Density Functional Theory Study of the Regioselectivity in Copolymerization of bis-Styrenic Molecules with Propylene Using Zirconocene Catalyst

Abstract

Density functional theory (DFT) was used to study the regioselectivity of the copolymerization of propylene and the bis-styrenic molecules (DVB and BVPE) using a zirconocene catalyst. This study reveals the following: when hydrogen is introduced to reactivate the catalyst on the vinyl bonds containing DVB or BVPE, the second vinyl bond is inserted into the polymer in a regio-irregular 1,2-way. (I) The 1,2-insertion mode forms more thermodynamically stable products. (II) The 2,1 insertion, DVB-PP_1, or BVPE-PP₁ needs to rotate 180° along the Zr-C₁ bond to complete the process; thus, it is easier to accomplish the 1,2 insertion. (III) The analysis of the local electrophilicity/nucleophilicity index and the Fukui functions also indicate that the 1,2-insertion mode is the optimal insertion mode. Investigating the mechanism of this experimental phenomenon is important in the development of a functionalization strategy for polypropylene (PP) polymers.

1. Introduction

Polyolefins are ubiquitous in our lives and are utilized in many fields, including agriculture, packaging, electronics, automobiles, machinery, medical treatment, transportation, and the military. Polyolefins are synthesized from very simple olefins and are inexpensive. They have many advantages, such as good mechanical properties and high recyclability. Of late, polyolefin materials have become the polymer materials with the largest output and the widest application [1,2,3,4,5,6].

Polyolefins are usually saturated, and general polypropylene materials lack polar functional groups; therefore, it is difficult to print and dye polyolefins. However, scientific researchers are investing in improving these properties; thus, they have proposed the introduction of a small quantity of polar monomers such as vinyl chloride and vinyl acetate into polyolefin chains to combine polyolefins with other polymers containing functional groups. This could improve the surface properties, including adhesion, solvent resistance, flexibility, rheology, and co-solubility and blending with other polymers and additives, thereby comprehensively upgrading polyolefin functions and performance to meet the needs of different fields [7,8,9,10].

Polyolefins are chemically inert polymers, and their material and molecular modifications are difficult. Scientists have proposed the introduction of polar functional groups to change the structure of polyolefins and to expand their application range [11,12,13]. The copolymerization of propylene with the bis-styrenic molecules (1,4-divinylbenzene (DVB) and 1,2-bis(4-vinylphenyl)-ethane (BVPE)) is a common modification method. In the propylene polymerization catalyzed by the racemic dimethylsilyl-bis(2-methyl-4-phenylindenyl)-zirconium dichloride (I)/methyl -aluminoxane (MAO), the polymer chain containing a styrene group was obtained under the action of hydrogen [14,15]. BVPE has two vinyl benzenes separated by an ethyl linker group, and its linker is longer than that of DVB, which weakens the degree of tight conjugation (Figure 1).

The monomers DVB and BVPE have a unique mode of M-C bond insertion during their polymerizations. The first vinyl bond is inserted via the 2,1 mode. However, when hydrogen is introduced to reactivate the inactivated catalyst, by inserting it into the second vinyl bond of either DVB or BVPE, the second vinyl bond is inserted into the polymer via the rare 1,2 mode. Chain reinsertion occurs in an irregular 1,2-way in this region. In previous studies, we studied the mechanism of the zirconocene-catalyzed and H₂-assisted chain transfer copolymerization of propylene and p-methylstyrene (pMS)-functionalized PP [16]. The results indicate that the 2,1 insertion of p-methylstyrene is more favorable owing to a thermodynamic control; the mechanism is the same as the first vinyl bond insertion of DVB and BVPE.

However, to the best of our knowledge, there have been no theoretical studies on the anomalous insertion mode of DVB and BVPE in which the second vinyl bond is inserted into the polymer via the 1,2 sequence. This study sought to understand, via calculations, the copolymerization mechanism after the introduction of hydrogen, focusing on why the reinsertion of the bis-styrenic (DVB and BVPE) chains occurs via the irregular 1,2 mode. A detailed mechanistic study of this experimental phenomenon will help to understand the mechanistic pathways of chain transfer copolymerization and develop a functionalization strategy for PP polymers.

2. Results and Discussion

Scheme 1 summarizes the reaction mechanism of the two vinyl bond insertions in the copolymerization of propylene with the bis-styrenic monomers (DVB and BVPE), as proposed by Dong [14,15]. DVB or BVPE was inserted into the intermediate [Zr]-PP₁, obtained via propylene polymerization, to form [Zr]-DVB-PP₁ or [Zr]-BVPE-PP₁, respectively. As a result of the spatial blocking effect in [Zr]-DVB-PP₁ or [Zr]-BVPE-PP₁, a high energy barrier for the subsequent propylene insertion ensued. Therefore, propylene cannot be further inserted into [Zr]-DVB-PP₁ or [Zr]-BVPE-PP₁ to inactivate the catalytic system. The sequence of insertions is similar to the copolymerization mechanism of propylene and p-methylstyrene [16]; the data are included in the Supplementary Materials (Figures S1–S6).

However, hydrogen can easily be inserted into [Zr]-DVB-PP₁ and [Zr]-BVPE-PP₁. In contrast to p-methylstyrene, the bis-styrenic molecules (DVB and BVPE) contain two vinyl bonds. When inserting the second vinyl bond of DVB or BVPE, it is inserted into the polymer in a rare 1,2-way, and the chain reinsertion introduces a regional irregularity. The irregularity begins with the introduction of hydrogen.

2.1. Hydrogen Reactivates the Reaction

Figure 2 lists the energies of the reaction coordinates transition states (TSs)/intermediates (IMs) involved in the hydrogen reaction process, and Figure 3 lists the main transition states and configurations of the intermediates for the DVB on to the zirconocene catalyst. The DVB unit in [Zr]-DVB-PP₁ is more spatially crowded than the propylene unit; therefore, further insertion of propylene into the zirconium–carbon bond of [Zr]-DVB-PP₁ to inactivate the catalytic system cannot occur easily. However, because hydrogen is smaller in size, it can be inserted into the zirconium–carbon bond of the [Zr]-DVB-PP₁ to form a coordinated DVB-PP₁ and into the catalytically active Zr-H site on the zirconocene.

H₂ first coordinates to the zirconium center across the transition state (TS1) to obtain the dihydro complex IM1 (Figure 2 and Figure 3). The bond length of Zr-C₁ (2.423 Å) is longer than that of [Zr]-DVB-PP₁ (2.355 Å), and the H₁-H₂ bond is slightly lengthened from 0.743 Å (in free H₂) to 0.744 Å in the configuration of the transition state TS1, owing to the insertion of H₂; the bond lengths of Zr-H₁ and Zr-H₂ are 3.314 Å and 3.311 Å, respectively. Relative to the reactant ([Zr]-DVB-PP₁ and H₂), the barrier for the transition state TS1 is 12.7 kcal/mol. Subsequently, the intermediate IM1 is formed; exothermic, 1.3 kcal/mol, compared with the transition state TS1. In the IM1 configuration, the Zr-C₁ (2.507 Å) and H₁-H₂ (0.783 Å) bonds are longer than those in the transition state, TS1; the Zr-H₁ (2.103 Å) and Zr-H₂ (2.081 Å) bonds are shorter than those in the transition state, TS1. Then, the intermediate, IM1, evolves to the four-member transition state, TS2, across an energy barrier of 2.8 kcal/mol, and the Zr-C₁ bond (2.601 Å) and H₁-H₂ bond (0.930 Å) become longer. After the transition state, TS2, the breaking of the H-H bond leads to the intermediate, IM2, which is exothermic, 18.8 kcal/mol. Compared with the TS2 configuration, the Zr-C₁ bond (4.411 Å) of IM2 is much longer, and the Zr-H₁ bond (1.818 Å) of IM2 is shortened by 0.112 Å. The intermediate IM2 is then decomposed into two parts: DVB-PP₁ and [Zr]-H; exothermic, 2.4 kcal/mol. The Zr-C₁ bond is broken. Due to DVB-PP₁ being separate from [Zr]-H in product, the distances between Zr and the center of the two side-C5 rings in [Zr]-H are 2.191 and 2.181 Å, respectively, which are shorter than those in intermediate IM2 (2.251 and 2.283 Å). The interaction between the central metal Zr and the two side-C₅ ring ligands becomes stronger, so the Zr-H₁ bond (1.828 Å) of [Zr]-H is slightly longer than that of IM2 by 0.010 Å.

During the entire hydrogen introduction reaction, the Zr-C₁ and H₁-H₂ bonds gradually become longer until they break, and the Zr-H₁ and C₁-H₂ bonds gradually become shorter until they form stable bonds. The Wiberg bond indices (WBI) and natural charges (NBO) for some key bonds and atoms of the reaction pathway involving hydrogen are shown in

Table 1. The Wiberg bond indices (WBI) and natural charges (Q_NBO) for some key bonds and atoms of the reaction pathway involving hydrogen; the values of BVPE are given in brackets.

	WBI				QNBO (e)
	B (Zr-C1)	B (H1-H2)	B (Zr-H1)	B (C1-H2)	Zr	H2
[Zr]-DVB[BVPE]-PP1 + H2	0.609 [0.619]	1.0 [1.0]			1.358 [1.362]	0.000 [0.0]
TS1	0.563 [0.571]	0.923 [0.942]	0.056 [0.040]	0.001 [0.001]	1.375 [1.403]	0.011 [0.005]
IM1	0.590 [0.596]	0.713 [0.712]	0.236 [0.236]	0.049 [0.050]	0.877 [0.879]	0.100 [0.100]
TS2	0.504 [0.509]	0.496 [0.496]	0.416 [0.417]	0.239 [0.239]	0.815 [0.815]	0.132 [0.132]
IM2	0.003 [0.003]	0.000 [0.000]	0.880 [0.882]	0.892 [0.895]	1.112 [1.089]	0.261 [0.259]
DVB[BVPE]-PP1 + [Zr]-H			0.877 [0.877]	0.902 [0.912]	1.311 [1.311]	0.245 [0.240]

. As the reaction proceeds, the WBI values of the Zr-C₁ bond (from 0.609 to 0.003) and those of the H₁-H₂ bond (from 1.000 to 0.000) gradually become smaller from the reactant ([Zr]-DVB-PP₁ and H₂) to the intermediate IM2, indicating the break of the Zr-C₁ and the H₁-H₂ bond. The Q_NBO values of the Zr atom also diminish from 1.358 e in the reactant [Zr]-DVB-PP₁ to 1.112 e in the intermediate IM2. Meanwhile, the WBI values of the Zr-H₁ (from 0.056 to 0.880) and the C₁-H₂ (from 0.001 to 0.892) bond gradually become larger from the transition state TS1 to the intermediate IM2, indicating the formation of the Zr-H₁ and the C₁-H₂ bond. The Q_NBO value of the H₂ atom also gradually increases from 0.000 e in the reactant to 0.261 e in the intermediate IM2. The WBI value (0.877) of the Zr-H₁ bond in [Zr]-H is slightly smaller than that of IM2 (0.880) by 0.003 Å, due to the interaction between the central metal Zr and the two side-C₅ ring ligands becoming stronger. The hydrogen introduction is an exothermic reaction (exothermic, 7.0 kcal/mol), and the reaction barrier is very low (14.2 kcal/mol), indicating that the reaction is thermodynamically feasible.

The mechanism for the activation reaction between zirconocene-BVPE and H₂ is similar to that for DVB. The respective energy values are given in the brackets in Figure 2 and represent the relative energy along the reaction coordinate for the BVPE reaction process; the main transition states (TSs) and configurations of the intermediates (IMs) are listed in Figure 4. The entire reaction passes through two TSs and two intermediates and finally reaches the product BVPE-PP₁ and [Zr]-H catalyst components. The reaction potential barrier is 12.5 kcal/mol, which is slightly lower than that of DVB, and the reaction is exothermic, 7.7 kcal/mol. It was also easy to perform the experimental reaction.

2.2. The Second Vinyl Bond of the bis-Styrenic Molecule (DVB and BVPE)

After hydrogen reactivates the catalyst, the intermediate, IM2, decomposes into two parts, DVB-PP₁ and [Zr]-H, and continues to insert. The subsequent insertion of the second vinyl bond of the bis-styrenic molecule (DVB) could be via one of two paths: a 1,2-mode insertion or a 2,1-mode insertion. From a configuration perspective, the 1,2 insertion is feasible if a slight forward translation of the vinyl bond of DVB-PP₁ occurs. For the 2,1 insertion, Zr-C₁ of the vinyl of DVB-PP₁ needs to rotate 180° to complete the 2,1 insertion. Thus, the 1,2 insertion is easier to complete.

Figure 5 illustrates in detail the manner in which the second vinyl bond of DVB or BVPE is inserted into the [Zr]-H bond; Figure 6 illustrates the optimized key TSs and intermediate states (IMs) for DVB. The 1,2-mode insertion and 2,1-mode insertion are all performed by first forming an intermediate (IM3_1,2 or IM3_2,1) and then form a quaternary TS (TS3_1,2 or TS3_2,1), resulting in the product (PR_1,2 or PR_2,1).

During the reaction, the second vinyl group of DVB-PP₁ slowly formed a bond with the Zr atom. According to the configurations of the intermediate, IM3_1,2; the transition state, TS3_1,2; and the product, PR_1,2, the bond lengths between the Zr and C₂ atoms in IM3_1,2, TS3_1,2, and PR_1,2 are 2.567, 2.417, and 2.170 Å, respectively, which decrease in turn. The bond lengths of the carbon bonds C₂-C₃ in IM3_1,2, TS3_1,2, and PR_1,2 are 1.375, 1.411, and 1.524 Å, respectively, which become longer as they form single bonds from double bonds. Simultaneously, the bond lengths between the Zr and H₁ atoms are 1.822 Å and 1.859 Å in IM3_1,2 and TS3_1,2, respectively, and they lengthen successively until the Zr-H₁ bond in PR_1,2 is broken and a stable product forms.

The relative energies of the species indicate that the 1,2-mode insertion is thermodynamically and kinetically preferred to the 2,1-mode insertion; the energies of TS3_1,2 and IM3_1,2 are 5.4 and 6.8 kcal/mol lower than those of TS3_2,1 and IM3_2,1, respectively. The energies of TS3_2,1 are higher than those of TS3_1,2 because the steric effect of the former is greater than that of the latter. In TS3_2,1, there is a spatial repulsion between the benzene ring of DVB and the H atom of the benzene ring of the ligand, and the H-H distance (2.200 Å). In TS3_1,2, the benzene ring of DVB is at a longer distance from the coordinated benzene of the catalyst, which reduces the spatial effect of TS3_1,2. The distances between Zr and the center of two side-C5 rings of TS3_1,2 are 2.234 and 2.242 Å, respectively, shorter than that inTS3_2,1 (2.282 and 2.306 Å); this also indicates that the steric effect of TS3_1,2 is smaller than that of TS3_2,1. Hence, PR_1,2 is more stable than PR_2,1. Therefore, for the whole reaction, a 1,2-mode insertion is preferred to the 2,1-mode insertion, which is consistent with the regional selectivity of the 1,2 insertion observed in the experiment. Relative to the DVB-PP₁ and [Zr]-H catalytic site, the potential barrier of the 1,2 insertion is 2.0 kcal/mol, while that of the 2,1 insertion is 7.4 kcal/mol. The total discharge energy for the 1,2 insertion is 12.2 kcal/mol, while that of the 2,1 insertion is 5.6 kcal/mol.

Table 2. The Wiberg bond indices (WBI) and natural charges (Q_NBO) for some key bonds and atoms for the reaction pathway of the second vinyl bond insertion; the values of BVPE are given in brackets.

	WBI				QNBO (e)
	B (Zr-H1)	B (C2-C3)	B (Zr-C2)	B (C3-H1)	Zr	C2
DVB[BVPE]-PP1+ [Zr]-H	0.877 [0.877]	1.897 [1.898]			1.311 [1.311]	−0.421 [−0.419]
IM31,2	0.889 [0.889]	1.595 [1.598]	0.345 [0.342]	0.006 [0.005]	1.095 [1.095]	−0.643 [−0.639]
TS31,2	0.604 [0.604]	1.392 [1.145]	0.529 [0.530]	0.283 [0.291]	1.148 [1.149]	−0.703 [−0.704]
PR1,2	0.144 [0.143]	1.024 [1.023]	0.788 [0.788]	0.782 [0.784]	1.319 [1.320]	−0.806 [−0.806]
	B (Zr-H1)	B (C2-C3)	B (Zr-C3)	B (C3-H1)	Zr	C3
IM32,1	0.817 [0.819]	1.693 [1.697]	0.235 [0.232]	0.067 [0.065]	0.940 [0.948]	−0.302 [−0.301]
TS32,1	0.636 [0.634]	1.497 [1.495]	0.383 [0.385]	0.261 [0.263]	0.890 [0.888]	−0.352 [−0.353]
PR2,1	0.181 [0.182]	1.081 [1.083]	0.650 [0.647]	0.747 [0.745]	1.043 [1.037]	−0.469 [−0.465]

shows the Wiberg bond indices and natural charges for some key bonds and atoms for the reaction pathway of the second vinyl bond insertion. The WBI values of the Zr-C₂ bond (0.529 and 0.788) and C₃-H₁ bond (0.283 and 0.782) for TS3_1,2 and PR_1,2 are larger than the corresponding values for the Zr-C₃ bond (0.383 and 0.650) and the C₃-H₁ bond (0.261 and 0.747) for TS3_2,1 and PR_2,1. On the contrary, the WBI values of the Zr-H₁ bond (0.604 and 0.144) and the C₂-C₃ bond (1.392 and 1.024) for TS3_1,2 and PR_1,2 are smaller than the corresponding values of the Zr-H₁ bond (0.636 and 0.181) and the C₂-C₃ bond (1.497 and 1.081) for TS3_2,1 and PR_2,1. These all indicate an interaction between [Zr]-H and DVB-PP₁ in TS3_1,2, and PR_1,2 is stronger than that in TS3_2,1 and PR_2,1. A similar conclusion can be drawn from the natural charges. The Q_NBO values of the Zr atom in TS3_1,2 and PR_1,2 are 1.148 e and 1.319 e, which are much larger than the Q_NBO values of the Zr atom (0.890 e and 1.043 e) in TS3_2,1 and PR_2,1, and the Q_NBO values of the C₂ atom in TS3_1,2 and PR_1,2 are −0.703 e and −0.806 e, which are much smaller than the corresponding Q_NBO values of the C₃ atom (−0.352 e and −0.469 e) in TS3_2,1 and PR_2,1.

The situation for BVPE is similar to that for DVB. The 1,2-mode insertion is thermodynamically preferred to the 2,1-mode insertion. The energy in the brackets in Figure 5 represents the energy in the BVPE reaction process, and Figure 7 lists the main TSs and the configurations of the intermediates. From an energy perspective, and for the relative stability of the activated zirconocene containing BVPE-PP₁ and [Zr]-H, the more feasible reaction pathway is the 1,2 insertion. The insertion of the vinyl bond of BVPE-PP₁ into [Zr]-H leads the transition state [TS3_1,2] via [IM3_1,2] before forming the product [PR_1,2]. The potential barrier of the whole process is 4.8 kcal/mol (slightly higher than 2.0 kcal/mol for DVB-PP₁), and the exothermic energy is 12.6 kcal/mol (similar to 12.2 kcal/mol for DVB-PP₁). In the second method, BVPE-PP₁ needs to rotate 180° along the Zr-C₁ bond, BVPE-PP₁, and insert into [Zr]-H to form [IM3_2,1], which transits to [TS3_2,1], leading to the product [PR_2,1]. The potential barrier of the whole process is 7.3 kcal/mol (similar to 7.4 kcal/mol for DVB-PP₁), and the exothermic energy is 5.5 kcal/mol (similar to 5.6 kcal/mol for DVB-PP₁). In comparison, the 1,2-insertion reaction path is more exothermic and has a lower energy barrier. Therefore, for the insertion of the second vinyl bond of the bis-styrenic molecule [BVPE], the 1,2-insertion mode is the optimal insertion mode.

To further investigate the reactions, the global reactivity index, local reactivity index, and Fukui functions values for some molecules were calculated (

Table 3. The global reactivity index, local reactivity index, and Fukui function values for some molecules.

	η a	μ b	ω c	NNud	ωlocale	NNu-localf		f+g	f−h
					Zr	C2	C3	Zr	C2	C3
[Zr]-DVB-PP1	4.594	−6.838	5.088	1.064	0.842	0.040	0.012	0.166	0.038	0.011
[Zr]-[BVPE]-PP1	4.295	−6.637	5.128	1.619	0.854	0.031	0.028	0.167	0.075	0.039
[Zr]-H	4.945	−7.212	5.260	0.588	1.298			0.247
DVB-PP1	8.748	−3.271	0.611	3.311		0.473	0.221		0.143	0.067
[BVPE]-PP1	8.145	−3.247	0.647	3.264		0.308	0.140		0.094	0.043

^a Chemical hardness (η, in eV). ^b Electronic chemical potential (μ, in eV). ^c Global electrophilicity (ω, in eV). ^d Global nucleophilicity (N_Nu, in eV). ^e Local electrophilicity (ω_local, in eV). ^f Local nucleophilicity (N_Nu-local, in eV). ^g Nucleophilic attack Fukui function for Zr (f⁺, in e). ^h Electrophilic attack Fukui function for C₂, C₃ (f⁻, in e).

). The complete local reactivity index and Fukui function values of these molecules are given in the Supplementary Materials (Table S1). The global reactivity index values of DVB-PP₁ and [BVPE]-PP₁ clearly reveal the nucleophilicities of the molecules with a global nucleophilicity (N_Nu) value of 3.311 and 3.264, respectively. The global reactivity index values of [Zr]-DVB-PP₁, [Zr]-[BVPE]-PP_1, and [Zr]-H reveal that they are electrophilic with global electrophilicity (ω) values of 5.088, 5.128, and 5.260, respectively. The results also show that the ω value of [Zr]-H is slightly higher than that of [Zr]-DVB-PP₁ and [Zr]-[BVPE]-PP₁, so that the electrophilicity of [Zr]-H is higher. Similar conclusions can be drawn from the local reactivity index values. The local electrophilicity (ω_local) value of Zr in [Zr]-H (1.298) is higher than those of [Zr]-DVB-PP₁ (0.842) and [Zr]-[BVPE]-PP₁ (0.854), indicating that Zr in [Zr]-H has greater reactivity.

The local nucleophilicity (N_Nu-local) index values of C₂ in DVB-PP₁ (0.473) and [BVPE]-PP₁ (0.308) are higher than those of C₃ (0.221 and 0.140), indicating that C₂ has greater reactivity; thus, it more easily reacts with Zr in [Zr]-H to form a Zr-C₂ bond to complete the 1,2-insertion reactions. The local nucleophilicity (N_Nu-local) index values of C₂ and C₃ in DVB-PP₁ (0.473 and 0.221) are higher those in [BVPE]-PP₁ (0.308 and 0.140), indicating that DVB-PP₁ has more reactivity; thus, it more easily reacts with [Zr]-H, consistent with the potential barrier of the DVB-PP₁ 1,2-insertion reaction process being lower than that of BVPE-PP₁ by 2.8 kcal/mol.

The Fukui function is often used to predict reactions. The site with a larger Fukui function value has a higher reactivity. The Fukui function information for some molecules is shown in Table 3 and Figure 8. The results show that the Fukui function value (f⁺) of Zr in [Zr]-H is higher than those of [Zr]-DVB-PP₁ and [Zr]-[BVPE]-PP₁, so the Zr in [Zr]-H is more reactive. The Fukui function values (f⁻) of C₂ in DVB-PP₁ (0.143) and [BVPE]-PP₁ (0.094) are higher than those of C₃ (0.067 and 0.043), indicating that C₂ has more reactivity; thus, it more easily reacts with Zr in [Zr]-H to form a Zr-C₂ bond to complete the 1,2-insertion reactions. Therefore, this also reveals why the 1,2-insertion mode is the optimal insertion mode.

3. Computational Methods

All standard DFT calculations were performed using the Gaussian 09 program [17]. All structures were optimized and characterized using frequency analysis calculations to be at a minimum (no virtual frequency) or a transition state (TS, with a unique virtual frequency) at the B3LYP [18,19]/BSI level. BSI denotes a basis set combining the SDD [20] for Zr and 6-31G (d, p) for other non-metal atoms. The pseudo-potential basis set was used for the Zr atom. To improve the energetic results, single-point energy calculations at the optimized structures were performed at the M06 [21,22]/BSII, with solvent effects being simulated via the SMD [23] solvent model, using toluene as the solvent. BSII represents a basis set combining SDD for Zr, and 6-311++G (d, p) for other non-metal atoms. The basis set superposition errors (BSSEs) were accounted for at the same level by using the standard counterpoise method [24,25], as implemented in Gaussian 09. The NBO charges [26] and Wiberg bond indices were obtained at the B3LYP/BSI level. The gas phase B3LYP/BSI harmonic frequency was used to modify the free energy by heat and entropy at 298.15 K and 1 atm pressure, respectively. BSSE-corrected free energies and enthalpies obtained at the M06 (SMD, solvent = toluene)/BSII level and free energies are discussed in the main text; the relative enthalpies are also given for reference. The reliability of the M06//B3LYP combination is demonstrated by its successful application in explaining various transition metal catalytic reactions [27,28,29,30,31,32,33,34,35,36]. The total energy and Cartesian coordinates of all the optimized structures are provided in the Supplementary Materials (Table S2).

The global reactivity index, local reactivity index, and Fukui functions values were performed using the Multiwfn program [37,38]. The calculations also used a mixed basis set (SDD for Zr and 6-31G(d) for other non-metal atoms).

Vertical ionization potential: $\mathrm{VIP}=E_{N-1}-E_N$,

Vertical electron affinity: $\mathrm{VEA}=E_{\mathrm{N}}-E_{N-1}$, where N denotes the number of electrons for a stable system.

Mulliken electronegativity: $\chi =\frac{\mathrm{VIP}+\mathrm{VEA}}{2}$,

Chemical potential: $\mu =-\chi$,

Chemical hardness: $\eta =\mathrm{VIP}-\mathrm{VEA}$ [39],

Electrophilicity index [40]: $\omega =\frac{{\mu }^2}{2\eta }$,

Nucleophilicity index: $N_{Nu}=E_{HOMO}(Nu)-E_{HOMO}(TCE)$, where Nu refers to nucleophile and TCE denotes tetracyanoethylene [41].

The Fukui function is defined as follows [42,43], where N denotes the number of electrons, the term $\upsilon$ is external potential.

$f\left(\mathrm{r}\right)={\left[\frac{\partial \rho \left(\mathrm{r}\right)}{\partial N}\right]}_{\upsilon }$

Nucleophilic attack: $f^{+}(r)={\rho }_{N+1}(r)-{\rho }_N(r)$,

Electrophilic attack: $f^{-}(r)={\rho }_N(r)-{\rho }_{N-1}(r)$.

4. Conclusions

DFT calculations were performed to study the regioselectivity of the vinyl bond reaction of the copolymerization of propylene and the bis-styrenic molecules. The calculations revealed that, when hydrogen is introduced to reactivate the inactivated catalyst and the vinyl bond containing DVB or BVPE is inserted, the second vinyl bond is inserted into the polymer in a rare 1,2 manner. This study yielded the following insights into the mechanism: (I) Upon insertion of the first vinyl bond of the DVB or BVPE into the Zr-C (PP₁), its second vinyl bond is more inclined to be inserted in the 1,2 mode. (II) The 2,1 insertion is thermodynamically and kinetically unfavorable for DVB-PP₁ or BVPE-PP₁, as the Zr-C₁ bond should rotate 180° to complete the insertion before the second insertion take place; thus, the 1,2 insertion is easier to complete. Because the 1,2 insertion is the preferred mode for the bulk DVB-PP₁ or BVPE-PP₁, in terms of both the kinetics and thermodynamics, it leads to a growth polymer with an irregularity and region selectivity of the second vinyl bond insertion into the PP_i. (III) The analysis of the local reactivity index and Fukui functions also indicate that the 1,2-insertion mode is the optimal insertion mode. A detailed mechanistic study of this is important in understanding the chain transfer copolymerization, and to develop a functionalization strategy for PP polymers.