## 2 Results and Discussion
### The Second Vinyl Bond of the bis-Styrene Molecule (DVB and BVPE)  
After hydrogen reactivates the catalyst, the intermediate, IM2, decomposes into two parts, DVB-PP\({}_{1}\) and [Zr]-H, and continues to insert. The subsequent insertion of the second vinyl bond of the _bis_-styrene 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-PP\({}_{1}\) occurs. For the 2,1 insertion, Zr-C\({}_{1}\) of the vinyl of DVB-PP\({}_{1}\) needs to rotate 180\({}^{\circ}\) 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\({}_{2,1}\)). Figure 4: Optimized structures of key TSs and intermediates (IMs) in the BVPE reaction pathway shown in Figure 2. The key length is in angstroms. During the reaction, the second vinyl group of DVB-PP\({}_{1}\) slowly formed a bond with the Zr atom. According to the configurations of the intermediate, IM3\({}_{1,2}\); the transition  
Figure 5: The reaction pathway of the second vinyl bond insertion; the relative free energy is given in kcal/mol, and the relative energy of BVPE is given in brackets; the relative enthalpy is also given in parentheses for reference (in kcal/mol). Figure 6: Optimized structures of key TSs and intermediates (IMs) in the DVB reaction pathway shown in Figure 5. The key length is in angstroms. state, TS3\({}_{1,2}\); and the product, PR\({}_{1,2}\), the bond lengths between the Zr and C\({}_{2}\) atoms in IM3\({}_{1,2}\), TS3\({}_{1,2}\), and PR\({}_{1,2}\) are 2.567, 2.417, and 2.170 A, respectively, which decrease in turn. The bond lengths of the carbon bonds C\({}_{2}\)-C\({}_{3}\) in IM3\({}_{1,2}\), TS3\({}_{1,2}\), and PR\({}_{1,2}\) are 1.375, 1.411, and 1.524 A, respectively, which become longer as they form single bonds from double bonds. Simultaneously, the bond lengths between the Zr and H\({}_{1}\) atoms are 1.822 A and 1.859 A in IM3\({}_{1,2}\) and TS3\({}_{1,2}\), respectively, and they lengthen successively until the Zr-H\({}_{1}\) 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 A). 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 A, respectively, shorter than that inTS3\({}_{2,1}\) (2.282 and 2.306 A); 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.