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

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.


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 ever, 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].

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].

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 singlepoint 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].  or Ti TS B ), ultimately generating the final product ( Ti PR H or Ti PR B ). Ti H and Ti B are halftitanocene catalysts containing N-heterocyclic carbene as a ligand, with the difference that in Ti B , one hydrogen of the N-heterocyclic carbene is substituted by B(C 6 F 5 ) 3 as the remote coordinating ligand. 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 ( Ti IMH or Ti IMB), followed by a four-member ring transition state ( Ti TSH or Ti TSB), ultimately generating the final product ( Ti PRH or Ti PRB). 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.   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 ( Ti IMH or Ti IMB), followed by a four-member ring transition state ( Ti TSH or Ti TSB), ultimately generating the final product ( Ti PRH or Ti PRB). 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 Ti IM Owing to the coordination effect, the bond distance between Ti and the N-heterocycl carbene (NHC) carbon atom (TiH-2 CH, 2.271 Å) in the Ti IMH structure was longer than tha of TiH (2.174 Å) by 0.097 Å. Additionally, the 3 CH-4 CH (1.435 Å) bond was longer than th in the C2H4 molecule (1.330 Å) by 0.105 Å. The TiH-3 CH and TiH-4 CH bond lengths wer  During the reaction process, the WBIs of Ti H -1 C H (from 0.634 to 0.094) and 3 C H -4 C H (from 2.039 to 1.012) bonds diminished from the reactant (Ti H + C 2 H 4 ) to the product Ti PR H . This decrease indicates the breakage of the Ti H -1 C H bond and the transition of the 3 C H -4 C H bond from a double to single bond. Meanwhile, the WBI gradually increased from 0.009 to 1.011 for the 1 C H -4 C H bond, thus indicating the formation of the 1 C H -4 C H bond. Compared with the reactant (Ti H + C 2 H 4 ), the energy of Ti TS H was higher by 27.6 kcal/mol, whereas that of Ti PR H was lower by 4.6 kcal/mol. The intermediate Ti IM H was highly stable, and its energy was lower than that of the product Ti PR H by 14.8 kcal/mol. Consequently, the reaction was prone to halt at the intermediate stage, thus rendering difficulty in yielding the product.

Ethylene Insertion into Titanium (TiH orTiB) Catalysts
In Ti B catalysts, one hydrogen of the N-heterocyclic carbene was substituted with B(C 6 F 5 ) 3 as the remote coordinating ligand. The Q NBO value of the Ti B atom (1.487 e) in the Ti B catalyst was higher than that of the Ti H atom (1.206 e) in the Ti H catalyst. The process of ethylene insertion into Ti B catalysts was similar to that of the Ti H catalyst. The free energies demonstrate that ethylene insertion into the Ti B catalyst is thermodynamically and kinetically preferred over the Ti H catalyst. Compared with the reactant (Ti B + C 2 H 4 ), the energy barrier for Ti TS B was 9.7 kcal/mol, which is significantly lower than that for the Ti H 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 Ti H catalyst. Unlike the highly stable Ti IM H , the energy of intermediate Ti IM B was slightly higher than that of the reactant by 2.7 kcal/mol. Further, the WBIs of Ti B -3 C B (0.270) and Ti B -4 C B (0.156) in Ti IM B were significantly lower than those (0.646 and 0.689) in Ti IM H , 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 ∆E = of the transition state into the distortion energy (E TS−dist ) and interaction energy (E TS−int ) between two reaction fragments (A: C 2 H 4 and B: Ti catalyst). Herein, this method was applied to analyze two transition states ( Ti TS H and Ti TS B ). As shown in Scheme 2I, the distortion energies were calculated as E TS-dist  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 ( Ti TSH and Ti TSB). As shown in Scheme 2I, the distortion energies were calculated as ETS-dist We also applied the same approach to decompose the two coordination energies of intermediates ( Ti IMH and Ti IMB) into distortion energy (EIM−dist) and interaction energy (EIM−int) between two reaction fragments (A: C2H4 and B: Ti catalyst). As shown in Scheme We also applied the same approach to decompose the two coordination energies of intermediates ( Ti IM H and Ti IM B ) into distortion energy (E IM−dist ) and interaction energy (E IM−int ) between two reaction fragments (A: C 2 H 4 and B: Ti catalyst). As shown in Scheme 2II, the distortion energies were calculated as  Table 2. Table 2. The decomposition of activation energies of the transition states ( Ti TS H and Ti TS B ) and coordination energies of intermediates ( Ti IM H and Ti IM B ) and into the distort energies and the interaction energies, given in kcal/mol.

1-Hexene Insertion into Titanium (Ti H or Ti B ) Catalysts
Following ethylene insertion into the Ti H or Ti B 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 Ti H or Ti B 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 Ti H21 (blue), Ti H12 (green), Ti B21 (black), and Ti B12 (yellow). Figure 4 shows the optimized structures of the 1-hexene insertion into Ti catalysts. The WBIs and Q NBO involved in 1-hexene insertion into the Ti H and Ti B catalysts are presented in Table 3.
For Ti H catalysts, two pathways exist for 1-hexene insertion reactions: 1,2 insertion (Ti H12 ) or 2,1 insertion (Ti H21 ). The free energies indicated that the Ti H21 pathway is thermodynamically and kinetically preferred over the Ti H12 pathway. Compared with the reactant ( Ti PR H + Hex), the free energy barrier of Ti TS H21 was 26.3 kcal/mol, which is lower than the 30.0 kcal/mol barrier for the Ti TS H12 catalyst. Furthermore, the reaction for the Ti H21 pathway was exothermic by 11.7 kcal/mol, which is higher than the 7.5 kcal/mol for the Ti H12 pathway.
In the 1-hexene insertion During the reaction process, the WBIs of the Ti H -3 C H (from 0.627 to 0.100) and 6 C H -7 C H bonds (from 1.980 to 0.999) decreased from the reactant ( Ti PR H + Hex) to the product Ti PR H21 . This decrease indicates the breakage of the Ti H -3 C H bond and the transition of the 6 C H -7 C H bond from a double to single bond. Meanwhile, the WBI for the 3 C H -6 C H bond gradually increased from 0.012 to 1.000, thus indicating the formation of the 3 C H -6 C H bond. Similar to the ethylene insertion reaction, the 1-hexene insertion intermediate Ti IM H21 was stable, with its energy being equal to that of the product Ti PR H21 .
For Ti B catalysts, 1,2 insertion (Ti B12 ) or 2,1 insertion (Ti B21 ) pathways exist for 1-hexene insertion reactions. The free energy results revealed that the Ti B21 pathway is thermodynamically preferred over the Ti B12 pathway. Compared with the reactant ( Ti PR B + Hex), the free energy barrier of Ti TS B21 was 12.4 kcal/mol, which is higher than the 6.5 kcal/mol for the Ti TS B12 catalyst. Additionally, the reaction for the Ti B21 pathway was exothermic by 14.6 kcal/mol, significantly larger than the 9.8 kcal/mol for the Ti B12 pathway. The energies of both transition states ( Ti TS B21 and Ti TS B12 ) were not high, thus allowing them to be easily crossed during the reaction. Consequently, the product ( Ti PR B21 ) with lower product energy Ti PR B21 became the main reaction product.    Reaction pathways for 1-hexene insertion into Ti catalysts: TiH21 (blue), TiH12 (green) (black), and TiB12 (yellow). Depending on which carbon ( 6 C or 7 C) in 1-hexene forms a C-C with 3 C carbon of [Ti]-alkyl, there are two insertion modes: the 1,2-insertion forming Ti-6 C an 3 C bonds and the 2,1-insertion forming Ti-7 C and 6 C-3 C bonds.  For TiH catalysts, two pathways exist for 1-hexene insertion reactions: 1,2 inserti (TiH12) or 2,1 insertion (TiH21). The free energies indicated that the TiH21 pathway is th modynamically and kinetically preferred over the TiH12 pathway. Compared with the actant ( Ti PRH + Hex), the free energy barrier of Ti TSH21 was 26.3 kcal/mol, which is low than the 30.0 kcal/mol barrier for the Ti TSH12 catalyst. Furthermore, the reaction for t TiH21 pathway was exothermic by 11.7 kcal/mol, which is higher than the 7.5 kcal/mol the TiH12 pathway.  Comparison between Ti H and Ti B catalysts in the 1-hexene insertion reaction revealed that both catalysts followed the dominant 2,1 insertion pathway (Ti H21 and Ti B21 ). The free energy barrier for Ti B21 was 12.4 kcal/mol, significantly lower than 26.3 kcal/mol for Ti H21 . Unlike the highly stable Ti IM H21 , the energy of the intermediate Ti IM B21 was 13.3 kcal/mol higher than that of the product Ti PR B21 . The WBIs of the Ti B -6 C B (0.341) and Ti B -7 C B (0.120) in Ti IM B21 were considerably lower than those in Ti IM H21 (0.693 and 0.677). Therefore, the 1-hexene insertion reaction for Ti B21 was easier to perform.
The comparison of the entire ethylene and 1-hexene insertion reaction process for Ti H and Ti B catalysts is shown in Figure 5. In the ethylene and 1-hexene insertion into Ti H catalysts, the energy of the transition state Ti TS H was the highest at 27.6 kcal/mol, whereas that of the final product Ti PR H21 was −16.3 kcal/mol. However, the energy of the intermediate Ti IM H was −19.4 kcal/mol, lower than that of the final product Ti PR H21 (−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 Ti B catalysts, compared with the reactant, the energy of the transition state Ti TS B was 9.7 kcal/mol, considerably lower than that of Ti TS H (27.6 kcal/mol). The energy of the final product Ti PR B21 was −23.3 kcal/mol, significantly lower than that of Ti PR H21 (−16.3 kcal/mol). Consequently, the entire ethylene and 1-hexene insertion reaction proceeded smoothly to reach the final product for the Ti B catalyst.  Table 4. Similar to the reaction pathway catalyzed by the Ti catalyst, the ethylene and 1-hexene insertion into V H or V B catalysts involved the formation of an intermediate, followed by a four-member ring transition state, thereby resulting in the final product. Both the V H and V B catalysts contain N-heterocyclic carbene as a ligand, with the difference that in the V B catalyst, one hydrogen of the N-heterocyclic carbene is substituted with B(C 6 F 5 ) 3 as the remote coordinating ligand. The Q NBO value for the V B atom (0.767 e) in the V B catalyst was larger than that for the V H atom (0.435 e) in the V H catalyst.  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 Nheterocyclic 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.   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 Nheterocyclic 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.  Depending on which carbon ( 6 C or 7 C) in 1-hexene forms a C-C bond with 3 C carbon of [V]-alkyl, there are two insertion modes for 1-hexene insertion: the 1,2-insertion forming V-6 C and 7 C-3 C bonds and the 2,1-insertion forming V-7 C and 6 C-3 C bonds. Figure 6. Reaction pathways for ethylene and 1-hexene insertion into VH (blue) or VB (black) catalysts. Depending on which carbon ( 6 C or 7 C) in 1-hexene forms a C-C bond with 3 C carbon of [V]alkyl, there are two insertion modes for 1-hexene insertion: the 1,2-insertion forming V-6 C and 7 C-3 C bonds and the 2,1-insertion forming V-7 C and 6 C-3 C bonds.       For ethylene insertion into vanadium (V H and V B ) catalysts, the energy results indicate that ethylene insertion into the V B catalyst is thermodynamically and kinetically preferred over the V H catalyst. Compared with the reactant, the energy barrier for V B ethylene insertion was 2.9 kcal/mol, significantly lower than the 13.1 kcal/mol for V H ethylene insertion. The reaction was exothermic by 20.7 kcal/mol for the V B catalyst, larger than the 7.9 kcal/mol for the V H catalyst. The intermediate V IM H was highly stable, with its energy being lower than that of the product V PR H 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 V IM B was higher than that of the product V PR B by 10.8 kcal/mol. Additionally, the WBIs of V B -3 C B (0.384) and V B -4 C B (0.200) in V IM B were significantly lower than those in V IM H (0.621 and 0.712). Consequently, the reaction proceeded smoothly to yield the product for the V B ethylene insertion.

Ethylene and 1-Hexene Insertion into V Catalysts
The results for the decomposition of activation energies of the transition states ( V TS H and V TS B ) and coordination energies of intermediates ( V IM H and V IM B ) into the distort energies and the interaction energies are presented in Table 5. The E IM−dist and E TS−dist (eff) values of V IM H and V TS H were 15.4 and 72.7 kcal/mol, respectively, higher than those of V IM B (5.4 kcal/mol) and V TS B (48.5 kcal/mol), respectively. This indicates that V IM H and V TS H underwent a more significant configuration change compared with the reactants, which is consistent with the IRI analysis. Figure 7II shows the IRI analysis of V IM H, V TS H , V IM B, and V TS B [48]. The interactions between the two reaction fragments (C 2 H 4 and V catalyst) in V IM H and V TS H were stronger than those in V IM B  The energy results indicate that the V B21 pathway is preferred over the V H12 pathway. As shown in Figure 6, the energy of the transition state V TS B21 was lower than that of V TS H12 by 13.9 kcal/mol. Moreover, the energy of product V PR B21 was lower than that of V PR H12 by 12.5 kcal/mol. Furthermore, the energy of V IM H12 was lower than that of the corresponding product V PR H12 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 V IM B21 was higher than that of the product V PR B21 by 11.5 kcal/mol. The WBIs of V B -6 C B (0.136) and V B -7 C B (0.257) in V IM B21 were significantly lower than those in V IM H12 (0.660 and 0.601). Thus, the reaction proceeded smoothly to yield the product for V B 1-hexene insertion.
In the insertion of ethylene and 1-hexene into V H catalysts, the transition state energy ( V TS H ) was 13.1 kcal/mol, whereas that of the final product energy V PR H12 was −15.0 kcal/mol. However, the energies of intermediates V IM H and V IM H12 were −20.5 and −23.0 kcal/mol, respectively, lower than that of the final product V PR H12 (−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 V B catalysts, the transition state energy V TS B was significantly lower at 2.9 kcal/mol compared with V TS H (13.1 kcal/mol). The energy of the final product V PR B21 was −27.5 kcal/mol, substantially lower than that of V PR H12 (−15.0 kcal/mol). Consequently, the ethylene and 1-hexene insertion reaction proceeded smoothly and yielded the final product when using the V B catalyst.
Further comparison between Ti B and V B catalysts revealed that the energy of transition state V TS B of the ethylene and 1-hexene insertion into V B catalysts was 2.9 kcal/mol, which is lower than that of Ti TS B (9.7 kcal/mol). Additionally, the energy of the final product V PR B21 was −27.5 kcal/mol, which is lower than that of Ti PR B21 (−23.3 kcal/mol). These results indicate that the V B catalyst has higher reaction activity than the Ti B 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 ( The ω value of V B (9.449) was slightly higher than that of Ti B (7.478); thus, V B exhibited greater electrophilicity and reactivity, which is in agreement with the experimental results [24,25].

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 Ti IMH was highly stable, with its energy even lower than that of the product Ti PRH, 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 Ti IMH, the energy of the intermediate Ti IMB 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 strate-  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 Ti H and V H with those of Ti B and V B revealed that the ELF values in the atomic regions of Ti B and V B were lower. This suggests that Ti B and V B atoms are more susceptible to nucleophilic attacks. These observations align with the conclusions drawn from previous discussions.

Conclusions
DFT calculations were employed to study the promotion of B(C 6 F 5 ) 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 Ti B was preferred over Ti H , both thermodynamically and kinetically. The intermediate Ti IM H was highly stable, with its energy even lower than that of the product Ti PR H , 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 Ti IM H , the energy of the intermediate Ti IM B 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 Ti H and Ti B catalysts, the 2,1 insertion reaction (Ti H21 and Ti B21 ) was the dominant reaction pathway for 1-hexene insertion. Moreover, the 1-hexene insertion reaction for Ti B21 was preferred over Ti H21 and was easier to perform. The entire ethylene and 1-hexene insertion reaction proceeded smoothly to reach the final product for the Ti B catalyst. (III) Similar to the case of Ti catalysts, V B was preferred over V H for the entire ethylene and 1-hexene insertion reaction. Furthermore, the V B catalyst exhibited higher reaction activity than the Ti B catalyst, which agrees with the experimental results. The ELF and GRI analyses also indicated that titanium (or vanadium) catalysts with B(C 6 F 5 ) 3 as a ligand demonstrated higher reactivity. This study is expected to enhance the understanding of the promotion of B(C 6 F 5 ) 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.