Understanding the reaction mechanism of the CO2 and cyclohexene oxide copolymerization catalyzed by zinc(II) and magnesium(II) catalysts: a DFT approach

The reaction mechanisms of carbon dioxide and cyclohexene oxide copolymerization catalyzed by four different zinc(II)-magnesium(II) (labeled as M1-M2) catalysts were computationally studied using density functional theory at the BP86-D3(BJ)/def2-TZVP/SMD//BP86-D3(BJ)/def2-SVP/SMD level of theory. The results showed that the most effective catalyst was the ZnMg system, in which poly(cyclohexene carbonate) was the preferred product, followed by the side product cis-cyclohexene carbonate. The QTAIM, NCI and ELF analysis performed to understand the role of metals in the reaction showed that ligands and substrates interact more strongly with zinc(II) centers compared to magnesium(II) centers. Furthermore, the Zn-I interaction at the M1 position was stronger than the Mg-I interaction at the same position. All these results indicate a synergism between the metals Zn and Mg, which makes Zn(II)Mg(II) the best combination for the reaction.


Introduction
The industrialization process faced since the 18th century has generated social and environmental changes that have brought significant challenges, which is leading us to a climate that is increasingly less suitable for life on Earth. Due to the generation of energy based on the burning of fossil fuels, the concentrations of carbon dioxide (CO 2 ) in the atmosphere have increased c.a. 75% since the 18th century, scenario that contributed significantly with the rise in the average global surface temperature by 0.6 °C in the last century [10,25,39]. Aiming to find solutions to overcome this alarming situation, scientists around the world are trying to reduce CO 2 emissions into the atmosphere by different strategies. Among the viable alternatives of CO 2 conversion, the chemical conversion into valuable products is already a relevant industrial process that uses CO 2 to synthesize products like salicylic acid, methanol, cyclic carbonates, urea and polymers such as polyether carbonates and polycarbonates [10,35].
Although the conversion of CO 2 into products will never be capable of compensating its emissions in the atmosphere, the conversion into materials that have large use in society such as polymers is an interesting alternative to mitigate the problem [25]. Polymers play a central role in modern societies in areas that have a wide range of uses, from personal uses, such as clothing, to materials used in the fabrication of water cleaners. The use of carbon dioxide as a reagent for the production of polymers has already reached the status of a commercial product, being an environmental alternative to polymers synthesized from petrochemical sources [43].
Ring opening and copolymerization reactions (ROCOP) employing CO 2 and a cyclic epoxide such as 1 3 cyclohexene carbonate (CHO) as a promising reaction to both use carbon dioxide as a reagent and to produce poly(cyclohexene carbonate) via a less harmful route than the traditional route that uses phosgene gas and transdiols such as bisphenol A in synthesis [25]. Bimetallic homogeneous catalysts are being employed to promote the ROCOP of CO 2 and CHO. The use of bimetallic catalysts relies on the synergistic effects between metals that are used to activate chemical bonds that in a single metal catalyst would not happen [11].
In Fig. 1 is presented the general scheme of the ROCOP reaction and the catalyst used in this work. The main product of these reactions, as described in Fig. 1, is poly(cyclohexene carbonate), and a minor product is formed in a side reaction, the cis-cyclohexene carbonate. The catalyst employed in this reaction is composed by two metals described in Fig. 1 as metals 1 (M 1 ) and 2 (M 2 ), in which homo-or hetero-bimetallic combinations could be used [35]. Combinations such as Zn(II)Zn(II) [9], Mg(II)Mg(II) [12,13], Ti(IV)Zn(II) [17], Fe(III)Fe(III) [8], Co(III)Co(II), Co(II)Co(II) [23], and Co(II)Mg(II) [12] were used at metal positions 1 and 2.
This work aims to study the reaction mechanism of the ROCOP catalyzed by bimetallic homogeneous catalysts composed of zinc(II) and magnesium(II) in homo-and hetero-bimetallic combinations (from now on named as MgMg, ZnMg, MgZn and ZnZn systems) by means of computational modeling employing the density functional theory (DFT) in calculations.

Computational details
All geometry optimizations, vibrational frequencies, and single point calculations were performed with ORCA 4.2 software [30,31] using the BP86 [6,32,33] density functional approximation (DFA) along with the def2-TZVP and def2-SVP basis set [42] for single point and geometry optimization/frequency calculations. Dispersion effects were accounted for using the D3 dispersion correction with Becke-Johnson damping [19,20]. Solvation effects were modeled by the implicit solvation model SMD using the parameters for the dibutyl ether solvent [28]. To accelerate the calculation of Coulomb and exchange integrals, the resolution of identity (RI) approximation [1,5,14,15,24,40] was used, in which the def2/J auxiliary basis set [41] was used to perform the RI approximation. To reach this level of theory, a benchmark was made comparing the performance of ten selected DFAs, where the results of this study can be found in the supplementary material.
Since some molecules in the catalytic cycle are nonrigid, a conformational analysis using CREST software [36] was performed prior to DFT geometry optimization and subsequent frequency calculation. The intermediaries Int3, Int6a, Int7a (Fig. 2) and the first monomer of the polymer produced in the reaction were submitted to this analysis and the structure with the lowest energy was taken as the initial structure for the DFT calculation. Conformational analysis and thermal corrections for the DFT calculations were performed at 393.15 K, the temperature commonly held in experiments in analogous systems. The transition states were identified as having only one imaginary eigenvalue of the hessian and confirmed by the IRC algorithm [22].
The final Gibbs free energy (G) for each molecule was calculated using the expression: where E elec is the electronic energy of the molecule at the BP86-D3(BJ)/def2-TZVP/SMD level of theory, the G corr is the thermal corrections from the frequency calculations at the BP86-D3(BJ)/def2-SVP/SMD level of theory and ΔG o solv is the correction to bring the molecules from the gas phase to solution at a concentration of 1 mol ⋅ L -1 in which the calculated value for 393.15 K is 10.5 kJ ⋅ mol -1 .

Catalytic cycle
In this article, two main products have their reaction mechanisms considered according to the experimental results on analogous systems [9,13,35]: (i) the catalytic cycle of poly(cyclohexene carbonate) formation (represented in Fig. 2 as the green path); and (ii) the catalytic cycle of cis-cyclohexene carbonate formation (represented as the orange path in Fig. 2). Both catalytic cycles have common steps that are represented as the black path, which comprehends the formation of intermediaries 1 (Int1), 2 (Int2), 3 (Int3) and 4 (Int4). The first step of the reaction is due to the coordination of a CHO molecule with the catalyst, which forms Int1; after the formation of Int1, Int2 is formed through TS1 by opening the CHO epoxide ring. With the coordination of CO 2 in M 1 in Int2, Int3 is formed, subsequently forming Int4 by a nucleophilic attack of the oxygen bonded to M 2 in the CO 2 carbon atom passing through TS2. Up to this point, the reaction could take two different paths, forming the poly(cyclohexene carbonate) or cis-cyclohexene carbonate. The formation of the poly(cyclohexene carbonate) occurs by first coordinating one more molecule of CHO, forming intermediary 5a (Int5a), and next forming intermediary 6a (Int6a) via a second CHO epoxide ring opening reaction passing through transition state 3a (TS3a), beginning the polymer propagation. Thus, to produce more monomers of the polymer, more molecules of CHO coordinate to M 1 , subsequently reacting to open the CHO epoxide ring. In this work we restricted ourselves to only one propagation step since other propagation steps are similar to the first one. Finally, we proposed a termination step to the reaction in which one acetic acid molecule coordinates to M 2 forming the intermediary 7a (Int7a), and after a proton transfer reaction through transition state 4a (TS4a) forming the intermediary 8a (Int8a), eventually regenerating the catalyst and releasing the first monomer of poly(cyclohexene carbonate).
The formation of cis-cyclohexene carbonate proceeds by, firstly, a geometrical rearrangement of Int4a, forming thus the intermediary 5b (Int5b). After, by a backbiting reaction, the intermediary 6b (Int6b) is formed passing through the transition state 3b (TS3b). Finally, the catalyst is regenerated and the cis-cyclohexene carbonate molecule is released.

Comparison between MgMg, ZnMg, MgZn and ZnZn energetic profiles
The energetic profile for the MgMg, ZnMg, MgZn and ZnZn systems is represented in Fig. 3. As can be seen, the opening of the epoxide ring of the CHO molecule is a step in which all systems have similar energies and, on the other hand, the nucleophilic attack on the CO 2 carbon atom occurs with different energetic barriers in which the trends of the barriers are inversed in the second step of the reaction. A remarkable feature of the four catalytic systems is that all considered barriers are feasible to take place in the given temperature, which implies that the modeled catalytic systems determine only how fast the reaction could occur (for a further The transition states 1 and 2 for the MgMg, ZnMg, MgZn and ZnZn systems are shown in Fig. 4. When analyzing the transition state structures, one can see that, especially for TS1, the structures are very similar, which is also reflected in the energetics of those molecules, as shown in Fig. 3. On the other hand, the structures for TS2 differ in two groups, in which the transition states of the molecules where the oxygen atom attacking CO 2 is bonded to Mg are earlier transition states than those bonded to Zn. Taking the energetics from the intermediary 1 (local minimum) to the energetics of the transition states, the two main barriers of this part of the catalytic cycle can be determined: (i) the barrier to reach TS1 from Int1 ( ΔG 1 ); and (ii) the barrier from Int1 to TS2 ( ΔG 2 ). Taking the Boltzmann weight ratio p 2∕p 1 = e −(ΔG 2 −ΔG 1 ) ∕RT the relative populations of each transition states can be calculated. This ratio is important to show how fast the reaction would proceed in the nucleophilic attack step on CO 2 compared to the opening of the epoxide ring of the CHO molecule because the barriers for the first part of the reaction are close to each other, and thus the second step of the reaction determines the best catalytic system. In Table 1 the calculated values of ΔG 1 , ΔG 2 , and p 2∕p 1 are shown.
The values shown in Table 1 show that although the ZnMg system has the second highest value ΔG 1 , ΔG 2 compensates by providing a faster reaction than the other systems, as can be seen from the relative populations of p 2∕p 1 . The general trend for the systems is ΔG 1 < ΔG 2 for systems with Mg at M 1 position and ΔG 2 < ΔG 1 for systems with Zn at M 1 .

Topological analysis
Once the TS2 presented such large difference between activation energies for distinct combinations of M 1 -M 2 , it was performed an AIM analysis of TS2 and its previous intermediate (Int3) in order to evaluate the effect of metal changes (M 1 and M 2 ) in the strength of some highlighted chemical bonds (or interactions) beyond its influence on the reactivity  of such systems. The quantum theory of atoms in molecules (QTAIM) was developed by Richard Bader [3,4] and has been widely applied in the evaluation and characterization of chemical bonds and noncovalent interactions [26,29]. This theory is based on the topological evaluation of the electronic density (r) to characterize the atoms in the properties of the molecules and their interactions. In broad terms, a chemical bond (or an interaction between atoms) can be investigated through the evaluation of its AIM properties at its Bond Critical Points (BCPs). The BCP is a critical point formed by the encounter of vector path lines of the electronic density gradient ∇ 2 CP that come from two distinct attractors (commonly atoms in a molecule). These path lines that connect two attractors through the same BCP are called Bond Path (BP). The presence of a BP connecting two attractors between a BCP features the presence of a chemical bond or a noncovalent interaction between them. The strength of such interactions can be estimated through the AIM properties at its respective BCP.
The AIM molecular graphs of Int3 and TS2 (MgMg, ZnMg, MgZn, and ZnZn, respectively) revealed several covalent and noncovalent interactions between catalysts and substrates (Figs. 5 and 6). Some interactions in these systems were highlighted to evaluate their AIM properties in detail, and the main interactions are displayed in Tables 2 and 3. The AIM properties for all the BCPs studied are shown in Tables S5-S12.
In general, the AIM analysis of Int3 and TS2 in the MgMg, ZnMg, MgZn, and ZnZn systems shows that Zn atoms have stronger interactions with O and N atoms (from the ligand). The electronic density (r) values of Zn-O and Zn-N bonds for Int3 and TS2 ranging between 0.05 and 0.07 ( e∕Bohr 3 ) (BCPs f, g, h, and i for ZnMg, BCPs j, k, l, and m for MgZn and BCPs f, g, h, i, j, k, l, and m for ZnZn) that  f, g, h, i, j, k, l, and m for MgMg, BCPs j, k, l, and m for ZnMg, and BCPs f, g, h, and i for MgZn) as can be verified at Tables S5-S12. In addition to that, the Zn-O and Zn-N bonds showed ‖V CP ‖ ∕G CP > 1 , which indicates that these interactions are covalent [16], while the Mg-O and Mg-N bonds showed ‖V CP ‖ ∕G CP < 1 , which indicates that these interactions are noncovalent. This behavior demonstrates that Zn atoms interact with the ligand more strongly than Mg atoms, and the strength of such interactions is reflected in the stability of the complexes and their reactivity.  Although this difference can seem low, by evaluating the difference between potential energy density ( V CP ) at the BCPs c and d for M 2 =Mg and M 2 =Zn we can achieve a difference about 0.13 Hartree∕Bohr 3 (or 80 kcal/mol) between TS2 in the MgMg and in the MgZn systems that is substantial.
Finally, the AIM analysis indicates that the I-M 1 interaction is considerably stronger for M 1 =Zn than for M 1 =Mg,  and this interaction contributes to the stabilization of Int3 and TS2 in the ZnMg and ZnZn systems. This behavior agrees with NCI finds that showed stronger interactions between I-Zn than I-Mg as can be verified in Fig. 8 and helps to understand its stabilization. Meanwhile, the stability exchange between ZnMg and ZnZn in TS2 could be related to the energetic balance between the two half-broken strong C-O bonds (BCPs c and d) to make a new single O-C bond (BCP b). The noncovalent interactions (presented in Fig. 8) between catalyst, CHO and CO 2 showed weak in comparison to the interactions highlighted and should not had great role on the stabilization of systems. The AIM and NCI analysis demonstrated that the interaction between Zn and I stabilizes the system. Beyond that, the Mg as M 2 favors the reaction because low O-M 2 interaction strength and the slightly difference between O-CO 2 interactions strength for Int3 and TS2 which reflects on a lower difference between Int3 and TS2 and a lower activation barrier, which also can be observed by the results of the ASM analysis presented in the Supplementary Information. Such synergy between M 1 =Zn and M 2 =Mg make the ZnMg a better candidate to catalyze this reaction, as verified through the other analyzes.

ZnMg full energetic profile
The full catalytic energetic profile of the ZnMg system is presented in Fig. 9. As expected by the experimental results [13], the formation of the first monomer of poly(cyclohexene carbonate) is both a thermodynamic and a kinetic product. An important feature of the energetic profile is that the steps that involve the opening of the CHO epoxide ring have larger barriers compared to the reaction with CO 2 , especially the opening of the first CHO epoxide ring, that is, ΔG ‡ TS1 configures the highest barrier to polymer formation. This trend of opening the first ring being the most energetic step in the reaction is in agreement with the experiments [12] and can be explained as being more energetic demanding than the ΔG ‡ TS3a because the TS3a is more stabilized by the term TΔS due to the higher number of degrees of freedom than TS1. The termination step proposed for this reaction seems to be a good suggestion because ΔG ‡ TS4a is a feasible barrier and also because it configures an irreversible step, as there is no documented expressive formation of side products from the polymer monomers.   The backbiting reaction occurs first by the formation of intermediary 5b (Int5b) which is more favorable than intermediary 5a (Int5a); however, ΔG ‡ TS3b is 22.6 kJ ⋅ mol -1 greater than ΔG ‡ TS3a and becomes the determining step of the formation of cis-cyclohexene carbonate. Since the barrier to TS3b is overcome, the formation of intermediary 6b (Int6b) is favorable and, like in the termination step of the polymerization reaction, the formation of Int6b is an irreversible step in the reaction. A notable characteristic of this path is that Int6b is more stable than the formation of the reaction product and the regeneration of the catalyst. Once TS3b became the rate-determinant step of the cyclohexene carbonate formation it was performed AIM and NCI analysis of TS3a and TS3b to investigate the influence of covalent and noncovalent interactions on their energetic differences. The AIM analysis (Table S13 and Figure S29 . In addition to this, the NCI analysis ( Figure S30) indicated the presence of stronger repulsive interactions in the new ring formation in the TS3b compared to the ring opening in the TS3a. These repulsive interactions, together with the weaker interactions between substrate and metals revealed by the AIM analysis, should be related to the higher energy of TS3b regarding TS3a. This behavior indicates that the interactions between substrate and catalyst can affect the energetic profile of the reaction. Therefore, better catalysts can be designed by understanding these interactions to optimize them employing different substituents to tune the interaction between metal and substrate molecules.
In summary, the reaction catalyzed by the ZnMg system proceeds with the formation of the first monomer of poly(cyclohexene carbonate) because this product is more stable than the cis-cyclohexene carbonate and also because since the reaction reaches Int4, passing through TS3a is faster than passing through TS3b, although Int5b is more stable than Int5a. A note about both paths is that all involved barriers are feasible to take place under experimental conditions; however, a key point, especially for path A, is that the more monomers are added to the substrate, the more the TΔ r S term in Δ r G contributes to stabilizing the product, and consequently, the polymer formation establishes as the most favorable product.
Taking into account the other three systems studied in this work and the reactivity presented up to the formation of Int4, the features of the energetic trend presented to the ZnMg systems would be similar, especially in the ZnZn system. However, in a system having both the ZnMg and the MgZn catalysts, the preferable route would be the reaction being catalyzed by ZnMg system because of the faster passage of this catalyst through TS2.

Conclusions
The reaction mechanism of the ring opening and copolymerization of CHO and CO 2 was studied at the BP86-D3(BJ)/ def2-TZVP/SMD//BP86-D3(BJ)/def2-SVP/SMD level of theory for the MgMg, ZnMg, MgZn and ZnZn systems using a model system. The characteristic that makes the ZnMg catalyst better than other studied catalysts is that the ratio p 2∕p 1 is smaller for this system than for the other ones, and consequently, in reaction media that initially contained the ZnMg and MgZn system, the most probable catalyst that acts in the reaction is ZnMg. The metal in position 2 has a key role in CO 2 activation since this metal influences directly the electron density of the oxygen atom that is attacking CO 2 carbon atom; the metal 1, on the other hand, works in the stabilization of Int2, and therefore the energetic demand to distort both Int2 and CO 2 to the geometry of TS2.
Poly(cyclohexene carbonate) formation involves four transition states, in which the opening of the CHO epoxide ring that passes through the TS1 is the bottleneck of the reaction, especially for ZnMg and ZnZn systems that share similar reactivities up to CO 2 activation. Already at the formation of the first monomer of poly(cyclohexene carbonate) we could observe that this is the most preferable product in the reaction and the main factor that influences in the formation of ciscyclohexene carbonate is the barrier to overcome the TS3b.
One point that is still unclear in the studied systems is how the stereoselectivity of the polymer produced is controlled in the reactions catalyzed by the studied bimetallic catalysts. Reddi and Cramer [37] have recently studied the ROCOP of CHO and CO 2 catalyzed by an indium(III) phosphasalen catalyst and described the intricacies that promote R,R as the preferred product in the reaction. Therefore, we believe that promoting a better understanding of the features that promote possible poly(cyclohexene carbonate) enantiomers would be of great importance in rationalizing the stereochemistry of this polymer. Code and data availability Inputs and outputs files of the calculations presented in the article are available in ioChem-BD and NOMAD repositories. The Python script used to perform ASM calculations is available in GitHub repository.