, 2+, and 3+: the higher the charge on the central metal, the higher the activity. This may be related to the donor−acceptor-type bond between metal and the ligand. In the case of 3-P2migratory, due to the electron delocalization over the phenyl rings that are electron withdrawing, the ligand is less electron donating as compared with that in 1-P2migratory and 2-P2migratory and thus increases the Lewis acidity of the central metal.2,58,59 This can be indicated by the distances between the Y atom and the geometrical center of the cyclopentadienyl, which are 2.35, 2.37, and 2.42 Å in 1-P2migratory, 2-P2migratory, and 3-P2migratory, respectively. Our previous model study indicated that the HOMO− LUMO energy gap of the reactants correlated well with the metal-dependent activity toward styrene polymerization promoted by rare-earth-metal complexes.52 In this study, the energy gap (ΔE) between the HOMO of styrene and the LUMO of P2migratory (Table 1 and Table S7) has also been E

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Figure 7. Optimized structures and relative energies of the stationary points involved in the 2,1-re insertion of styrene into the Y−CH2SiMe3 bond of [(Flu−Py)Y(CH2SiMe3)]+. Energies are relative to 4+ and the monomer. All the hydrogen atoms are omitted for clarity.

Figure 8. Computed energy profiles (free energies in kcal/mol) and transition structures (distances in Å) for the second (left) and third (right) styrene insertions into 4-P12,1‑re and 4-P2migratory, respectively. Energies are relative to corresponding reactants involved. All the hydrogen atoms have been omitted for clarity. The C3H9Si group is replaced by a purple ball.

analyzed. However, the current result shows no correlation between the energy gap and the ligand-dependent activity. These results suggest that, for styrene polymerization catalyzed by rare-earth-metal complexes, the activities of the catalysts with architecture-related ligands and the same central metal may correlate with the charges on the central metal. This is possibly due to the fact that the activity-related metal charge varies with the electron-donating ability of these architecturerelated ancillary ligands, while for the catalysts holding the same ligand and different central metals, their activities may correlate with the HOMO−LUMO energy gap of the reactants. In this case, the metal of active species with high activity induced more orbital contribution from the surrounding ligand to the LUMO and reduced the LUMO energy and thus decreased the HOMO−LUMO energy gap of the reactants (active species and styrene monomer).52 Styrene Polymerization Catalyzed by [(Flu−Py)Y(CH2SiMe3)]+ (4+). Considering the structural similarity of 3+ and 4+, the most favorable 2,1-re insertion10,55,60 is again calculated for the insertion of the first monomer in the case of 4+. The structures of stationary points together with their relative energies are shown in Figure 7. As shown in this figure, the π-adduct has a relative energy of −0.7 kcal/mol and the energy barrier (ΔG⧧) of 14.1 kcal/mol should be overcome for achieving the insertion process. The overall energy profile for the styrene insertion into 4+ is similar to the cases of [(RCH2− Py)Y(CH2SiMe3)]+ (1+, 2+, and 3+). For the insertion of the second monomer, we also considered the favorable migratory insertion into the 4-P12,1‑re. Kinetically, the reaction has a quite low energy barrier of 10.5 kcal/mol (Figure 8), which is lower than that for the corresponding insertion in the case 3+. The third monomer insertion into 4P2migratory has also been calculated to be a feasible process, as suggested by the insertion energy barrier of 19.2 kcal/mol (Figure 8). However, this result is inconsistent with the experimental finding that the precursor 4 showed very low activity toward styrene polymerization.2,19

In a previous experimental study, it was speculated that the low activity of the precursor 4 was ascribed to the η3-allyl coordination mode of the Cp moiety that inhibited electron delocalization over the phenyl ring of the ligand.19 However, the optimized cationic species 4+ shows an η5-cyclopentadienyl/κ1 coordination mode rather than the η3-allyl/κ1 mode observed in the corresponding neutral complex. Moreover, the charge on the central metal of 4-P2migratory (1.16) is similar to 3-P2migratory (1.19). Therefore, the electron delocalization could not be suppressed during the 4+-mediated styrene polymerization. This situation drove us to further explore the origin of low activity of precursor 4. A comparison of the X-ray structures of 1, 2, 3, and 4 indicates that the distance of Y···OTHF in precursor 4 (2.308 Å) is significantly shorter than that in 1, 2, and 3 (2.429, 2.401, and 2.402 Å), suggesting a stronger coordination of the THF molecule to the Y center in 4. Actually, the calculated dissociation enthalpies of the THF molecule from the metal center are 9.25, 12.7, 12.6, and 22.2 kcal/mol for complexes 1, 2, 3, and 4, respectively. This suggests that the AliBu3promoted decoordination of the THF molecule is more difficult in 4 than that in 1, 2, and 3.52,53 The binding of THF molecule with AliBu3 is calculated to be exothermic by 18.9 kcal/mol. Therefore, in the case of 4, the abstraction of a THF molecule by AliBu3 is less thermochemically favorable (18.9 vs 22.2 kcal/mol). The THF molecule could recoordinate to the central metal and block the coordination of the styrene monomer. The calculations revealed that the complexation energy and energy barrier for the first styrene insertion into the THF-ligated system (thf4+) (13.4 and 25.4 kcal/mol, Figure S5) are 14.1 and 11.3 kcal/mol higher than that of the system without THF (4+), respectively. Our previous DFT calculations also suggested that the decoordination of THF to generate a vacancy for monomer coordination is crucial for styrene polymerization.52,54 Therefore, the coordination of the THF molecule to the central metal could be responsible for the low activity of complex 4+.52,54 F

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Organometallics Styrene Polymerization Catalyzed by [(Flu−CH2CH2− NHC)Y(CH2SiMe3)]+ (5+). Considering that the ancillary ligand of species 5+ shows a more significant difference in structure compared with 1+−4+, two possible scenarios (1,2-si and 2,1-re insertions avoiding the repulsion between the ancillary ligand and the phenyl ring) were computed for insertion of the first styrene molecule into cationic species 5+. The calculated free energy profiles are presented in Figure 9. As expected, there is

Figure 11. Computed energy profile (free energy in kcal/mol) and transition structures (distances in Å) for the insertion of a second styrene into 5-P12,1‑re. Energies are relative to 5-P12,1‑re and the monomer. All the hydrogen atoms have been omitted for clarity.

On the basis of the current calculation results, we speculated that the steric hindrance of trimethylphenyl of the 5+ group blocks the coordination of the second styrene insertion. To confirm this, we replaced its trimethylphenyl group with the methyl group and H atom, respectively, to see the situation of coordination and insertion of the second styrene monomer. This thus led to two model complexes, 6+ and 7+, as shown in Figure 12. As expected, the adduct of cationic species and monomer was located for both cases, and the complexation energy and insertion free energy barrier for the methyl case are higher than those for the case of a hydrogen substituent (5.3 vs 2.8 kcal/mol and 19.2 vs 14.3 kcal/mol, Table S4). This result suggests that the substituent hindrance of the carbene moiety plays an important role in the activity of 5+, and the smaller substituent group on the N-heterocyclic carbene could be beneficial for increasing the activity of such cationic species toward styrene polymerization. A structure comparison of 3+ with 5+ indicates that the side arm of the former connects with a Flu moiety and one methylene group, but two methylene groups are involved in the latter. This led us to wonder whether the length of the alkyl chain of the side arm contributes to the activity discrepancy. For this purpose, on the basis of 3+, we computationally designed cationic species 8+, where two methylene groups connect the Py and Flu moieties (Figure 13 and Figure S6). The insertion of the third styrene molecule was considered for the case of 8+ since the activity discrepancy appeared in this step (vide supra). The calculated results show that the complexation energy of the monomer to the metal center is 12.1 kcal/mol, which is higher than that for the case of 3+ (9.3 kcal/mol, Figure 6). However, the energy barrier of 22.9 kcal/ mol for this insertion is the same as that for the case of 3+ (Figure 6). These results suggest that the longer bridge makes

Figure 9. Computed energy profiles (free energy in kcal/mol) for insertion of the first styrene molecule into the Y−C σ-bond of the cationic species [(Flu−CH2CH2−NHC)Y(CH2SiMe3)]+ (5+). Energies are relative to 5+ and the monomer.

an obvious kinetic preference for the 2,1-re insertion. Unexpectedly, 5+-mediated 2,1-insertion of the first styrene molecule has a moderate free energy barrier of 17.2 kcal/mol. It is noteworthy that the metal center of 5-P12,1‑re is wrapped by the bulky ligand and phenyl ring of the inserted styrene unit. It is therefore supposed that such a structure may hamper the insertion reaction of the incoming monomer.24,30 To test this hypothesis, the insertion of second styrene molecule has been calculated. Both migratory and stationary insertions were considered in this case. Due to the steric hindrance around the metal center of 5-P12,1‑re, as shown in Figure 10, attempts to locate a coordination complex or transition state for migratory insertion were fruitless. The free energy profile of the stationary insertion is shown in Figure 11. The energy barrier for the insertion of a second styrene molecule is significantly higher (ΔG⧧ = 31.7 kcal/mol) than the case of 1+, 2+, and 3+ species, and the reaction is unlikely to occur under the experimental conditions.52 The phenyl group of the preinserted styrene blocks the coordination of the incoming monomer. The Lewis acidity of 5-P12,1‑re could be lower than 3-P12,1‑re, as suggested by the Mulliken charge on the metal (1.06 for 5-P12,1‑re vs 1.27 for 3-P12,1‑re). This is because of the highly electron-donating nature of the Nheterocyclic carbene (NHC) moiety in 5-P12,1‑re.

Figure 10. Optimized structures and relative energies of the stationary points involved in the 2,1-re insertion of styrene into the Y−CH2SiMe3 bond of [(Flu−CH2CH2−NHC)Y(CH2SiMe3)]+. Energies are relative to 5+ and the monomer. All the hydrogen atoms were omitted for clarity. G

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Figure 12. Replacement of trimethylphenyl in cationic species 5+ with a methyl group (6+) and H atom (7+).

also account for the higher activity of precursor 3 compared with precursor 4. The tiny value of ΔΔH′ (0.1 kcal/mol) suggests that the activation of 3 and 5 by [Ph3C][B(C6F5)4] is thermodynamically comparable.

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CONCLUSION We have computationally investigated styrene polymerization catalyzed by five cationic rare-earth-metal complexes, [(RCH2− Py)Y(CH2SiMe3)]+ (R = C5Me4 (Cp′), 1+; R = C9H6 (Ind), 2+; R = C13H8 (Flu), 3+), [(Flu−Py)Y(CH2SiMe3)]+ (4+), and [(Flu−CH2CH2−NHC)Y(CH2SiMe3)]+ (5+), respectively. It has been found that the 2,1-insertion reaction is more favorable than 1,2-insertion since the latter has a higher free energy barrier and is less exergonic. On the basis of the calculated energy profiles, the experimentally observed activity difference has been rationalized. The insertion of the first monomer into the Y−C bond of 1+, 2+, and 3+ has a similar complexation energy and energy barrier, suggesting that there is no significant activity difference in the chain initiation mediated by 1+, 2+, and 3+. The free energy profiles have been computed for both migratory and stationary insertions during the chain propagation, and the results indicate a clear kinetic preference for frontside insertion, resulting in a syndiotactic enchainment of the monomer units. This advantage of frontside insertion could be responsible for the experimentally observed preference of high syndioselectivity. The current results suggest that the charge on the central metal could account for the activity of these cationic species: the higher the charge on the central metal, the higher the activity. The low activity of 4+ could be ascribed to the coordination of a THF molecule to the central metal and thermodynamically less favorable generation of the active species. In the case of 5+, the resulting product of the first styrene insertion is stable and its central metal is wrapped by the bulky ligand and phenyl ring of the inserted styrene unit, being responsible for the absolute inertness toward styrene polymerization. In addition, the theoretical results also suggest that a longer alkyl chain of the side arm of the ancillary ligand might deter monomer coordination and thus decrease polymerization activity. These results could provide valuable

Figure 13. Ethylene-bridged cationic species 8+.

the monomer coordination more difficult and thus results in lower activity. Formation of Contact Ion Pairs. In this study, we further considered the effect of formation of a contact ion pair (CIP) on the catalytic activities of 3+, 4+, and 5+. The anion B(C6F5)4− could coordinate to the Y atom via its two F atoms, viz., paraand meta-F or ortho- and meta-F atom. First, the structures of CIP were optimized, and the results show that the anion favorably adopts ortho- and meta-F atoms rather than para- and meta-F atoms to coordinate to the Y center (Figure 14 and Figure S7). This coordination manner (κ2-F fashion) was also observed in the solid structure of similar ion pairs.61,62 To see whether such ion pairs could also be formed in solution, the ion pair CIP3 is chosen as an example for geometrical optimization in toluene solution. The computed formation free energy (3+ + B(C6F5)4− → CIP3) is −29.7 kcal/mol, suggesting that the formation of a contact ion pair in solution is likely to occur. Like that in our previous work,42 we assume that the reaction enthalpies of reactions 1, 2, and 3 are ΔH1, ΔH2, and ΔH3 (Scheme 1), respectively. Let (1) minus (2) give (4), and (1) minus (3) give (5). The reaction enthalpies of (4) and (5) are therefore ΔH1 − ΔH2 and ΔH1 − ΔH3, respectively. Let ΔΔH = ΔH1 − ΔH2 and ΔΔH′ = ΔH1 − ΔH3. According to the calculated enthalpies based on optimized structures of [(Flu− CH2−Py)Y(CH2SiMe3)][B(C6F5)4], [(Flu−Py)Y(CH 2 SiMe3 )][B(C 6 F 5 ) 4 ], and [(Flu−CH 2 CH 2 −NHC)Y(CH2SiMe3)][B(C6F5)4], the ΔΔH and ΔΔH′ were computed to be −5.2 and 0.1 kcal/mol, respectively. The large negative value of ΔΔH suggests that reaction 1 is more exothermic than reaction 2. That is to say, it is thermodynamically easier for precursor 3 to be activated by [Ph3C][B(C6F5)4] and to give corresponding active species in comparison with 4. This could

Figure 14. Optimized structures of contact ion pairs (distances in Å). H

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Scheme 1. Formation of Contact Ion Pairs [(Flu−CH2−Py)Y(CH2SiMe3)][B(C6F5)4], [(Flu−Py)Y(CH2SiMe3)][B(C6F5)4], and [(Flu−CH2CH2−NHC)Y(CH2SiMe3)][B(C6F5)4]

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information on the design of new organo-rare-earth-metal polymerization catalysts.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.organomet.6b00558. Relative Gibbs free energies and enthalpies of stationary points involved in the chain initiation and the chain propagation, comparison of complexation energies with the B3PW91, M06, and MPW1K methods, 3D structures of TS1, A2migratory, and P2migratory, optimized structures for contact ion pair, computed potential energy surface for the insertion of styrene monomer into P26‑migratory, and the imaginary frequencies of transition states (PDF) Optimized Cartesian coordinates with the self-consistentfield energies (at the MPW1K(PCM)//B3PW91 level) (XYZ)

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AUTHOR INFORMATION

Corresponding Author

*E-mail (Y. Luo): [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was partly supported by the NSFC (Nos. 21174023, 21429201, 21674014) and the Fundamental Research Funds for the Central Universities (DUT2016TB08). The authors also thank RICC (RIKEN Integrated Cluster of Clusters) and the Network and Information Center of Dalian University of Technology for part of the computational resources.

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