Introduction

Nonheme mononuclear and dinuclear complexes are involved in many catalytic reactions such as C–H activation, oxygen transfer, alcohol oxidation, and deformylation reactions [1,2,3,4,5,6,7]. C–H bond activation in hydrocarbons is highly inert, and biomimetic species can provide a direct way to introduce functional groups, cost-effectively, and has high industrial applications [8,9,10]. C–H bond activation is inspired by models of CytP450 and Rieske dioxygenase and these hydroxylate unactivated C–H bonds with higher selectivity at fast rates [11, 12]. Selective functionalization of the C–H bond in organic compounds is a “grand challenge” in catalysis science [13,14,15,16,17,18]. To carry out selective C–H bond activation, many heme [19,20,21] and nonheme [22,23,24,25,26,27,28,29] iron-containing complexes have been used with dioxygen as an oxidant. Dioxygen (O2) is an ideal oxidant due to several reasons as it is abundant in nature, is a renewable chemical oxidant, has water as a byproduct, and is nontoxic at most of the conditions, and its reduction potential is more than sufficient to carry many chemical transformations [30,31,32,33,34,35]. Nonheme complexes with a tetradentate N-atom donor ligand having cis labile sites (FeN4) show great promise for selective C–H bond activation [36,37,38,39]. Iron is ubiquitous, has low toxicity, and can exist in multiple redox states making its chemistry interesting and acts as a key intermediate in many biotransformation reactions, occurring via C–H and O–H activation, including biological O2 activation [40,41,42,43,44,45].

A tetraamido macrocyclic ligand (TAML) activator is widely used in chemical and biological agents such as petroleum refining, water treatment, textiles, and cleaning [46]. TAML activators have about 10,000 turnovers per hour in many applications [47]. The TAML-coordinated metal species being environment friendly have been tested [48]. To investigate the catalytic properties, many experimental and theoretical studies such as Mossbauer, EPR, density functional theory (DFT), and transient- and steady-state kinetics have been used [39, 49, 50]. In the last two decades, the tetradentate TAML-ligated iron species becomes a popular oxidant to achieve an effective small biomimetic molecule of oxidizing enzymes for green oxidation chemistry [30, 51]. It has biological elements like C, H, N, O, and Fe and is devoid of toxic functionalities [52]. There are several Fe–TAML complexes such as mononuclear iron oxo/peroxo/superoxo/hydroperoxo as well as oxygen-bridged dinuclear species that are observed in the previous literature [50, 53,54,55,56]. Some of the species are also well characterized by X-rays and spectroscopic parameters [49, 50, 57]. These species are also important intermediates generated during various metal-mediated catalytic transformation reactions such as alkane hydroxylation, olefin epoxidation, and sulfoxidation [58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74] occurring via C–H bond activation. These reactions are also important in synthetic pharmaceutical [13] and biological processes such as medicine, photosystem II, and naphthalene dioxygenase [75, 76].

The growing interest in TAML-ligated iron species motivated us to explore structures and spin-state energetics of mononuclear oxo/peroxo/superoxo/hydroperoxo and oxygen-bridged dinuclear species as a possible oxidant in many catalytical transformation reactions. Here, we would like to underpin and compare electronic structures, bonding, magnetic interactions, and spin-state energetic aspects of Fe(III/IV/V)–O/O2 and Fe(IV)–μ-O1/O2–Fe(IV) species. By a study of structures and bonding of the species, we also like to comment on their reactivity.

Computational details

All calculations were carried out by using Gaussian09 programs [77]. In our earlier work, we have performed DFT calculations on iron species employing a bunch of functionals such as B3LYP, B3LYP-D2, wB97XD, B97D, M06-2X, OLYP, TPPSh, and MP2 methods [71, 73]. Among the tested functionals, B3LYP incorporating dispersion correction (B3LYP-D2 functional) was found to be superior in predicting the correct spin ground state of iron species [71, 73]. So here we have restricted geometry optimizations using only the B3LYP-D2 functional [78]. The LACVP basis set comprising the LanL2DZ–Los Alamos effective core potential for the iron [79,80,81] and a 6-31G [82] basis set for the other atoms (C, H, N, and O) have been employed for geometry optimization. The identification of the geometry that is located at the lowest point on the potential energy surface is made by frequency calculations which were performed on optimized geometry and confirmed by the absence of imaginary frequencies, and free-energy corrections were also found by frequency calculation. Single point energy calculations were made by using a TZVP [75, 83, 84] basis set on all atoms of the optimized geometries. For computing the solvation energies using acetonitrile as a solvent, the PCM solvation model was used. The quoted DFT energies are B3LYP-D2 solvation including free-energy corrections with the TZVP basis set at the temperature of 298.15 K. From the optimized geometries, structural parameters, vibrational wavenumbers, and other molecular properties like HOMO-LUMO and NBO were analyzed. The vibrational energy distribution analysis (VEDA) program was used to calculate the partial energy distribution (PED) [85], by using PED fundamental vibrational modes which were characterized. Theoretical and valuable information about intra- and intermolecular charge transfer (ICT) and conjugation and hyperconjugation of the molecular system [86, 87] is provided by natural bonding orbital (NBO) analysis. Using the Mulliken population analysis (MPA) method with the B3LYP-D2 functional, charges on the atoms of complexes were calculated. In the Gaussian09 fragment approach available which was employed to aid smooth convergence. In the diiron species, the magnetic exchange between both the iron centers is calculated by employing the following spin Hamiltonian:

$$ \hat{\boldsymbol{H}}=-\boldsymbol{J}\ {\mathbf{S}}_{\mathbf{1}}.{\mathbf{S}}_{\mathbf{2}} $$

Where J is the magnetic exchange coupling constant; positive J values show the ferromagnetic coupling while negative J values show the antiferromagnetic coupling. Noodleman’s broken symmetry is used to compute the magnetic exchange coupling (J) constant [88, 89]. A common notation of multAspin state is used throughout where the mult, A, and spin state denote the total multiplicity, the species, and the possible spin states, respectively.

Results and discussion

Here, we will thoroughly discuss the electronic structures, bonding nature, and spin state energetics of biomimetic [FeIII(TAML)]− (species I) and its possible mononuclear derivatives end-on [(TAML)FeIV–ƞ1–O2]•− (species II), side-on [(TAML)FeIV–(ƞ2–O2)]2− (species IIIa), [(TAML)FeIII–(ƞ2–O2)]3− (species IIIb), [(TAML)FeIV–OOH] − (species IV), [(TAML)FeIV–O]2− species (V), and [(TAML)FeV–O] − species (VI) and dinuclear derivatives [(TAML)FeIV–μO–(TAML)FeIV]2− (species VII) and [(TAML)FeIV–μO2–FeIV(TAML)]2− (species VIII) followed by a comparative study.

Electronic structure and energetics of [FeIII(TAML)]− (species I)

It is a tetraamido macrocyclic species containing the iron ion, which is a very efficient and selective catalyst [22,23,24,25,26,27,28,29]. In species I (See Scheme 1), iron is surrounded by four deprotonated N-amido ligands and is almost square planar species [39]. This is well characterized by X-ray, UV-vis, EPR, and EXAFS [39]. We have optimized species I on the surfaces of S = 5/2 (sextet; 6Ihs) and S = 3/2 (quartet; 4Iis), and our DFT calculations reveal that the quartet state is computed to be the ground state and the sextet state lies at 89.0 kJ/mol higher in energy (see Fig. 1). This ground state is also supported by the experimental report [39]. The optimized structure of the ground state and the corresponding spin density plot are shown in Fig. 2a,b. The computed Fe–Navg bond length of the ground state is found to be 1.865 Å, and this is in good agreement with the X-ray structure (see Table S1 of ESI) [39]. A spin density of ρ = 2.663 is located at the iron center (see Fig. 2b and Table S2 of ESI). The eigenvalue plot of the ground state is shown in Fig. S1 of ESI, and the electronic configuration at the metal center is found to be (dyz)2, (dxz)1, (dz2)1, (dxy,)1, and (dx2-y2)0. The HOMO-LUMO gap of the ground state is 4.446 eV (see Fig. 2c). By the reaction of [FeIII(TAML)]− species with dioxygen, it can form mononuclear end-on {[(TAML)FeIV–ƞ1–O2]•−}/side-on species {[(TAML)FeIII/IV–ƞ2–O2]3/2−} or dinuclear μ-oxo{[(TAMLFeIV)2(μ-oxo)]2−}/peroxo {[(TAMLFeIV)2(peroxo(O2)]2−}bridged species which can also consequently form iron(IV/V)-oxo species [55]. After reactions of species I with dioxygen, the iron metal center is no longer in the plane but it gets out of the plane due to repulsion between charges of the coordinated nitrogen atoms and the axial ligands that forces the iron atom out of the plane. The distance of the shift of iron metal out of the plane depends upon the elastic force that drives the iron metal back into the plane [39].

Scheme 1
scheme 1

A schematic diagram of tetraamido macrocyclic ligand-coordinated iron [FeIII(TAML)]− species [39, 50]

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Fig. 1
figure 1

B3LYP-D2-computed relative energies (in kJ/mol) of species I–VIII

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Fig. 2
figure 2

a B3LYP-D2-optimized structure of 4Iis (bond length in Å) and b its spin density plot and c HOMO-LUMO frontier molecular orbitals of 4Iis

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Electronic structure and energetics of end-on [(TAML)FeIV–ƞ1–O2]•− (species II)

When the binding mode of oxygen is ƞ1, it can generate end-on iron superoxo species [90, 91]. Five spin interactions can be possible due to the presence of four unpaired electrons at the iron center and one unpaired electron at distal oxygen (see Scheme S1 of ESI). We have optimized all spin states of this species except 6IIhs (due to the spin convergence issue). The antiferromagnetically coupled intermediate spin state (2IIis) is found to be the ground state with the 4IIhs, 4IIis, and 2IIis lying at 23.8, 77.7, and 13.2 kJ/mol, respectively (see Table S3 of ESI), and the ground state is also inconsistent with similar species in the previous report [56]. The optimized structure and spin density plot of the ground state are shown in Fig. 3a,b. The average Fe–Navg bond of species II is larger than that of species I by 0.013 Å. The Fe–O1 and O1–O2 bond lengths are computed to be 2.173 Å and 1.296 Å, respectively. The O1–O2 bond length is in agreement with the other metal superoxo species that are ca. 1.2–1.3 Å [91,92,93,94,95,96]. The stretching frequencies of the Fe–O and O–O bonds are computed to be v314 cm−1 and v1200 cm−1 that are also in agreement with the calculated stretching frequency of other superoxide species [91,92,93,94,95]. The iron center of this species is found to be shifted by 0.08 Å (see Table S4 of ESI) above the plane along with the axial bond concerning species I, and this is due to repulsion between charges of equatorial ligated nitrogen atoms and axial superoxo ligands that forces the iron atom out of the plane and suggested species II is relatively less planar. The HOMO-LUMO gap of species II is 1.524 eV (see Fig. 3c), and the gap is smaller than that of species I. The eigenvalue plot of the ground state is shown in Fig. 4, and the electronic configuration at the metal center is found to be (dxz)2, (dyz)1, (dxy,)1, (dz2)0, and (dx2-y2)0. The spin density values at iron and distal oxygen centers are computed to be 2.586 and − 0.881 suggesting that the presence of antiferromagnetic coupling between them and a significant spin density at distal oxygen can activate the C–H and O–H bonds [56, 61, 96].

Fig. 3
figure 3

a B3LYP-D2-optimized structure (bond length in Å) of 2IIis, b its spin density plot, and c the HOMO-LUMO frontier molecular orbitals of 2IIis

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Fig. 4
figure 4

Computed eigenvalue plot incorporating energies computed for d-based orbitals for alpha and beta spin corresponding to the ground state (2IIis) (energies are given in eV)

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Electronic structure and energetics of side-on [(TAML)FeIV–(ƞ2–O2)]2− (species IIIa) and [(TAML)FeIII–(ƞ2–O2)]3− (species IIIb)

When the binding mode of oxygen is ƞ2, the side-on species can be formed [95, 96]. Similar to species II, we have tried to optimize all three possible spin surfaces (such as 5IIIahs, 3IIIais, and 1IIIals) of species III but here we have got only one optimization, i.e., the low spin surface (see details in Fig. S2 of ESI). So, here we have also taken side-on species with oxidation state + 3 at the iron center and attempted to optimize all three possible spin states (6IIIbhs, 4IIIbis, and 2IIIbls) for species IIIb. Our DFT calculations predicted that the sextet spin state (6IIIbhs) is found to be the ground state with 4IIIbis and 2IIIbls lying at 23.0 kJ/mol and 47.9 kJ/mol, respectively. The optimized structure and spin density plot of the ground state are shown in Fig. 5a,b. The Fe–Navg bond is computed to be 2.093 Å, and this is higher than that of species II. The computed Fe–O1 and Fe–O2 bond lengths are 2.009 Å and 1.994 Å, respectively, which are also observed in similar architecture [97]. The computed parameters suggest that the oxygen binds with iron symmetrically. The iron–oxygen bond length is found to be smaller while the O1–O2 bond length is slightly higher than the lengths of end-on species II, and these are also confirmed by the computed stretching frequency of Fe–O (v448 cm−1) and O–O (v821 cm−1) bonds [94]. The computed bond angle of O1–Fe–O2 is found to be 45.1° indicating the pseudo-square pyramidal geometry of species IIIb. The shift in the position of the iron atom is computed to be 0.72 Å (see Table S4 of ESI). The spin density value of 3.887 is located at the iron center, and both the oxygen atoms occupied similar spin density that indicates a symmetrical binding mode (see Fig. 5b). The eigenvalue plot of the ground state is shown in Fig. S4 of ESI. The electronic configuration on Fe metal is found to be (dxy)1, (dxz)1, (dyz)1, (dz2)1, and (dx2-y2)1. The HOMO-LUMO gap of species IIIb is calculated to be 3.698 eV (see Fig. 5c), and this is greater than that of species II which may indicate the possibility of lesser electron transfer compared to that in species II. The significant spin densities at both the oxygen atoms can participate in catalytic reactions [61,62,63,64]. The NBO plots of the ground state show that orbital contributions between both the oxygen atoms and iron center are involved in making the σ-bond confirming the presence of the σ-bond between both the oxygen atoms and iron center (see Fig. S5 of ESI).

Fig. 5
figure 5

a B3LYP-D2-optimized structure (bond length in Å) of 6IIIbhs, b its spin density plot, and c the HOMO-LUMO frontier molecular orbitals of 6IIIbhs

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Electronic structure and energetics of hydroperoxo [(TAML)FeIV–OOH]− (species IV)

After the abstraction of hydrogen from organic substrates by superoxo/peroxo species, hydroperoxo species can be formed. Similar to the above species, there are three possible spin states of species IV, in which intermediate spin (S = 1) is found to be the ground state, and other spin states, S = 2 and S = 0, lie at 49.1 and 77.9 kJ/mol higher in energy, respectively. The optimized structure and spin density plot of the ground state are shown in Fig. 6. The Fe–O1 and O1–O2 bond lengths are computed to be 1.889 Å and 1.486 Å, respectively. The Fe–O1 bond length decreases while the O1–O2 bond length increases from superoxo species II. The computed shift in the position of the iron atom is computed to be 0.19 Å. The decrease in the Fe–O1 bond length is due to the overlap between d-orbital of Fe and p-orbital of the oxygen atom. The HOMO-LUMO gap also decreases to 0.059 eV compared to that of species II and IIIb (see Fig. S6 of ESI). The NBO analysis shows that iron dz2 orbital has a 20.1% orbital contribution whereas pz orbital of oxygen has a 79.9% orbital contribution (see the NBO plot in Fig. S7 of ESI). There is a reduction of spin density at the oxygen atoms. The eigenvalue plot is shown in Fig. 7. The electronic configuration at the metal center is found to be (dxz)2, (dyz)1, (dxy,)1, (dz2)0, and (dx2-y2)0. The stretching frequency of the Fe–O and O–O bond is computed to be v420 cm−1 and v823 cm−1, respectively, and a decrease in O–O stretching frequency by v373 cm−1 compared to that of end-on [(TAML)FeIV-ƞ1-O2]•− species supported an increase in the O1–O2 bond length.

Fig. 6
figure 6

a B3LYP-D2-optimized structure (bond length in Å) of 3IVis and b its spin density plot

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Fig. 7
figure 7

Computed eigenvalue plot incorporating energies computed for d-based orbitals for alpha and beta spin corresponding to the ground state (3IVis) (energies are given in eV)

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Electronic structure and spin energetics of [(TAML)FeIV–O]2− (species V)

The first direct evidence for the generation of a nonheme FeIV–O complex was reported by Grapperhaus et al. at the start of this millennium [98], and this is well characterized by X-ray and spectroscopy. Nonheme FeIV–O species became a popular active oxidant that can show reactivity towards C–H, O–H, N–H, oxygen atom transfer reactions, etc. in detail [68, 69]. Here, we have also optimized high (quintet, S = 2), intermediate (triplet, S = 1), and low spin (singlet, S = 1) states of the species, and our DFT calculations reveal that the triplet state is found to be the ground state with the quintet and singlet states lying at 86.4 kJ/mol and 112.6 kJ/mol higher in energy, respectively (see Fig. 1) and this ground state is inconsistent with earlier experimental and theoretical reports [54, 65,66,67,68]. The optimized structure and spin density plot of the ground state are shown in Fig. 8a,b. The calculated Fe–Navg bond length is 1.929 Å, higher than that of species I (see Table S1 of ESI). The Fe–O bond length is found to be 1.653 Å, shorter than that of the other spin surface quintet and singlet states (see Table S1 of ESI), and this shorter bond length is due to the formation of π bond between iron and oxygen revealing a double-bond character (see Scheme S2 of ESI). The Fe–O bond length matches with previous experimental and theoretical studies [53].

Fig. 8
figure 8

a B3LYP-D2-optimized structure (bond length in Å) of 3Vis, b its spin density plot, and c computed NBO plots of 3Vis

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The orbital contribution of iron dz2 (36.6%) and oxygen pz (63.4%) suggests the formation of the σ-bond (see Fig. 8c). However, additional orbital contributions between iron and oxygen atoms show the formation of the π-bond and unfold the presence of a double-bond character between them. The electronic configuration of the ground state is computed to be (dxy)2, (dyz)1, (dxz,)1, (dz2)0, and (dx2-y2)0 (see Fig. 9), also supporting the formation of the π-bond between dyz and p-orbital of the oxygen (see Fig. 8c). A similar electronic configuration is also found with other iron(IV)-oxo species [53]. Here, the dx2-y2 orbital has higher energy than the dz2 due to the strong equatorial ligand field of the TAML ligand. The stretching frequency of the Fe–O bond is found to be 880 cm−1 revealing the strength of the bond. The computed Fe–Navg bond length is found to be 1.971 Å, and this is longer than that of species I. The iron center of this species is also shifted towards the z-axis by 0.35 Å (see Table S3 of ESI). The computed HOMO-LUMO gap is 3.605 eV (see Fig. 10a). The computed spin density value of 1.347 is located at the iron center and the ferryl oxygen has also acquired spin density (ρ = 0.584). The coordinated nitrogen atoms also gained some spin density via electron delocalization. A significant spin density at the oxygen atom can activate the C–H/O–H bond of aliphatic/aromatic hydrocarbons [71,72,73,74].

Fig. 9
figure 9

Computed eigenvalue plot incorporating energies computed for d-based orbitals for alpha and beta spin corresponding to the ground state (5Vis) (energies are given in eV)

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Fig. 10
figure 10

The HOMO-LUMO frontier molecular orbitals of a species V and b species VI

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Electronic structure and spin energetics of [(TAML)FeV–O]− species (VI)

One electron oxidation of species V can produce the [(TAML)FeV–O]− (species VI), and this species with sufficient thermal stability for extensive spectroscopic characterization was generated by de Oliveira et al. [50]. In our previous study, we have found that the low spin state (S = 1/2) of species VI is the ground state with the high spin lying at 5.2 kJ/mol higher in energy [99]. The computed Fe–O bond length is found to be smaller than that of species V (see Table S1 of ESI), and this is due to the increment in the double-bond character between the iron center and oxygen atom. The computed HOMO-LUMO gap is 1.423 eV, smaller than that of species V (see Fig. 10). The shift in the position of the iron atom is computed to be 0.40 Å. The redox potential change upon the oxidation at the iron center can also increase the reactivity of species (VI) [71, 100]. From the NBO calculations, we see that iron dz2 (39.2%) which is greater than species VI and oxygen pz (60.8%) suggests a stronger bond between iron and oxygen than species V (see Fig. 8c and S8 of ESI). A spin density at the oxygen atom can help in C–H/O–H bond activation as well as in olefin epoxidation/sulfoxidation [50, 101].

Electronic structure and energetics of [(TAML)FeIV–μO–(TAML)FeIV]2− (species VII)

The well-characterized [(TAML)FeV–O]− species can react with FeIII(TAML)]־ species I to generate μ-oxo dinuclear derivative [(TAML)FeIV–μO–FeIV(TAML)]2− (species VII) [50, 53]. This μ-oxo-bridged dinuclear species is also well characterized in previous studies [55]. The dimer [(TAML)FeIV–μO–FeIV(TAML)] (species VII) possesses the same ligand, and one can assume that both the iron centers are likely to have an identical spin on both the iron centers. There are five possible spin states such as 9VIIhs, 1VIIhs, 5VIIis, 1VIIis, and 1VIIls for species VII, and the schematically electronic interactions for each of the iron centers are shown in Table 1. We have optimized all five spin surfaces of species VII, and our DFT calculations predicted that the intermediate spin state (1VIIis) with antiferromagnetic coupling between both the iron centers is found to be the ground state and other spin surfaces such as 9VIIhs, 1VIIhs, 5VIIis, and 1VIIls lie at 68.8, 82.4, 3.3, and 186.1 kJ/mol higher in energy, respectively. This ground state is also supported by experimental observation [55]. The optimized structure and spin density plot of the ground state (1VIIis) and 5VIIis are shown in Fig. 11. The Fe1/Fe2–Navg bond lengths are found to be 1.913 Å and 1.895 Å which are greater than those of species I, and these are also in agreement with the experimental data [55]. The bond angle of Fe–O–Fe is found to be 160.5°, and this bending around the bridged oxygen atom is aroused due to the ligated nitrogen atom donating the electron density to the empty dz2 which overlaps to the p-orbital of the oxygen atom, and this also includes the double-bond formation between iron and oxygen atoms.

Table 1 Possible spin states of [(TAML)FeIV–μO–FeIV(TAML)]2− species
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Fig. 11
figure 11

a B3LYP-D2-optimized structure (bond length in Å) of 1VIIis and its b spin density plot and c optimized structure (bond length in Å) of 5VIIis and d its spin density plot

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Our calculations also reveal that both the iron centers have equivalent formal charges, but there is a significant difference in Fe–O bond lengths. Computed Fe1–μ-oxo and Fe2–μ-oxo bond distances are found to be 1.835 Å and 1.711 Å, respectively, and these are also observed on similar structures in previous reports [73]. Selected bond length and spin density values are shown in Tables S1 and S2 of ESI.

The iron atom (Fe2) possessing a beta electron (the negative spin density in Fig. 11b) has a shorter Fe–O bond length compared to the other Fe atom. From the NBO analysis, σ-bonding effects are also observed between the iron Fe1 (19%) and μ-oxo (81%) whereas the Fe2–μ-oxo possesses the additional π-bond character as the Fe2 (25.9%) and μ-oxo (74.1%) orbital contribution is detected (see Fig. 12). Spin density on both the iron centers is found to be 2.351 and − 1.524, respectively. There is also a significant electron density found at the oxygen atom. From the earlier report, di-μ-oxo-diiron(VII) species and two μ-oxo groups yield a symmetric Fe(IV)-oxo environment [102]. Here, our calculations suggest an asymmetric environment with one shorter and other longer Fe–O bond lengths due to the presence of one μ-oxo group [73]. The Fe–Fe bond distance is 3.495 Å. From Table S4 of ESI, we see that the displacements along the z-axis are − 0.41 Å and 0.42 Å, and these opposite signs indicate that both iron centers are approaching towards each other. Nitrogen atoms coordinated to the iron atom gain significant electron density via the electron delocalization mechanism. The bridged oxygen atom possesses a significant electron density that can help in C–H/O–H bond activation [72, 73]. The eigenvalue plot is shown in Fig. 13, and both the Fe atoms have the similar electronic configuration of (dxy)2, (dyz)1, (dxz,)1, (dz2)0, and (dx2-y2)0 with alpha electrons in dxz and dyz at the Fe1 center and beta electrons in dxz and dyz at the Fe2 center (see Fig. 13). The dz2 and dx2-y2 are unoccupied due to being much higher in energy. The HOMO-LUMO gap is 0.939 eV (see Fig. 14a).

Fig. 12
figure 12

Computed NBO plots of the ground state of species VII

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Fig. 13
figure 13

Computed eigenvalue plot incorporating energies computed for d-based orbitals for alpha and beta spin corresponding to the ground state (1VIIis) (energies are given in eV)

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Fig. 14
figure 14

The HOMO-LUMO frontier molecular orbitals of species VII (1VIIis) and species VIII (5VIIIis)

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The computed magnetic exchange coupling constant is found to be J = − 88.82 cm−1, and this shows that antiferromagnetic coupling occurs between both the iron centers. The stretching frequencies for Fe1–μO and Fe2–μO are ʋ349 cm−1 and ʋ766 cm−1 respectively, and these frequencies are supported by the iron–μ-oxo bond distances.

Electronic structure and spin energetics of [(TAML)FeIV–O–O–FeIV(TAML)]2− (species VIII)

When they react in 1:2 of species I and dioxygen, oxygen-bridged dinuclear (μ–1,2-peroxo) species ([(TAML)FeIV–O–O–FeIV(TAML)]2− (species VIII) can be generated [55]. Similar to species VII, we have also optimized five possible spin states (see Table S6 of ESI) and our DFT calculations show that the 5VIIIis is found to be the ground state with 9VIIIhs, 1VIIIis, and 1VIIIls lying at 36.2, 13.0, 12.9, and 356.3 kJ/mol higher in energy, respectively. The optimized structure and spin density plot of the 5VIIIis (ground state) and the corresponding spin state (1VIIIis) are shown in Fig. 15. The calculated Fe1–μO1 and Fe2–μO2 bond lengths of the 5VIIIis state are found to be 2.124 Å and 2.127 Å, respectively, and are higher than the corresponding bond lengths of species IVIIis. The O1–O2 bond length is 1.334 Å, in agreement with that of the other –1,2-peroxo species [103], and the computed stretching frequency for the O–O bond is v1050 cm−1 corresponding to the formation of the peroxo linkage. The same stretching frequencies (v258 cm−1) are found for both Fe1–O1 and Fe2–O2 bonds, smaller than those of the μ-oxo-bridged species, indicating that the Fe–O bond length is longer in μ–1,2-peroxo species and suggesting the presence of a single bond between both the iron–oxygen bonds (see Table S1 of ESI). The Fe1–Navg and Fe2–Navg bond distances are computed to be 1.882 Å and 1.883 Å, respectively. The spin density plot of the ground state shows that both the iron centers possess the same sign of spin density suggesting the presence of ferromagnetic coupling between iron centers, and this is also supported by the estimation of the magnetic exchange with the value of 777.44 cm−1, although the experimental magnetic exchange value of the species is not observed yet. The coordinated nitrogen atoms to the iron center also acquired electron density due to electron delocalization. The computed HOMO-LUMO gap is smaller than that of species VII (see Fig. 14b). Similar to species VII, here also, displacements along the z-axis have an opposite sign 0.04 Å and -0.07 Å— indicating that both iron centers are approaching towards each other, this displacement is smaller as compared to that of species VII. The eigenvalue plot also describes the electronic configurations around both the iron centers (see Fig. 16). It is also found that orbitals of both the Fe atoms are found to be at the same energy levels, and the electronic configuration is found to be (dxy)2, (dyz)1, (dxz,)1, (dz2)0, and (dx2-y2)0. The dz2 and dx2-y2 are unoccupied due to being much higher in energy. The cleavage of the peroxo linkage can generate [(TAML)FeIV–O]2− species V and [(TAML)FeV–O]− species VI. Significant electron densities are also located at both the bridged oxygen atoms which can activate C–H and O–H bonds of aliphatic and aromatic compounds [71, 73, 98]. The HOMO-LUMO gap is shown in Fig. 14b, and the gap in species VII is smaller than that in species VIII. NBO analysis shows 6.7% of Fe1–py and 93.3% of O–px and 6.7% of Fe2-py and 93.3% of O-px (see Fig. S9 of ESI). The contribution of the iron orbital is small as compared to that of the μ-oxo-bridged complex iron atom, and this may be due to the longer bond length and also the absence of the π-bond between Fe1/2 and μO1/2 as compared to Fe1–O1 and Fe2-O1 of μ-oxo-bridged species.

Fig. 15
figure 15

a B3LYP-D2-optimized structure (bond length in Å) of 5VIIIis and b its spin density plot and c optimized structure (bond length in Å) of 1VIIIis and d its spin density plot

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Fig. 16
figure 16

Computed eigenvalue plot incorporating energies computed for d-based orbitals for alpha and beta spin corresponding to the ground state (5VIIIis) (energies are given in eV)

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Comparative study

Species formed after the reactions depend upon the binding modes of dioxygen either ƞ1 (end-on species) or ƞ2 (side-on species). Here, species I–VI are mononuclear whereas species VII–VIII are bridged dinuclear. Our computed parameters also show that the Fe1–O1 bond distance of species II (2.173 Å) is longer than that of species III (1.994 Å), whereas the O1–O2 bond length of species II (1.321 Å) is smaller than that of species III (1.537 Å) due to both the oxygen atoms coordinated to the iron center in species III, and these are also supported by computed stretching frequencies. The shifting of the iron center of species II (0.08 Å) out of the plane is found to be smaller than that of species III (0.72 Å), due to repulsion between charges of the coordinated atoms of both the oxygen atoms that forces the iron atom out of the plane which is comparatively more in species III. The HOMO-LUMO gap of species II (1.524 eV) is computed to be smaller than that of species III (3.698 eV). The Fe–O1 bond distance of species IV (1.889 Å) is smaller than that of species II (2.173 Å) and species III (1.994 Å) which may be due to being protonated at the distal oxygen atom (–OOH). The HOMO-LUMO gap in species IV (0.059 eV) is smaller than that in species II and species III. The shift of the iron atom out of the plane in species V (0.19 Å) is larger than that in species II (0.08 Å) but smaller than that in species III (0.72 eV).

In species V, the Fe–Navg (1.911 Å) and Fe–O (1.653 Å) bond lengths are longer than those in species VI (1.892 Å and 1.630 Å for Fe–Navg and Fe–O). The shift of the iron atom out of the plane in species VI (0.40 Å) is calculated to be larger than that in species V (0.35 Å), and this may be due to the reflection of higher charge at the iron center. The HOMO-LUMO gap of species V (3.605 eV) is larger than that of species VI (1.423 eV) indicating higher reactivity of species VI which is also observed in previous reports [53, 71, 104, 105]. From the NBO analysis of species V and species VI, we have observed that both species V and species VI have a double-bond character, In species VI, the iron atom has 39.2% contribution which is slightly greater than that in species V (36.6%) which indicates that the Fe–O bond has a more double-bond character in species VI than in species V.

In dinuclear species VII and VIII, the Fe1/Fe2–Navg computed bond distances (1.913 Å and 1.895 Å, respectively) are longer than the corresponding bond (1.882 Å and 1.883 Å, respectively) in species VIII, but iron–μ-oxo bond lengths (1.835 Å and 1.777 Å, respectively) of species VII are longer than iron–oxygen bonds (2.124 Å and 2.127 Å, respectively) of species VIII, and these are also supported by the computed stretching frequencies. From the NBO analysis of species VII, we have found that orbital contribution of 19% at the Fe1 center and 25.9% at the Fe2 center indicates that Fe2–O1 has a double-bond contribution which is also supported by the smaller bond Fe2–O1 bond distance. NBO analysis for species VIII has a small contribution at iron centers (6.7%) supporting the longer Fe1–O1 and Fe2–O2 bond lengths. The shift of the iron atom out of plane along the bridged oxygen (axial ligand) of species VII (− 0.41 Å/0.42 Å for Fe1/Fe2) is longer than that of species VIII (0.04 Å/− 0.07 Å for Fe1/Fe2). The HOMO-LUMO gap of species VII (0.939 eV) is larger than that of species VIII (0.881 eV). Both the iron centers in species VII are antiferromagnetically coupled, while in species VIII, both iron centers are ferromagnetically coupled. The HOMO-LUMO gap in binuclear species is relatively smaller than that in mononuclear species except for species IV.

Conclusions

Tetraamido macrocyclic ligand-coordinated iron species are of great interest because of their wide role in catalytic reactions, and they mimic properties of metalloenzymes. Here, we have undertaken the DFT study on mononuclear and dinuclear iron–TAML species for analyzing structures, bonding, energetics, and magnetic interactions. Some salient conclusions derived from this work are highlighted below:

  1. (i)

    Our computed DFT energies using dispersion-corrected hybrid B3LYP-D2 functional predicted the intermediate spin state for [FeIII(TAML)]− (species I), [(TAML)FeIV–ƞ1–O2]•− (species II), [(TAML)FeIV–OOH]− (species IV), [(TAML)FeIV–O]2− (species V), [(TAML)FeIV–μO–(TAML)FeIV]2− (species VII), and [(TAML)FeIV–μO2–FeIV(TAML)]2− (species VIII); the high spin state for [(TAML)FeIII–ƞ1–O2]3− (species IIIa) and the low spin state for [(TAML)FeV–O]− species (VI) are computed as the ground state. These ground states are in good agreement with the available experimental species [39, 53, 55, 56].

  2. (ii)

    Our computed DFT results also show that antiferromagnetic coupling between both iron centers is found to be in μ-oxo-bridged species VII whereas ferromagnetically coupling is in μ–(1,2-peroxo) species VIII.

  3. (iii)

    Here, we have also observed that the computed Fe–Navg bond length of species I is smaller than that of the rest of the studied species (species II–VIII).

  4. (iv)

    The increase in the oxidation state increases the bond strength confirmed by decreases in the bond length and an increase in stretching frequency.

  5. (v)

    The iron atom gets out of the plane on reaction with dioxygen, the shift of the position of the iron atom along the z-axis of the mononuclear species is computed to be 0.08 Å (species II), 0.72 Å (species III), 0.19 Å (species IV), 0.35 Å (species V), and 0.40 Å (species VI), and the shift of the position of the iron atom along the z-axis of the dinuclear species is computed to be − 0.41 Å/0.42 Å for Fe1/Fe2 (species VII) and 0.04 Å/− 0.07 Å for Fe1/Fe2 (species VIII).

  6. (vi)

    NBO analysis, orbital contributions of iron and oxygen, and iron atoms explained the ionic and the covalent nature of a metal–oxygen bond along with the formation of the π-bond.

  7. (vii)

    The nitrogen atom coordinated to the iron atom gains electron density via the electron delocalization mechanism. The significant spin density at the oxygen atom can be a witness for C–H/O–H/N–H bond activation.

To this end, these findings have direct relevance to the community working in the area of iron complexes/bioinorganic chemistry and related interface of chemistry.