## 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_-styrene 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 H\({}_{2}\)-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_-styrene (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.