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Article

Promotion of B(C6F5)3 as Ligand for Titanium (or Vanadium) Catalysts in the Copolymerization of Ethylene and 1-Hexene: A Computational Study

by
Shuyuan Yu
,
Chenggen Zhang
*,
Fei Wang
,
Xinru Liang
,
Mengyao Yang
and
Mengyu An
College of Chemistry and Material Science, Langfang Normal University, Langfang 065000, China
*
Author to whom correspondence should be addressed.
Polymers 2023, 15(11), 2435; https://doi.org/10.3390/polym15112435
Submission received: 11 April 2023 / Revised: 21 May 2023 / Accepted: 23 May 2023 / Published: 24 May 2023
(This article belongs to the Special Issue Molecular Simulation of Polymers)
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Abstract

:
Density functional theory (DFT) is employed to investigate the promotion of B(C6F5)3 as a ligand for titanium (or vanadium) catalysts in ethylene/1-hexene copolymerization reactions. The results reveal that (I) Ethylene insertion into TiB (with B(C6F5)3 as a ligand ) is preferred over TiH, both thermodynamically and kinetically. (II) In TiH and TiB catalysts, the 2,1 insertion reaction (TiH21 and TiB21) is the primary pathway for 1-hexene insertion. Furthermore, the 1-hexene insertion reaction for TiB21 is favored over TiH21 and is easier to perform. Consequently, the entire ethylene and 1-hexene insertion reaction proceeds smoothly using the TiB catalyst to yield the final product. (III) Analogous to the Ti catalyst case, VB (with B(C6F5)3 as a ligand) is preferred over VH for the entire ethylene/1-hexene copolymerization reaction. Moreover, VB exhibits higher reaction activity than TiB, thus agreeing with experimental results. Additionally, the electron localization function and global reactivity index analysis indicate that titanium (or vanadium) catalysts with B(C6F5)3 as a ligand exhibit higher reactivity. Investigating the promotion of B(C6F5)3 as a ligand for titanium (or vanadium) catalysts in ethylene/1-hexene copolymerization reactions will aid in designing novel catalysts and lead to more cost-effective polymerization production methods.

1. Introduction

Polyolefins possess excellent properties and are widely used across various applications. The development of innovative and efficient olefin polymerization catalysts has consistently been a focal point for academic and industrial research. Progress in olefin polymerization catalytic systems has accelerated the development of functionalized polyolefin materials [1,2]. Titanium and vanadium complexes demonstrate efficient and controllable performance in polymerization catalysis. Additionally, the ligands within these complexes are crucial for enhancing catalyst activity [3,4].
In 1995, Linden et al., synthesized titanium complexes utilizing binaphthoxy and bisphenoxy as ligands for olefin polymerization. The stereomodification of ligands influences the degree of polymerization and significantly impacts the stereoregularity of polyhexene [5]. In 2004, Fujita et al., synthesized a series of titanium complexes using 2-pyrimidine derivatives as ligands. They discovered that various ligands exhibit different catalytic activities in ethylene polymerization. Titanium catalysts can also be used to prepare block copolymers for ethylene/propylene copolymerization and monodisperse polyethylene with high molecular weight [6,7]. Li et al., reported titanium complexes using β-enaminoketonato as chelate ligands. These catalysts exhibit high activity after activation by the cocatalyst methylaluminoxane (MAO). The resulting ethylene polymers display narrow molecular weight distribution and high molecular weight characteristics. Additionally, they demonstrated that the spatial and electronic effects of the substituents influenced the polymerization yield, catalytic activity, and molecular weight [8]. Hu et al., reported a class of titanium complexes featuring tridentate ligands [O–N–P], which exhibited high activity and stability in ethylene polymerization after activation by MAO. The polymer produced was highly linear polyethylene with excellent copolymerization ability in ethylene/1-hexene and ethylene/norbornene copolymerizations [9]. Nomura et al., synthesized phenoxy monotitanocene complexes with various structures capable of copolymerizing ethylene and 1-butene (or 1-hexene). The study revealed that different substituents on cyclopentadienyl affect the catalytic polymerization activity. Minor changes in the ligand structure can cause significant alterations in the polymerization activity [10]. In 2016, Dong et al., demonstrated that bulky dibenzhydryl-substituted aryloxide semititanocene complexes can copolymerize ethylene with 1-hexene. When the ligands near Ti are relatively constrained, the catalytic activity decreases, particularly affecting larger comonomers that lack sufficient space for coordination to achieve polymerization [11]. Matthias et al., designed titanium catalysts based on phenol oxides, which regulate the coordination environment around the central metal by altering the substitutions at the phenol oxide coordination sites. Additionally, they introduced the ligand structure of imidazoline-2-imide to coordinate with titanium complexes, thereby resulting in improved stabilization of the central metal titanium [12]. In 2020, Zhao et al., synthesized titanium complexes with different-size substituents and investigated their propylene polymerization performances. The results indicated that the spatial and electronic effects of substituents considerably regulate the polymerization behavior, including activity and polymer molecular weight [13].
Li et al., developed trivalent vanadium complexes using pyridinedimide, pyridinamine imine, and pyridinediamine as chelating ligands. In the presence of cocatalysts, these catalysts exhibit high activity and high-temperature stability, thereby resulting in high relative molecular weight and single-peak distribution polyethylene [14,15,16]. Wu et al., synthesized novel trivalent vanadium complexes with single (double) salicylaldehyde imines as ligands. Under normal temperature and pressure, these vanadium complexes can efficiently catalyze ethylene polymerization, thereby producing linear polyethylene. Moreover, adjusting the ligand structure can effectively regulate the molecular weight of polyethylene [15,16]. Nomura et al., discovered that vanadium complexes with imines as ligands exhibit polymerization activity during ethylene polymerization, resulting in linear polyethylene with high molecular weight. Their studies also demonstrated that the activity of the catalyst is affected by the substituents on the imino aromatic ring of the ligand or the substituents on the phenoxy group [17,18]. Czaja et al., reported a series of vanadium chloride (IV) complexes chelated with bidentate and tetradentate salicylaldehyde imines. The results revealed that changing the substituents on salicylaldehyde imines impacted the ethylene polymerization activity [19,20]. Gambarotta et al., investigated the influence of ligand structure on ethylene polymerization catalyzed by vanadium complexes. By introducing different ligands to adjust the catalyst, ethylene/propylene copolymerization can be highly active in cyclohexane solvent [21].
In 2015, Trofymchuk et al., analyzed the ability of nickel catalysts with boron adducts for ethylene polymerization using density functional theory (DFT). The results revealed that adding boron adducts transformed the nickel catalysts into Lewis acids, activating them for ethylene polymerization [22]. In 2017, Johnson et al., prepared a palladium catalyst using B(C6F5)3 as a ligand. The results indicated that the remote combination of B(C6F5)3 enhanced the catalyst activity for ethylene polymerization [23].
Recently, Nomura et al., explored titanium (or vanadium) complexes with B(C6F5)3 as ligands. They discovered that titanium (or vanadium) catalysts exhibit high activity for ethylene/1-hexene copolymerization [24,25,26]; the ethylene polymerization catalytic activity reached 4590 kg-PE/mol-Ti·h [24] and 11,000 kg-PE/mol-V·h [25], respectively. However, the promotion mechanism of B(C6F5)3 as a ligand for titanium (or vanadium) catalysts in ethylene/1-hexene copolymerization remains unclear. Therefore, this study employed DFT calculations to investigate the promotion of B(C6F5)3 as a ligand for titanium (or vanadium) catalyst in ethylene/1-hexene copolymerization. A detailed mechanistic study can help understand the promotion mechanism of B(C6F5)3 as a ligand for olefin polymerization catalysts and design a new catalyst. Scheme 1 summarizes the structure diagram of titanium (or vanadium) catalysts and the reaction pathway of ethylene/1-hexene copolymerization [24,25].

2. Computational Methods

DFT calculations were performed using the Gaussian 16 software [27]. All structures were optimized and determined by frequency analysis to be a minimum (no imaginary frequency) or transition state (TS, with an imaginary frequency) at the B3LYP-D3 (BJ) [28,29,30,31]/BSI level. BSI represents a basis set combining the SDD [32] for Ti, V, and 6–31 G (d) for nonmetal atoms. The pseudopotential basis set was employed for Ti and V atoms. The intrinsic reaction coordinate (IRC) [33] method was used to confirm transition states connecting reactants and products. The energetic results were refined at the M06-2X [34,35]/def2-TZVP level using the SMD [36] solvent effects model (with toluene as the solvent) through single-point energy calculations. The gas phase B3LYP/BSI harmonic frequency was employed to adjust the free energy using heat and entropy at 298.15 K (experimental temperature). Free energies derived at the M06-2X (SMD, solvent = toluene)/BSII level are discussed in the main text. The natural bond orbital (NBO) charges [37] and Wiberg bond indices (WBIs) were obtained at the B3LYP/BSI level. The reliability of the M06-2X/B3LYP combination in solving various transition metal catalytic reactions has been established [38,39,40,41,42,43,44,45,46,47].
The cubic files for the interaction region indicator (IRI) [48], electron localization function (ELF) [49,50], and global reactivity index (GRI) [51,52,53,54] analyses were implemented using the Multiwfn program 3.8 [55]. The results were visualized by the VMD program 1.9.3 [56].

3. Results and Discussion

3.1. Ethylene Insertion into Titanium (TiH or TiB) Catalysts

Figure 1 depicts the pathway of ethylene insertion to titanium (TiH or TiB) catalysts. The optimized structures and IRI analysis of key structures are shown in Figure 2. Table 1 presents the WBIs and natural charges (QNBO) for certain key bonds and atoms. Evidently, the ethylene insertion to titanium (TiH or TiB) catalysts initially formed an intermediate (TiIMH or TiIMB), followed by a four-member ring transition state (TiTSH or TiTSB), ultimately generating the final product (TiPRH or TiPRB). TiH and TiB are half-titanocene catalysts containing N-heterocyclic carbene as a ligand, with the difference that in TiB, one hydrogen of the N-heterocyclic carbene is substituted by B(C6F5)3 as the remote coordinating ligand.
In TiH catalysts, ethylene initially bonded to Ti, thereby forming intermediate TiIMH. Owing to the coordination effect, the bond distance between Ti and the N-heterocyclic carbene (NHC) carbon atom (TiH–2CH, 2.271 Å) in the TiIMH structure was longer than that of TiH (2.174 Å) by 0.097 Å. Additionally, the 3CH–4CH (1.435 Å) bond was longer than that in the C2H4 molecule (1.330 Å) by 0.105 Å. The TiH–3CH and TiH–4CH bond lengths were 2.186 and 2.137 Å, respectively, with large WBIs of TiH–3CH (0.646) and TiH–4CH (0.689). Compared with reactants (TiH + C2H4), the energy of TiIMH was lower by 19.4 kcal/mol, thus indicating that TiIMH is highly stable. After TiIMH, the reaction reached a four-member ring transition state, TiTSH, with the TiH–3CH bond (2.160 Å) being shorter than that in TiIMH(2.186 Å) by 0.026 Å. The WBIs of TiH–3CH (0.572) and TiH–4CH (0.275) in TiTSH were lower than those in TiIMH. Following TiTSH, the product of ethylene insertion, TiPRH formed. The 1CH–4CH (1.537 Å) and TiH–3CH (2.138 Å) bonds in TiPRH were shorter than those in TiTSH by 0.545 and 0.022 Å, respectively. Conversely, the 3CH–4CH bond (1.538 Å) in TiPRH was longer than that in TiTSH by 0.105 Å.
During the reaction process, the WBIs of TiH–1CH (from 0.634 to 0.094) and 3CH–4CH (from 2.039 to 1.012) bonds diminished from the reactant (TiH + C2H4) to the product TiPRH. This decrease indicates the breakage of the TiH–1CH bond and the transition of the 3CH–4CH bond from a double to single bond. Meanwhile, the WBI gradually increased from 0.009 to 1.011 for the 1CH–4CH bond, thus indicating the formation of the 1CH–4CH bond. Compared with the reactant (TiH + C2H4), the energy of TiTSH was higher by 27.6 kcal/mol, whereas that of TiPRH was lower by 4.6 kcal/mol. The intermediate TiIMH was highly stable, and its energy was lower than that of the product TiPRH by 14.8 kcal/mol. Consequently, the reaction was prone to halt at the intermediate stage, thus rendering difficulty in yielding the product.
In TiB catalysts, one hydrogen of the N-heterocyclic carbene was substituted with B(C6F5)3 as the remote coordinating ligand. The QNBO value of the TiB atom (1.487 e) in the TiB catalyst was higher than that of the TiH atom (1.206 e) in the TiH catalyst. The process of ethylene insertion into TiB catalysts was similar to that of the TiH catalyst. The free energies demonstrate that ethylene insertion into the TiB catalyst is thermodynamically and kinetically preferred over the TiH catalyst. Compared with the reactant (TiB + C2H4), the energy barrier for TiTSB was 9.7 kcal/mol, which is significantly lower than that for the TiH catalyst (27.6 kcal/mol). Additionally, the reaction was exothermic by 8.7 kcal/mol, which is larger than the 4.6 kcal/mol for the TiH catalyst. Unlike the highly stable TiIMH, the energy of intermediate TiIMB was slightly higher than that of the reactant by 2.7 kcal/mol. Further, the WBIs of TiB–3CB (0.270) and TiB–4CB (0.156) in TiIMB were significantly lower than those (0.646 and 0.689) in TiIMH, thus indicating that the reaction proceeded smoothly to yield the product.
Bickelhaupt’s activation strain analysis is frequently employed to gain insight into the origin of the various contributions [57,58,59]. This analysis decomposes the electronic activation energy ΔE≠ of the transition state into the distortion energy (ETS−dist) and interaction energy (ETS−int) between two reaction fragments (A: C2H4 and B: Ti catalyst). Herein, this method was applied to analyze two transition states (TiTSH and TiTSB). As shown in Scheme 2I, the distortion energies were calculated as ETS-dist(A) = ETS−A − EA and ETS−dist(B) = ETS−B − EB, where EA (or EB) and ETS−A (or ETS−B) are the energies of A (or B) in reactant ground state and transition state geometries, respectively. The interaction energies between A and B in the transition state were calculated by ETS−int = ΔE≠ − ETS−dist + BE(AB), where ETS−dist = ETS−dist(A) + ETS−dist(B), BE(AB) is the binding energy between A and B in the intermediate complex AB, and ΔE≠ is the electronic activation energy for ethylene insertion reaction. When considering the intermediate complex AB as the reference, the electronic activation energy ΔE≠ = ETS−dist(eff) + ETS−int, so ETS−dist(eff)= ETS−dist − BE(AB) represent the effective distortion energy.
We also applied the same approach to decompose the two coordination energies of intermediates (TiIMH and TiIMB) into distortion energy (EIM−dist) and interaction energy (EIM−int) between two reaction fragments (A: C2H4 and B: Ti catalyst). As shown in Scheme 2II, the distortion energies were calculated as EIM−dist(A) = EIM−A − EA and EIM−dist(B) = EIM-B − EB, where EA (or EB) and EIM−A (or EIM−B) are the energies of A (or B) in reactant ground state and intermediate geometries, respectively. The interaction energies between A and B in the intermediates were calculated by EIM−int = ΔE − EIM−dist, where EIM−dist = EIM−dist(A) + EIM−dist(B), and ΔE is the binding energy between A and B in the intermediate complex AB. The results are presented in Table 2.
The EIM−dist and ETS−dist(eff) values of TiIMH and TiTSH were 30.2 and 75.8 kcal/mol, respectively, which are much higher than those of TiIMB (9.6 kcal/mol) and TiTSB (36.1 kcal/mol), respectively. This indicates that TiIMH and TiTSH undergo a more significant configuration change compared to reactants. This is consistent with the IRI analysis. Figure 2II shows the IRI analysis of TiIMH, TiTSH, TiIMB, and TiTSB [48]. Evidently, the interactions between the two reaction fragments (C2H4 and Ti catalyst) in TiIMH and TiTSH were stronger than those in TiIMB and TiTSB.
The EIM−int of TiIMH (−65.3 kcal/mol) was much lower than that of TiIMB (−20.6 kcal/mol). This indicates that TiIMH is more stable, and the reaction for the TiH catalyst is prone to halt at the intermediate stage, whereas that for the TiB catalyst proceeds smoothly to yield the product. The ETS-int of TiTSH (−64.2 kcal/mol) was lower than that of TiTSB (−41.7 kcal/mol) by 22.5 kcal/mol. However, the ETS−dist(eff) (75.8 kcal/mol) of TiTSH was much higher than that (36.1 kcal/mol) of TiTSB by 39.7 kcal/mol. This explains why the energy barrier of TiTSB is lower than TiTSH, thus rendering the TiB catalyst more efficient in catalyzing ethylene polymerization.

3.2. 1-Hexene Insertion into Titanium (TiH or TiB) Catalysts

Following ethylene insertion into the TiH or TiB catalysts, the 1-hexene insertion reaction can be accomplished through 1,2 insertion or 2,1 insertion reactions. The 1-hexene 1,2 insertion and 2,1 insertion into the TiH or TiB catalysts involve an intermediate, followed by a four-member ring transition state, which yields the final product. Figure 3 illustrates the reaction pathways of 1-hexene insertion into Ti catalysts, namely TiH21 (blue), TiH12 (green), TiB21 (black), and TiB12 (yellow). Figure 4 shows the optimized structures of the 1-hexene insertion into Ti catalysts. The WBIs and QNBO involved in 1-hexene insertion into the TiH and TiB catalysts are presented in Table 3.
For TiH catalysts, two pathways exist for 1-hexene insertion reactions: 1,2 insertion (TiH12) or 2,1 insertion (TiH21). The free energies indicated that the TiH21 pathway is thermodynamically and kinetically preferred over the TiH12 pathway. Compared with the reactant (TiPRH + Hex), the free energy barrier of TiTSH21 was 26.3 kcal/mol, which is lower than the 30.0 kcal/mol barrier for the TiTSH12 catalyst. Furthermore, the reaction for the TiH21 pathway was exothermic by 11.7 kcal/mol, which is higher than the 7.5 kcal/mol for the TiH12 pathway.
In the 1-hexene insertion TiH21 pathway, 1-hexene initially bonded to Ti, thereby forming the intermediate TiIMH21. Owing to the coordination effect, the 6CH–7CH bond (1.457 Å) was significantly longer than that in the 1-hexene (Hex) molecule (1.332 Å) by 0.125 Å. The TiH–6CH and TiH–7CH bond were 2.129 and 2.148 Å in length, respectively, with large WBIs of TiH–6CH (0.693) and TiH–7CH (0.677). Compared with reactants (TiPRH + Hex), the free energy of TiIMH21 was lower by 16.3 kcal/mol, thus indicating its stability. After TiIMH21, the reaction reached a four-member ring transition state, TiTSH21, with the TiH–7CH (2.266 Å) being longer than that in TiIMH21 (2.148 Å) by 0.118 Å. The WBIs of TiH–6CH (0.192) and TiH–7CH (0.393) in TiTSH21 were lower than those in TiIMH21. Following TiTSH21, the product of 1-hexene insertion, TiPRH21, formed. Compared with the TiTSH21 configuration, the 3CH–6CH (1.535 Å) and TiH–7CH (2.123 Å) bonds in TiPRH21 were shorter, whereas the 6CH–7CH bond (1.537 Å) in TiPRH21 was longer.
During the reaction process, the WBIs of the TiH–3CH (from 0.627 to 0.100) and 6CH–7CH bonds (from 1.980 to 0.999) decreased from the reactant (TiPRH + Hex) to the product TiPRH21. This decrease indicates the breakage of the TiH–3CH bond and the transition of the 6CH–7CH bond from a double to single bond. Meanwhile, the WBI for the 3CH–6CH bond gradually increased from 0.012 to 1.000, thus indicating the formation of the 3CH–6CH bond. Similar to the ethylene insertion reaction, the 1-hexene insertion intermediate TiIMH21 was stable, with its energy being equal to that of the product TiPRH21.
For TiB catalysts, 1,2 insertion (TiB12) or 2,1 insertion (TiB21) pathways exist for 1-hexene insertion reactions. The free energy results revealed that the TiB21 pathway is thermodynamically preferred over the TiB12 pathway. Compared with the reactant (TiPRB + Hex), the free energy barrier of TiTSB21 was 12.4 kcal/mol, which is higher than the 6.5 kcal/mol for the TiTSB12 catalyst. Additionally, the reaction for the TiB21 pathway was exothermic by 14.6 kcal/mol, significantly larger than the 9.8 kcal/mol for the TiB12 pathway. The energies of both transition states (TiTSB21 and TiTSB12) were not high, thus allowing them to be easily crossed during the reaction. Consequently, the product (TiPRB21) with lower product energy TiPRB21 became the main reaction product.
Comparison between TiH and TiB catalysts in the 1-hexene insertion reaction revealed that both catalysts followed the dominant 2,1 insertion pathway (TiH21 and TiB21). The free energy barrier for TiB21 was 12.4 kcal/mol, significantly lower than 26.3 kcal/mol for TiH21. Unlike the highly stable TiIMH21, the energy of the intermediate TiIMB21 was 13.3 kcal/mol higher than that of the product TiPRB21. The WBIs of the TiB–6CB (0.341) and TiB–7CB (0.120) in TiIMB21 were considerably lower than those in TiIMH21 (0.693 and 0.677). Therefore, the 1-hexene insertion reaction for TiB21 was easier to perform.
The comparison of the entire ethylene and 1-hexene insertion reaction process for TiH and TiB catalysts is shown in Figure 5. In the ethylene and 1-hexene insertion into TiH catalysts, the energy of the transition state TiTSH was the highest at 27.6 kcal/mol, whereas that of the final product TiPRH21 was −16.3 kcal/mol. However, the energy of the intermediate TiIMH was −19.4 kcal/mol, lower than that of the final product TiPRH21 (−16.3 kcal/mol), thus indicating that the intermediate is highly stable. Therefore, the reaction was prone to halt at the intermediate rather than proceed to yield the product. Conversely, for the entire ethylene and 1-hexene insertion into TiB catalysts, compared with the reactant, the energy of the transition state TiTSB was 9.7 kcal/mol, considerably lower than that of TiTSH (27.6 kcal/mol). The energy of the final product TiPRB21 was −23.3 kcal/mol, significantly lower than that of TiPRH21 (−16.3 kcal/mol). Consequently, the entire ethylene and 1-hexene insertion reaction proceeded smoothly to reach the final product for the TiB catalyst.

3.3. Ethylene and 1-Hexene Insertion into V Catalysts

Figure 6 shows the reaction pathways for ethylene and 1-hexene insertion into vanadium (VH or VB) catalysts. The key optimized structures and IRI analysis of important structures are shown in Figure 7. The WBIs and QNBO involved in the ethylene and 1-hexene insertion into VH or VB catalysts are presented in Table 4. Similar to the reaction pathway catalyzed by the Ti catalyst, the ethylene and 1-hexene insertion into VH or VB catalysts involved the formation of an intermediate, followed by a four-member ring transition state, thereby resulting in the final product. Both the VH and VB catalysts contain N-heterocyclic carbene as a ligand, with the difference that in the VB catalyst, one hydrogen of the N-heterocyclic carbene is substituted with B(C6F5)3 as the remote coordinating ligand. The QNBO value for the VB atom (0.767 e) in the VB catalyst was larger than that for the VH atom (0.435 e) in the VH catalyst.
For ethylene insertion into vanadium (VH and VB) catalysts, the energy results indicate that ethylene insertion into the VB catalyst is thermodynamically and kinetically preferred over the VH catalyst. Compared with the reactant, the energy barrier for VB ethylene insertion was 2.9 kcal/mol, significantly lower than the 13.1 kcal/mol for VH ethylene insertion. The reaction was exothermic by 20.7 kcal/mol for the VB catalyst, larger than the 7.9 kcal/mol for the VH catalyst. The intermediate VIMH was highly stable, with its energy being lower than that of the product VPRH by 12.6 kcal/mol. Therefore, the reaction was prone to halt at the intermediate stage, thus rendering difficulty in yielding the product. However, the energy of the intermediate VIMB was higher than that of the product VPRB by 10.8 kcal/mol. Additionally, the WBIs of VB–3CB (0.384) and VB–4CB (0.200) in VIMB were significantly lower than those in VIMH (0.621 and 0.712). Consequently, the reaction proceeded smoothly to yield the product for the VB ethylene insertion.
The results for the decomposition of activation energies of the transition states (VTSH and VTSB) and coordination energies of intermediates (VIMH and VIMB) into the distort energies and the interaction energies are presented in Table 5.
The EIM−dist and ETS−dist(eff) values of VIMH and VTSH were 15.4 and 72.7 kcal/mol, respectively, higher than those of VIMB (5.4 kcal/mol) and VTSB (48.5 kcal/mol), respectively. This indicates that VIMH and VTSH underwent a more significant configuration change compared with the reactants, which is consistent with the IRI analysis. Figure 7II shows the IRI analysis of VIMH, VTSH, VIMB, and VTSB [48]. The interactions between the two reaction fragments (C2H4 and V catalyst) in VIMH and VTSH were stronger than those in VIMB and VTSB.
The EIM−int of VIMH (−49.5 kcal/mol) was considerably lower than that of VIMB (−28.0 kcal/mol). This suggests that the intermediate VIMH was more stable, and the ethylene insertion reaction for the VH catalyst was prone to halt at the intermediate. Conversely, for the VB catalyst, the ethylene insertion reaction proceeded smoothly to yield the product. The ETS−int of VTSH (−73.7 kcal/mol) was lower than that of vTSB (−59.5 kcal/mol) by 14.2 kcal/mol. However, the ETS−dist(eff) (72.7 kcal/mol) of vTSH was significantly larger than that of vTSB (48.5 kcal/mol) by 24.2 kcal/mol. This explains why the energy barrier of VTSB was lower than that of VTSH, thus rendering the VB catalyst more efficient in catalyzing ethylene polymerization. After ethylene insertion into VH and VB catalysts, the subsequent 1-hexene insertion reaction occurred through 1,2 insertion or 2,1 insertion reactions. The 1-hexene 1,2 insertion and 2,1 insertion into VH and VB catalysts involve an intermediate, followed by a four-member ring transition state, leading to the final product. For clarity, this study focused on the optimal reaction pathways (VH12 and VB21), and the detailed reaction pathways are shown in Figures S1 and S2. VH12 and VB21 are the dominant 1-hexene insertion reaction pathways for VH and VB catalysts, respectively.
The energy results indicate that the VB21 pathway is preferred over the VH12 pathway. As shown in Figure 6, the energy of the transition state VTSB21 was lower than that of VTSH12 by 13.9 kcal/mol. Moreover, the energy of product VPRB21 was lower than that of VPRH12 by 12.5 kcal/mol. Furthermore, the energy of VIMH12 was lower than that of the corresponding product VPRH12 by 8.0 kcal/mol, thus indicating its high stability. Therefore, the reaction was prone to halt at the intermediate rather than proceed to yield the product. However, the energy of intermediate VIMB21 was higher than that of the product VPRB21 by 11.5 kcal/mol. The WBIs of VB–6CB (0.136) and VB–7CB (0.257) in VIMB21 were significantly lower than those in VIMH12 (0.660 and 0.601). Thus, the reaction proceeded smoothly to yield the product for VB 1-hexene insertion.
In the insertion of ethylene and 1-hexene into VH catalysts, the transition state energy (VTSH) was 13.1 kcal/mol, whereas that of the final product energy VPRH12 was −15.0 kcal/mol. However, the energies of intermediates VIMH and VIMH12 were −20.5 and −23.0 kcal/mol, respectively, lower than that of the final product VPRH12 (−15.0 kcal/mol). This indicates that the intermediate stages were highly stable, thus rendering the reaction prone to stopping at the intermediate stages and difficult to yield the final product. Conversely, for the ethylene and 1-hexene insertion into VB catalysts, the transition state energy VTSB was significantly lower at 2.9 kcal/mol compared with VTSH (13.1 kcal/mol). The energy of the final product VPRB21 was −27.5 kcal/mol, substantially lower than that of VPRH12 (−15.0 kcal/mol). Consequently, the ethylene and 1-hexene insertion reaction proceeded smoothly and yielded the final product when using the VB catalyst.
Further comparison between TiB and VB catalysts revealed that the energy of transition state VTSB of the ethylene and 1-hexene insertion into VB catalysts was 2.9 kcal/mol, which is lower than that of TiTSB (9.7 kcal/mol). Additionally, the energy of the final product VPRB21 was −27.5 kcal/mol, which is lower than that of TiPRB21 (−23.3 kcal/mol). These results indicate that the VB catalyst has higher reaction activity than the TiB catalyst, which is in agreement with the experimental results. Further, the catalytic activity reached 4590 kg-PE/mol-Ti·h and 11,000 kg-PE/mol-V·h for ethylene polymerization [24,25].
To thoroughly investigate the reaction, both the GRI and ELF analyses were conducted on key molecules (Table 6 and Figure 8). The VB and TiB catalysts exhibited the largest electrophilicity (ω) values, 9.449 and 7.478, respectively, thus signifying their electrophilic nature. By contrast, VH and TiH exhibited substantial global nucleophilicity (NNu) values of 5.650 and 6.356, thus indicating that they are nucleophilic. The C2H4 and Hex molecules displayed moderate NNu values of 1.863 and 2.361, thus suggesting a certain level of nucleophilicity. Thus, VB and TiB catalysts can facilitate olefin polymerization reactions, whereas VH and TiH do not. The ω value of VB (9.449) was slightly higher than that of TiB (7.478); thus, VB exhibited greater electrophilicity and reactivity, which is in agreement with the experimental results [24,25].
Figure 8 presents the ELF analysis for key molecules, including TiH, TiB, VH, and VB. The ELF analysis, which is typically used to analyze nucleophilic attack sites, was employed herein to obtain the ELF isosurface maps for these molecules (Figure 8). A comparison of the ELF isosurface maps for TiH and VH with those of TiB and VB revealed that the ELF values in the atomic regions of TiB and VB were lower. This suggests that TiB and VB atoms are more susceptible to nucleophilic attacks. These observations align with the conclusions drawn from previous discussions.

4. Conclusions

DFT calculations were employed to study the promotion of B(C6F5)3 as a ligand for titanium (or vanadium) catalysts in the copolymerization of ethylene and 1-hexene. The results revealed that: (I) Ethylene insertion into TiB was preferred over TiH, both thermodynamically and kinetically. The intermediate TiIMH was highly stable, with its energy even lower than that of the product TiPRH, thus it was easy for the reaction to stall at the intermediate stage and difficult to reach the product. In contrast to the very stable TiIMH, the energy of the intermediate TiIMB was slightly higher than the reactant by 2.7 kcal/mol, thereby allowing the reaction to proceed smoothly to reach the product. (II) For both TiH and TiB catalysts, the 2,1 insertion reaction (TiH21 and TiB21) was the dominant reaction pathway for 1-hexene insertion. Moreover, the 1-hexene insertion reaction for TiB21 was preferred over TiH21 and was easier to perform. The entire ethylene and 1-hexene insertion reaction proceeded smoothly to reach the final product for the TiB catalyst. (III) Similar to the case of Ti catalysts, VB was preferred over VH for the entire ethylene and 1-hexene insertion reaction. Furthermore, the VB catalyst exhibited higher reaction activity than the TiB catalyst, which agrees with the experimental results. The ELF and GRI analyses also indicated that titanium (or vanadium) catalysts with B(C6F5)3 as a ligand demonstrated higher reactivity. This study is expected to enhance the understanding of the promotion of B(C6F5)3 as a ligand for titanium (or vanadium) catalysts, aid in developing new strategies for polymerization catalyst design, and lead to more cost-effective polymerization production methods.

Supplementary Materials

The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/polym15112435/s1. Figure S1. The details pathway of 1-hexene insertion into V catalysts, VH12 (blue), VH21 (green), VB21 (black), and VB12 (yellow). Figure S2. Optimized structures of 1-hexene insertion into V catalysts reaction pathway shown in Figure S1. Table S1: Additional computational details. Table S2: Energies and Cartesian coordinates of all the optimized structures.

Author Contributions

Conceptualization, C.Z. and S.Y.; data curation, F.W., X.L., M.Y. and M.A.; formal analysis, F.W. and X.L.; funding acquisition, C.Z.; investigation, S.Y.; project administration, C.Z. All authors have read and agreed to the published version of the manuscript.

Funding

This work was financially supported by the Science and Technology Project of Hebei Education Department (ZD2021090), the Fundamental Research Funds for the Universities in Hebei Province (JYT202101), and the Innovation and Entrepreneurship Training Program of Langfang Normal University (X202210100016).

Institutional Review Board Statement

Not applicable.

Data Availability Statement

The data presented in this study are available in the Supplementary Materials.

Conflicts of Interest

The authors declare no conflict of interest.

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Polymers 15 02435 sch001 550
Scheme 1. Schematic of the structure diagram of titanium (or vanadium) catalysts and the reaction pathway of ethylene/1-hexene copolymerization. (a) Structural diagram of titanium catalysts (TiH and TiB). (b) Structural diagram of vanadium catalysts (VH and VB). (c) Reaction pathway of ethylene (I) and 1-hexene (II) copolymerization.
Scheme 1. Schematic of the structure diagram of titanium (or vanadium) catalysts and the reaction pathway of ethylene/1-hexene copolymerization. (a) Structural diagram of titanium catalysts (TiH and TiB). (b) Structural diagram of vanadium catalysts (VH and VB). (c) Reaction pathway of ethylene (I) and 1-hexene (II) copolymerization.
Polymers 15 02435 sch001
Polymers 15 02435 g001 550
Figure 1. Reaction pathway of ethylene insertion into TiH (blue) or TiB (black) catalysts.
Figure 1. Reaction pathway of ethylene insertion into TiH (blue) or TiB (black) catalysts.
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Polymers 15 02435 g002a 550Polymers 15 02435 g002b 550
Figure 2. (I) Optimized structures of the reaction pathway for ethylene insertion into Ti catalysts (shown in Figure 1) with key bond lengths in angstroms. Most hydrogen atoms are omitted for clarity. (II) Interaction region indicator (IRI) analysis of TiIMH, TiTSH, TiIMB, and TiTSB, with key interactions highlighted by red circles.
Figure 2. (I) Optimized structures of the reaction pathway for ethylene insertion into Ti catalysts (shown in Figure 1) with key bond lengths in angstroms. Most hydrogen atoms are omitted for clarity. (II) Interaction region indicator (IRI) analysis of TiIMH, TiTSH, TiIMB, and TiTSB, with key interactions highlighted by red circles.
Polymers 15 02435 g002aPolymers 15 02435 g002b
Polymers 15 02435 sch002 550
Scheme 2. The scheme used to calculate the distortion and interaction energies between the C2H4 (A) and M catalyst (B), (M = Ti or V).
Scheme 2. The scheme used to calculate the distortion and interaction energies between the C2H4 (A) and M catalyst (B), (M = Ti or V).
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Polymers 15 02435 g003 550
Figure 3. Reaction pathways for 1-hexene insertion into Ti catalysts: TiH21 (blue), TiH12 (green), TiB21 (black), and TiB12 (yellow). Depending on which carbon (6C or 7C) in 1-hexene forms a C–C bond with 3C carbon of [Ti]–alkyl, there are two insertion modes: the 1,2-insertion forming Ti-6C and 7C–3C bonds and the 2,1-insertion forming Ti-7C and 6C–3C bonds.
Figure 3. Reaction pathways for 1-hexene insertion into Ti catalysts: TiH21 (blue), TiH12 (green), TiB21 (black), and TiB12 (yellow). Depending on which carbon (6C or 7C) in 1-hexene forms a C–C bond with 3C carbon of [Ti]–alkyl, there are two insertion modes: the 1,2-insertion forming Ti-6C and 7C–3C bonds and the 2,1-insertion forming Ti-7C and 6C–3C bonds.
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Polymers 15 02435 g004a 550Polymers 15 02435 g004b 550
Figure 4. Optimized structures of the reaction pathway for 1-hexene insertion into Ti catalysts shown in Figure 3, with key bond lengths in angstroms. Most hydrogen atoms are omitted for clarity.
Figure 4. Optimized structures of the reaction pathway for 1-hexene insertion into Ti catalysts shown in Figure 3, with key bond lengths in angstroms. Most hydrogen atoms are omitted for clarity.
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Polymers 15 02435 g005 550
Figure 5. Comparison of the entire ethylene and 1-hexene insertion reaction process for TiH (blue) and TiB (black) catalysts.
Figure 5. Comparison of the entire ethylene and 1-hexene insertion reaction process for TiH (blue) and TiB (black) catalysts.
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Polymers 15 02435 g006a 550Polymers 15 02435 g006b 550
Figure 6. Reaction pathways for ethylene and 1-hexene insertion into VH (blue) or VB (black) catalysts. Depending on which carbon (6C or 7C) in 1-hexene forms a C–C bond with 3C carbon of [V]–alkyl, there are two insertion modes for 1-hexene insertion: the 1,2-insertion forming V–6C and 7C–3C bonds and the 2,1-insertion forming V–7C and 6C–3C bonds.
Figure 6. Reaction pathways for ethylene and 1-hexene insertion into VH (blue) or VB (black) catalysts. Depending on which carbon (6C or 7C) in 1-hexene forms a C–C bond with 3C carbon of [V]–alkyl, there are two insertion modes for 1-hexene insertion: the 1,2-insertion forming V–6C and 7C–3C bonds and the 2,1-insertion forming V–7C and 6C–3C bonds.
Polymers 15 02435 g006aPolymers 15 02435 g006b
Polymers 15 02435 g007a 550Polymers 15 02435 g007b 550
Figure 7. (I) Optimized structures of ethylene and 1-hexene insertion into V catalysts reaction pathway shown in Figure 6, with key bond lengths in angstroms. Most hydrogen atoms are omitted for clarity. (II) Interaction region indicator (IRI) analysis of VIMH, VTSH, VIMB, and VTSB, with key interactions highlighted by red circles.
Figure 7. (I) Optimized structures of ethylene and 1-hexene insertion into V catalysts reaction pathway shown in Figure 6, with key bond lengths in angstroms. Most hydrogen atoms are omitted for clarity. (II) Interaction region indicator (IRI) analysis of VIMH, VTSH, VIMB, and VTSB, with key interactions highlighted by red circles.
Polymers 15 02435 g007aPolymers 15 02435 g007b
Polymers 15 02435 g008 550
Figure 8. Isosurface maps of electron localization function for TiH, TiB, VH, and VB.
Figure 8. Isosurface maps of electron localization function for TiH, TiB, VH, and VB.
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Table
Table 1. WBIs and QNBO for some important bonds and atoms for ethylene insertion into Ti catalysts.
Table 1. WBIs and QNBO for some important bonds and atoms for ethylene insertion into Ti catalysts.
WBIQNBO (e)
B (TiH–1CH)B (TiH–3CH)B (TiH–4CH)B (3CH–4CH)B (1CH–4CH)TiH1H
TiH + C2H40.634 2.039 1.2060.251
TiIMH0.7970.6460.6891.2110.0091.1130.254
TiTSH0.4640.5720.2751.2630.4731.0560.248
TiPRH0.0940.6270.0421.0121.0111.1420.248
B (TiB–1CB)B (TiB–3CB)B (TiB–4CB)B (3CB–4CB)B (1CB–4CB)TiBB(C6F5)3
TiB + C2H40.861 2.039 1.487−0.497
TiIMB0.8820.2700.1561.7990.0041.460−0.518
TiTSB0.7430.5220.1711.4730.3511.233−0.524
TiPRB0.2520.8900.1220.9780.9671.344−0.518
Table
Table 2. The decomposition of activation energies of the transition states (TiTSH and TiTSB) and coordination energies of intermediates (TiIMH and TiIMB) and into the distort energies and the interaction energies, given in kcal/mol.
Table 2. The decomposition of activation energies of the transition states (TiTSH and TiTSB) and coordination energies of intermediates (TiIMH and TiIMB) and into the distort energies and the interaction energies, given in kcal/mol.
ComplexΔG≠ΔE≠BE(AB)ETS−dist(A)ETS−dist(B)ETS−distETS−dist(eff)ETS−int
TiTSH27.611.6−35.121.818.940.775.8−64.2
TiTSB9.7−5.6−11.09.515.625.136.1−41.7
ComplexΔGΔE EIM−dist(A)EIM−dist(B) EIM−distEIM−int
TiIMH−19.4−35.1 18.411.8 30.2−65.3
TiIMB2.7−11.0 1.28.4 9.6−20.6
Table
Table 3. WBIs and QNBO for some important bonds and atoms for the 1-hexene insertion into Ti catalysts.
Table 3. WBIs and QNBO for some important bonds and atoms for the 1-hexene insertion into Ti catalysts.
WBIQNBO (e)
B (TiH−3CH)B (TiH−7CH)B (TiH−6CH)B (6CH−7CH)B (3CH−6CH)TiH1H
TiPRH + Hex0.627 1.980 1.1420.248
TiIMH210.6540.6770.6931.1320.0121.3250.256
TiTSH210.5280.3930.1921.4310.3680.8440.248
TiPRH210.1000.5880.0480.9991.0001.1540.248
B (TiH−3CH)B (TiH−6CH)B (TiH−7CH)B (6CH−7CH)B (3CH−7CH)TiH1H
TiIMH120.7530.6480.6361.1800.0091.2040.255
TiTSH120.4850.5060.1941.3250.4311.0470.247
TiPRH120.1030.6250.0380.9960.9861.1190.248
B (TiB−3CB)B (TiB−7CB)B (TiB−6CB)B (6CB−7CB)B (3CB−6CB)TiBB(C6F5)3
TiPRB + Hex0.890 1.980 1.344−0.518
TiIMB210.9360.1200.3411.6870.0021.395−0.533
TiTSB210.7640.4750.1931.4630.3321.273−0.534
TiPRB210.2340.8930.1160.9620.9681.401−0.528
B (TiB−3CB)B (TiB−6CB)B (TiB−7CB)B (6CB−7CB)B (3CB−7CB)TiBB(C6F5)3
TiIMB120.9210.3340.1201.6910.0031.432−0.533
TiTSB120.7230.5670.1521.3830.3611.296−0.533
TiPRB120.2510.9000.0970.9680.9491.414−0.525
Table
Table 4. WBIs and QNBO for some important bonds and atoms for the ethylene and 1-hexene insertion into V catalysts.
Table 4. WBIs and QNBO for some important bonds and atoms for the ethylene and 1-hexene insertion into V catalysts.
WBIQNBO (e)
B (VH–1CH)B (VH–3CH)B (VH–4CH)B (3CH–4CH)B (1CH–4CH)VH1H
VH + C2H40.830 2.039 0.4350.250
VIMH0.8410.6210.7121.2740.0150.5550.254
VTSH0.6600.6860.2601.1890.5590.1790.247
VPRH0.1720.7050.0391.0101.0070.6350.250
B (VH–3CH)B (VH–7CH)B (VH–6CH)B (6CH–7CH)B (3CH–6CH)VH1H
VPRH + Hex0.705 1.980 0.6350.250
VIMH120.7570.6010.6601.2420.0140.8070.254
VTSH120.6390.6920.2561.1190.5810.2140.248
VPRH120.1380.6710.0290.9980.9900.7340.250
B (VB–1CB)B (VB–3CB)B (VB–4CB)B (3CB–4CB)B (1CB–4CB)VBB(C6F5)3
VB + C2H40.982 2.039 0.767−0.482
VIMB1.0180.3840.2001.6920.0040.911−0.519
VTSB0.8610.5960.1621.4400.3550.596−0.528
VPRB0.2660.9740.1320.9660.9600.692−0.517
B (VB–3CB)B (VB–7CB)B (VB–6CB)B (6CB–7CB)B (3CB–6CB)VBB(C6F5)3
VPRB + Hex0.974 1.980 0.692−0.517
VIMB210.9780.2570.1361.7500.0330.947−0.529
VTSB210.8680.5450.1671.4270.3510.679−0.535
VPRB210.3340.9370.1570.9440.9350.752−0.526
Table
Table 5. The decomposition of activation energies of the transition states (VTSH and VTSB) and coordination energies of intermediates (VIMH and VIMB) and into the distort energies and the interaction energies, given in kcal/mol.
Table 5. The decomposition of activation energies of the transition states (VTSH and VTSB) and coordination energies of intermediates (VIMH and VIMB) and into the distort energies and the interaction energies, given in kcal/mol.
ComplexΔG≠ ΔE≠ BE(AB)ETS−dist(A)ETS−dist(B)ETS−distETS−dist(eff)ETS−int
VTSH13.1−1.0−34.128.110.538.672.7−73.7
VTSB2.9−11.0−22.69.816.125.948.5−59.5
ComplexΔGΔE EIM−dist(A)EIM−dist(B) EIM−distEIM−int
VIMH−20.5−34.1 14.41.0 15.4−49.5
VIMB−9.9−22.6 2.03.4 5.4−28.0
Table
Table 6. The global reactivity index for some key molecules.
Table 6. The global reactivity index for some key molecules.
η aμ bω cNNu d
TiH3.930−1.8550.3026.356
TiB3.823−7.7947.4780.857
VH4.318−2.0830.4215.650
VB3.334−8.0669.4490.811
C2H413.714−3.5080.5921.863
Hex12.307−3.0530.6192.361
a Chemical hardness (η, in eV). b Electronic chemical potential (μ, in eV). c Global electrophilicity (ω, in eV). d Global nucleophilicity (NNu, in eV).
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Yu, S.; Zhang, C.; Wang, F.; Liang, X.; Yang, M.; An, M. Promotion of B(C6F5)3 as Ligand for Titanium (or Vanadium) Catalysts in the Copolymerization of Ethylene and 1-Hexene: A Computational Study. Polymers 2023, 15, 2435. https://doi.org/10.3390/polym15112435

AMA Style

Yu S, Zhang C, Wang F, Liang X, Yang M, An M. Promotion of B(C6F5)3 as Ligand for Titanium (or Vanadium) Catalysts in the Copolymerization of Ethylene and 1-Hexene: A Computational Study. Polymers. 2023; 15(11):2435. https://doi.org/10.3390/polym15112435

Chicago/Turabian Style

Yu, Shuyuan, Chenggen Zhang, Fei Wang, Xinru Liang, Mengyao Yang, and Mengyu An. 2023. "Promotion of B(C6F5)3 as Ligand for Titanium (or Vanadium) Catalysts in the Copolymerization of Ethylene and 1-Hexene: A Computational Study" Polymers 15, no. 11: 2435. https://doi.org/10.3390/polym15112435

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