Theoretical Study on Electronic Structural Properties of Catalytically Reactive Metalloporphyrin Intermediates

: Metalloporphyrins have attracted great attention in the potential application of biomimetic catalysis. Especially, they were widely investigated as green catalysts in the chemical oxidation of various hydrocarbons through the catalytic activation of molecular oxygen. The structural properties of active central metal ions were reported to play a decisive role in catalytic activity. However, those delicate structural changes are di ﬃ cult to be experimentally captured or elucidated in detail. Herein, we explored the electronic structural properties of metalloporphyrins (metal porphyrin (PM II , PM III Cl)) and their corresponding catalytically active intermediates (metal(III)-peroxo(PM III -O 2 ), metal(III)-hydroperoxo(PM III -OH), and metal(IV)-oxo(PM IV = O), (M = Fe, Mn, and Co)) through the density functional theory method. The ground states of these intermediates were determined based on the assessment of relative energy and the corresponding geometric structures of ground states also further conﬁrmed the stability of energy. Furthermore, our analyses of Mulliken charges and frontier molecular orbitals revealed the potential catalytic behavior of reactive metalloporphyrin intermediates. accurate results, the triple- ζ plus polarization slater-type orbital basis sets (TZP) and a ﬁne mesh numerical integration of the matrix elements were employed. The sub-valence 3s and 3p shells of the metal center were included in the valence set. For C and N atoms, 2s and 2p were considered as valence shells, respectively. The other shells of lower energy, such as [Ne] for the metal and [He] for C / N, were described as the core. The speciﬁc structures of calculated intermediates are listed in Figure 1. M-O-O (~124.3 ◦ ) are than of Co-O-O (~110 ◦ ) in Co porphyrin. angles of Fe / Mn-O-O close to 120 ◦ these orbitals property of 2 -like bonding. Speciﬁcally, the O-O bond length in these metalloporphyrin adducts with end-on oxygen was 1.275 (Fe), 1.382 (Mn), and 1.280 (Co) Å, respectively. As compared to regular O-O bond length in molecular oxygen, these bond length values indicated that O 2 has been greatly elongated in the PM III -O 2 adducts. Due to the elongation of O-O bond, we presumed that high valent metalloporphyrin species can be generated from the cleavage of O-O bond. Fe and Mn porphyrins with the side-on oxygen showed a much lower M-O-O angle value ( > 50 ◦ ) than those observed in end-one model. However, Mn-O-O angle was slightly higher (~ 10 ◦ ) than that of Fe-O-O. H atom from C-H bond in


Introduction
Metalloporphyrins have been widely used as impressive catalysts in broad chemical reactions [1][2][3][4][5][6][7], including hydroxylation [8,9], epoxidation [10,11], reduction of nitric oxide [12], oxidation of sulfides [13], radical reactions [14,15], halogenation [16], cycloaddition [17,18], and reduction [19,20]. During the application of metalloporphyrins, the characterization of reactive intermediates is of great importance for the understanding of reaction mechanism. For example, Ali et al. explored the electronic structure, spin-states, and spin-crossover reaction of heme-related Fe-porphyrins based on density functional theory (DFT) calculations [21]. In the mechanistic studies, high-valent iron(IV)-oxo species have been implicated as the key reactive intermediates in the catalytic cycles of alkanes oxidation by heme and non-heme iron enzymes [22][23][24], as well as the Mn and Co-oxo species [25][26][27][28][29]. In addition, spectroscopic characterization found a hydroperoxo-heme intermediate converted from a side-on peroxo to an end-on hydroperoxo complex [30]. The low-spin end-on ferric peroxo heme intermediate has been proposed as an alternative reactive intermediate in the one electron reduction of a ferric heme [31]. Furthermore, the electronic structure of substituted iron(II) porphyrins has been theoretically studied with intermediate or high spin state [32]. The oxygen activation associated with Co, Mn, and Mo porphyrins has been studied by quantum chemical methods [33]. Moreover, ferric-superoxo complexes in the oxygen activation by non-heme iron(II) complex were understood by the theoretical calculations [34]. Hydrogen peroxide activated by high-valent heme centers was investigated by density functional theory, implicating its catalytic ability in the catalytic cycle [35]. Therefore, theoretical calculation and spectroscopic characterization are mostly employed for the mechanistic studies of these catalytic reactions involved with metalloporphyrins.
To the best of our knowledge, porphyrins and metalloporphyrins are considered as the most popular biometric catalysts in the functionalization of C-H with various substrates. For instance, alkane can be readily activated by a homogeneous manganese (III) porphyrin-iodosyl benzene oxidizing system [36]. Manganese porphyrins could also selectively catalyze the halogenations of C-H bond [3]. Oxidation of cyclohexene via molecular oxygen can be completed by cobalt porphyrin complexes immobilized on montmorillonite [37]. In addition to these experimental studies, theoretical studies were also widely performed to understand the catalytic role of these metalloporphyrins. For example, a DFT study found that tetra-amido macrocyclic ligands were substantially noninnocent to high-valent iron, cobalt, and nickel tetraamidomacrocyclic ligand (TAML) complexes [38]. A quantitative structure-activity relationship model (QSAR) study on metalloporphyrin catalysts was carried out in the oxidation of cyclohexane to adipic acid [39]. Theoretical studies were performed to explore a unique class of reactive molecules of iron(III)-nitro porphyrins [40,41]. Despite the diversity of active sites reported, a common mechanistic hypothesis for dioxygen activation is emerging. In this unified approach [42][43][44], dioxygen might initially bind to a reduced metal center to form a metal-superoxo complex, and subsequently the peroxo intermediates [42,45]. Then, O-O bond cleavage of metal-hydroperoxo species possibly results in the formation of high-valent metal-oxo oxidants [4, 46,47], which are considered as the reactive species to oxidize the substrates. Therefore, it is significantly important to determine the corresponding reactive intermediates and evaluate their chemical properties.
Although the wide utilization of metalloporphyrins in the catalytic oxidation of alkanes, the reactive intermediates are difficult to be captured and the electronic structure properties of intermediates are still unclear thus far. In fact, the electronic structure of these reaction intermediates of metalloporphyrins plays a key role in the determination of their function and reactivity [48]. In this work, we explored the intermediates of electronic and geometric properties in the activation of molecular oxygen via metalloporphyrins based on the DFT calculations. Firstly, the ground state of the metalloporphyrin intermediates was evaluated by calculating the relative energy of intermediates. Then, the geometric structure of the ground state intermediates was compared with the data of experiments and then the electronic structure of ground state was confirmed to be stable. Finally, the electronic property of the intermediates was analyzed to give a deep insight into catalytic behavior of porphyrin in the oxidation reaction of alkanes.

Computational Methods
The selection of proper calculation methods is essentially important to obtain reliable molecular structures and properties. In this study, DFT calculations were carried out using the Amsterdam density functional (ADF2009.01) program package developed by Baerends and his co-workers [49][50][51]. All metalloporphyrin compounds were optimized with OLYP (unrestricted formalism) generalized gradient approximations based on the OPTX exchange functional [52,53]. The OLYP functional was reported to show great performance in the calculation of metal-complexes [54,55]. Various density functional predict methods could provide greatly different results. Specifically, OLYP was proved to be an appropriate model for the oxygen bonding with metalloporphyrins [54,[56][57][58]. Any spin contamination observed in our calculation was ignored due to their low influence (<5%). To obtain Catalysts 2020, 10, 224 3 of 17 accurate results, the triple-ζ plus polarization slater-type orbital basis sets (TZP) and a fine mesh numerical integration of the matrix elements were employed. The sub-valence 3s and 3p shells of the metal center were included in the valence set. For C and N atoms, 2s and 2p were considered as valence shells, respectively. The other shells of lower energy, such as [Ne] for the metal and [He] for C/N, were described as the core. The specific structures of calculated intermediates are listed in Figure 1.
Catalysts 2020, 10, x FOR PEER REVIEW 3 of 17 influence (< 5%). To obtain accurate results, the triple-ζ plus polarization slater-type orbital basis sets (TZP) and a fine mesh numerical integration of the matrix elements were employed. The sub-valence 3s and 3p shells of the metal center were included in the valence set. For C and N atoms, 2s and 2p were considered as valence shells, respectively. The other shells of lower energy, such as [Ne] for the metal and [He] for C/N, were described as the core. The specific structures of calculated intermediates are listed in Figure 1.

The Ground State
To determine the ground states of the metalloporphyrins and intermediates shown in Figure 1, the relative energy of metalloporphyrins with various possible spin states were calculated. As listed in Table 1, PFe II has an S=1 ground state, arising from the (dxy) 2 (dz 2 ) 2 (dπ) 2 configuration. Typically, Fe II ion (d 6 ) has a 5 T2g ground state from the ligand field. Therefore, our calculated results were consistent with both experimental and theoretical observations [59,60]. The S=2 state of PFe II is an intermediate state with an energy level of 112.90 kcal•mol −1 higher than the ground state. In addition, the S=0 state of PFe II is the high spin state with an energy of 191.66 kcal.mol −1 . For PMn II species, we obtained an S=3/2 ground state, which is in agreement with Liao's theoretical work [61]. Furthermore, our results indicate that PCo II has an S=1/2 ground state, which is consistent with the configuration assignment (dxy) 2 (dπ) 4 (dz 2 ) 1 reported by the Lin group based on those Electron Spin Resonance (ESR) spectra [62].

The Ground State
To determine the ground states of the metalloporphyrins and intermediates shown in Figure 1, the relative energy of metalloporphyrins with various possible spin states were calculated. As listed in Table 1, PFe II has an S=1 ground state, arising from the (dxy) 2 (dz 2 ) 2 (dπ) 2 configuration. Typically, Fe II ion (d 6 ) has a 5 T 2g ground state from the ligand field. Therefore, our calculated results were consistent with both experimental and theoretical observations [59,60]. The S=2 state of PFe II is an intermediate state with an energy level of 112.90 kcal·mol −1 higher than the ground state. In addition, the S=0 state of PFe II is the high spin state with an energy of 191.66 kcal.mol −1 . For PMn II species, we obtained an S=3/2 ground state, which is in agreement with Liao's theoretical work [61]. Furthermore, our results indicate that PCo II has an S=1/2 ground state, which is consistent with the configuration assignment (dxy) 2 (dπ) 4 (dz 2 ) 1 reported by the Lin group based on those Electron Spin Resonance (ESR) spectra [62].  [61,63] and the high-spin one (S=5/2) [64,65]. As shown in Table 1, our calculated results show that spin quantum number (S) of the ground state is 3/2 for PFe III Cl, while the high spin (S=5/2) was obtained with a slightly higher energy level of 18.38 kcal.mol −1 . This result suggests that a mixed state of S=3/2 and 5/2 might be observed for PFe III Cl complex, consistent with spin states studied by magnetic moments and Moessbauer parameters [66]. Furthermore, the ground state of Mn III complexes was determined to be S=2 state, which agrees with the DFT theoretical results reported by Kepenekian et al. [67]. The high spin ground state of PMn III Cl probably resulted from the redistribution of both σ and π charges. Co III cation with d 6 electronic configuration PCo III Cl was obtained with an S=0 ground state according to our calculation results.
These mononuclear meta-dioxygen (PM III -O 2 ) adducts were implicated as key intermediates in dioxygen activation reactions catalyzed by metalloenzymes. Thus, the structural and the electronic properties of these reactive species are helpful to understand their biological or chemical roles of catalytic activities. As mentioned above, dioxygen may be bound to the metal center through either end-on or side-on approach. According to the data listed in Table 2, the DFT energetic results suggested that both side-on PFe III -O 2 and end-on PFe III -O 2 have the S=0 ground state. The side-on PMn III O 2 has an S=3/2 ground state, while the end-on PMn III -O 2 has an S=5/2 ground state. Additionally, the end-on PCo III -O 2 has an S=1/2 ground state. The oxidative manganese (IV) intermediates were reported to include either hydroxo or oxo ligand. The high-valent iron(IV)-oxo species have been proposed as an oxidant intermediate in the C-H abstraction reaction. As shown in Table 3, PFe IV O was calculated to have an S=1 ground state and an S=2 active state. This intermediate had a high spin (S=2) iron(IV)-oxo unit with a double bond character between iron center and oxygen atom. In contrast, PMn IV O had an S=1/2 ground state with three unpaired electrons distributed between manganese and oxygen atom in a ratio of 1:2. The active state had a higher energy level (68.26 kcal.mol −1 ) than the ground state. Based on Shaik's two-state theory [68], the high spin state of PFe IV O was assumed to have a higher catalytic reactivity in the C-H oxidation. Our energetic calculations found that PCo IV O had an S=3/2 ground state and an S=5/2 active state. These calculated energetic results demonstrate reasonable spin sate for the high-valent species. PMn III OH species was reported to have a similar hydrogen abstraction capability as compared to PMn IV =O [69]. As the reductant of high-valent species, PFe III OH was predicted to have an S=3/2 ground state, which was different from that of PFeO III H reported in the literature [70]. Furthermore, Catalysts 2020, 10, 224

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PMn III OH was found with a high-spin ground state (S=2). However, PCo III OH was shown with a low-spin ground state (S=0).

The Geometric Structure
To understand the specific structural features, the geometric structure of the ground state intermediates was optimized to confirm the ground state of intermediates. The geometric structure model of intermediates is shown in Figure 2. The calculated geometry parameters are recorded in Figure S1. The data of C m -C α , C α -C β , C α -C β, and C α -N obtained from PFe II species agreed well with those parameters reported in the crystal structure [71]. The Fe-N bond length was calculated to be 1.997 Å, which is close to that of 2.003 Å reported by Rauk [72]. Typically, the Fe II was set in plane of the porphyrin. Thus, these calculated geometric parameters of PFe II are consistent with experimental values obtained from crystal structures.

The Geometric Structure
To understand the specific structural features, the geometric structure of the ground state intermediates was optimized to confirm the ground state of intermediates. The geometric structure model of intermediates is shown in Figure 2. The calculated geometry parameters are recorded in Figure S1. The data of Cm-Cα, Cα-Cβ, Cα-Cβ, and Cα-N obtained from PFe II species agreed well with those parameters reported in the crystal structure [71]. The Fe-N bond length was calculated to be 1.997 Å, which is close to that of 2.003 Å reported by Rauk [72]. Typically, the Fe II was set in plane of the porphyrin. Thus, these calculated geometric parameters of PFe II are consistent with experimental values obtained from crystal structures.  Figure S2. The bond length of Fe-Cl in PFe III Cl was 2.224 Å (exp. 2.221 Å) and Fe-N bond was 2.213 Å (exp. 2.087 Å). These calculated bond lengths were consistent with experimental data [73]. The degree of ∠NαFeNβ was 148.8°, which indicated that Fe atom was stretched out of the plane defined by four N atoms toward the axial chloride atom. As compared to PFe II , Fe-N bond distance in PFe III Cl was elongated by about 0.2 Å. For PMn III Cl, Mn-N bond length was 2.002 Å and the axial Mn-Cl distance was 2.297 Å. Thus, Mn atom was out of the plane by 0.16 Å [74]. Mn-N bond had a length of 1.965 Å, which was slightly longer than the experimental value of 1.947 Å [75]. In the model of PCo III Cl, the calculated Co-N bond length was 2.006 Å, which was shorter than both Mn-N and Fe-N bonds. The C-C bond length was comparable with that of the low-spin cobalt porphyrin reported by the Scheidt group [76]. Thus, our calculated ground states of these complexes were in great agreement with their crystal structures.
The geometric structure parameters of PM III O2 were compared with the experimental data to confirm the ground state. As shown in Figure S3 Figure S2. The bond length of Fe-Cl in PFe III Cl was 2.224 Å (exp. 2.221 Å) and Fe-N bond was 2.213 Å (exp. 2.087 Å). These calculated bond lengths were consistent with experimental data [73]. The degree of ∠N α FeN β was 148.8 • , which indicated that Fe atom was stretched out of the plane defined by four N atoms toward the axial chloride atom. As compared to PFe II , Fe-N bond distance in PFe III Cl was elongated by about 0.2 Å. For PMn III Cl, Mn-N bond length was 2.002 Å and the axial Mn-Cl distance was 2.297 Å. Thus, Mn atom was out of the plane by 0.16 Å [74]. Mn-N bond had a length of 1.965 Å, which was slightly longer than the experimental value of 1.947 Å [75]. In the model of PCo III Cl, the calculated Co-N bond length was 2.006 Å, which was shorter than both Mn-N and Fe-N bonds. The C-C bond length was comparable with that of the low-spin cobalt porphyrin reported by the Scheidt group [76]. Thus, our calculated ground states of these complexes were in great agreement with their crystal structures.
The geometric structure parameters of PM III O 2 were compared with the experimental data to confirm the ground state. As shown in Figure S3    PFe III OH (1.740 Å) or PCo III OH (1.850 Å). We expected that a longer M-O bond can facilitate the transfer of active oxygen. In addition, the angle of Fe-O-H was 105.5° in PFe III OH, which is slightly smaller than those of Mn-O-H and Co-O-H. To the best of our knowledge, PFe III OH was considered to react with alkane radical and to form Fe-O-C in the OH rebound step. The relative smaller M-O-H angle is likely to facilitate the combination of PFe III OH and alkane radical.

Mulliken Charge
To explore the dedicate structure of intermediates, the Mulliken charge of these metalloporphyrins was also analyzed (see Figure 5A). Interestingly, for all these complexes, the metal center is the most positive site, while N atoms are present with the most negative charges. Additionally, no great difference was observed in all H and C atoms from these metalloporphyrins. Specifically, the charge distributed on Fe, Mn, and Co atom was 1.02, 1.276, and 0.846, respectively. Thus, a more positive charge was observed on Mn III than Fe III and Co III cations. For negative change on N atoms, those N atoms from Mn III porphyrin had slightly lower negative charge than those present in Fe and Co porphyrins. The charge distribution property of these metalloporphyrins with chloride as axial ligand is similar to the order of that derived from metalloporphyrins without chloride ligand. The metal center and N atoms in PMn III Cl complex have the highest positive charge and mostly negative charge, respectively. Furthermore, the axial Cl ligand in PMn III Cl complex also show much negative charge (−0.5), which had a decreased effect on the charge of Co II ion. We presumed that the electronic structure can greatly influence the catalytic reactivity, because these metal centers are the active sites for the oxygen absorption and activation. Based on our Mulliken charge distribution results, we concluded that PMn II was much easier to combine with molecular oxygen than Fe and Co porphyrins, due to the presence of most positive charge on Mn center.
With the incorporation of oxygen on metal centers, it is clearly observed that Mulliken charges distribution in PM III -O 2 complexes have been greatly changed as compared to those without oxygen. Furthermore, the charge on end-on PMn III -O 2 complex was different from metal centers in PFe III O 2 -endon and PCo III O 2 -endon adducts (see Figure 5B). Typically, Mn center has a slightly higher positive charge than Fe and Co Centers. The oxygen located in β positions also demonstrate certain differences in the negative charge. In contrast, the negative charge of oxygen atoms in α position show little difference. Additionally, atoms of H m , C β , and H presented in the end-on PMn III -O 2 complex have much lower negative charge than those presented in the other PM III -O 2 complexes.
Mulliken charges on PM IV =O and PM III OH complexes are shown in Figure 5C. All metal centers have the most positive charge. In addition, we can see that the charge on Co IV ion was lower than that of Fe IV and Mn IV ions for high valent species. The charge on O atom was −0.508 |e| for PFe IV  show much negative charge (−0.5), which had a decreased effect on the charge of Co II ion. We presumed that the electronic structure can greatly influence the catalytic reactivity, because these metal centers are the active sites for the oxygen absorption and activation. Based on our Mulliken charge distribution results, we concluded that PMn II was much easier to combine with molecular oxygen than Fe and Co porphyrins, due to the presence of most positive charge on Mn center. With the incorporation of oxygen on metal centers, it is clearly observed that Mulliken charges distribution in PM III -O2 complexes have been greatly changed as compared to those without oxygen. Furthermore, the charge on end-on PMn III -O2 complex was different from metal centers in PFe III O2endon and PCo III O2-endon adducts (see Figure 5B). Typically, Mn center has a slightly higher positive charge than Fe and Co Centers. The oxygen located in β positions also demonstrate certain differences For all hydroxy species, O atoms have more negative charge than these high valent species (PM IV O). Indeed, PFe III OH was considered to combine with alkane radical in the OH radical rebound Catalysts 2020, 10, 224 9 of 17 step. The more negative charge on O can promote the combination of iron-hydroxo species with alkane radical. The O atom of PMn III OH is more negative than that of PFe III OH and PCo III OH. Previously, the iron-hydroperoxo species was assumed to be a sluggish oxidant. The oxidation ability of the intermediate cannot compete with that of high-valent iron(IV)-oxo species, while both iron-oxo and iron-hydroperoxo species have been recently proposed as oxidants in cytochrome P450. The O atom of PFe III OH is more negative than that in PFe IV O, inferring that Fe III OH was expected to be a stronger nucleophilic agent.

Frontier Molecular Orbitals
The bonding properties of metalloporphyrins are important to understand the nature of catalytic process. As shown in Figure 6, HOMO of PFe II was mainly constituted by Fe-dxz orbital, while LUMO was made up by Fe-dz 2 orbital. In fact, Fe-dz 2 orbital protruded out of porphyrin surface, which was therefore stereochemically active. In addition, 92.79% of HOMO in PMn II complex was dxy orbital. Unlike Fe center in PFe II , Mn metal was located within porphyrin plane, exhibiting less stereochemical activity than typical dz 2 orbital. Frontier molecular orbital (FMO) of PCo II was active in stereochemistry, which is similar to that of PFe II . However, PCo II energy levels of FMO were lower than those of PFe II and PMn II . Indeed, LUMO played an important role with respect to the activation of dioxygen. Once oxygen was coordinated to central iron, oxygen was considered to be activated. The LUMO in these complexes served as an electron acceptor to accept electron from HOMO of oxidant. The lower E LUMO reduced FMO energy gap between metalloporphyrin and molecular oxygen, which is favorable in the electron transfer between the catalyst and the oxidant. FMO analysis revealed that PFe II and PCo II were more stereochemically favorable than PMn II in the activation of dioxygen. However, PCo II was considered to be the most advantageous in orbital energy. For PFe III Cl, the LUMO was made up with Fe-dxy orbital, while PMn III Cl consisted of Mn-dx 2 -z 2 orbital. Both HOMOs of PFe III Cl and PMn III Cl were admixed with Cl-pz orbital to form the hybrid dz 2 -pz orbital that is much less stereochemically active. The axial chloride lowered energy level of HOMO and LUMO for PFe III Cl as compared with their counterparts. In contrast to the unligated oxidation, oxidation may occur under the HOMO control approach.
The relative extent of iron-porphyrin interactions can be qualitatively evaluated through spin population and orbital contribution analyses. As shown in Figure 7, the nature of ground state of ferrous ion critically depended upon the energy of d z 2 orbital relative to those of d xz and d yz orbitals.
For most of porphyrin derivatives, the ground state was 3 A 2g , which was strongly perturbed by the closely lying 3 E g excited state. This strong mixing with spin-orbit coupling explained the large orbital contribution to magnetic susceptibility of these complexes. A small axial perturbation could induce a reversal of ground state with corresponding inversion of magnetic anisotropy. This was promoted by the back-bonding between the filled dxz orbital of heme-iron and the empty p orbital of carbine. The manganese (IV) species with a Mn IV OH group had a higher redox potential. A ligand σ* back bonding interaction existed only in the side-on complexes.
The characteristics of frontier molecular orbital were greatly associated with the properties of catalytic intermediates. Such a state was interpreted in term of a molecular orbital. As shown in Figure 8, The HOMO of S=1 PFe IV O was consisted of dxy orbital and O-py orbital, in which they interacted to form π orbital. In this case, π orbital of PFe IV O attacks the C-H bond, and the attack orientation is near to 90 • (perpendicularly). In general, dz 2 is a σ *-type orbital, but the S=2 Fe IV =O intermediate provides occupied and unoccupied π FMOs. These have different orientation dependencies, providing an active site flexibility in using this orientation to control the reactivity. Whereas PMn IV =O species provides the occupied π FMOs, PCo IV =O complex gives unoccupied σ FMOs.
the LUMO was made up with Fe-dxy orbital, while PMn III Cl consisted of Mn-dx 2 -z 2 orbital. Both HOMOs of PFe III Cl and PMn III Cl were admixed with Cl-pz orbital to form the hybrid dz 2 -pz orbital that is much less stereochemically active. The axial chloride lowered energy level of HOMO and LUMO for PFe III Cl as compared with their counterparts. In contrast to the unligated oxidation, oxidation may occur under the HOMO control approach. The relative extent of iron-porphyrin interactions can be qualitatively evaluated through spin population and orbital contribution analyses. As shown in Figure 7, the nature of ground state of ferrous ion critically depended upon the energy of dz 2 orbital relative to those of dxz and dyz orbitals. For most of porphyrin derivatives, the ground state was 3 A2g, which was strongly perturbed by the closely lying 3 Eg excited state. This strong mixing with spin-orbit coupling explained the large orbital contribution to magnetic susceptibility of these complexes. A small axial perturbation could induce a reversal of ground state with corresponding inversion of magnetic anisotropy. This was promoted closely lying 3 Eg excited state. This strong mixing with spin-orbit coupling explained the large orbital contribution to magnetic susceptibility of these complexes. A small axial perturbation could induce a reversal of ground state with corresponding inversion of magnetic anisotropy. This was promoted by the back-bonding between the filled dxz orbital of heme-iron and the empty p orbital of carbine. The manganese (IV) species with a Mn IV OH group had a higher redox potential. A ligand σ* back bonding interaction existed only in the side-on complexes. The characteristics of frontier molecular orbital were greatly associated with the properties of catalytic intermediates. Such a state was interpreted in term of a molecular orbital. As shown in Figure 8, The HOMO of S=1 PFe IV O was consisted of dxy orbital and O-py orbital, in which they interacted to form π orbital. In this case, π orbital of PFe IV O attacks the C-H bond, and the attack orientation is near to 90° (perpendicularly). In general, dz 2 is a σ *-type orbital, but the S=2 Fe IV =O intermediate provides occupied and unoccupied π FMOs. These have different orientation dependencies, providing an active site flexibility in using this orientation to control the reactivity. Whereas PMn IV =O species provides the occupied π FMOs, PCo IV =O complex gives unoccupied σ FMOs.
As shown in Figure 8, LUMO of PFe III OH was consisted with Fe-dxz and O-px, to form the π *

Conclusions
To summarize, ground states of PM II (M=Fe, Mn, and Co) were determined by energy assessment and confirmed by experimental results. The geometric structure of intermediates was further analyzed to confirm the ground state. Mulliken charges suggested that non-ligated metalloporphyrin was favorable to activate dioxygen. Mn II showed higher activity to dioxygen than PFe II and PCo II . Our results also indicate that O atom of iron-hydroxo species (PFe III OH) carried more negative charge than that of high-valent species that showed the potential oxidant ability. Specifically, PCo III OH provided flexible orientation for C-H bond attack. Frontier molecular orbital analysis demonstrated As shown in Figure 8, LUMO of PFe III OH was consisted with Fe-dxz and O-px, to form the π * orbital of PFe III OH. The HOMO of PFe III OH was made up by Fe-dyz and O-py, generating the π orbital of PFe III OH. They provided the px,y characters, which is perpendicular to the Fe-O bond. PMn III OH was observed to σ bond with Mn-dx 2 -y 2 and O-p x orbitals, which provided a character for C-H bond attacking along with the Fe-O bond. Finally, for the PCo III OH, LUMO has a character of d z was dπ FMO that is composed of Co-pxz and O-p z , facilitating C-H bond attacked perpendicular to Co-O bond. The FMO of PCo III OH provided flexible orientation for C-H bond attack and it implied a potential oxidant for PCo III OH.

Conclusions
To summarize, ground states of PM II (M=Fe, Mn, and Co) were determined by energy assessment and confirmed by experimental results. The geometric structure of intermediates was further analyzed to confirm the ground state. Mulliken charges suggested that non-ligated metalloporphyrin was favorable to activate dioxygen. Mn II showed higher activity to dioxygen than PFe II and PCo II . Our results also indicate that O atom of iron-hydroxo species (PFe III OH) carried more negative charge than that of high-valent species that showed the potential oxidant ability. Specifically, PCo III OH provided flexible orientation for C-H bond attack. Frontier molecular orbital analysis demonstrated that non-ligated PM II facilitated activating the dioxygen. These metalloporphyrins provided the flexible orbital orientation that were beneficial to the adduct of dioxygen. The PFe IV O had two π and π * type orbitals for C-H bond attack that is perpendicular to Fe-O bond. PMn IV =O only had one π type orbital, which facilitated the C-H perpendicular attack. PCo IV =O might benefit to the C-H bond attack in the orientation than PFe IV O and PMn IV =O. PCo III OH exhibited a strong oxidant ability since the C-H bond provided the flexible orientation for C-H bond attack. Currently, research on the mechanism of C-H bond attacking by possible reactive metalloporphyrin intermediates is undergoing in our lab. These studies give novel insights into geometric and electronic structure properties of catalytically active sites, which are likely to provide new understanding of the selective redox roles of metalloporphyrins in biomimetic catalysis and the catalytic behavior of related metaloenzymes in biological processes.
Supplementary Materials: The following are available online at http://www.mdpi.com/2073-4344/10/2/224/s1, Figure S1: Geometric parameters of the ground state for PM II (*presents the experimental value), Figure S2: Geometric parameters of the ground state for PM III Cl (*presents the experimental value), Figure S3