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 (cIM1
A or tIM1
A) followed by a quaternary TS (cTS1
A or tTS1
A), resulting in the final product (cPR1
A or tPR1
A). 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 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
2H
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 (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 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.
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 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.
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 (ΔG = +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 (ΔG = −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 (ΔG = +10.0 kcal/mol). Τhe 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 (ΔG = −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 (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 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.
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 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
2Ph
2), indicating that the decomposition of cyclopropenone form free CO and C
2Ph
2. Although Path A
CO 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 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 (ΔG = −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 (ΔG = +7.2 kcal/mol). Τhe 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 (ΔG = −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 (ΔG = +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 (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 (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 (ΔG = −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.
3.5. 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.
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 (ΔG = −4.0 kcal/mol). Owing to the coordination effect, the Pd-C
9 bond (2.080 Å) in the IM
ACO configuration is longer than that in PR
AE2 (2.049 Å). The Q
NBO value of the Pd atom decreases from 0.232 e in PR
AE2 to 0.026 e in the intermediate IM
ACO. Meanwhile, the Q
NBO values of the C
11 (0.665 e) and O
2 (−0.415 e) atoms in the intermediate IM
ACO are higher than those in PR
AE2 (0.506 e and −0.506 e). After the formation of IM
ACO, the reaction reaches the three-member transition state, TS
ACO (ΔG = +13.9 kcal/mol). Τhe 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 (ΔG = −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 (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 PR
ACO, forming the intermediate IM
ACOE (ΔG = −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 (ΔG = +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
2H
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 (ΔG = −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 (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 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 (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 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.
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 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.
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 C
a and C
b atoms in C
2H
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.