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Article

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

by
Chenggen Zhang
1,*,
Shuyuan Yu
1,2,*,
Fei Wang
1,
Fuping Wang
1,
Jian Cao
1,
Huimin Zheng
1,
Xiaoyu Chen
1 and
Aijin Ren
1
1
College of Chemistry and Material Science, Langfang Normal University, Langfang 065000, China
2
College of Chemistry and Chemical Engineering, University of Chinese Academy of Sciences, Beijing 100049, China
*
Authors to whom correspondence should be addressed.
Polymers 2022, 14(23), 5273; https://doi.org/10.3390/polym14235273
Submission received: 13 November 2022 / Revised: 29 November 2022 / Accepted: 1 December 2022 / Published: 2 December 2022
(This article belongs to the Special Issue Advances in Synthesis and Applications of Polymeric Biorenewable Materials via Metal Catalyzed Polymerizations)
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Abstract

:
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.

Graphical Abstract

1. 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 in-chain 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].

2. 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.

3. Results and Discussion

3.1. 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 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 cIM1A (endothermic; 1.5 kcal/mol). Owing to the coordination effect, in the cIM1A configuration, the Pd-C1 bond (2.047 Å) is longer than that in CatA (2.018 Å). Additionally, the C2-C3 (1.388 Å) bond is longer than that in C2H4 molecule (1.331 Å). After the formation of the intermediate, cIM1A, the reaction reaches the transition state, cTS1A (ΔG = +12.9 kcal/mol), and the Pd-C1 (2.234 Å) and C2-C3 bonds (1.428 Å) are longer. After the transition state, cTS1A, the product of the first ethylene insertion, the cPR1A form, is attained (ΔG = −30.4 kcal/mol). Compared to the cTS1A configuration, the C1-C2 (1.531 Å) and Pd-C3 bonds (2.017 Å) in the product cPR1A are shortened by 0.605 and 0.045 Å, respectively. In contrast, the C2-C3 bond (1.512 Å) in the product cPR1A is elongated by 0.084 Å.
The C2-C3 bond lengthens during the entire ethylene insertion reaction from a double bond to form a single bond, while the Pd-C1 bond lengthens until it breaks. The Wiberg bond indices (WBIs) and natural charges (QNBO) 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-C1 (from 0.704 to 0.010) and C2-C3 bonds (from 2.039 to 1.069) gradually decrease from the reactant (CatA + C2H4) to the product cPR1A, indicating the breaking of the Pd-C1 bond and the C2-C3 bond change from a double bond to a single bond. The QNBO values of the C1 atom also diminish from −0.819 e in CatA to −0.666 e in the product cPR1A. Meanwhile, the WBI gradually increases from 0.408 to 0.672 for the Pd-C3 bond and from 0.538 to 1.108 for the C1-C2 bond, indicating the formation of the Pd-C3 and C1-C2 bonds. The cis-mode ethylene insertion reaction is exothermic (ΔG = −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 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.

3.2. 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 slightly higher than TS1A by 1.3 kcal/mol. Compared to the reactant (cPR1A + 1a), the energy barrier for Path A1a is 24.0 kcal/mol, and the reaction is exothermic (ΔG = −22.3 kcal/mol), implying that it is thermodynamically feasible.
In Path B1a of the cyclopropenone reaction, the C4-O1 bond of cyclopropenone is first inserted into the Pd-C3 bond of cPR1A, forming a four-member carbonyl insertion transition state TS3A (ΔG = +42.2 kcal/mol). The lengths of Pd-C3 (2.299 Å) and C4-O1 (1.315 Å) bonds in the TS3A configuration are longer than those (2.017 and 1.217 Å) in the reactant (cPR1A + 1a). Thereafter, the intermediate 3A is formed (ΔG = −28.8 kcal/mol). In the 3A configuration, the C4-O1 (1.396 Å) bond and C4-C5 (1.499 Å) bond are longer than those (1.315 Å and 1.444 Å) in TS3A. The Pd-O1 (1.979 Å) bond is shorter than that (2.012 Å) in TS3A. Afterward, the intermediate, 3A, evolves to another four-member migratory insertion TS, TS4A (ΔG = +2.5 kcal/mol). Meanwhile, the Pd-O1 (1.994 Å) and C4-C5 bonds (1.670 Å) elongate. Afterward, the C4-C5 bond breakage leads to the product, 4A (ΔG = −38.2 kcal/mol). Compared to the TS4A configuration, the Pd-C5 bond (2.018 Å) of 4A is shorter than that in the TS4A (2.615 Å) configuration by 0.597 Å. The frontier orbitals (HOMO and LUMO) of the transition states TS3A and TS4A show their respective carbonyl insertion and migratory insertion reaction characteristics.
The energy of TS3A is higher than that of TS4A by 26.3 kcal/mol. Compared to the reactant (cPR1A + 1a), the energy barrier for Path B1a is 42.2 kcal/mol, which is higher than that for Path A1a (24.0 kcal/mol). Consequently, Path A1a is a more favorable reaction route than Path B1a. The barrier for cyclopropenone Path A1a is 9.6 kcal/mol higher than that of the initial ethylene insertion reaction. However, the reaction for cyclopropenone Path A1a is 6.3 kcal/mol more exothermic than ethylene insertion.

3.3. 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.
For the second ethylene insertion, 4A and C2H4 first form a coordination intermediate IMAE1 (ΔG = +4.0 kcal/mol). In the IMAE1 configuration, Pd-C7 and Pd-C8 bond lengths are 2.162 and 2.152 Å, respectively. After the formation of the intermediate IMAE1, the reaction reaches the transition state TSAE1 (ΔG = +8.6 kcal/mol). Τhe Pd-C5 (2.139 Å) and C7-C8 bonds (1.423 Å) become longer, while the Pd-C7 bond (2.084 Å) becomes shorter. After the TSAE1, the product PRAE1 is formed (ΔG = −16.7 kcal/mol). The C7-C8 bond (1.531 Å) in the product PRAE1 is 0.108 Å longer than that in the TSAE1 configuration. The energy barrier for the pathway of the second ethylene insertion is 12.6 kcal/mol, and the reaction is exothermic (ΔG = −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 (IMAE2) is first formed, followed by a quaternary TS (TSAE2), finally resulting in the product (PRAE2). 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 (ΔG = −11.0 kcal/mol), releasing more energy than the second ethylene insertion (ΔG = −4.1 kcal/mol), which indicates that the reaction is feasible.

3.4. 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 ACO) and with a Pd catalyst (Path BCO; 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.
In the Path ACO, cyclopropenone (1a) decomposes without a catalyst. The reaction first forms a transition state (TS11a). The C4-C6 bond (1.881 Å) is longer than that of 1a (1.430 Å), whereas the C4-O1 bond length has decreased from 1.217 Å in 1a to 1.185 Å in the TS11a configuration. Relative to 1a, the barrier for TS11a is 35.9 kcal/mol. Subsequently, the intermediate IM11a is formed through an exothermic reaction with ΔG = −2.3 kcal/mol, relative to TS11a. The C4-C6 (2.229 Å) and C4-C5 (1.418 Å) bonds in the IM11a configuration are longer than those in the TS11a, whereas the C4-O1 (1.166 Å) bond is shorter. IM11a is followed by the formation of another transition state, TS21a, across a small barrier of 1.1 kcal/mol. The C4-C5 bond (1.619 Å) increases in length. Afterward, the C4-C5 bond breakage leads to the product CO + C2Ph2, through an exothermic reaction (ΔG = −44.5 kcal/mol). Τhe 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 C4-O1 bond lengths gradually decrease until they form a free CO molecule. WBI and QNBO 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 TS21a, the WBIs gradually decrease, from 1.078 to 0.806 for the C4-C5 bond and from 1.078 to 0.391 for the C4-C6 bond, indicating the breakage of these bonds. Meanwhile, the WBIs of the C4-O1 (from 1.682 to 2.250) and the C5-C6 (from 1.478 to 2.660) bonds gradually increase from 1a to the product (CO + C2Ph2), indicating that the decomposition of cyclopropenone form free CO and C2Ph2. Although Path ACO is an exothermic reaction (ΔG = −9.8 kcal/mol), the barrier is very high (35.9 kcal/mol), implying that the reaction is laborious.
In Path BCO, 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 (C3) transfer transition state (TS1AEtCO). The Pd-C3 (2.298 Å) bond is longer in the TS1AEtCO configuration than that in 2A (2.069 Å), and the C3-C5 bond length decreases from 2.820 (in 2A) to 2.126 Å. Relative to 2A, the barrier for TS1AEtCO is 8.1 kcal/mol. Thereafter, the intermediate IM1AEtCO forms through an exothermic reaction (ΔG = −48.6 kcal/mol). In the IM1AEtCO configuration, the C3-C5 (1.522 Å) bond is significantly shorter than that in the TS1AEtCO (2.126 Å). Afterward, the Pd-C3 bond breaks. The intermediate IM1AEtCO is followed by the endothermic formation of another carbon (C6) transfer transition state, TS2AEtCO (ΔG = +7.2 kcal/mol). Τhe C4-C6 bond length is 1.954 Å, which is longer than that in IM1AEtCO (1.487 Å). After TS2AEtCO, the C4-C6 bond breaks leading to IM2AEtCO (ΔG = −5.3 kcal/mol). In the IM2AEtCO configuration, the C4-C6 (2.619 Å) bond is considerably longer than that in TS2AEtCO (1.954 Å). The intermediate IM2AEtCO is followed by the formation of the transition state TS3AEtCO (ΔG = +14.5 kcal/mol), and the Pd-C4 bond (2.463 Å) becomes longer than that in IM2AEtCO (1.870 Å). Thereafter, the reaction releases CO molecules and produces CO + PRAEtCO, through an exothermic reaction (ΔG = −5.9 kcal/mol).
In Path BCO, the Pd-C3 and Pd-C5 bonds gradually elongates until their breakage, and the Pd-C6 bonds gradually shortens until they form stable bonds. From 2A to the intermediate IM2AEtCO, the WBI of the Pd-C3 bond decreases from 0.629 to 0.020 and that of the Pd-C5 bond decreases from 0.564 to 0.031, indicating the breakage of these bonds. Meanwhile, the WBI of the Pd-C6 bond increases from 0.080 in 2A to 0.605 in IM2AEtCO, indicating the formation of the Pd-C6 bond. The QNBO value of the C6 atom also gradually increases from −0.184 e in 2A to −0.091 e in the intermediate IM2AEtCO.
Because 2A is an intermediate of the cyclopropenone reaction pathway (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.

3.5. 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.
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 (C11) in CO is first coordinated with the Pd metal atom of the PRAE2, forming the intermediate IMACO (ΔG = −4.0 kcal/mol). Owing to the coordination effect, the Pd-C9 bond (2.080 Å) in the IMACO configuration is longer than that in PRAE2 (2.049 Å). The QNBO value of the Pd atom decreases from 0.232 e in PRAE2 to 0.026 e in the intermediate IMACO. Meanwhile, the QNBO values of the C11 (0.665 e) and O2 (−0.415 e) atoms in the intermediate IMACO are higher than those in PRAE2 (0.506 e and −0.506 e). After the formation of IMACO, the reaction reaches the three-member transition state, TSACO (ΔG = +13.9 kcal/mol). Τhe Pd-C9 (2.340 Å) and C11-O2 bonds (1.170 Å) become longer, whereas the Pd-C11 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 TSACO. After TSACO, the product of the CO insertion, PRACO, forms through an exothermic reaction (ΔG = −5.2 kcal/mol). The C9-C11 bond length in PRACO is 1.570 Å, which is 0.228 Å smaller than that in the TSACO configuration. Additionally, the Pd-C11 (1.908 Å) and C11-O2 bonds (1.186 Å) in PRACO are longer by 0.039 and 0.016 Å, respectively. As the CO insertion reaction proceeds, the WBI of the Pd-C9 bond decreases from 0.701 in the intermediate IMACO to 0.158 in the product PRACO, indicating the Pd-C9 bond breakage. Meanwhile, the WBI of the C9-C11 bond increases from 0.076 in the intermediate IMACO to 0.919 in the product PRACO, indicating the formation of the C9-C11 bond. The CO insertion reaction is endothermic (ΔG = +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 PRACO, forming the intermediate IMACOE (ΔG = −14.0 kcal/mol). Owing to the coordination effect, the Pd-C11 bond in the IMACOE configuration is 2.016 Å and is longer than that in PRACO (1.908 Å). After the formation of the intermediate IMACOE, the reaction reaches the four-member transition state, TSACOE (ΔG = +9.1 kcal/mol). The Pd-C11 (2.285 Å) and C12-C13 bonds (1.465 Å) become longer, while the C13-C11 bond (1.891 Å) becomes shorter. As shown in Figure 10B, the characteristics of the C2H4 insertion reaction can be determined from the frontier orbitals (HOMO and LUMO) of TSACOE. After the TSACOE, the product of the ethylene insertion, PRACOE, is formed through an exothermic reaction (ΔG = −25.8 kcal/mol). PRACOE contains UnitB. Compared to the TSACOE configuration, the C12-C13 bond (1.538 Å) in PRACOE is elongated by 0.073 Å. As the ethylene insertion reaction proceeds, the WBI of the Pd-C11 bond decreases from 0.748 in PRACO to 0.022 in PRACOE and that of the C12-C13 bond decreases from 2.039 to 1.010, indicating the breakage of the Pd-C11 bond, and the C12-C13 bond changes from a double bond to a single bond. Meanwhile, the WBIs of the Pd-C12 (from 0.411 to 0.705) and C11-C13 (from 0.051 to 1.026) bonds gradually increases from the intermediate IMACOE to the product PRACOE, indicating the formation of the Pd-C12 and C11-C13 bonds. The ethylene insertion reaction is exothermic (ΔG = −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 TSACO is the highest. Compared to the free energy of the reactant (PRAE2 + CO), the reaction pathway for the generation of UnitB is exothermic (ΔG = −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 TS1A, 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.

3.6. 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 PRAE2. 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 QNBO values for certain key bonds and atoms of the reaction pathway of the AAc insertion are listed in Table 5.
The AAc insertion reaction could be via Path AAAc or Path BAAc. In Path AAAc, AAc and PRAE2 first form a quaternary transition state TS21AAc (ΔG = +22.5 kcal/mol). Τhe Pd-C9 (2.278 Å) and C14-C15 bonds (1.425 Å) become longer. Afterward, the product of the AAc insertion, PR21AAc, is formed (ΔG = −30.0 kcal/mol). Compared to the TS21AAc configuration, the C14-C15 bond (1.541 Å) in the product PR21AAc is lengthened by 0.116 Å. As the reaction proceeds, the WBI of the Pd-C9 bond decreases from 0.706 to 0.066, indicating the breakage of the Pd-C9 bond. The WBI of the C14-C15 bond decreases from 2.039 to 1.014, implying the transition from a double bond to single bond. Meanwhile, the WBIs of the Pd-C15 (from 0.518 to 0.663) and C9-C14 (from 0.487 to 1.004) bonds gradually increase from TS21AAc to PR21AAc, indicating the formation of the Pd-C15 and C9-C14 bonds. Path AAAc is an exothermic reaction (ΔG = −7.5 kcal/mol) with a barrier of 22.5 kcal/mol, implying that the reaction is feasible. Similar to Path AAAc, in Path BAAc, a quaternary transition state (TS12AAc) is first formed, resulting in the product (PR12AAc). Path BAAc is an exothermic reaction (ΔG = −6.5 kcal/mol) with an energy barrier of 22.2 kcal/mol, indicating that Path AAAc and Path BAAc 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 (ΔG = −22.3 kcal/mol) releases significantly more energy than the AAc insertion reaction (ΔG = −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 (NNu) value of 3.105, indicating that it is also nucleophilic. The NNu 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 Ca and Cb atoms in C2H4 are the highest. Meanwhile, the Fukui function values (f−) of Ca and Cb atoms in 1a and AAc, respectively, are the highest except for the oxygen atom. This indicates that Ca and Cb are more reactive, easily reacting with Pd in CatA to complete the reactions.

4. 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: https://www.mdpi.com/article/10.3390/polym14235273/s1. Table S1: Energies of all the optimized structures. Table S2: Additional computational details and detailed data of Fukui functions values for some molecules [54,55,56,57,58,59,60].

Author Contributions

Conceptualization, C.Z. and S.Y.; data curation, S.Y., F.W. (Fuping Wang), H.Z., X.C., and A.R.; formal analysis, F.W. (Fei Wang) and J.C.; funding acquisition, C.Z., F.W. (Fuping Wang) and J.C.; investigation, S.Y. and F.W. (Fuping Wang); project administration, C.Z. All authors have read and agreed to the published version of the manuscript.

Funding

This work was financially supported by the Science and Technology Project of Hebei Education Department (ZD2021090), the S&T Program of Hebei (B2020408007), the Science and Technology Research Projects of Langfang Normal University (XBQ202011), the Fundamental Research Funds for the Universities in Hebei Province (JYT202101), and the Innovation and Entrepreneurship Training Program of Langfang Normal University (X202210100016).

Data Availability Statement

The data presented in this study are available in the Supplementary Materials.

Conflicts of Interest

The authors declare no conflict of interest.

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Polymers 14 05273 sch001 550
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).
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).
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Polymers 14 05273 g001 550
Figure 1. The reaction pathway of the first ethylene insertion, cis-mode (black) and trans-mode (blue); the relative free energy is given in kcal/mol.
Figure 1. The reaction pathway of the first ethylene insertion, cis-mode (black) and trans-mode (blue); the relative free energy is given in kcal/mol.
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Polymers 14 05273 g002 550
Figure 2. (A) Optimized structures in the first ethylene insertion reaction pathway shown in Figure 1, cis-mode (black) and trans-mode (blue), the key length is in angstroms. (B) Interaction region indicator (IRI) analysis of key structures with the noncovalent weak interactions highlighted by the red circles.
Figure 2. (A) Optimized structures in the first ethylene insertion reaction pathway shown in Figure 1, cis-mode (black) and trans-mode (blue), the key length is in angstroms. (B) Interaction region indicator (IRI) analysis of key structures with the noncovalent weak interactions highlighted by the red circles.
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Polymers 14 05273 g003 550
Figure 3. The reaction pathway of cyclopropenone, Path A1a (black) and Path B1a (blue); the relative free energy is given in kcal/mol.
Figure 3. The reaction pathway of cyclopropenone, Path A1a (black) and Path B1a (blue); the relative free energy is given in kcal/mol.
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Polymers 14 05273 g004 550
Figure 4. (A) Optimized structures in the cyclopropenone reaction pathway shown in Figure 3, Path A1a (black) and Path B1a (blue), the key length is in angstroms. For clarity, the hydrogen atom is omitted. (B) The frontier orbital (HOMO and LUMO) of the transition states.
Figure 4. (A) Optimized structures in the cyclopropenone reaction pathway shown in Figure 3, Path A1a (black) and Path B1a (blue), the key length is in angstroms. For clarity, the hydrogen atom is omitted. (B) The frontier orbital (HOMO and LUMO) of the transition states.
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Polymers 14 05273 g005 550
Figure 5. The reaction pathway for continuing ethylene insertion; the relative free energy is given in kcal/mol.
Figure 5. The reaction pathway for continuing ethylene insertion; the relative free energy is given in kcal/mol.
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Polymers 14 05273 g006 550
Figure 6. Optimized structures for continuing ethylene insertion reaction pathway shown in Figure 5, the key length is in angstroms. For clarity, the hydrogen atom is omitted.
Figure 6. Optimized structures for continuing ethylene insertion reaction pathway shown in Figure 5, the key length is in angstroms. For clarity, the hydrogen atom is omitted.
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Polymers 14 05273 g007 550
Figure 7. Generation CO from cyclopropenone decomposition reaction pathway without catalyst (Path ACO, blue) or with pd catalyst (Path BCO, black; Path B’CO, red); the relative free energy is given in kcal/mol.
Figure 7. Generation CO from cyclopropenone decomposition reaction pathway without catalyst (Path ACO, blue) or with pd catalyst (Path BCO, black; Path B’CO, red); the relative free energy is given in kcal/mol.
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Polymers 14 05273 g008 550
Figure 8. Optimized structures in the pathway of generation CO from cyclopropenone shown in Figure 7 (Path ACO, blue; Path BCO, black; Path B’CO, red), the key length is in angstroms. For clarity, the hydrogen atom is omitted.
Figure 8. Optimized structures in the pathway of generation CO from cyclopropenone shown in Figure 7 (Path ACO, blue; Path BCO, black; Path B’CO, red), the key length is in angstroms. For clarity, the hydrogen atom is omitted.
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Polymers 14 05273 g009 550
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.
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Polymers 14 05273 g010 550
Figure 10. (A) Optimized structures in the reaction pathway for generation of UnitB shown in 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.
Figure 10. (A) Optimized structures in the reaction pathway for generation of UnitB shown in 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.
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Polymers 14 05273 g011 550
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. 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.
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Polymers 14 05273 g012 550
Figure 12. Optimized structures in the allyl acetate (AAc) insertion reaction pathway shown in Figure 11, Path AAAc (black) and Path BAAc (blue), the key length is in angstroms. For clarity, the hydrogen atom is omitted.
Figure 12. Optimized structures in the allyl acetate (AAc) insertion reaction pathway shown in Figure 11, Path AAAc (black) and Path BAAc (blue), the key length is in angstroms. For clarity, the hydrogen atom is omitted.
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Polymers 14 05273 g013 550
Figure 13. Isosurface maps of Fukui functions for Pd (f+) in CatA and Ca, Cb (f−) in C2H4, 1a and AAc.
Figure 13. Isosurface maps of Fukui functions for Pd (f+) in CatA and Ca, Cb (f−) in C2H4, 1a and AAc.
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Table
Table 1. The Wiberg bond indices (WBIs) and natural charges (QNBO) for some key bonds and atoms of the reaction pathway for the first ethylene insertion.
Table 1. The Wiberg bond indices (WBIs) and natural charges (QNBO) for some key bonds and atoms of the reaction pathway for the first ethylene insertion.
WBIQNBO (e)
B (Pd-C1)B (C2-C3)B (Pd-C3)B (C1-C2)PdC1
CatA + C2H40.7042.039 0.318−0.819
cIM1A0.7181.5500.408 0.243−0.768
cTS1A0.4061.3100.5530.5380.161−0.739
cPR1A0.0101.0690.6721.1080.219−0.666
B (Pd-C1)B (C2-C3)B (Pd-C2)B (C1-C3)PdC1
tIM1A0.7431.6800.297 0.194−0.782
tTS1A0.3651.2960.5770.6180.210−0.769
tPR1A 0.0350.7271.0070.316−0.666
Table
Table 2. The Wiberg bond indices (WBIs) and natural charges (QNBO) for some key bonds and atoms of the reaction pathway for cyclopropenone.
Table 2. The Wiberg bond indices (WBIs) and natural charges (QNBO) for some key bonds and atoms of the reaction pathway for cyclopropenone.
WBIQNBO (e)
Path A1aB (Pd-C3)B (Pd-C4)B (Pd-C5)B (C4-C5)B (C3-C4)PdC4C5
cPR1A + 1a0.672 1.078 0.2190.521−0.016
TS1A0.6910.1810.2980.7300.0250.1850.567−0.051
2A0.6290.5770.5640.1370.0920.1660.5870.021
TS2A0.3290.2630.6670.0850.5540.2000.5840.018
4A0.017 0.6850.0611.0080.3700.5830.022
Path B1aB (Pd-C3)B (Pd-O1)B (C4-O1)B (C4-C5)B (Pd-C5)PdC4O1
cPR1A + 1a0.672 1.6821.078 0.2190.521−0.594
TS3A0.3370.5071.1761.034 0.3400.364−0.596
3A0.0150.5880.9580.9210.0200.4150.271−0.686
TS4A0.0170.5571.0780.7440.1480.4140.320−0.641
4A0.0170.3941.4490.0610.6850.3700.583−0.556
Table
Table 3. The Wiberg bond indices (WBIs) and natural charges (QNBO) for some key bonds and atoms of the pathway of generation CO from cyclopropenone.
Table 3. The Wiberg bond indices (WBIs) and natural charges (QNBO) for some key bonds and atoms of the pathway of generation CO from cyclopropenone.
WBIQNBO (e)
Path ACOB (C4-O1)B (C4-C5)B (C4-C6)B (C5-C6) C4C5C6O1
1a1.6821.0781.0781.478 0.521−0.016−0.016−0.594
TS11a1.8871.2690.5661.505 0.656−0.2210.060−0.476
IM11a2.0251.1890.4151.585 0.687−0.3140.090−0.405
TS21a2.0630.8060.3911.964 0.557−0.2220.102−0.442
CO + C2Ph22.250 2.660 0.5060.0060.006−0.506
Path BCOB (Pd-C3)B (Pd-C5)B (C3-C5)B (Pd-C6)B (Pd-C4)B (C4-C6)PdC4C6O1
2A0.6290.5640.1360.0800.5771.1090.1660.587−0.184−0.499
TS1AEtCO0.3160.4290.5360.1170.6331.5440.1360.557−0.146−0.504
IM1AEtCO0.0170.2061.0090.2060.6501.0460.2150.352−0.1360.016
TS2AEtCO0.0120.0341.0030.4040.8340.5000.0890.604−0.171−0.454
IM2AEtCO0.0200.0310.9960.6050.9080.1310.0790.669−0.091−0.424
TS3AEtCO0.0140.0510.9980.6440.4670.0180.1280.616−0.031−0.475
PRAEtCO0.0100.0500.9950.562 0.2730.506−0.051−0.506
Path B’COB (Pd-C3)B (Pd-C4)B (Pd-C5)B (C4-C6)B (C5-C6)B (C3-C5)PdC4C6O1
2A0.6290.5770.5641.1091.5480.1360.1660.587−0.184−0.499
TS1ACOEt0.6750.1150.3680.6191.8150.0220.1550.549−0.023−0.441
IM1ACOEt0.701 0.200 2.4310.0260.2050.506−0.0240.506
TS2ACOEt0.368 0.291 1.8720.5670.180 0.006
PRAEtCO0.010 0.050 1.2331.2450.273 −0.051
Table
Table 4. The Wiberg bond indices (WBIs) and natural charges (QNBO) for some key bonds and atoms of the reaction pathway for generation of UnitB.
Table 4. The Wiberg bond indices (WBIs) and natural charges (QNBO) for some key bonds and atoms of the reaction pathway for generation of UnitB.
WBIQNBO (e)
CO InsertionB (Pd-C11)B (Pd-C9)B (C9-C11)B (C11-O2)PdC11O2
PRAE2 + CO 0.706 1.1380.2320.506−0.506
IMACO0.8150.7010.0762.2240.0260.665−0.415
TSACO0.7980.3060.6682.0010.2160.571−0.455
PRACO0.7480.1580.9191.9210.2580.554−0.459
C2H4 insertionB (Pd-C11)B (Pd-C12)B (C12-C13)B (C11-C13)PdC11C12C13
PRACO0.748 2.039 0.2580.554−0.427−0.427
IMACOE0.6500.4111.5220.0510.1870.554−0.490−0.441
TSACOE0.2590.5981.2060.6180.1670.548−0.505−0.546
PRACOE0.0220.7051.0101.0260.2400.652−0.589−0.564
Table
Table 5. The Wiberg bond indices (WBIs) and natural charges (QNBO) for some key bonds and atoms of the reaction pathway of the allyl acetate (AAc) insertion.
Table 5. The Wiberg bond indices (WBIs) and natural charges (QNBO) for some key bonds and atoms of the reaction pathway of the allyl acetate (AAc) insertion.
WBIQNBO (e)
B (Pd-C9)B (Pd-C15)B (C14-C15)B (C9-C14)PdC9C15C14
PRAE2 + AAc0.706 2.039 0.232−0.517−0.427−0.427
TS21AAc0.4060.5181.3020.4870.168−0.465−0.339−0.445
PR21AAc0.0660.6631.0141.0040.244−0.440−0.345−0.489
B (Pd-C9)B (Pd-C14)B (C14-C15)B (C9-C15)PdC9C14C15
PRAE2 + AAc0.706 2.039 0.232−0.517−0.427−0.427
TS12AAc0.3820.5471.3020.4860.145−0.473−0.511−0.270
PR12AAc0.0160.6891.0100.9880.222−0.465−0.544−0.305
Table
Table 6. The global reactivity index (GRI) and Fukui function values for some molecules.
Table 6. The global reactivity index (GRI) and Fukui function values for some molecules.
η aμ bω cNNu df+ef−f
PdCaCb
CatA6.534−4.1751.4733.1050.228
C2H413.705−3.5090.5921.865 0.3130.313
1a7.360−4.1081.3033.283 0.0590.057
AAc11.579−3.5240.7711.972 0.1670.116
a Chemical hardness (η, in eV). b Electronic chemical potential (μ, in eV). c Global electrophilicity (ω, in eV). d Global nucleophilicity (NNu, in eV). e Nucleophilic attack Fukui function for Pd (f+, in e). f Electrophilic attack Fukui function for Ca, Cb (f−, in e).
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Zhang, C.; Yu, S.; Wang, F.; Wang, F.; Cao, J.; Zheng, H.; Chen, X.; Ren, A. Density Functional Theory Analysis of the Copolymerization of Cyclopropenone with Ethylene Using a Palladium Catalyst. Polymers 2022, 14, 5273. https://doi.org/10.3390/polym14235273

AMA Style

Zhang C, Yu S, Wang F, Wang F, Cao J, Zheng H, Chen X, Ren A. Density Functional Theory Analysis of the Copolymerization of Cyclopropenone with Ethylene Using a Palladium Catalyst. Polymers. 2022; 14(23):5273. https://doi.org/10.3390/polym14235273

Chicago/Turabian Style

Zhang, Chenggen, Shuyuan Yu, Fei Wang, Fuping Wang, Jian Cao, Huimin Zheng, Xiaoyu Chen, and Aijin Ren. 2022. "Density Functional Theory Analysis of the Copolymerization of Cyclopropenone with Ethylene Using a Palladium Catalyst" Polymers 14, no. 23: 5273. https://doi.org/10.3390/polym14235273

APA Style

Zhang, C., Yu, S., Wang, F., Wang, F., Cao, J., Zheng, H., Chen, X., & Ren, A. (2022). Density Functional Theory Analysis of the Copolymerization of Cyclopropenone with Ethylene Using a Palladium Catalyst. Polymers, 14(23), 5273. https://doi.org/10.3390/polym14235273

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