Comparison of the Reactivity and Structures for the Neutral and Cationic Bis(imino)pyridyl Iron and Cobalt Species by DFT Calculations

: Density Functional Theory (DFT) method was adopted to investigate and compare the reaction mechanisms of ethylene polymerization catalyzed by neutral, cationic bis(imino)pyridyl (PDI) iron and cobalt derivatives. The electronic structure and the oxidation states of the metal center and the PDI ligand were analyzed by taking spin states, natural bond orbital (NBO) charge distribution, etc. into consideration, revealing that the reactivity is closely related to the valence electron numbers instead of the charge numbers. The neutral Co(0) had the lowest reactivity as it possessed the most electrons. During the formation of the cationic Co( + ) / Fe( + ), one electron was mainly lost from PDI ligand rather than the metal center while the metal center maintained + II valence state through the process. Moreover, a special unsymmetrically bidentate NˆN coordination manner was found to provide the deﬁcient metal surroundings with 14e, which may initiate the reactivity of some unsymmetrical species with rich electrons. Finally, an anion [AlMe 4 ] − participating process was proposed to explain the presence of the experimentally observed LCo( + )B(C 2 H 4 ). A special intermediate, Co( + )B(C 2 H 4 ) [AlMe 4 ] − with Co in + I and absence of Co–C σ bond, was obtained. These calculation results may provide fundamental information for further understanding and designing the ethylene polymerization catalysts.

Talsi and coworkers [30][31][32] remarked the catalytic behavior of the bis(imino)pyridine iron and cobalt dihalide precatalyst upon addition of MAO or AlMe 3 , demonstrating the different types of active sites precursors present in different catalytic systems. Erker and colleagues [33] found that in the ( Ar PDI)CoCH 3 /Li[B(C 6 F 5 ) 4 ]/ethylene system ( Ar PDI = [bis(N-aryliminoethyl-κN,N )pyridine-κN]), Li + ions may interact with the "arms" of chelated donor ligands forming a reactive cationic reactant on the open coordination site. According to Talsi's results [34], the interaction of L 3Me Co(II)Cl 2 and AlMe 3 at −10 • C reduced cobalt (II) (L 3Me Co(II)Cl 2 ) into a cobalt (I) complex (L 3Me Co(II)(µ-Me)(µ-Cl)AlMe 2 ). Furthermore, in the presence of ethylene, newly formed complexes, such as ( iPr PDI)Co(I)C 2 H 4 + , were also observed. However, up to now, the nature of the active species and the reaction mechanism of this special PDI-based iron or cobalt species were still in dispute.
In addition to experimental researches on the catalytic mechanism of the cobalt and iron catalysts based on a PDI backbone, many studies on theoretical calculations that overlay the mechanism were also reported [35][36][37]. In 1999, Gibson et al. [38] performed full ab initial computations on the bis(imino)pyridyl iron catalytic system for ethylene polymerization, and identified the key structure of ( Ar PDI)Fe(II)CH 3 C 2 H 4 as the product of the first monomer insertion into the cationic alkyl using the BP86 functionals. While just the singlet multiplicities was considered during calculation, this was proved to not be accurately described [39]. Later, Morokuma etc. theoretically investigated the mechanisms of chain propagation and β-hydride transfer (BHT) by considering three potential energy surfaces of the catalyst model, in which two cationic bis(imino)pyridyl-Fe(II) systems were explored with different steric effect [40]. They found that the BHT pathway could be suppressed by increasing the steric bulk and the chain propagation took place mainly on quintet or triplet surfaces. In order to explore the effect of cocatalyst in the catalytic process, Burin and coworkers [41] chose different additives including (AlMeO) 6 (AlMe 3 ), (PhOAlMe 2 ) 2 and TMA and calculated the activation and termination process of ethylene polymerization catalyzed by bis(imino)pyridyl iron catalysts using the unrestricted M06 functional. Altogether, the "alkyl-free" theory of polymerization catalyzed by bis(imino)pyridyl cobalt and polymerization mechanism have not been finalized and further researches are still necessary.
The reactivity differed due to the different charge or spin states of the active center. Herein, we used Density Functional Theory (DFT) to investigate and compare the reactivities of the cationic ( Ar PDI)MCH 3 + and neutral ( Ar PDI)MCH 3 (Ar = 2,6-Me 2 Ph, M = Fe, Co) of the iron and cobalt active species for the ethylene polymerization. Due to the limitation of the DFT calculations, just the following reaction processes were investigated: the first and second ethylene coordination and insertion, β-hydrogen transfer (BHT) to monomer and β-hydrogen elimination (BHE) reaction. Further, two kinds of spin states were considered. The differences of the electronic properties such as the NBO charge distribution, valence electron number and oxidation states and so on between the neutral and cationic iron or cobalt species were studied in detail. Moreover, in the case of the cobalt complex, a new reaction mechanism involving the cocatalyst ions (AlMe 4 − ) was also simply analyzed.

Results and Discussion
To gain insight into the nature of the active species formed upon treatment of the corresponding metal dihalide complexes with MAO, various alkyl species based on bis(imino)pyridyl iron and cobalt complexes have been isolated in the experiments [2,27,42]. However, the activities and structures of the isolated species are related to the methodologies and additives which the researchers used during their alkylation synthesis. That means the actual electronic structures of the active centers varies in the charge distribution, spin states and the oxidation levels. Since the LMCH 3 (M = Fe and Co, L = Ar PDI) species are always considered as the initiated species towards ethylene polymerization, we select it as the model to explore the comparison between the iron and cobalt species by considering their neutral and cationic structures with different spin states. As shown in Scheme 1, the following reaction process are studied: the first coordination of the ethylene (Coord I), first insertion (Ins I), the second coordination (Coord II), second insertion (Ins II), β-hydrogen transfer (BHT) and β-hydrogen elimination (BHE). Comparison of energy curves (such as ethylene insertion and β-hydrogen transfer) demonstrated that there are some differences between the behavior of iron and cobalt complexes in polymerization, and also the spin states. The energy interval between the energy level of π-complex and sum of ethylene and catalyst energies could give the monomer coordination energy. Thus, the bond order of the special LCoCH 3 and LCoCH 3 -C 2 H 4 (2) and orbitals of the reaction intermediates were analyzed. Additionally, the charge distribution of the system and the oxidation state for the PDI ligand were discussed. Finally, the effect of cocatalyst ions on the ethylene reaction process by cobalt system was also considered and compared.
Catalysts 2020, 11, x FOR PEER REVIEW 3 of 20 species by considering their neutral and cationic structures with different spin states. As shown in Scheme 1, the following reaction process are studied: the first coordination of the ethylene (Coord I), first insertion (Ins I), the second coordination (Coord II), second insertion (Ins II), β-hydrogen transfer (BHT) and β-hydrogen elimination (BHE). Comparison of energy curves (such as ethylene insertion and β-hydrogen transfer) demonstrated that there are some differences between the behavior of iron and cobalt complexes in polymerization, and also the spin states. The energy interval between the energy level of π-complex and sum of ethylene and catalyst energies could give the monomer coordination energy. Thus, the bond order of the special LCoCH3 and LCoCH3-C2H4(2) and orbitals of the reaction intermediates were analyzed. Additionally, the charge distribution of the system and the oxidation state for the PDI ligand were discussed. Finally, the effect of cocatalyst ions on the ethylene reaction process by cobalt system was also considered and compared.

Energy Profiles and Structures
For clear description, the symbol s M(q)-i was used to represent the intermediates in Scheme 1, where the 'M' could be the iron or cobalt metals, the 's' is the spin quantum number, 'q' denotes charges and the 'i' corresponds to the intermediates in Scheme 1. For example, the initiated LCoCH3 will be 1 Co(0)-1 when it is neutral in the triplet.   Figures S1 and S2. The energies of the reactants: 1 Co(0)-1 + C2H4 were taking as the starting point, as the triplet 1 Co(0)-1 has lower energy than the singlet 0 Co(0)-1. Although both the singlet and triplet states were considered, the energies of most of the intermediates and transition state (TS) structures in triplet state 1 Co(0) are lower than the corresponding singlet 0 Co(0). The diffidence is 13.5~15.9 kcal/mol for the intermediates and 3.2~8.9 kcal/mol for the TS states. Although the energy differences between 0 Co(0)-1 and triplet 1 Co(0)-1 (1' in Figure 1) is not much, it seems that the behavior of neutral cobalt species tend to be in high spin states instead of the low spin state. However, the BHE process is a bit different. The transition state Co(0)-TS3/9 for the hydrogen transferred to the cobalt metal center, is lower in energy for its singlet state than triplet state. Thus, spin crossover behavior exists in Scheme 1. The reaction pathway of ethylene polymerization catalyzed by LMCH 3 (M = Fe and Co) species.

Energy Profiles and Structures
For clear description, the symbol s M(q)-i was used to represent the intermediates in Scheme 1, where the 'M' could be the iron or cobalt metals, the 's' is the spin quantum number, 'q' denotes charges and the 'i' corresponds to the intermediates in Scheme 1. For example, the initiated LCoCH 3 will be 1 Co(0)-1 when it is neutral in the triplet. Figure 1 shows the relative zero-point energy profile of the corresponding reaction in Scheme 1 for the neutral cobalt species, s Co(0). The optimized structures of all the points in Figure 1 are listed in Figures S1 and S2. The energies of the reactants: 1 Co(0)-1 + C 2 H 4 were taking as the starting point, as the triplet 1 Co(0)-1 has lower energy than the singlet 0 Co(0)-1. Although both the singlet and triplet states were considered, the energies of most of the intermediates and transition state (TS) structures in triplet state 1 Co(0) are lower than the corresponding singlet 0 Co(0). The diffidence is 13.5~15.9 kcal/mol for the intermediates and 3.2~8.9 kcal/mol for the TS states. Although the energy differences between 0 Co(0)-1 and triplet 1 Co(0)-1 (1 in Figure 1) is not much, it seems that the behavior of neutral cobalt species tend to be in high spin states instead of the low spin state. However, the BHE process is a Catalysts 2020, 10, 1396 4 of 20 bit different. The transition state Co(0)-TS3/9 for the hydrogen transferred to the cobalt metal center, is lower in energy for its singlet state than triplet state. Thus, spin crossover behavior exists in the BHE process of the neutral cobalt alkyl complexes. This phenomenon has been reported by Holland in his special concentration on the BHE process [43].

Energy Profiles and Structures of the Neutral LCoCH 3 System
second insertion (Ins II) for chain growth, β-hydrogen transfer (BHT) and β-hydrogen elimination (BHE) for chain terminations. BHE just requires transferring the β-hydrogen to the metal center while Ins II and BHT need to coordinate another ethylene firstly. Obviously, the BHE process is more advantageous than BHT and Ins II. The overall barrier of BHE in the triplet state is 4.37 kcal/mol, while it is only 1.99 kcal/mol in the singlet TS via a spin crossover. Then the singlet BHE complex 0 Co(0)-9 is provided. Since the overall barrier of the BHT is much higher than that of BHT and Ins II reaction paths, it will not be considered as a termination process for the neutral cobalt alkyls species. So BHE process is kinetically favored over the thermodynamically favored Ins II to form the propagated cobalt alkyl complexes by 7.5 kcal/mol. For the bis(imino)pyridyl metal species with low steric substituents, the BHE is competitive chain termination mechanism for producing short oligomer chains with unsaturated end group [44].  Then, by overcoming a considerable overall energy barrier of 21.25 kcal/mol, the coordinated ethylene inserts into the Co-C bond in 1 Co(0)-2, producing the cobalt alkyl complex 1 Co(0)-3 (LCoC 3 H 7 ) with releasing energy of −23.62 kcal/mol. The second ethylene insertion (Ins II) starts from 3 reacting with the second ethylene, which was separated from the Ins I in Figure 1 for clarity. The energy barrier of Ins II is much higher than the Ins I. However, it could be compensated partly by the releasing energy from the formation of 1 Co(0)-3, then the overall barrier for Ins II will be 9.50 kcal/mol. Additionally, in comparison with the first one (−2.86 kcal/mol), the coordination of the second ethylene to 1 Co(0)-3 is unfavorable (binding energy of 7.47 kcal/mol). These results indicate that, in the ethylene polymerization catalyzed by the active species with similar electronic properties to the neutral Co(0)-1, the first ethylene insertion process could be the rate-determining step with exothermic energies ready for further reactions.
As shown in Scheme 1, after the formation of 1 Co(0)-3, three reaction pathways could proceed: second insertion (Ins II) for chain growth, β-hydrogen transfer (BHT) and β-hydrogen elimination (BHE) for chain terminations. BHE just requires transferring the β-hydrogen to the metal center while Ins II and BHT need to coordinate another ethylene firstly. Obviously, the BHE process is more advantageous than BHT and Ins II. The overall barrier of BHE in the triplet state is 4.37 kcal/mol, while it is only 1.99 kcal/mol in the singlet TS via a spin crossover. Then the singlet BHE complex 0 Co(0)-9 is provided. Since the overall barrier of the BHT is much higher than that of BHT and Ins II reaction paths, it will not be considered as a termination process for the neutral cobalt alkyls species. So BHE process is kinetically favored over the thermodynamically favored Ins II to form the propagated cobalt alkyl complexes by 7.5 kcal/mol. For the bis(imino)pyridyl metal species with low steric substituents, the BHE is competitive chain termination mechanism for producing short oligomer chains with unsaturated end group [44]. Figure 2 shows the binding information of the ethylene coordinated 0 Co(0)-2, 1 Co(0)-2, 1 Co(0)-4 and 1 Co(0)-6. The binding energy ∆E is defined as ∆E = E 2 -(E 1 + E C2H4 ) where E 2 refers to the zero point energies of the coordinated species 1 Co(0)-2 or 1 Co(0)-4 etc., and E 1 is for the precoordinated 1 Co(0)-1 or 1 Co(0)-3. It is found that the distance between the cobalt atom and the coordinated ethylene in 0 Co(0)-2 is smaller than 1 Co(0)-2 complex (2.08, 2.08 Å vs 2.43, 2.33 Å). The double bond of the coordinated ethylene is longer in the 0 Co(0)-2 (1.39 Å) than 1 Co(0)-2 (1.35 Å). These exhibited stronger interactions in 0 Co(0)-2 than in 1 Co(0)-2. However, the binding energy of 1 Co(0)-2 has negative values (−2.86 kcal/mol) while it is positive in 0 Co(0)-2 (3.63 kcal/mol). Asymmetrical coordination was found between the bis(imino)pyridyl ligand and the cobalt metal center in 1 Co(0)-2, as may contribute to the more binding energies than 0 Co(0)-2 The asymmetric coordination could be easily observed from the distances between cobalt metal center and the nitrogen atoms in the bis(imino)pyridyl ligand. They are 2.24, 1.95 and 2.24 Å in 1 Co(0)-1, while they turn to 2.71, 2.03 and 2.08 Å in 1 Co(0)-2. The same phenomena was also observed in the ethylene coordinated 1 Co(0)-4 and 1 Co(0)-6, which is the intermediates for the further Ins II or BHT reactions. It is special to find this kind of asymmetrical coordination between the PDI ligand and the metal atom in the neutral triplet cobalt species. Therefore, the PDI ligand is bidentate rather than tridentate when interacts with the cobalt ( Figure 2). As reported for the structure of the iron species, it is generally considered that the active center is 14-electron alkyl divalent cation structure [42,45]. It can be speculated that the cobalt species may also become a 14-electron structure by forming the bidentate coordination structure during the process of catalyzing ethylene polymerization. Chirik et al. [10] speculate that when bis(imino)pyridyl cobalt catalyzes the [2 + 2] cycloadditions, the cobalt will de-coordinate with one of the nitrogen on both sides, which is consistent with the optimized intermediate structure 1 Co(0)-2 and 1 Co(0)-4. This special intermediate may provide new electronic properties for the interactions between the cobalt complexes and the coordinated ethylene.
Catalysts 2020, 11, x FOR PEER REVIEW 5 of 20 Figure 2 shows the binding information of the ethylene coordinated 0 Co(0)-2, 1 Co(0)-2, 1 Co(0)-4 and 1 Co(0)-6. The binding energy ΔE is defined as ΔE = E2-(E1 + EC2H4) where E2 refers to the zero point energies of the coordinated species 1 Co(0)-2 or 1 Co(0)-4 etc., and E1 is for the precoordinated 1 Co(0)-1 or 1 Co(0)-3. It is found that the distance between the cobalt atom and the coordinated ethylene in 0 Co(0)-2 is smaller than 1 Co(0)-2 complex (2.08, 2.08 Å vs 2.43, 2.33 Å ). The double bond of the coordinated ethylene is longer in the 0 Co(0)-2 (1.39 Å ) than 1 Co(0)-2 (1.35 Å ). These exhibited stronger interactions in 0 Co(0)-2 than in 1 Co(0)-2. However, the binding energy of 1 Co(0)-2 has negative values (−2.86 kcal/mol) while it is positive in 0 Co(0)-2 (3.63 kcal/mol). Asymmetrical coordination was found between the bis(imino)pyridyl ligand and the cobalt metal center in 1 Co(0)-2, as may contribute to the more binding energies than 0 Co(0)-2 The asymmetric coordination could be easily observed from the distances between cobalt metal center and the nitrogen atoms in the bis(imino)pyridyl ligand. They are 2.24, 1.95 and 2.24 Å in 1 Co(0)-1, while they turn to 2.71, 2.03 and 2.08 Å in 1 Co(0)-2. The same phenomena was also observed in the ethylene coordinated 1 Co(0)-4 and 1 Co(0)-6, which is the intermediates for the further Ins II or BHT reactions. It is special to find this kind of asymmetrical coordination between the PDI ligand and the metal atom in the neutral triplet cobalt species. Therefore, the PDI ligand is bidentate rather than tridentate when interacts with the cobalt ( Figure 2). As reported for the structure of the iron species, it is generally considered that the active center is 14-electron alkyl divalent cation structure [42,45]. It can be speculated that the cobalt species may also become a 14-electron structure by forming the bidentate coordination structure during the process of catalyzing ethylene polymerization. Chirik et al. [10] speculate that when bis(imino)pyridyl cobalt catalyzes the [2 + 2] cycloadditions, the cobalt will de-coordinate with one of the nitrogen on both sides, which is consistent with the optimized intermediate structure  In the transition state (TS) structures of ethylene insertion 0 Co(0)-2/3 and 1 Co(0)-2/3 (see Supporting Information Figures S1 and S2), the distance between the cobalt atom and γ-hydrogen on the connected polymer chain indicates an agnostic interaction leading to stabilization of structure. Further, the bidentate interactions recover to the tridentate manner during the transition state process.
To further clarify the special unsymmetrically bidentate NN coordination character in the πcomplexes 1 Co(0)-2, Mayer bond order analysis was performed by Multiwfn [46]. The bond order of the bonds in the active center for 1 Co(0)-2 and 0 Co(0)-2 are listed in Table 1 where the concerned atom numbers are illustrated in Scheme 2. The greater the value of bond order, the stronger the bond between atoms. Usually, the bond order for one π-bond equals two, and for one σ-bond equals one. In the transition state (TS) structures of ethylene insertion 0 Co(0)-2/3 and 1 Co(0)-2/3 (see Supporting Information Figures S1 and S2), the distance between the cobalt atom and γ-hydrogen on the connected polymer chain indicates an agnostic interaction leading to stabilization of structure. Further, the bidentate interactions recover to the tridentate manner during the transition state process.
To further clarify the special unsymmetrically bidentate NN coordination character in the π-complexes 1 Co(0)-2, Mayer bond order analysis was performed by Multiwfn [46]. The bond order of the bonds in the active center for 1 Co(0)-2 and 0 Co(0)-2 are listed in Table 1 where the concerned atom numbers are illustrated in Scheme 2. The greater the value of bond order, the stronger the bond between atoms. Usually, the bond order for one π-bond equals two, and for one σ-bond equals one.
As shown in Table 1, the bond order value of most carbon-carbons bond is greater than 1.4, but differs between the 0 Co(0)-2 and 1 Co(0)-2. The bond orders are 1.41/1.42 in the aromatic pyridine ring (C(1)~C(5)) for 0 Co(0)-2, indicating well delocalized π-bonds. In contrast, less conjugation degree exist in the pyridine ring of 1 Co(0)-2, which could be derived from the broad range of the bond order value (1.33~1.49) in the ring.  Table 1. Bond order of the bonds in the active center for 1 Co(0)-2 and 0 Co(0)-2 by Mayer bond order analysis( "---" represents coordination interaction and "-" represents a chemical bond).
Further, the interactions between the cobalt metal and the three nitrogen atoms are intramolecular coordination bonds in which the bond order is mostly less than 0.5. Among the three Co---N interactions, stronger values were found between the central nitrogen on pyridine and the cobalt metal center. Additionally, they are weaker in 1 Co(0)-2 than in 0 Co(0)-2. The binding levels of N(6)---Co(66), N(12)---Co(66) and N(13)---Co(66) are 0.42, 0.11 and 0.39 in 1 Co(0)-2, but they are 0.61, 0.47 and 0.48 in 0 Co(0)-2. The weak bond of the N(12)---Co(66) (0.11) on one arm of the 1 Co(0)-2 suggests that there is almost no coordination interaction between the N(12) and the cobalt metal. As a result, the cobalt atom has more interaction with one of the 'arms' (C(5)-C(11)-N(12)) than the other, and the delocalization degree of this arm is smaller. Thus, the PDI ligand interacts with the cobalt in 1 Co(0)-2 by a bidentate coordination instead of the normal tridentate. By this way, the deficient 14electron metal center may be created to inspire the activity of neutral cobalt LCo-R towards ethylene insertion.

Scheme 2.
Atom labels around the active centers and fragmental units for the ethylene coordinated s M(q)-2 π-complexes. The hydrogen atoms were omitted for charity. Table 1. Bond order of the bonds in the active center for 1 Co(0)-2 and 0 Co(0)-2 by Mayer bond order analysis ("-" represents coordination interaction and "-" represents a chemical bond).
Further, the interactions between the cobalt metal and the three nitrogen atoms are intramolecular coordination bonds in which the bond order is mostly less than 0.5. Among the three Co-N interactions, stronger values were found between the central nitrogen on pyridine and the cobalt metal center. Additionally, they are weaker in 1 Co(0)-2 than in 0 Co(0)-2. The binding levels of N(6)-Co(66), N(12)-Co(66) and N(13)-Co(66) are 0.42, 0.11 and 0.39 in 1 Co(0)-2, but they are 0.61, 0.47 and 0.48 in 0 Co(0)-2. The weak bond of the N(12)-Co(66) (0.11) on one arm of the 1 Co(0)-2 suggests that there is almost no coordination interaction between the N(12) and the cobalt metal. As a result, the cobalt atom has more interaction with one of the 'arms' (C(5)-C(11)-N(12)) than the other, and the delocalization degree of this arm is smaller. Thus, the PDI ligand interacts with the cobalt in 1 Co(0)-2 by a bidentate coordination instead of the normal tridentate. By this way, the deficient 14-electron metal center may be created to inspire the activity of neutral cobalt LCo-R towards ethylene insertion.
In order to clearly demonstrate and compare the electronic properties of the 1 Co(0)-2 and 0 Co(0)-2, their HOMO orbitals were obtained by Multiwfn (Figure 3). The distribution of the HOMO orbitals of singlet 0 Co(0)-2 are well symmetrically delocalized in the structures. In contrast, the distribution in triplet 1 Co(0)-2 is asymmetric about the axis of the cobalt atom and the central nitrogen atom on the pyridine. This may be due to the fact the two unpaired electrons in 1 Co(0)-2 arise the unsymmetrically bidentate NN coordination character.
In order to clearly demonstrate and compare the electronic properties of the 1 Co(0)-2 and 0 Co(0)-2, their HOMO orbitals were obtained by Multiwfn (Figure 3). The distribution of the HOMO orbitals of singlet 0 Co(0)-2 are well symmetrically delocalized in the structures. In contrast, the distribution in triplet 1 Co(0)-2 is asymmetric about the axis of the cobalt atom and the central nitrogen atom on the pyridine. This may be due to the fact the two unpaired electrons in 1 Co(0)-2 arise the unsymmetrically bidentate NN coordination character. For the LCo(+)CH3 (Co(+)-1) species, the doublet 1/2 Co(+)-1 is more stable in energy than the quartet 3/2 Co(+)-1 by 1.16 kcal/mol. Differently, the ethylene coordinated Co(+)-2 is more stable in the quartet state than the doublet. It is interesting to find that for the cationic cobalt alkyl species, all the coordinated intermediates such as Co(+)-2, Co(+)-4, Co(+)-6, Co(+)-7 have lower energy in quartet than in doublet state. However, the transition process of Ins I and II prefer to proceed in doublet state instead of quartet. Overall, except for the two transition states Co(+)TS4/5 and Co(+)TS6/7, the energy differences between the quartet and the doublet states are not much within 3.5 kcal/mol. This means that for the cationic cobalt alkyl species, the spin crossover may occur throughout the reaction pathway considered in Scheme 1.
It is obvious that the overall energy barrier of the Ins I (19.31 kcal/mol) is higher than Ins II (4.24 kcal/mol), BHT (7.59 kcal/mol) and BHE (2.39 kcal/mol), predicting the Ins I to be the rate determining step.
In comparison with the neutral cobalt species (Figure 1), the overall barrier for the process considered in Scheme 1 has lower energies for the corresponding cationic species (Figure 4). However, the energy released from the formation of the cobalt alkyl species is greater in the neutral system. For example, the energies of the overall transition barriers for Ins I and II in the neutral system are 21.25 and 9.5 kcal/mol, respectively, while they are 19.31 and 4.24 kcal/mol in the cationic. The formation of the neutral 1 Co(0)-3 and 1 Co(0)-5 are -23.62 and -42.74 kcal/mol, respectively, while they are −15.10 and −34.53 kcal/mol for 3/2 Co(+)-3 and 3/2 Co(+)-5. So, the cationic system may have better reactivities than the neutral one. The energy difference between the favorable BHE and the second favorable process Ins II is just 1.85 kcal/mol in Co(+) species while it is 7.51 kcal/mol in Co(0), indicating that the cationic species are more favorable for the chain propagation to generate polymers. The energetically unfavorable BHE in cationic could also facilitate the chain growth to polymers. For either the neutral or the cationic system, the Ins I is the rate-determining step.
Similar to the neutral π-coordinated species, the 3/2 Co(+)-4 (quartet 4' in Figure 4) and 3/2 Co(+)-6 ( Figure S4) exhibits slightly asymmetry between metal center and nitrogen atoms in the bis(imino)pyridyl ligand.  Figures S3 and S4. For the LCo(+)CH 3 (Co(+)-1) species, the doublet 1/2 Co(+)-1 is more stable in energy than the quartet 3/2 Co(+)-1 by 1.16 kcal/mol. Differently, the ethylene coordinated Co(+)-2 is more stable in the quartet state than the doublet. It is interesting to find that for the cationic cobalt alkyl species, all the coordinated intermediates such as Co(+)-2, Co(+)-4, Co(+)-6, Co(+)-7 have lower energy in quartet than in doublet state. However, the transition process of Ins I and II prefer to proceed in doublet state instead of quartet. Overall, except for the two transition states Co(+)TS4/5 and Co(+)TS6/7, the energy differences between the quartet and the doublet states are not much within 3.5 kcal/mol. This means that for the cationic cobalt alkyl species, the spin crossover may occur throughout the reaction pathway considered in Scheme 1.   It is obvious that the overall energy barrier of the Ins I (19.31 kcal/mol) is higher than Ins II (4.24 kcal/mol), BHT (7.59 kcal/mol) and BHE (2.39 kcal/mol), predicting the Ins I to be the rate determining step.
In comparison with the neutral cobalt species (Figure 1), the overall barrier for the process considered in Scheme 1 has lower energies for the corresponding cationic species (Figure 4). However, the energy released from the formation of the cobalt alkyl species is greater in the neutral system. For example, the energies of the overall transition barriers for Ins I and II in the neutral system are 21.25 and 9.5 kcal/mol, respectively, while they are 19.31 and 4.24 kcal/mol in the cationic. The formation of the neutral 1 Co(0)-3 and 1 Co(0)-5 are −23.62 and −42.74 kcal/mol, respectively, while they are −15.10 and −34.53 kcal/mol for 3/2 Co(+)-3 and 3/2 Co(+)-5. So, the cationic system may have better reactivities than the neutral one. The energy difference between the favorable BHE and the second favorable process Ins II is just 1.85 kcal/mol in Co(+) species while it is 7.51 kcal/mol in Co(0), indicating that the cationic species are more favorable for the chain propagation to generate polymers. The energetically unfavorable BHE in cationic could also facilitate the chain growth to polymers. For either the neutral or the cationic system, the Ins I is the rate-determining step.

Energy Profiles and Structures of the Cationic LFe + CH 3 System
Previous theoretical works on the PDI-derived catalysts are mostly for cationic iron species. Ziegler examined the reactivity of the bis-ortho aryl substituted [(PDI)Fe(C 3 H 7 )] + complex towards ethylene polymerization by BP86 [35]. Along with transition states for Ins, BHT and BHE, metal−alkyl and ethylene π coordination structures were reported. However, only singlet spin state energy profile was reported [40]. Later, Musaev reported the same structures and catalytic behaviors by B3LYP, in which high spin-state structures are more favorable. They also found that the BHT is favorable than the Ins process when the ligand steric is low. By B3LYP methods, the reactivity of the [(PDI)Fe(CH 3 )] + was studied by de Bruin [47]. It was suggested that the termination via the BHT transition state has around 10 kcal/mol lower activation enthalpy than ethylene insertion. Further, the [(PDI)Fe(CH 3 )] 2+ with iron in +III oxidation state has a much lower insertion barrier than BHT.
In order to compare the different charge effect between iron and cobalt complexes the computational study was carried out on both of the neutral and cationic bis(imino)pyridine (PDI) iron complexes. The energy profiles for the cationic PDI iron species were depicted in Figure 5. Further, the optimized structures were listed in Figures S5 and S6. For most of the points shown in Figure 5, the quintet state is more stable in energy than the triplet state. The transition state of Ins II located on the triplet spin state is consistent with the results reported by Musaev who has examined the ethylene insertion to the [(PDI)-FeC 3 H 7 ] + structure [47].
Similar to the cobalt species, Ins I process is also the rate determining step. Close overall transition barriers were found for the three reaction pathways of Ins II, BHT, and BHE in the cationic iron species, in which the energy difference is just 3.14 kcal/mol. It seems that the BHE has lower transition energy. However, BHE is an energetically unfavorable process producing 2 Fe(+) and C 3 H 6 , with endothermal energy of 2.75 kcal/mol.
Despite the transition barrier is not high, the BHE process of both cationic cobalt and iron species occurs with a bit endothermal energy. The overall energy of the rate-determining transition barrier is 19.35 kcal/mol in Fe(+) while it is 19.31 kcal/mol in Co(+). Identical reactivity may exist in the cationic iron and cobalt systems. However, it is difficult for the active species to possess strictly positive charge in the actual catalytic process, since the anion ions interact with them more or less in the real experiments. Similar to the cobalt species, Ins I process is also the rate determining step. Close overall transition barriers were found for the three reaction pathways of Ins II, BHT, and BHE in the cationic iron species, in which the energy difference is just 3.14 kcal/mol. It seems that the BHE has lower transition energy. However, BHE is an energetically unfavorable process producing 2 Fe(+) and C3H6, with endothermal energy of 2.75 kcal/mol.
Despite the transition barrier is not high, the BHE process of both cationic cobalt and iron species occurs with a bit endothermal energy. The overall energy of the rate-determining transition barrier is 19.35 kcal/mol in Fe(+) while it is 19.31 kcal/mol in Co(+). Identical reactivity may exist in the cationic iron and cobalt systems. However, it is difficult for the active species to possess strictly positive charge in the actual catalytic process, since the anion ions interact with them more or less in the real experiments.

Energy Profiles and Structures of the Neutral LFeCH3 System
As shown in Figure 6, the energy profiles for the neutral iron species Fe(0) were illustrated and the optimized structures were listed in Figure S7 and S8. Almost all the quartet state species is more stable in energy than doublet state species, indicating that for neutral bis(imino)pyridyl (PDI) iron complexes, doublet state species have an overwhelming superiority.

Energy Profiles and Structures of the Neutral LFeCH 3 System
As shown in Figure 6, the energy profiles for the neutral iron species Fe(0) were illustrated and the optimized structures were listed in Figures S7 and S8. Almost all the quartet state species is more stable in energy than doublet state species, indicating that for neutral bis(imino)pyridyl (PDI) iron complexes, doublet state species have an overwhelming superiority.
The barrier for Ins I is also the rate determining step for Fe(0). The value for it is 16.13 kcal/mol, as it is lower than either neutral Co(0) or cationic Co(+) and Fe(+). Different from Fe(+) and Co(0), the BHT process for Fe(0) is more favorable than the BHE. Overall, in comparison with Ins II and BHE, the BHT is the most preferred reaction paths. Similar with neutral Co(0), the neutral iron alkyl intermediates Fe(0)-3 and Fe(0)-5 are very stable with considerable exothermic energies indicating that the neutral systems tend to form stable metal alkyls. Moreover, the binding energies of 3/2 Fe(0)-1 with ethylene to form 3/2 Fe(0)-2 is −5.74 kcal/mol, which is more stable than that of 1 Co(0)-2. However, it may be due to the one less electron in the 3/2 Fe(0)-2 than the 1 Co(0)-2, the unsymmetrical coordination has not been observed in the neutral iron system.

Oxidation Level of the PDI Ligand
Wieghardt and colleagues found a structural parameter (∆) to determine electron exchange between the metal and the bis(imino)pyridyl ligand along with the oxidation level of metal according to the following Equation (1) [29]; Each factor was defined as depicted in Scheme 3. Based on the equation, we found the changes linearly with the reduction of (PDI 0 ) ligand. This finding could be helpful for the electronic exchange definitions between the metal and bis(imino)pyridine skeleton structure. The barrier for Ins I is also the rate determining step for Fe(0). The value for it is 16.13 kcal/mol, as it is lower than either neutral Co(0) or cationic Co(+) and Fe(+). Different from Fe(+) and Co(0), the BHT process for Fe(0) is more favorable than the BHE. Overall, in comparison with Ins II and BHE, the BHT is the most preferred reaction paths. Similar with neutral Co(0), the neutral iron alkyl intermediates Fe(0)-3 and Fe(0)-5 are very stable with considerable exothermic energies indicating that the neutral systems tend to form stable metal alkyls. Moreover, the binding energies of 3/2 Fe(0)-1 with ethylene to form 3/2 Fe(0)-2 is −5.74 kcal/mol, which is more stable than that of 1 Co(0)-2. However, it may be due to the one less electron in the 3/2 Fe(0)-2 than the 1 Co(0)-2, the unsymmetrical coordination has not been observed in the neutral iron system.

Oxidation Level of the PDI Ligand
Wieghardt and colleagues found a structural parameter (Δ) to determine electron exchange between the metal and the bis(imino)pyridyl ligand along with the oxidation level of metal according to the following equation (1) [29]; Each factor was defined as depicted in Scheme 3. Based on the equation, we found the changes linearly with the reduction of (PDI 0 ) ligand. This finding could be helpful for the electronic exchange definitions between the metal and bis(imino)pyridine skeleton structure. To figure out how the electronic exchange occurred between the metal and the bis(imino)pyridine skeleton structure, we calculated the Δ value of the structures for the Ins I and II process and listed in Figure 7 (for more details see Supporting Information in Tables S1-S8). To figure out how the electronic exchange occurred between the metal and the bis(imino)pyridine skeleton structure, we calculated the ∆ value of the structures for the Ins I and II process and listed in Figure 7 (for more details see Supporting Information in Tables S1-S8).
It is necessary to have an overall cognition about the structure parameter ∆ of iron and cobalt species before analyzing the data in  To figure out how the electronic exchange occurred between the metal and the bis(imino)pyridine skeleton structure, we calculated the Δ value of the structures for the Ins I and II process and listed in Figure 7 (for more details see Supporting Information in Tables S1-S8). It is necessary to have an overall cognition about the structure parameter Δ of iron and cobalt species before analyzing the data in Figure 7. It is characteristic of neutral (PDI) 0 ligands when the values are in the range of 0.15-0.19 Å (av 0.17 Å ). The Δexp values in the range 0.09～0.12 Å (average, 0.102 Å) are typical for a π-radical anion (PDI) 1− . Structures with an average Δexp value of 0.062 ± 0.02 Å have been found for complexes containing a dianion (PDI) 2− . Having this in mind, the calculated Δ in this work will reflect the oxidation level of the PDI ligand.
As illustrated in Figure 7, it is clear that for most cationic systems, the calculated values Δ are located in the range of 0.15～0.19 Å , which indicates that the PDI ligands are neutral. Then, the oxidation state of the metal center will be +II, which is normally accepted in the related reports. There are some differences between the high and low spin states for the cationic species, in which the latter has lower values than the former. This means that the interactions between the PDI ligand and metal center are stronger in the low spin state than the high spin state. Further, it could also be supported from the shorter bond in optimized structures in Figures S1-S8. In comparison with the iron system, the values of the cationic cobalt species are always greater. Especially for the low spin cationic species, the values of iron system are in the range of 0.144～0.159 while they are 0.165～0.174 for cobalt. The values for the high spin states are almost the same for the iron and cobalt species.
For most of the neutral iron and cobalt structures, the Δ values are within 0.09 ～ 0.13 Å . Theoretically, that the PDI ligand is an anion revealing the +II oxidation level of the metal center in the neutral LMCH3 structure, which is exhibits as +I in appearance. According to the results As illustrated in Figure 7, it is clear that for most cationic systems, the calculated values ∆ are located in the range of 0.15~0.19 Å, which indicates that the PDI ligands are neutral. Then, the oxidation state of the metal center will be +II, which is normally accepted in the related reports. There are some differences between the high and low spin states for the cationic species, in which the latter has lower values than the former. This means that the interactions between the PDI ligand and metal center are stronger in the low spin state than the high spin state. Further, it could also be supported from the shorter bond in optimized structures in Figures S1-S8. In comparison with the iron system, the values of the cationic cobalt species are always greater. Especially for the low spin cationic species, the values of iron system are in the range of 0.144~0.159 while they are 0.165~0.174 for cobalt. The values for the high spin states are almost the same for the iron and cobalt species.
For most of the neutral iron and cobalt structures, the ∆ values are within 0.09~0.13 Å. Theoretically, that the PDI ligand is an anion revealing the +II oxidation level of the metal center in the neutral LMCH 3 structure, which is exhibits as +I in appearance. According to the results mentioned above, the ground state of these neutral species is high spin state. It is similar to the cationic species, the ∆ values for high spin states are almost the same for iron and cobalt system. However, lower values are found in 0 Co(0) structures. Particularly, the ∆ values of the transition barrier for the Ins I and Ins II in 0 Co(0) are rather low. They are 0.061 and 0.058, respectively, suggesting that PDI is dianion during the insertion step.
Overall, in comparison with the cationic species, the one more extra electron in the neutral species may mainly transfer to the PDI ligand instead of the metal center. By this way, the metal center does always keep the +II valence in either cationic or neutral species.

Charge Distribution
In order to figure out the difference of the charge distribution among s M(q)-1 and the ethylene coordinated s M(q)-2, we do the electronic population analysis by natural bond orbital (NBO) method [48]. Firstly, the model molecule in Scheme 2 is divided into four moieties: PDI ligand, M center, CH 3 and two Ars (aromatic rings connected to the two nitrogen atoms in PDI ligand). The NBO charge distribution of s M(q)-1 was illustrated in Figure 8a and Table S9. The charge changes aroused by the coordination of the ethylene in s M(q)-2 were listed in Figure 8b.
In order to figure out the difference of the charge distribution among s M(q)-1 and the ethylene coordinated s M(q)-2, we do the electronic population analysis by natural bond orbital (NBO) method [48]. Firstly, the model molecule in Scheme 2 is divided into four moieties: PDI ligand, M center, CH3 and two Ars (aromatic rings connected to the two nitrogen atoms in PDI ligand). The NBO charge distribution of s M(q)-1 was illustrated in Figure 8a and Table S9. The charge changes aroused by the coordination of the ethylene in s M(q)-2 were listed in Figure 8b. As shown in Figure 8a, for both of the cationic and neutral species, the metal center and the two Ars possess positive charges while the CH3 moiety that binds to the metal has negative values. The positive values for the two Ars decrease slightly from the cationic species (0.492~0.515) to the neutral ones (0.327~0.385). Similarly, the fluctuation of the negative charges in the CH3 moiety is also not great. Additionally, it is obvious that the cationic complex has more positive charges than the neutral. The NBO charge distributions here could strongly support the conclusion that the PDI ligand is almost neutral in the cationic species while it is anion in the neutral species. The charge values of PDI in both of the neutral iron and cobalt species are close to zero while they are the most negative moiety As shown in Figure 8a, for both of the cationic and neutral species, the metal center and the two Ars possess positive charges while the CH 3 moiety that binds to the metal has negative values. The positive values for the two Ars decrease slightly from the cationic species (0.492~0.515) to the neutral ones (0.327~0.385). Similarly, the fluctuation of the negative charges in the CH 3 moiety is also not great. Additionally, it is obvious that the cationic complex has more positive charges than the neutral. The NBO charge distributions here could strongly support the conclusion that the PDI ligand is almost neutral in the cationic species while it is anion in the neutral species. The charge values of PDI in both of the neutral iron and cobalt species are close to zero while they are the most negative moiety in the neutral species. Therefore, the loss of one electron from the neutral system is mainly from the PDI ligand instead of the metal center.
After coordination of ethylene molecules, the charge distribution changes slightly in the cationic species while it changes more in the neutral species. In s M(q)-2, the C 2 H 4 moiety has positive NBO charges in both cationic and neutral systems, indicating that some of the electrons from C 2 H 4 are transferred to other moieties, mainly to the metal center. Additionally, the electrons transferred from C 2 H 4 moiety are less in the neutral s M(0)-2 than the cationic s M(+)-2. Besides the metal center, there are significant changes of charges on the CH 3 and PDI moieties in the neutral due to the coordination. For 3/2 Fe(0)-2, the iron atom become more positively charged while CH 3 moiety is more negatively. In contrast, for the 1/2 Fe(0)-2, 1 Co(0)-2 and 0 Co(0)-2, the metal atoms receive less positive charges while CH 3 less negative.

General Comparison on Valence Electrons
For all the four species, Co(+), Co(0), Fe(+), Fe(0), the first ethylene insertion step is the rate determining one. Additionally the energies of the transition barriers increase in the sequence of Fe(0) (16.13 kcal/mol) < Co(+)(19.31 kcal/mol) < Fe(+)(19.35 kcal/mol) < Co(0)(21.25 kcal/mol), though the difference is not much, within 5.12 kcal/mol. The neutral cobalt system Co(0) has the lowest reactivity because it possesses the most more electrons; however, the Fe(+), which lacks the electrons most, is not the most active one here. As for the spin states of the Co(+), Fe(0), and Fe(+), Ins I and Ins II process have lower energy in the high spin states, but spin crossover may exist for the BHT and BHE process in most cases. Additionally, the spin crossover is almost throughout the Co(+) species. BHT or BHE is the kinetically favorable process in comparison with the Ins II as they have a low steric substituent, but they are always energetically unfavorably. The Co(0) and Fe(+) tend to undergo hydrogen transfer through BHE for the possible chain termination, while Fe(0) and Co(+) through BHT.
As demonstrated in Scheme 4, the valence electron numbers were considered generally. The unpaired electron numbers are the same for Co(+) and Fe(0), which is one electron less, and better reactivity, than the Co(0). Additionally, the unpaired electrons are located mainly at the cobalt metal center for Co(+) whereas those in Fe(0) are distributed in both of the iron metal and the PDI ligand. This may explain the occurrence of more spin crossover in Co(+) system. Additionally, the loss of one electron from the Co(0) to form the Co(+) is mainly from the PDI ligand instead of the cobalt metal, as is the same for Fe(0) to Fe(+). The better reactivity of neutral Fe(0) may be attributed to the almost 14e deficient electrons around the iron atom. For the cobalt species, it could also reach the 14e center by losing the CH 3 anion group from Co(0) to afford the Co(+) B (the symbol B to mark the bare nature or no alkyl coordination of the cobalt center) which could be supported by the observation of the alkyl free intermediate in the experiment [27,28]. In the next part, the coordination of ethylene or the cocatalyst anion groups to the Co(+) B will be analyzed for the possible reaction mechanism.

Possible Catalytic Process for the Cobalt Species
The electron deficient metal alkyl species [LM-R] + was well accepted mode for both early and late transition metal complexes when LnMX2 activated by MAO. However, Gibson [27,28] [34], neutral complexes of LCo(μ-Me)2AlMe2 were observed in the catalyst systems LCoCl2/AlMe3. However, in the presence of ethylene, the proposed structure of [LCo(η-C2H4)] + [AlMe3Cl] − is the major cobalt species. The polymerization manner catalyzed by the cobalt complex initiated with cocatalysts is still unclear. Even the exact nature of MAO and MMAO remains somewhat unclear, previous computational work showed that explicit inclusion of a MAO model did not significantly alter energy and structures for modeling ethylene oligomerization [50]. Thus, the [AlMe4] − was considered as the anion ions that function as the cocatalysts.
To further explore the intrinsic mechanism of ethylene reactions catalyzed by the cobalt species, as depicted in Figure 9 and Scheme 5, we contrast the energy profiles of the reactions of L s Co(+) B with C2H4 and anion ions [CH3] − and [AlMe4] − , respectively. Only the first ethylene insertion process was considered, as it appears to be the rate-determining step in the above calculated results. Both of It is worth mentioning that the numbers of the valence electrons in Co(0) is 16e, but when one of the nitrogen atoms in the PDI lost interactions with the metal center (as shown in Scheme 4), the 14e deficient center may be formed by an unsymmetrical manner. The good activity in the single cyclopenta ring fused PDI cobalt system towards the ethylene oligomerization in the experiments [49] could be attributed to the NNN unsymmetrically loose coordination manner in the metal center.

Possible Catalytic Process for the Cobalt Species
The electron deficient metal alkyl species [LM-R] + was well accepted mode for both early and late transition metal complexes when LnMX 2 activated by MAO. However, Gibson [27,28] [34], neutral complexes of LCo(µ-Me) 2 AlMe 2 were observed in the catalyst systems LCoCl 2 /AlMe 3 . However, in the presence of ethylene, the proposed structure of [LCo(η-C 2 H 4 )] + [AlMe 3 Cl] − is the major cobalt species. The polymerization manner catalyzed by the cobalt complex initiated with cocatalysts is still unclear. Even the exact nature of MAO and MMAO remains somewhat unclear, previous computational work showed that explicit inclusion of a MAO model did not significantly alter energy and structures for modeling ethylene oligomerization [50]. Thus, the [AlMe 4 ] − was considered as the anion ions that function as the cocatalysts.
To further explore the intrinsic mechanism of ethylene reactions catalyzed by the cobalt species, as depicted in Figure 9 and Scheme 5, we contrast the energy profiles of the reactions of L s Co(+) B with C 2 H 4 and anion ions [CH 3 ] − and [AlMe 4 ] − , respectively. Only the first ethylene insertion process was considered, as it appears to be the rate-determining step in the above calculated results. Both of the single and triplet states were considered with the optimized structures listed in Figures S9 and S10. The triplet is lower in energy than the singlet spin state. It was found that the reactions of both of the anion ions [ In comparison with anion ions [CH 3 ] − and [AlMe 4 ] − , the coordination of C 2 H 4 to the bare cationic L 1 Co(+) B produces less energy, but the formation of the L 1 Co(+)C 2 H 4 (1B) is still considerably stable in energy by 16.27 kcal/mol. The electron deficient 14e L 1 Co(+) B which is electron deficient has better binding abilities than either the cationic L 3/2 Co(+)CH 3 (3.62 kcal/mol) or the neutral L 1 Co(0)CH 3 (−2.86 kcal/mol) to coordinate the ethylene monomers. This may explain the experimental observation of the LCo(η-C 2 H 4 )] + . Additionally, for the process of the ethylene insertion, the energy barrier for the [AlMe 4 ] − participating one is lower than the [CH 3 ] − by 5.46 kcal/mol.
As mentioned above, the loss of electrons between the neutral and cationic species mainly caused the reduction of the oxidation state of the PDI ligand instead of the metal center. This means the metal center keeps the +II valence state in both the neutral and cationic systems. The oxidation state of the PDI ligand in the processes in Figure 9 was monitored and compared by calculating the structure parameter ∆. As listed in Table 2, similar to the cationic s Co(+)-1, the ∆ value of L 1 Co(+) B is 0.181 Å, indicating the neutral character of the PDI ligand. Consequently, the valence state of the cobalt metal center in L 1 Co(+) B is +I instead of +II. The neutral PDI ligand and the +I valence cobalt metal center were retained in the ethylene coordinated cationic L 1 Co(+)C 2 H 4 (1B in Figure 9). However, the ∆ values of 0.123 Å, 0.119 Å and 0.114 Å for 1A, 1C and 3A/3B indicated the presence of a monoanionic PDI ligand (more details see Tables S10 and S11). 2B could be generated from the 1B (neutral PDI and +I cobalt center) and 1C (monoanionic PDI and +II Cobalt center). Particularly, the calculated ∆ value of the structure 2B appears to be 0.168 Å which is in the range of the neutral PDI. Additionally, there is no Co-C σ bond formed in 2B, as is different from 2A. In 2B, the carbon atom in methyl group forms σ bond neither with Cobalt nor with Aluminum. Thus, the bonding in 2B appears to be a 3-center 2-electron character. Additionally, the valence state of cobalt should be +I in 2B. Moreover  As mentioned above, the loss of electrons between the neutral and cationic species mainly caused the reduction of the oxidation state of the PDI ligand instead of the metal center. This means the metal center keeps the +II valence state in both the neutral and cationic systems. The oxidation state of the PDI ligand in the processes in Figure 9 was monitored and compared by calculating the structure parameter Δ. As listed in Table 2, similar to the cationic s Co(+)-1, the Δ value of L 1 Co(+) B is 0.181 Å , indicating the neutral character of the PDI ligand. Consequently, the valence state of the cobalt metal center in L 1 Co(+) B is +I instead of +II. The neutral PDI ligand and the +I valence cobalt metal center were retained in the ethylene coordinated cationic L 1 Co(+)C2H4 (1B in Figure 9). However, the Δ values of 0.123 Å, 0.119 Å and 0.114 Å for 1A, 1C and 3A/3B indicated the presence As mentioned above, the loss of electrons between the neutral and cationic species mainly caused the reduction of the oxidation state of the PDI ligand instead of the metal center. This means the metal center keeps the +II valence state in both the neutral and cationic systems. The oxidation state of the PDI ligand in the processes in Figure 9 was monitored and compared by calculating the structure parameter Δ. As listed in Table 2, similar to the cationic s Co(+)-1, the Δ value of L 1 Co(+) B is 0.181 Å , indicating the neutral character of the PDI ligand. Consequently, the valence state of the cobalt metal center in L 1 Co(+) B is +I instead of +II. The neutral PDI ligand and the +I valence cobalt metal center were retained in the ethylene coordinated cationic L 1 Co(+)C2H4 (1B in Figure 9). However, the Δ values of 0.123 Å, 0.119 Å and 0.114 Å for 1A, 1C and 3A/3B indicated the presence

Computational Methods
Density functional theory (DFT) calculation was performed using the Gaussian 09 software package [51]. The geometric structures of the relevant species were optimized in the gas phase with the hybrid B3LYP which was used to produce reasonable results by other researchers [43,52]. In the investigation performed by Busico et al. [53], the B3LYP demonstrated moderate accuracy among the 22 functionals on transition states energies, agostic interactions, reaction energies and π-coordination energies for transition metal catalysts. The standard 6-311G(d) basis set was used for nonmetal atoms, while the SDD was chosen for the metal atom [54]. Vibration frequencies were calculated to check that the reaction intermediates were all positive and the TSs had only one imaginary frequency. The zero-point energy changes (∆E) were used to discuss the catalytic reaction process. Additionally, possible spin states were considered for all the investigated systems. Bruin et al [41] have confirmed that the inclusion of solvent or expansion of the wave function in a larger basis set did not affect the calculations performance in the gas phase. Then, in this theoretical calculation solvent effect was not considered. Intrinsic reaction coordinate (IRC) calculations [55,56] were also performed to check a TS connects two appropriate local minima in some of the reaction paths. In addition, natural bond orbital (NBO) analysis [46,49,57,58] was conducted on the optimized structures to acquire a further insight into the charge distributions of the system [59]. Some of the bond order was also analyzed by the Mayer bond order analysis by Multiwfn [46].

Conclusions
The reactivities and electronic structures of the neutral, cationic bis(imino)pyridyl iron and cobalt species were explored and compared in this work by DFT calculations. Different spin states were considered for the four species Co(+), Co(0), Fe(+), Fe(0). The results revealed that for all the species, the rate-determining step is the first ethylene insertion. The neutral cobalt system Co(0) had the lowest reactivity as it possessed the most electrons. As for the spin states in Co(+), Fe(0) and Fe(+), the Ins I and Ins II processes prefer to take place in high spin states, but the BHT and BHE tend to occur along with spin crossover. Additionally, the spin crossover is almost throughout the Co(+) species. Overall, due to the low steric substituent in the investigated species here, the BHT or BHE is the kinetically favorable process in comparison with the Ins II, but they are always energetically unfavorable. The Co(0) and Fe(+) tend to perform chain termination through BHE, while Fe(0) and Co(+) through BHT.
Additionally, the electron numbers are the same for Co(+) and Fe(0), which is one electron less and better reactivity than the neutral Co(0). The unpaired electrons are located mainly on the cobalt metal center in Co(+) while they are on both of the iron metal center and the PDI ligand in Fe(0). The more electrons in the cobalt metal center may explain the occurrence of more spin crossover in Co(+) system. Additionally the loss of one electron from the Co(0) to form the Co(+) is mainly from the PDI ligand instead of the cobalt metal, as is the same for Fe(0) to Fe(+).
Moreover, a special unsymmetrically NN coordination manner was found between the PDI ligand and the cobalt metal in the neutral cobalt species Co(0). This may result in 14e deficient center. Through this center, the good activity in some asymmetric structures of electron-rich cobalt in the experiments may be explained. Furthermore, a process involving [AlMe 4 ] − was proposed to explain the experimentally observed LCo(+) B (C 2 H 4 )(1B) which could be generated from the LCo(+) B with 14e deficient center by ethylene coordination. A special intermediate, Co(+)B(C 2 H 4 )[AlMe 4 ] − with Co in +I and absence of Co-C σ bond, was obtained. In this intermediate, the interaction of the cobalt metal atom with the [AlMe 4 ] − was less strong than with the coordinated ethylene. The chain growth in the cobalt species may proceed by attacking the carbon atom of the binding C 2 H 4 from the methyl group in [AlMe 4 ] − . These calculations results may provide fundamental information for understanding and designing the catalysts of ethylene polymerization.
Supplementary Materials: The following are available online at http://www.mdpi.com/2073-4344/10/12/1396/s1, Figure S1 The DFT optimized structures of the neutral cobalt system 0 Co(0) in Figure 1, Figure S2 The DFT optimized structures of the neutral cobalt system 1 Co(0) in Figure 1, Figure S3 The DFT optimized structures of the cationic cobalt system 1/2 Co(+) in Figure 3, Figure S4 The DFT optimized structures of the cationic cobalt system 3/2 Co(+) in Figure 3, Figure S5 The DFT optimized structures of the cationic iron system 1 Fe(+) in Figure 5, Figure S6 The DFT optimized structures of the cationic iron system 2 Fe(+) in Figure 5, Figure S7 The DFT optimized structures of the neutral iron system 1/2 Fe(0) in Figure 6, Figure S8 The DFT optimized structures of the neutral iron system 3/2 Fe(0) in Figure 6, Figure S9 The DFT optimized structures of the cobalt system 0 LCo(+) B in Figure 9, Figure S10 The DFT optimized structures of the cobalt system 1 LCo(+) B in Figure 9, Table S1 The factors for calculating the structure parameter ∆ in 0 Co(0), Table S2 The factors for calculating the structure parameter ∆ in 1 Co(0), Table S3 The factors for calculating the structure parameter ∆ in 1/2 Co(+), Table S4 The factors for calculating the structure parameter ∆ in 3/2 Co(+), Table S5 The factors for calculating the structure parameter ∆ in 1 Fe(+), Table S6 The factors for calculating the structure parameter ∆ in 2 Fe(+), Table S7 The factors for calculating the structure parameter ∆ in 1/2 Fe(0), Table S8 The factors for calculating the structure parameter ∆ in 3/2 Fe(0), Table S9 The NBO charge distribution for s M(q)-1 and s M(q)-2, M includes iron and cobalt, s means the spin states and the q refers to the charge number, Table S10 The factors for calculating the structure parameter ∆ in 0 Co(+) B , Table S11 The factors for calculating the structure parameter ∆ in 1 Co(+) B .