Density Functional Theory Analysis of the Copolymerization of Cyclopropenone with Ethylene Using a Palladium Catalyst

Density functional theory has been used to elucidate the mechanism of Pd copolymerization of cyclopropenone with ethylene. The results reveal that introducing ethylene and cyclopropenone to Pd catalyst is thermodynamically feasible and generates the α,β-unsaturated ketone unit (UnitA). Cis-mode insertion and Path A1a are the most favorable reaction routes for ethylene and cyclopropenone, respectively. Moreover, cyclopropenone decomposition can generate CO in situ without a catalyst or with a Pd catalyst. The Pd-catalyzed decomposition of cyclopropenone exhibits a lower reaction barrier (22.7 kcal/mol) than its direct decomposition. Our study demonstrates that incorporating CO into the Pd catalyst can generate the isolated ketone unit (UnitB). CO is formed first; thereafter, UnitB is generated. Therefore, the total energy barrier of UnitB generation, accounting for the CO barrier, is 22.7 kcal/mol, which is slightly lower than that of UnitA generation (24.0 kcal/mol). Additionally, the possibility of copolymerizing ethylene, cyclopropenone, and allyl acetate (AAc) has been investigated. The free energy and global reactivity index analyses indicate that the cyclopropenone introduction reaction is more favorable than the AAc insertion, which is consistent with the experimental results. Investigating the copolymerization mechanism will help to develop of a functionalization strategy for polyethylene polymers.


Introduction
Polyolefin materials are extensively being used in various applications. However, the chain structure of olefin polymers is generally saturated because their chains are composed of saturated C-C and C-H bonds. The wide application prospect of polymers is primarily owing to the polar groups on their chains and is determined by their properties. Therefore, it is crucial to introduce highly reactive polar groups into the chains to improve the surface characteristics, adhesion, dyeing and printing properties, solvent resistance, and compatibility and blending with other polymer materials [1][2][3].
Catalysts containing metals are commonly utilized in the copolymerization of olefins and polar monomers to achieve functional modifications. This widely used method can alter the polymer chain structure without applying high temperatures and pressures, significantly increasing the efficiency and yield. Late transition metals, such as Pd and Ni, have been recently proven superior to early transition metals in catalyzing the functionalization of polyolefins.
Since Brookhart et al. first utilized α-diimide Pd and Ni catalyst systems in the polymerization of olefins in 1995 [4], Pd and Ni catalysts have received significant research attention. Compared to other transition metals, Pd and Ni exhibit lower oxygen affinity and improve tolerance to polar functional groups. In 2002, Drent et al. reported another type of revolutionary phosphine sulfonate Ni and Pd catalysts [5] to produce highly linear copolymers of ethylene and acrylate. In functional polyethylene reactions, phosphine sulfonate Pd catalyst is suitable for polar monomers [6], including acrylate [7], acrylic acid [8], vinyl acetate [9], vinyl ether [10], acrylamide [11], and maleic anhydride [12].
In 2012, Guo et al. demonstrated that using a large steric ligand α-diimide Pd catalyst can provide a copolymer with a high degree of polar monomer incorporation [13]. According to Carrow et al., bisphosphine monoxide Pd catalysts produced highly linear copolymers [14,15]. Brookhart et al. showed that the ratio of methyl acrylate in copolymer increases linearly with the increase in methyl acrylate concentration in the presence of a Pd catalyst in 2015 [16]. Sui et al. reported a cationic Pd catalyst, which can copolymerize methyl acrylate and ethylene and generate a copolymer with a high molecular weight [17]. Nozaki et al. developed Pd catalysts based on carbene ligands and propylene copolymers. A series of polar monomers were produced using the Pd catalysts [18], which can copolymerize 1,1-disubstituted ethylene with ethylene [19,20]. In 2016, the Nozaki Group demonstrated that the large, sterically hindered bulky alkyl groups could improve the molecular weight and regioselectivity of the copolymers using phosphine sulfonate Pd catalysts [21]. In 2018, Zhang et al. reported a new cationic phosphonic diamide phosphine Pd catalyst. This catalyst can successfully catalyze ethylene and polar monomers to obtain high-molecular-weight linear copolymers [22]. Chen et al. reported a five-member ring phosphine nitrogen phosphine oxide Pd catalyst. This Pd catalyst can produce copolymers with low molecular weights [23].
The Chen Group recently synthesized a series of functional polyolefins with Pd phosphine sulfonate catalysts and evaluated their performance. They demonstrated that polar polyolefin materials exhibit excellent performance compared to conventional polyolefins [24][25][26]. In 2018, Wang et al. developed chain-end-functionalized polar polyethylenes using a Pd catalyst, introducing a carbene species as the comonomer, and copolymerized ethylene with polar monomers [27].
Phosphine sulfonate Pd catalysts have been confirmed to be tolerant with extensive polar monomers. In addition, Matsuda et al. found that N-Heterocyclic carbene Pd catalysts can catalyze ring opening of diphenylcyclopropenone, and react with phenylacetylene to produce alkenyl alkynyl ketone [28,29]. In 2019, Wang et al. [30] first applied a Pd catalyst (CatA) to catalyze the ring opening copolymerization of cyclopropenone and ethylene, in which cyclopropenone was used as C3 polar monomer [31,32]. They introduced cyclopropenone to the long chain of polyethylene and obtained a copolymer with inchain α,β-unsaturated ketone units (UnitA) in addition to an isolated ketone (UnitB), which was incorporated into polyethylene. However, the detailed reaction mechanism remains unclear. No theoretical studies have been conducted on the mechanism of the Pd-catalyzed copolymerization of cyclopropenone with ethylene. Therefore, this study employed density functional theory (DFT) calculations to understand the mechanism of the incorporation of UnitA and UnitB into the chain. A detailed mechanistic study of this experimental phenomenon will help understand the copolymerization mechanism and develop a functionalization strategy for olefin polymers. Scheme 1 summarizes the reaction mechanism of the Pd-catalyzed copolymerization of ethylene with cyclopropenone [30]. Scheme 1. Schematic illustration of Pd-catalyzed copolymerization of ethylene with cyclopropenone mechanism. (I) Insterion of the first ethylene into the palladium catalyst (CatA), generates the polymerization product. (II) Cyclopropenone is added and the α,β-unsaturated ketone unit (UnitA) is generated. (III) The second and third ethylene keep inserting and increase the chain. (IV) In-situ generation of CO from cyclopropenone. The palladium-catalyzed decomposition of cyclopropenone has a lower reaction barrier than the direct decomposition. (V) Incorporating CO to generate the isolated ketone unit (UnitB). (VI) Investigating the possibility of copolymerizing ethylene, cyclopropenone and allyl acetate (AAc).

Computational Methods
DFT calculations were performed using the Gaussian 16 software [33]. All structures were optimized and identified to be at a minimum (no virtual frequency) or a transition state (TS, with a specific virtual frequency) via frequency analysis at the B3LYP-D3(BJ) [34][35][36][37]/BSI level. BSI represents a basis set combining the SDD [38] for Pd and 6-31G (d) for non-metal atoms. The pseudo-potential basis set was used for the Pd atom. The energetic results were refined at the M06-2X [39,40]/BSII level via the SMD [41] solvent effects model (toluene as the solvent) using single-point energy calculations. BSII represents a basis set combining SDD for Pd and 6-311++G (d, p) for non-metal atoms. The gas phase B3LYP/BSI harmonic frequency was employed to modify the free energy using heat and entropy at 353.15 K (experimental temperature) and 1 atm pressure, respectively. Notably, the temperature change has negligible effects on the reaction barrier in the calculation of this system. Free energies derived at the M06-2X (SMD, solvent = toluene)/BSII level are discussed in the main text. The NBO charges [42] and Wiberg bond indices were obtained at the B3LYP/BSI level. The reliability of the M06-2X//B3LYP combination is demonstrated by its effective use in addressing various transition metal catalytic reactions [43][44][45][46][47][48][49][50][51][52]. The total energy of all the optimized structures are shown in Table S1.
The cubic files for interaction region indicator (IRI) [53], the global reactivity index [54][55][56][57] and Fukui functions [58,59] analyses were performed using the Multiwfn program 3.8 [60], and the results were visualized by the VMD program 1.9.3 [61]. Additional computational details and detailed data of Fukui functions values for some molecules are shown in Table S2.

First Ethylene Insertion to Phosphine Sulfonate Pd Catalyst
We initially investigated the first ethylene insertion to the phosphine sulfonate Pd catalyst (CatA). Figure 1 shows the reaction pathway of the first ethylene insertion and the associated energies. Two possible routes exist for the initial ethylene insertion reaction, Scheme 1. Schematic illustration of Pd-catalyzed copolymerization of ethylene with cyclopropenone mechanism. (I) Insterion of the first ethylene into the palladium catalyst (CatA), generates the polymerization product. (II) Cyclopropenone is added and the α,β-unsaturated ketone unit (UnitA) is generated. (III) The second and third ethylene keep inserting and increase the chain. (IV) In-situ generation of CO from cyclopropenone. The palladium-catalyzed decomposition of cyclopropenone has a lower reaction barrier than the direct decomposition. (V) Incorporating CO to generate the isolated ketone unit (UnitB). (VI) Investigating the possibility of copolymerizing ethylene, cyclopropenone and allyl acetate (AAc).

Computational Methods
DFT calculations were performed using the Gaussian 16 software [33]. All structures were optimized and identified to be at a minimum (no virtual frequency) or a transition state (TS, with a specific virtual frequency) via frequency analysis at the B3LYP-D3 (BJ) [34][35][36][37]/BSI level. BSI represents a basis set combining the SDD [38] for Pd and 6-31G (d) for non-metal atoms. The pseudo-potential basis set was used for the Pd atom. The energetic results were refined at the M06-2X [39,40]/BSII level via the SMD [41] solvent effects model (toluene as the solvent) using single-point energy calculations. BSII represents a basis set combining SDD for Pd and 6-311++G (d, p) for non-metal atoms. The gas phase B3LYP/BSI harmonic frequency was employed to modify the free energy using heat and entropy at 353.15 K (experimental temperature) and 1 atm pressure, respectively. Notably, the temperature change has negligible effects on the reaction barrier in the calculation of this system. Free energies derived at the M06-2X (SMD, solvent = toluene)/BSII level are discussed in the main text. The NBO charges [42] and Wiberg bond indices were obtained at the B3LYP/BSI level. The reliability of the M06-2X//B3LYP combination is demonstrated by its effective use in addressing various transition metal catalytic reactions [43][44][45][46][47][48][49][50][51][52]. The total energy of all the optimized structures are shown in Table S1.
The cubic files for interaction region indicator (IRI) [53], the global reactivity index [54][55][56][57] and Fukui functions [58,59] analyses were performed using the Multiwfn program 3.8 [60], and the results were visualized by the VMD program 1.9.3 [61]. Additional computational details and detailed data of Fukui functions values for some molecules are shown in Table S2.

First Ethylene Insertion to Phosphine Sulfonate Pd Catalyst
We initially investigated the first ethylene insertion to the phosphine sulfonate Pd catalyst (CatA). Figure 1 shows the reaction pathway of the first ethylene insertion and the associated energies. Two possible routes exist for the initial ethylene insertion reaction, the cis-mode (ethylene cis to phosphorus atom) and trans-mode (ethylene trans to phosphorus the cis-mode (ethylene cis to phosphorus atom) and trans-mode (ethylene trans to phosphorus atom) insertion [62]. Cis-and trans-mode insertion involves the formation of an intermediate (cIM1A or tIM1A) followed by a quaternary TS (cTS1A or tTS1A), resulting in the final product (cPR1A or tPR1A). The main optimized structures are shown in Figure 2.    Pd catalyst (CatA) has two ligands, phosphine and sulfonate. In cis-mode insertion, the ethylene first coordinate to the catalyst's center metal, forming intermediate cIM1 A (endothermic; 1.5 kcal/mol). Owing to the coordination effect, in the cIM1 A configuration, the Pd-C 1 bond (2.047 Å) is longer than that in CatA (2.018 Å). Additionally, the C 2 -C 3 (1.388 Å) bond is longer than that in C 2 H 4 molecule (1.331 Å). After the formation of the intermediate, cIM1 A , the reaction reaches the transition state, cTS1 A (∆G = +12.9 kcal/mol), and the Pd-C 1 (2.234 Å) and C 2 -C 3 bonds (1.428 Å) are longer. After the transition state, cTS1 A , the product of the first ethylene insertion, the cPR1 A form, is attained (∆G = −30.4 kcal/mol). Compared to the cTS1 A configuration, the C 1 -C 2 (1.531 Å) and Pd-C 3 bonds (2.017 Å) in the product cPR1 A are shortened by 0.605 and 0.045 Å, respectively. In contrast, the C 2 -C 3 bond (1.512 Å) in the product cPR1 A is elongated by 0.084 Å.
The C 2 -C 3 bond lengthens during the entire ethylene insertion reaction from a double bond to form a single bond, while the Pd-C 1 bond lengthens until it breaks. The Wiberg bond indices (WBIs) and natural charges (Q NBO ) for certain key bonds and atoms involved in the ethylene insertion reaction are presented in Table 1. As the reaction proceeds, the WBIs of the Pd-C 1 (from 0.704 to 0.010) and C 2 -C 3 bonds (from 2.039 to 1.069) gradually decrease from the reactant (CatA + C 2 H 4 ) to the product cPR1 A , indicating the breaking of the Pd-C 1 bond and the C 2 -C 3 bond change from a double bond to a single bond. The Q NBO values of the C 1 atom also diminish from −0.819 e in CatA to −0.666 e in the product cPR1 A . Meanwhile, the WBI gradually increases from 0.408 to 0.672 for the Pd-C 3 bond and from 0.538 to 1.108 for the C 1 -C 2 bond, indicating the formation of the Pd-C 3 and C 1 -C 2 bonds. The cis-mode ethylene insertion reaction is exothermic (∆G = −16.0 kcal/mol), and the barrier is low at 14.4 kcal/mol, suggesting that the experiment should be simple to perform.
The process of trans-mode ethylene insertion is similar to that of the cis-mode insertion. The energy results indicate that cis-mode insertion is thermodynamically and kinetically preferred to trans-mode insertion. Although the energy of cIM1 A is 6.9 kcal/mol higher than tIM1 A , meanwhile, the energies of cTS1 A and cPR1 A are 7.5 and 15.3 kcal/mol lower than tTS1 A and tPR1 A , respectively. This energy difference can be partly attributed to noncovalent weak interactions. As shown in Figure 2A, the hydrogen bonds in tIM1 A (2.559, 2.726, and 2.694 Å) are shorter than those in cIM1 A (2.630, 2.955, and 2.701 Å). However, the hydrogen bonds in tTS1 A (3.102, 3.013, and 3.995 Å) are longer than those in cTS1 A (2.453, 2.717, and 2.768 Å); the hydrogen bond in tPR1 A (2.866 Å) is longer than that in cPR1 A (2.692 Å). Figure 2B shows the interaction region indicator (IRI) analysis of key structures with weak key interactions highlighted using red circles [53]. As shown in Figure 2B, the noncovalent weak interactions in tIM1 A are stronger than the interactions in cIM1 A . However, the weak interactions in tTS1 A and tPR1 A are weaker than those in cTS1 A and cPR1 A . Consequently, cis-mode insertion is preferred to trans-mode insertion during the entire reaction, which is consistent with the previous results demonstrated by Sun [63] and Nozaki [64]. Therefore, only the favorable cis-mode ethylene insertion was considered in this following study.

Reaction of Cyclopropenone
After the ethylene insertion into the catalyst, the subsequent reaction of cyclopropenone (1a) could occur via one of two paths. Path A 1a and Path B 1a result in the same product (4A), by first forming a transition state (TS1 A or TS3 A ) and then an intermediate (2A or 3A), followed by the formation of another TS (TS2 A or TS4 A ). Figure 3 illustrates the reaction pathway of cyclopropenone, and Figure 4 shows the main optimized structures for the cyclopropenone reaction. The process of trans-mode ethylene insertion is similar to that of the cis-mode insertion. The energy results indicate that cis-mode insertion is thermodynamically and kinetically preferred to trans-mode insertion. Although the energy of cIM1A is 6.9 kcal/mol higher than tIM1A, meanwhile, the energies of cTS1A and cPR1A are 7.5 and 15.3 kcal/mol lower than tTS1A and tPR1A, respectively. This energy difference can be partly attributed to noncovalent weak interactions. As shown in Figure 2A, the hydrogen bonds in tIM1A (2.559, 2.726, and 2.694 Å) are shorter than those in cIM1A (2.630, 2.955, and 2.701 Å). However, the hydrogen bonds in tTS1A (3.102, 3.013, and 3.995 Å) are longer than those in cTS1A (2.453, 2.717, and 2.768 Å); the hydrogen bond in tPR1A (2.866 Å) is longer than that in cPR1A (2.692 Å). Figure 2B shows the interaction region indicator (IRI) analysis of key structures with weak key interactions highlighted using red circles [53]. As shown in Figure 2B, the noncovalent weak interactions in tIM1A are stronger than the interactions in cIM1A. However, the weak interactions in tTS1A and tPR1A are weaker than those in cTS1A and cPR1A. Consequently, cis-mode insertion is preferred to trans-mode insertion during the entire reaction, which is consistent with the previous results demonstrated by Sun [63] and Nozaki [64]. Therefore, only the favorable cis-mode ethylene insertion was considered in this following study.

Reaction of Cyclopropenone
After the ethylene insertion into the catalyst, the subsequent reaction of cyclopropenone (1a) could occur via one of two paths. Path A1a and Path B1a result in the same product (4A), by first forming a transition state (TS1A or TS3A) and then an intermediate (2A or 3A), followed by the formation of another TS (TS2A or TS4A). Figure 3 illustrates the reaction pathway of cyclopropenone, and Figure 4 shows the main optimized structures for the cyclopropenone reaction.   In Path A1a, the C4-C5 bond of cyclopropenone first coordinates to the Pd metal of cPR1A, forming a three-member oxidative addition transition state, TS1A (ΔG = +22.7 kcal/mol). The length (1.648 Å) of the C4-C5 bond in the configuration of the transition state TS1A is longer than that of 1a (1.430 Å) by 0.218 Å. Subsequently, the intermediate 2A is formed (ΔG = −8.7 kcal/mol), completing the oxidative addition process. Compared to the TS1A, in the 2A configuration, the C4-C5 (2.605 Å) bond is longer than that (1.648 Å) in the TS1A. The Pd-C4 (2.059 Å) and Pd-C5 (2.036 Å) bonds are shorter than those in the TS1A. Thereafter, the intermediate, 2A, evolves to another three-member carbon migration transition state, TS2A (ΔG = +10.0 kcal/mol). Τhe Pd-C3 (2.239 Å) and Pd-C4 bonds (2.289 Å) become longer. Afterward, the Pd-C3 bond breakage leads to the product, 4A, which contains UnitA (ΔG = −46.3 kcal/mol). The C3-C4 bond (1.504 Å) of 4A is shorter than that in the TS2A (1.963 Å) configuration by 0.459 Å. The highest occupied orbital (HOMO) and the lowest unoccupied orbital (LUMO) of TS1A and TS2A also indicate their oxidative addition and carbon migration reaction characteristics, respectively. The WBI and QNBO values for certain key bonds and atoms involved in the cyclopropenone reaction are listed in Table 2. As the reaction Path A1a proceeds from TS1A to the product 4A, the WBI decreases from 0.691 to 0.017 for the Pd-C3 bond and from 0.730 to 0.061 for the C4-C5 bond. This decrease indicates the breakage of Pd-C3 and C4-C5 bonds. From the TS1A to the 4A, the WBI progressively increases from 0.298 to 0.685 for the Pd-C5 bond and from 0.025 to 1.008 for the C3-C4 bond, indicating the formation of these bonds. The free energy of TS2A is In Path A 1a , the C 4 -C 5 bond of cyclopropenone first coordinates to the Pd metal of cPR1 A , forming a three-member oxidative addition transition state, TS1 A (∆G = +22.7 kcal/mol). The length (1.648 Å) of the C 4 -C 5 bond in the configuration of the transition state TS1 A is longer than that of 1a (1.430 Å) by 0.218 Å. Subsequently, the intermediate 2A is formed (∆G = −8.7 kcal/mol), completing the oxidative addition process. Compared to the TS1 A , in the 2A configuration, the C 4 -C 5 (2.605 Å) bond is longer than that (1.648 Å) in the TS1 A . The Pd-C 4 (2.059 Å) and Pd-C 5 (2.036 Å) bonds are shorter than those in the TS1 A . Thereafter, the intermediate, 2A, evolves to another three-member carbon migration transition state, TS2 A (∆G = +10.0 kcal/mol). The Pd-C 3 (2.239 Å) and Pd-C 4 bonds (2.289 Å) become longer. Afterward, the Pd-C 3 bond breakage leads to the product, 4A, which contains UnitA (∆G = −46.3 kcal/mol). The C 3 -C 4 bond (1.504 Å) of 4A is shorter than that in the TS2 A (1.963 Å) configuration by 0.459 Å. The highest occupied orbital (HOMO) and the lowest unoccupied orbital (LUMO) of TS1 A and TS2 A also indicate their oxidative addition and carbon migration reaction characteristics, respectively. The WBI and Q NBO values for certain key bonds and atoms involved in the cyclopropenone reaction are listed in Table 2. As the reaction Path A 1a proceeds from TS1 A to the product 4A, the WBI decreases from 0.691 to 0.017 for the Pd-C 3 bond and from 0.730 to 0.061 for the C 4 -C 5 bond. This decrease indicates the breakage of Pd-C 3 and C 4 -C 5 bonds. From the TS1 A to the 4A, the WBI progressively increases from 0.298 to 0.685 for the Pd-C 5 bond and from 0.025 to 1.008 for the C 3 -C 4 bond, indicating the formation of these bonds. The free energy of TS2 A is slightly higher than TS1 A by 1.3 kcal/mol. Compared to the reactant (cPR1 A + 1a), the energy barrier for Path A 1a is 24.0 kcal/mol, and the reaction is exothermic (∆G = −22.3 kcal/mol), implying that it is thermodynamically feasible. Table 2. The Wiberg bond indices (WBIs) and natural charges (Q NBO ) for some key bonds and atoms of the reaction pathway for cyclopropenone.  and C 4 -C 5 bonds (1.670 Å) elongate. Afterward, the C 4 -C 5 bond breakage leads to the product, 4A (∆G = −38.2 kcal/mol). Compared to the TS4 A configuration, the Pd-C 5 bond (2.018 Å) of 4A is shorter than that in the TS4 A (2.615 Å) configuration by 0.597 Å. The frontier orbitals (HOMO and LUMO) of the transition states TS3 A and TS4 A show their respective carbonyl insertion and migratory insertion reaction characteristics.

WBI Q NBO (e)
The energy of TS3 A is higher than that of TS4 A by 26.3 kcal/mol. Compared to the reactant (cPR1 A + 1a), the energy barrier for Path B 1a is 42.2 kcal/mol, which is higher than that for Path A 1a (24.0 kcal/mol). Consequently, Path A 1a is a more favorable reaction route than Path B 1a . The barrier for cyclopropenone Path A 1a is 9.6 kcal/mol higher than that of the initial ethylene insertion reaction. However, the reaction for cyclopropenone Path A 1a is 6.3 kcal/mol more exothermic than ethylene insertion.

Second and Third Ethylene Insertion
After introducing cyclopropenone into the reaction chain, ethylene insertion into the chain occurs continuously. We explored the reaction mechanism by performing the second and third ethylene insertion. Figure 5 illustrates the pathway for continuous ethylene insertion, while Figure 6 shows the main optimized structures of this reaction.     After the TS AE1 , the product PR AE1 is formed (∆G = −16.7 kcal/mol). The C 7 -C 8 bond (1.531 Å) in the product PR AE1 is 0.108 Å longer than that in the TS AE1 configuration. The energy barrier for the pathway of the second ethylene insertion is 12.6 kcal/mol, and the reaction is exothermic (∆G = −4.1 kcal/mol), implying that the reaction is feasible.
Similar to the second ethylene insertion, in the reaction pathway for the third ethylene insertion, an intermediate (IM AE2 ) is first formed, followed by a quaternary TS (TS AE2 ), finally resulting in the product (PR AE2 ). The barrier for the third ethylene insertion is 15.9 kcal/mol, which is slightly higher than that of the second ethylene insertion (12.6 kcal/mol). The reaction is exothermic (∆G = −11.0 kcal/mol), releasing more energy than the second ethylene insertion (∆G = −4.1 kcal/mol), which indicates that the reaction is feasible.

Generation of CO from Cyclopropenone
Cyclopropenone can break down into CO and alkynes [65,66]. This study investigated the decomposition of cyclopropenone without a catalyst (Path A CO ) and with a Pd catalyst (Path B CO ; Path B' CO ). Figure 7 illustrates the pathway of generation of CO from cyclopropenone. The main optimized structures involved in the generation of CO from cyclopropenone decomposition are shown in Figure 8.
Similar to the second ethylene insertion, in the reaction pathway for the third ylene insertion, an intermediate (IMAE2) is first formed, followed by a quaternar (TSAE2), finally resulting in the product (PRAE2). The barrier for the third ethylene inse is 15.9 kcal/mol, which is slightly higher than that of the second ethylene insertion kcal/mol). The reaction is exothermic (ΔG = −11.0 kcal/mol), releasing more energy tha second ethylene insertion (ΔG = −4.1 kcal/mol), which indicates that the reaction is feasib

Generation of CO from Cyclopropenone
Cyclopropenone can break down into CO and alkynes [65,66]. This study inv gated the decomposition of cyclopropenone without a catalyst (Path ACO) and with catalyst (Path BCO; Path B'CO). Figure 7 illustrates the pathway of generation of CO cyclopropenone. The main optimized structures involved in the generation of CO cyclopropenone decomposition are shown in Figure 8.   In the Path ACO, cyclopropenone (1a) decomposes without a catalyst. The reacti first forms a transition state (TS11a). The C4-C6 bond (1.881 Å) is longer than that of (1.430 Å), whereas the C4-O1 bond length has decreased from 1.217 Å in 1a to 1.185 Å the TS11a configuration. Relative to 1a, the barrier for TS11a is 35.9 kcal/mol. Subsequent the intermediate IM11a is formed through an exothermic reaction with ΔG = −2.3 kcal/m relative to TS11a. The C4-C6 (2.229 Å) and C4-C5 (1.418 Å) bonds in the IM11a configurati are longer than those in the TS11a, whereas the C4-O1 (1.166 Å) bond is shorter. IM11 followed by the formation of another transition state, TS21a, across a small barrier of kcal/mol. The C4-C5 bond (1.619 Å) increases in length. Afterward, the C4-C5 bond breaka leads to the product CO + C2Ph2, through an exothermic reaction (ΔG = −44.5 kcal/mol). Τ C4-O1 bond (1.138 Å) of CO is 0.028 Å shorter than that in the TS21a configuration.
In Path ACO, the C4-C6 bond lengths gradually increase until they break, while the O1 bond lengths gradually decrease until they form a free CO molecule. WBI and Q values for certain key bonds and atoms involved in the generation of CO from cyclop penone are listed in Table 3. As the reaction proceeds from the reactant (1a) to TS21a, WBIs gradually decrease, from 1.078 to 0.806 for the C4-C5 bond and from 1.078 to 0.3 In the Path A CO , cyclopropenone (1a) decomposes without a catalyst. The reaction first forms a transition state (TS1 1a ). The C 4 -C 6 bond (1.881 Å) is longer than that of 1a (1.430 Å), whereas the C 4 -O 1 bond length has decreased from 1.217 Å in 1a to 1.185 Å in the TS1 1a configuration. Relative to 1a, the barrier for TS1 1a is 35.9 kcal/mol. Subsequently, the intermediate IM1 1a is formed through an exothermic reaction with ∆G = −2.3 kcal/mol, relative to TS1 1a . The C 4 -C 6 (2.229 Å) and C 4 -C 5 (1.418 Å) bonds in the IM1 1a configuration are longer than those in the TS1 1a , whereas the C 4 -O 1 (1.166 Å) bond is shorter. IM1 1a is followed by the formation of another transition state, TS2 1a , across a small barrier of 1.1 kcal/mol. The C 4 -C 5 bond (1.619 Å) increases in length. Afterward, the C 4 -C 5 bond breakage leads to the product CO + C 2 Ph 2 , through an exothermic reaction (∆G = −44.5 kcal/mol). The C 4 -O 1 bond (1.138 Å) of CO is 0.028 Å shorter than that in the TS2 1a configuration.
In Path A CO , the C 4 -C 6 bond lengths gradually increase until they break, while the C 4 -O 1 bond lengths gradually decrease until they form a free CO molecule. WBI and Q NBO values for certain key bonds and atoms involved in the generation of CO from cyclopropenone are listed in Table 3. As the reaction proceeds from the reactant (1a) to TS2 1a , the WBIs gradually decrease, from 1.078 to 0.806 for the C 4 -C 5 bond and from 1.078 to 0.391 for the C 4 -C 6 bond, indicating the breakage of these bonds. Meanwhile, the WBIs of the C 4 -O 1 (from 1.682 to 2.250) and the C 5 -C 6 (from 1.478 to 2.660) bonds gradually increase from 1a to the product (CO + C 2 Ph 2 ), indicating that the decomposition of cyclopropenone form free CO and C 2 Ph 2 . Although Path A CO is an exothermic reaction (∆G = −9.8 kcal/mol), the barrier is very high (35.9 kcal/mol), implying that the reaction is laborious. In Path B CO , cyclopropenone (1a) decomposes with a Pd catalyst (CatA). An intermediate (2A) initially forms in the cyclopropenone reaction pathway, as shown in Figure 3. The reaction first forms a three-member alkyl (C 3 ) transfer transition state (TS1 AEtCO ). The Pd-C 3 (2.298 Å) bond is longer in the TS1 AEtCO configuration than that in 2A (2.069 Å), and the C 3 -C 5 bond length decreases from 2.820 (in 2A) to 2.126 Å. Relative to 2A, the barrier for TS1 AEtCO is 8.1 kcal/mol. Thereafter, the intermediate IM1 AEtCO forms through an exothermic reaction (∆G = −48.6 kcal/mol). In the IM1 AEtCO configuration, the C 3 -C 5 (1.522 Å) bond is significantly shorter than that in the TS1 AEtCO (2.126 Å). Afterward, the Pd-C 3 bond breaks. The intermediate IM1 AEtCO is followed by the endothermic formation of another carbon (C 6 ) transfer transition state, TS2 AEtCO (∆G = +7.2 kcal/mol). The C 4 -C 6 bond length is 1.954 Å, which is longer than that in IM1 AEtCO (1.487 Å). After TS2 AEtCO , the C 4 -C 6 bond breaks leading to IM2 AEtCO (∆G = −5.3 kcal/mol). In the IM2 AEtCO configuration, the C 4 -C 6 (2.619 Å) bond is considerably longer than that in TS2 AEtCO (1.954 Å). The intermediate IM2 AEtCO is followed by the formation of the transition state TS3 AEtCO (∆G = +14.5 kcal/mol), and the Pd-C 4 bond (2.463 Å) becomes longer than that in IM2 AEtCO (1.870 Å). Thereafter, the reaction releases CO molecules and produces CO + PR AEtCO , through an exothermic reaction (∆G = −5.9 kcal/mol).
In Path B CO , the Pd-C 3 and Pd-C 5 bonds gradually elongates until their breakage, and the Pd-C 6 bonds gradually shortens until they form stable bonds. From 2A to the intermediate IM2 AEtCO, the WBI of the Pd-C 3 bond decreases from 0.629 to 0.020 and that of the Pd-C 5 bond decreases from 0.564 to 0.031, indicating the breakage of these bonds. Meanwhile, the WBI of the Pd-C 6 bond increases from 0.080 in 2A to 0.605 in IM2 AEtCO , indicating the formation of the Pd-C 6 bond. The Q NBO value of the C 6 atom also gradually increases from −0.184 e in 2A to −0.091 e in the intermediate IM2 AEtCO .
Because 2A is an intermediate of the cyclopropenone reaction pathway (Figure 3), the energy of the reactant (cPR1 A + 1a) and the first transition state (TS1 A ) for the cyclopropenone reaction should be considered when analyzing the barrier and exothermic conditions of Path B CO . Compared to the reactant of cyclopropenone reaction (cPR1 A + 1a), the reaction Path B CO is an exothermic reaction (∆G = −16.0 kcal/mol). The barrier of TS1 A (22.7 kcal/mol) is 0.6 kcal/mol higher than that of TS1 AEtCO (22.1 kcal/mol). The energy barrier of Path B CO is 22.7 kcal/mol, which is significantly lower than that of Path A CO (35.9 kcal/mol), indicating that Path B CO is favorable, and the reaction is feasible.
Path B' CO is another pathway for cyclopropenone (1a) to decompose with a Pd catalyst (CatA). Path B' CO begins from the intermediate (2A) (Figure 3) of the cyclopropenone reaction pathway. In Path B' CO , 2A first forms a transition state (TS1 ACOEt ) and then releases CO molecules to the intermediate (IM1 ACOEt ). Next, another alkyl (C 3 ) transfer TS (TS2 ACOEt ) is formed, resulting in the same product with Path B CO (PR AEtCO ). The main difference between Path B' CO and Path B CO is that in Path B' CO , CO is first released, and then, the alkyl transfer occurs to afford the product, while in Path B CO, CO is released after the alkyl transfer. Compared with the reactant of cyclopropenone reaction (cPR1 A + 1a), the barrier of the reaction Path B' CO is 48.1 kcal/mol, which is higher than that of Path B CO (22.7 kcal/mol), implying that Path B' CO is not feasible.

Reaction Pathway for the Generation of UnitB
PR AE2 , the product obtained after the second and third ethylene insertions ( Figure 5), can continue reacting with CO to form UnitB. Figure 9 shows the reaction pathway for the generation of UnitB. The main optimized structures for the reaction pathway for the generation of UnitB are shown in Figure 10. Table 4 lists the WBI and Q NBO values for certain key bonds and atoms of the reaction pathway for the generation of UnitB.  (Figure 3), the energy of the reactant (cPR1A + 1a) and the first transition state (TS1A) for the cyclopropenone reaction should be considered when analyzing the barrier and exothermic conditions of Path BCO. Compared to the reactant of cyclopropenone reaction (cPR1A + 1a), the reaction Path BCO is an exothermic reaction (ΔG = −16.0 kcal/mol). The barrier of TS1A (22.7 kcal/mol) is 0.6 kcal/mol higher than that of TS1AEtCO (22.1 kcal/mol). The energy barrier of Path BCO is 22.7 kcal/mol, which is significantly lower than that of Path ACO (35.9 kcal/mol), indicating that Path BCO is favorable, and the reaction is feasible.
Path B'CO is another pathway for cyclopropenone (1a) to decompose with a Pd catalyst (CatA). Path B'CO begins from the intermediate (2A) (Figure 3) of the cyclopropenone reaction pathway. In Path B'CO, 2A first forms a transition state (TS1ACOEt) and then releases CO molecules to the intermediate (IM1ACOEt). Next, another alkyl (C3) transfer TS (TS2ACOEt) is formed, resulting in the same product with Path BCO (PRAEtCO). The main difference between Path B'CO and Path BCO is that in Path B'CO, CO is first released, and then, the alkyl transfer occurs to afford the product, while in Path BCO, CO is released after the alkyl transfer. Compared with the reactant of cyclopropenone reaction (cPR1A + 1a), the barrier of the reaction Path B'CO is 48.1 kcal/mol, which is higher than that of Path BCO (22.7 kcal/mol), implying that Path B'CO is not feasible.

Reaction Pathway for the Generation of UnitB
PRAE2, the product obtained after the second and third ethylene insertions ( Figure 5), can continue reacting with CO to form UnitB. Figure 9 shows the reaction pathway for the generation of UnitB. The main optimized structures for the reaction pathway for the generation of UnitB are shown in Figure 10. Table 4 lists the WBI and QNBO values for certain key bonds and atoms of the reaction pathway for the generation of UnitB. Figure 9. The reaction pathway for generation of UnitB; the relative free energy is given in kcal/mol. Figure 9. The reaction pathway for generation of UnitB; the relative free energy is given in kcal/mol.    Figure 9, the key length is in angstroms. For clarity, the hydrogen atom is omitted. (B) The frontier orbital (HOMO and LUMO) of the transition states. Table 4. The Wiberg bond indices (WBIs) and natural charges (Q NBO ) for some key bonds and atoms of the reaction pathway for generation of UnitB.

WBI Q NBO (e)
CO Insertion B (Pd-C 11 ) B (Pd-C 9 ) B (C 9 -C 11 ) B (C 11  The reaction pathway for the generation of UnitB can be divided into two parts, the CO insertion reaction and the ethylene insertion reaction. In the CO insertion reaction, the carbon atom (C 11 ) in CO is first coordinated with the Pd metal atom of the PR AE2 , forming the intermediate IM ACO  the reaction reaches the three-member transition state, TS ACO (∆G = +13.9 kcal/mol). The Pd-C 9 (2.340 Å) and C 11 -O 2 bonds (1.170 Å) become longer, whereas the Pd-C 11 bond (1.869 Å) becomes shorter. As shown in Figure 10B, the characteristics of the CO insertion reaction can be determined from the frontier orbitals (HOMO and LUMO) of TS ACO . After TS ACO , the product of the CO insertion, PR ACO, forms through an exothermic reaction (∆G = −5.2 kcal/mol). The C 9 -C 11 bond length in PR ACO is 1.570 Å, which is 0.228 Å smaller than that in the TS ACO configuration. Additionally, the Pd-C 11 (1.908 Å) and C 11 -O 2 bonds (1.186 Å) in PR ACO are longer by 0.039 and 0.016 Å, respectively. As the CO insertion reaction proceeds, the WBI of the Pd-C 9 bond decreases from 0.701 in the intermediate IM ACO to 0.158 in the product PR ACO , indicating the Pd-C 9 bond breakage. Meanwhile, the WBI of the C 9 -C 11 bond increases from 0.076 in the intermediate IM ACO to 0.919 in the product PR ACO , indicating the formation of the C 9 -C 11 bond. The CO insertion reaction is endothermic (∆G = +4.7 kcal/mol), with a barrier of only 9.9 kcal/mol, indicating that the CO insertion reaction is feasible.
For the ethylene insertion reaction, the ethylene is first coordinated to the Pd metal atom in PR ACO , forming the intermediate IM ACOE (∆G = −14.0 kcal/mol). Owing to the coordination effect, the Pd-C 11 bond in the IM ACOE configuration is 2.016 Å and is longer than that in PR ACO (1.908 Å). After the formation of the intermediate IM ACOE , the reaction reaches the four-member transition state, TS ACOE (∆G = +9.1 kcal/mol). The Pd-C 11 (2.285 Å) and C 12 -C 13 bonds (1.465 Å) become longer, while the C 13 -C 11 bond (1.891 Å) becomes shorter. As shown in Figure 10B, the characteristics of the C 2 H 4 insertion reaction can be determined from the frontier orbitals (HOMO and LUMO) of TS ACOE . After the TS ACOE , the product of the ethylene insertion, PR ACOE , is formed through an exothermic reaction (∆G = −25.8 kcal/mol). PR ACOE contains UnitB. Compared to the TS ACOE configuration, the C 12 -C 13 bond (1.538 Å) in PR ACOE is elongated by 0.073 Å. As the ethylene insertion reaction proceeds, the WBI of the Pd-C 11 bond decreases from 0.748 in PR ACO to 0.022 in PR ACOE and that of the C 12 -C 13 bond decreases from 2.039 to 1.010, indicating the breakage of the Pd-C 11 bond, and the C 12 -C 13 bond changes from a double bond to a single bond. Meanwhile, the WBIs of the Pd-C 12 (from 0.411 to 0.705) and C 11 -C 13 (from 0.051 to 1.026) bonds gradually increases from the intermediate IM ACOE to the product PR ACOE , indicating the formation of the Pd-C 12 and C 11 -C 13 bonds. The ethylene insertion reaction is exothermic (∆G = −30.7 kcal/mol), and the barrier is very low, indicating that the ethylene insertion reaction is feasible. In the reaction pathway for the generation of UnitB, the free energy of TS ACO is the highest. Compared to the free energy of the reactant (PR AE2 + CO), the reaction pathway for the generation of UnitB is exothermic (∆G = −26.0 kcal/mol), and the barrier is only 9.9 kcal/mol, suggesting that the reaction is viable.
For producing UnitB, CO should be formed first, implying that CO generation should be considered in the determination of the total energy barrier of UnitB. The energy barrier of CO generation is 22.7 kcal/mol (i.e., the energy of TS1 A , as shown in Figure 3), which is higher than 9.9 kcal/mol. Therefore, the total energy barrier for UnitB generation is 22.7 kcal/mol, which is slightly lower than that for UnitA generation (24.0 kcal/mol), as shown in Figure 3. However, CO gas is generated in situ, and not all the generated CO can be smoothly inserted into the polymerization chain. Consequently, the UnitB generation in the polymerization chain increases only when the CO generation increases.

Reaction Pathway of the Allyl Acetate (AAc) Insertion
To examine the possibility of the copolymerization of ethylene, cyclopropenone, and AAc, we investigated the reaction mechanism of introducing AAc into PR AE2 . Figure 11 illustrates the reaction pathway of the AAc insertion. Figure 12 shows the main optimized structures for the reaction pathway of the AAc insertion. The WBI and Q NBO values for certain key bonds and atoms of the reaction pathway of the AAc insertion are listed in Table 5.    Figure 11. The reaction pathway of the allyl acetate (AAc) insertion, Path AAAc (black) and Path BAAc (blue); the relative free energy is given in kcal/mol.    Figure 11, Path A AAc (black) and Path B AAc (blue), the key length is in angstroms. For clarity, the hydrogen atom is omitted.
The AAc insertion reaction could be via Path A AAc or Path B AAc . In Path A AAc , AAc and PR AE2 first form a quaternary transition state TS 21AAc (∆G = +22.5 kcal/mol). The Pd-C 9 (2.278 Å) and C 14 -C 15 bonds (1.425 Å) become longer. Afterward, the product of the AAc insertion, PR 21AAc, is formed (∆G = −30.0 kcal/mol). Compared to the TS 21AAc configuration, the C 14 -C 15 bond (1.541 Å) in the product PR 21AAc is lengthened by 0.116 Å. As the reaction proceeds, the WBI of the Pd-C 9 bond decreases from 0.706 to 0.066, indicating the breakage of the Pd-C 9 bond. The WBI of the C 14 -C 15 bond decreases from 2.039 to 1.014, implying the transition from a double bond to single bond. Meanwhile, the WBIs of the Pd-C 15 (from 0.518 to 0.663) and C 9 -C 14 (from 0.487 to 1.004) bonds gradually increase from TS 21AAc to PR 21AAc , indicating the formation of the Pd-C 15 and C 9 -C 14 bonds. Path A AAc is an exothermic reaction (∆G = −7.5 kcal/mol) with a barrier of 22.5 kcal/mol, implying that the reaction is feasible. Similar to Path A AAc , in Path B AAc , a quaternary transition state (TS 12AAc ) is first formed, resulting in the product (PR 12AAc ). Path B AAc is an exothermic reaction (∆G = −6.5 kcal/mol) with an energy barrier of 22.2 kcal/mol, indicating that Path A AAc and Path B AAc compete with each other. The reaction barrier of the cyclopropenone introduction is 24.0 kcal/mol (Figure 3), which is slightly higher than that of the AAc insertion reaction (22.5 or 22.2 kcal/mol). However, the exothermic cyclopropenone reaction (∆G = −22.3 kcal/mol) releases significantly more energy than the AAc insertion reaction (∆G = −7.5 or −6.5 kcal/mol). These findings indicate that the cyclopropenone introduction reaction is more likely to occur, which is consistent with the experimental results [30].
To further investigate the reactions, we calculated the global reactivity index (GRI) and Fukui function values for certain molecules (Table 6). Compared to the other three molecules, the catalyst (CatA) has the largest electrophilicity (ω) value of 1.473, indicating that it is electrophilic. Meanwhile, CatA has a large global nucleophilicity (N Nu ) value of 3.105, indicating that it is also nucleophilic. The N Nu value of 1a (3.283) is higher than that of AAc (1.972); therefore, the electrophilicity of 1a is higher, and it exhibits higher reactivity. This is consistent with the experimental results [30]. The Fukui function is often employed to predict reactions. The site with a higher Fukui function value has a higher reactivity. The Fukui function information for certain molecules is presented in Table 6 and Figure 13. The complete Fukui function values of these molecules are provided in Table S2. The results show that the Fukui function value (f + ) of the Pd atom is the most significant parameter of CatA; therefore, the Pd atom in CatA is more reactive. The Fukui function values (f − ) of C a and C b atoms in C 2 H 4 are the highest. Meanwhile, the Fukui function values (f − ) of C a and C b atoms in 1a and AAc, respectively, are the highest except for the oxygen atom. This indicates that C a and C b are more reactive, easily reacting with Pd in CatA to complete the reactions.

Conclusions
We performed DFT calculations to investigate the mechanism of Pd-catalyzed copolymerization of cyclopropenone with ethylene. The results demonstrated that introducing ethylene and cyclopropenone to Pd catalyst is thermodynamically feasible and generated UnitA. Cis-mode insertion and Path A1a is the most favorable reaction route for ethylene and cyclopropenone, respectively. The energy barrier for cyclopropenone Path A1a is higher than that for the ethylene insertion reaction. However, more energy (6.3 kcal/mol) is released in the cyclopropenone exothermic reaction than in the ethylene insertion. Additionally, cyclopropenone can decompose to generate CO in situ without a catalyst or with a Pd catalyst. The Pd-catalyzed decomposition of cyclopropenone has a lower reaction barrier than the direct decomposition of cyclopropenone. The energy barrier of CO generation is 22.7 kcal/mol. Incorporating CO into a Pd catalyst can generate UnitB. CO should be formed first, and then, UnitB is generated. Therefore, the total energy barrier of UnitB generation should be determined by considering the energy barrier of CO generation. The energy barrier of incorporating CO to a Pd catalyst is 9.9 kcal/mol, which is lower than that of CO generation. Therefore, the total energy barrier for UnitB generation is 22.7 kcal/mol, which is slightly lower than that for UnitA generation (24.0 kcal/mol). Moreover, the possibility of copolymerizing ethylene, cyclopropenone, and AAc was investigated. The free energy and the GRI analyses indicate that the cyclopropenone insertion reaction is more favorable than AAc insertion, which is consistent with the experimental results. A thorough mechanistic study of this phenomenon will contribute to understanding the copolymerization of cyclopropenone with ethylene and developing a functionalization strategy for PE polymers.
Supplementary Materials: The following supporting information can be downloaded at: www.mdpi.com/xxx/s1. Table S1: Energies of all the optimized structures. Table S2: Additional computational details and detailed data of Fukui functions values for some molecules.

Conclusions
We performed DFT calculations to investigate the mechanism of Pd-catalyzed copolymerization of cyclopropenone with ethylene. The results demonstrated that introducing ethylene and cyclopropenone to Pd catalyst is thermodynamically feasible and generated UnitA. Cis-mode insertion and Path A 1a is the most favorable reaction route for ethylene and cyclopropenone, respectively. The energy barrier for cyclopropenone Path A 1a is higher than that for the ethylene insertion reaction. However, more energy (6.3 kcal/mol) is released in the cyclopropenone exothermic reaction than in the ethylene insertion. Additionally, cyclopropenone can decompose to generate CO in situ without a catalyst or with a Pd catalyst. The Pd-catalyzed decomposition of cyclopropenone has a lower reaction barrier than the direct decomposition of cyclopropenone. The energy barrier of CO generation is 22.7 kcal/mol. Incorporating CO into a Pd catalyst can generate UnitB. CO should be formed first, and then, UnitB is generated. Therefore, the total energy barrier of UnitB generation should be determined by considering the energy barrier of CO generation. The energy barrier of incorporating CO to a Pd catalyst is 9.9 kcal/mol, which is lower than that of CO generation. Therefore, the total energy barrier for UnitB generation is 22.7 kcal/mol, which is slightly lower than that for UnitA generation (24.0 kcal/mol). Moreover, the possibility of copolymerizing ethylene, cyclopropenone, and AAc was investigated. The free energy and the GRI analyses indicate that the cyclopropenone insertion reaction is more favorable than AAc insertion, which is consistent with the experimental results. A thorough mechanistic study of this phenomenon will contribute to understanding the copolymerization of cyclopropenone with ethylene and developing a functionalization strategy for PE polymers.