## 2 Results and Discussion
### Mechanistic Study of CO\({}_{2}\) Cycloaddition
#### 2.3.2 Reaction Pathway Analysis  
Previous studies suggested a three-stage CO\({}_{2}\) cycloaddition mechanism: (1) GO ring-opening, (2) CO\({}_{2}\) insertion, and (3) GLC ring-closing [16]. Through modeling and transition state analysis (Figure 9), we confirmed this pathway for P-BVIMCI. Energy calculations (Figure 10) revealed that the GO ring-opening step had the highest energy barrier (48.04 kcal/mol), and this rate-determining step aligned with prior mechanistic studies [45; 46].  
Figure 8: The (**a**) average local ionization energy (red: maximum; blue: minimum.) and (**b**) dual descriptor Fukui function analysis of P-BVIMCI.  
Figure 10: Energy barrier of cycloaddition reaction process relative energy of CO\({}_{2}\) cycloaddition (**a**) without catalysts and (**b**) catalyzed by P-BVIMCI.  
Figure 9: The reaction process of CO\({}_{2}\) cycloaddition catalyzed by P-BVIMCI.  
To investigate the interactions among P-BVIMCl, epoxides, and CO\({}_{2}\) molecules, we conducted Interaction Region Indicator (IRI) analysis on the transition states of three reaction stages [47; 48] (Figure 11). Blue isosurfaces corresponded to strong intermolecular attractions (e.g., hydrogen bonds, halogen bonds), red isosurfaces represented strong repulsions (e.g., ring strain), and green isosurfaces indicated van der Waals interactions. Ring-opening stage (Figure 11a,b): Blue-green isosurfaces between Cl\({}^{-}\) and the \(\beta\)-C atom of GO demonstrated halogen bond-like interactions, indicating the formation of a new C-Cl bond. Blue isosurfaces between the imidazole C-H group and the oxygen atom (O\({}^{-}\)) of the opened GO ring confirmed strong hydrogen-bonding interactions (C-H\(\cdots\)O), facilitating ring-opening. CO\({}_{2}\) molecules adopt an activated bent configuration (176.11\({}^{\circ}\)) under the synergistic effect of Cl\({}^{-}\) and imidazole groups, promoting subsequent insertion. CO\({}_{2}\) insertion stage (Figure 11c,d): The newly formed C-Cl bond was evidenced by characteristic peaks in the IRI scatter plot (sign(\(\uplambda_{2}\)) \(\rho<-0.05\) regions). Blue isosurfaces emerged between the CO\({}_{2}\) carbon atom and the O\({}^{-}\) ion from the opened GO ring, signaling the formation of a new C-O bond. GLC ring-closure stage (Figure 11e,f): Red and blue isosurfaces between the newly formed O\({}^{-}\) ion and the original \(\beta\)-C atom of GO indicated cyclic C-O bond formation. The disappearance of the C-Cl bond peak in Figure 11d confirmed Cl\({}^{-}\) departure, marking reaction completion. This analysis systematically revealed the bond formation/breaking sequence and interaction evolution during the catalytic cycle.  
We proposed the CO\({}_{2}\) catalytic cycloaddition mechanism over P-BVIMCl (Figure 12). The process involved three key steps: 1. Nucleophilic Activation: Cl\({}^{-}\) attacked the \(\beta\)-C of GO while activating CO\({}_{2}\), and the imidazole C-H acted as an electrophilic site to protonate GO's oxygen, triggering ring-opening to form an O\({}^{-}\) intermediate. 2. CO\({}_{2}\) Insertion: The  
Figure 11: IRI analysis of transition states of (**a,b**) GO ring-opening step, (**c,d**) CO\({}_{2}\) insert step, and (**e,f**) CPC ring-closing step.  
activated CO\({}_{2}\) (bent at 176.11\({}^{\circ}\)) is inserted into GO under O\({}^{-}\) attraction, forming a GLC precursor. 3. Cyclization: The terminal O\({}^{-}\) attacks \(\beta\)-C, expelling Cl\({}^{-}\) and closing the ring to generate GLC. This mechanism highlighted the dual role of Cl\({}^{-}\) (nucleophilic) and imidazole C-H (electrophilic) in driving CO\({}_{2}\) conversion.