Estimations of Fe-N2 Intrinsic Interaction Energies of Iron-Sulfur/Nitrogen-Carbon Sites: A Deeper Bonding Insight by EDA-NOCV Analysis of a Model Complex of the Nitrogenase Cofactor.

The MoFe7S9C1- unit of the nitrogenase cofactor (FeMoco) attracts chemists and biochemists due to its unusual ability to bind aerial dinitrogen (N2) at ambient condition and catalytically convert it into ammonia (NH3). The mode of N2 binding and its reaction pathways are yet not clear. An important conclusion has been made based on the very recent synthesis and isolation of model Fe(I/0)-complexes with sulfur-donor ligands under the cleavage of one Fe-S bond followed by binding of N2 at the Fe(0) center. These complexes are structurally relevant to the nitrogenase cofactor (MoFe7S9C1-). Herein, we report the EDA-NOCV analyses and NICS calculations of the dinitrogen-bonded dianionic complex Fe0-N2 (1) (having a CAr ← Fe π-bond) and monoanionic complex FeI-N2 (2) (having a CAr-Fe σ-bond) to provide a deeper insight into the Fe-N2 interacting orbitals and corresponding pairwise interaction energies (EDA-NOCV = energy decomposition analysis coupled with natural orbital for chemical valence; NICS = nucleus-independent chemical shifts). The orbital interaction in the Fe-N2 bond is significantly larger than Coulombic interactions, with major pairwise contributions coming from d(Fe) orbitals to the empty π* orbitals of N2 (three Fe → N2). ΔE int values are in the range of -61 to -77 kcal mol-1. Very interestingly, NICS calculations have been carried out for the fragments before and after binding of the N2 molecule. The computed σ- and π-aromaticity values are attributed to the position of the Fe atoms, oxidation states of Fe centers, and Fe-C bond lengths of these two complexes.

Introduction

Dinitrogen (N2) binding and catalytic reductive protonation leading to the formation of ammonia (NH3) are some of the most important biochemical natural processes on the planet.[1−3] The reduced forms of N2 (bio-organic molecules such as amino acid, peptide, nucleotide and nucleic acid etc.) are the parts of different forms that are the building blocks of the living organism, plants, and animals.[4] However, most of the living species on the earth cannot directly utilize the aerial N2 molecule although it is 78% of atmosphere of our planet. This is due to the kinetic inertness of molecular dinitrogen. The detailed bonding analysis (energy decomposition analysis coupled with natural orbital for chemical valence (EDA-NOCV))[5] of N2 suggests that the Wiberg bond order of N2 is little above three (3.03), possessing two π-bonds and one σ-bond with overall 70% covalent orbital (ΔEorb) and 30% electrostatic (ΔEelstat) contributions. The σ and π contributions are 65.6 and 34.4%, respectively. The very short N–N distance of 1.102 Å contributes to a high Pauling repulsion (ΔEPauli) energy.[5] Molecular N2 (:N≡N:) contains two low-lying pairs of electrons (σ/σ*) in 2σg+/2σu+ that are not efficient for σ-donation, while its doubly degenerate filled π-orbitals (1πu) (HOMO–1; Scheme , top) and doubly occupied 3σg+ (HOMO) orbital are higher in energy and are available for bonding with acceptors in certain circumstances.[6] The LUMO and LUMO+1 are the doubly degenerate π* (1πg) orbital and σ* orbital (3σu+) of N2,[5] respectively, which are available for π-backdonations from metal atoms (Scheme ) to accept electron densities, leading to the crucial elongation/activation of the N–N bond.

Scheme 1

(Top) Shape of the MO of Bonding and Antibonding Orbitals and (Bottom) End-On Orbital Interactions between Metal-Atom (M) and the N2 Molecule

Diazotrophs are bacteria and archaea that can bind areal N2 and transform it into a more stable reduced form such as ammonia. They live in the soil. A family of plants, called legume, whose roots are infected with nitrogen-fixing bacteria such as azotobacter start living in the plant’s root. This bacterium provides nitrogen products to legume pants by utilizing direct N2 from air. The active enzyme of azotobacter is nitrogenase, which possesses a monoanionic inorganic cluster [Mo(+3)Fe(+2.5)4Fe(+3)2Fe(+2)S(−2)9C(−4); (MoFe7S9C)1–].[7] This coordination cluster is protected from undergoing aerial oxidation by the protein part of this enzyme. Two Fe–S/Fe–Mo–S hetero-cubane units (Fe4S3 and MoFe3S3) are connected by a hexacoordinate lighter element (carbon) and three μ3-S bridges to form the monoanionic inorganic core MoFe7S9C1– having nine bridging anions S2– and one μ6-C4– anion. MoFe7S9C1– (Scheme ; top right) has a ground-state spin S = 3/2 in the resting state.[1,2] Kinetic studies have shown that it does not bind to molecular N2 in the resting state. Rather it binds with N2 under reduced form (Scheme , top right) when another Fe4S4 unit (P-cluster) transfers the required number of electrons.[1,2] However, the modes of N2 binding and the reaction paths of N2 reduction by nitrogenase are still not clear. Several model Fe complexes have been reported over the past two decades to shed light on the structure, electronic properties, and reactivity of the nitrogenase enzyme.[7−27] Based on the experimental evidences, it has been concluded that one of the six Fe centers that are bonded to the central C-atom is expected to bind with N2 under reduced state with the cleavage of one Fe–S bond. The coordination geometry of that particular Fe center is speculated to be four, with an S2CN coordination environment (Scheme ).[26] Recently, the group of Holland has designed an S2(η2-CAr)-donor ligand (Scheme ), which has been further utilized for the syntheses of Fe(II/I/0) complexes. Holland et al. experimentally observed that under reduced condition, one Fe–S–Ar of the modelled complex is broken with the formation of the Fe–N2 bond (Scheme ).[26] Very recently they have suggested[26] that cleavage of the Fe–S bond is more likely rather than elongation of the Fe–Ccentral bond or dissociation of the Fe–Ccentral bond of the MoFe7S9C cluster of the nitrogenase enzyme under reduced condition during binding of N2 (Schemes and ).

Scheme 2

Speculated N2 Binding by the Fe Center of the FeMoCo Cluster of the Nitrogenase Enzyme (Top) and Previously Reported Model Complex[26] under Reduced State with Cleavage of the Fe–S Bond

Scheme 3

Axial (Left; Fe–C Bond Elongation) and Equatorial (Right) N2 Bonding at the Fe Center of Nitrogenase

Syntheses of several modelled complexes have been reported, having M–N2 bonds for the purpose of dinitrogen reduction to ammonia.[8−26] The importance of activation of the N2 bond has been emphasized, and the extent of backdonation has been correlated with υN–N IR stretching frequency. However, there is no report of any theoretical study on estimation of the Fe–N2 interaction energy for efficient binding of the N2 molecule with the Fe center that could rationalize the syntheses and characterizations of this class of complexes.

Herein, we report on the DFT, NBO, QTAIM, NICS calculations, and, most importantly, EDA-NOCV analysis of previously reported dinitrogen-bonded Fe0–N2 (1) and Fe+1–N2 (2) complexes[26,27] to give a deeper insight into the nature of Fe–N2 bonds and corresponding pairwise interaction energies. Interestingly, nucleus-independent chemical shift (NICS) calculations even gave a deeper insight into the extent of Fe → CAr backdonation before and other binding with the N2 molecule.

Results and Discussion

Holland and co-workers have isolated and crystallographically characterized N2-bonded Fe complexes catering to two different applications:[26,27] dianionic dithiolate Fe–N2 complex, designed to mimic and explain the N2 binding of the nitrogenase enzyme,[26] and monoanionic L-Fe(N2)(Ph) [L = β-diketiminate] complex, as an intermediate in the activation of benzene and N2 leading to the formation of aniline derivatives,[27] which we designate as complexes A and B, respectively (Schemes and ). The Fe center of A is coordinated by two sulfur and two carbon atoms of the η2-aryl ring, whereas the Fe center of complex B is coordinated to two nitrogen atoms of β-diketiminate and one carbon atom of the phenyl group. Besides, the Fe atom of complex A interacts with the π cloud of the aromatic carbon ring, while in complex B the Fe–C interaction is mostly a σ type (Scheme ). Despite their structural differences, the precursors of both complexes A and B bind with N2 only under the reduced condition at low temperatures to produce A–B,[26,27] which is similar to the FeMoco cofactor of the nitrogenase enzyme.[26] However, complex A deviates from the nitrogenase enzyme in the Fe–C interaction (Fe···C2(Ar); Scheme ), where it is an σ-type bond (complex B, Fe–Ph; Scheme right) in the latter and a π type in the former (A). Both A and B show a pseudotetrahedral geometry at the iron site after binding to N2. While the Fe–N bond distances are 1.790–1.839 Å, the N–N bond lengths of pseudoterminally bonded N2 are 1.131–1.136 Å in the reported complexes A and B, respectively. Though these two complexes have been intended for different applications, the common theme they share is dinitrogen binding. Intrigued by this, we have modelled and optimized simplified versions of the reported complexes A and B, which we designate as complexes 1 and 2 (Scheme ), respectively, to shed some light on the strength of N2 binding to the Fe centers. We have optimized complex 1 in both singlet and triplet electronic states, while complex 2 was reported in the electronic quartet state and also in doublet state, in both the gas phase and THF at BP86-D3(BJ)/Def2TZVPP level (Scheme , Figure ). The details of the computational methods are provided in the Supporting Information. The calculations suggest the energy of solvation as 127.4 (1) and 39.6 (2) kcal mol–1; the geometrical parameters of the gas phase and THF optimized complexes are very close in both gas phase and solution. Herein, we report the geometrical parameters of the gas phase optimized structures. Complex 1 is comparatively more stable in the triplet state by 7.35 kcal mol–1 in the gas phase and 6.93 kcal mol–1 in THF solution. The authors have experimentally and theoretically proven the preference for the triplet state geometry over the singlet state in the reported complex A. However, in the case of complex 2, calculations suggest that doublet state is more stable than the quartet state, by 6.4 kcal mol–1 in the gas phase and 6.91 kcal mol–1 in THF. Although the energy difference between the doublet and quartet states of complex 2 is small, we assume that it can exist in both states under experimental conditions. The coordinated sulfur atoms of complex 1 are at a distance of 2.294–2.351 Å from the Fe center with an S–Fe–S bond angle of 118.4°, while the coordinated carbon atom of the aromatic ring is at a distance of 2.039 (1) Å, which is very close to the experimental values (2.037 (1), 2.049 (2) Å) of original complexes A–B.[26,27] The optimized values correlate well with the reported Fe–S (2.320(16)–2.355(16) Å) and Fe–C (2.037(5) (1) Å) distances and S–Fe–S bond angle of 114.3° (A)/118.4° (1) (Figure ). The Fe–C distances of A are 2.037 and 2.24 Å, which are close to those of 1 (2.05, 2.08 Å). The difference in the second Fe–C bond length can be attributed to the steric hindrance in A.[26]

Scheme 4

Simplified Structures of Complexes 1 and 2 that Have Been Modelled

Figure 1

Optimized geometries of complexes 1, 2 at BP86-D3(BJ)/Def2TZVPP level of theory and of previously reported complex B.

The Fe(I) center (3d7) of complex 2 has adopted a slightly distorted tetrahedral geometry. The deviation from perfect tetrahedral geometry can lift the degeneracy of the t2g level of the Fe(I) ion. Hence, 2 has been optimized in both quartet (S = 3/2; 2-quartet) and doublet (S = 1/2; 2-doublet). The coordinated nitrogen atoms of the ligand of 2-quartet (Scheme , Figure ) are equidistant (1.969 Å) from the Fe center, with the N–Fe–N bond angle of 96.9°. The Fe–CPh bond distance of 2-quartet is 2.022 Å. The optimized values concur well with those of the experimentally reported Fe–N (2.036 Å) and Fe–C (2.049 Å) bond lengths and the N–Fe–N bond angle of 93.7° of B.[27] The slight widening of the S–Fe–S and N–Fe–N bond angles in complexes 1 and 2-quatret from the reported bond angles is owing to the presence of less bulky substituents, which reduces the steric repulsion (Figure ). The structures of 1, 2-quartet, and B with selected bond parameters are given in Figure . The comparison between the bond parameters 2-quartet and 2-doublet clearly suggests that the spin ground state of B is most likely 3/2 (quartet). The Fe–NN2 (1.838 Å, B) bond length is significantly farther from that of 2-doublet (1.737 Å), but rather closer to 2-quartet (1.824 Å). Other Fe–NL bond distances of B are little over 2 Å. The corresponding bond parameters of 2-doublet are significantly shorter than those of B/2-quartet. The bulky substitution (like Dip-group = 2,6-disiopropylphenyl) on two N atoms of the β-diketiminate ligand (L) must have exerted a significant amount of steric effect/distortion, leading to a quartet as the ground state of 2. Structural optimization with smaller substitutions (Me-group) at the BP86-D3(BJ)/Def2TZVPP level of theory favors the doublet state (2-doublet) over the quartet state (2-quartet) of 2.

The Fe–N2 bond length of complex 1 is slightly shorter (1.801 Å) than that of complex 2 (1.824 Å). However, the N–N bond lengths of coordinated N2 in both complexes 1 and 2 are similar (1.147 Å) and are slightly elongated compared to the N≡N bond length of free N2 (1.102 Å), suggesting strong Fe → N2 backdonation. The Fe–N2 bond dissociation energies [(L)Fe–N2 → (L)Fe + N2] of 1 and 2 are slightly endothermic both in the gas phase (20.9 (1), 15.8 (2) kcal mol–1) and in THF (17.1 (1), 16.1 (2) kcal mol–1). The energy of dissociation in the gas phase is 33.2 and 27.0 kcal mol–1 for 1 and 2, respectively.

Computational Method

The EDA-NOCV method[28−37] is more appropriate in explaining the nature of the bond as one of the major strengths of the method is its ability to provide the best bonding model to represent the bonding situation in the equilibrium geometry.[35,36] However, the EDA-NOCV analysis of paramagnetic species is quite challenging as the main problem of EDA-NOCV calculations of paramagnetic species is to reflect physically meaningful orbital occupations in both possible situations: the bound complex and the isolated fragments. Especially in complexes involving 3d metal ions, it is a challenge to identify the d-orbitals with unpaired electrons to achieve meaningful orbital occupations in the isolated fragments, and thus in the bound complex, for accurate EDA-NOCV analysis.[37] The EDA-NOCV method[28−37] decomposes the intrinsic interaction energy (ΔEint) between two fragments into four energy components as given belowwhere the electrostatic term (ΔEelstat) arises from the interpenetrating charges of the nuclei of the two fragments that attract the electron cloud of the opposite fragment, and the orbital term (ΔEorb) comes from the mixing and relaxation of the orbitals, charge transfer, and polarization between the isolated fragments. The dispersion energy (ΔEdisp) arises from the noncovalent interactions, and, in particular, weak London forces between the two interacting fragments. The above-mentioned terms represent attractive forces; the Pauli term (ΔEPauli) arises due to the repulsion between the same electron spins of the two fragments when sharing the same bonding space. The corresponding deformation electron densities are represented by the direction of the charge flow red → blue.[36] The N2 has been considered in singlet, and ligand-Fe is either in S = 1 or in 1/2 or 3/2 spin state for our EDA-NOCV fragmentations and analyses.[37]

We have employed charge and energy density methods like natural bond orbital (NBO), quantum theory of atoms in molecules (QTAIM), and energy decomposition analysis coupled with natural orbitals for chemical valence (EDA-NOCV) methods to study the nature of the Fe–N2 bond. The natural charge distribution of the dianionic dithiolate-Fe complex, a precursor of complex 1, shows the concentration of charge on the sulfur atoms and faint positive charge on the Fe center. Upon binding to N2, the charge gets depleted on the sulfur atoms, and rather charge concentration can be observed on the Fe center and the otherwise neutral N2 (Table ). This indicates the direction of charge flow (CAr)(S2) → Fe → N2. On the contrary, for monoanionic [(NacNac)(C6H5)]Fe, the precursor of complex 2 shows a positive charge on the Fe center and a negative charge on the ligand nitrogen atoms. However, after binding to N2, the shift of charge is much more akin to complex 1 and the charge flows in the direction (CPh)(N2)L → Fe → N2. The NBO calculation suggests a Wiberg bond index of 0.96, 0.85 for Fe–N bond and 2.48 for N–N bond in complex 1 and 2, respectively.[26] The Fe–N and N–N bond orders are consistent with the Fe–N and N–N bond lengths in both the complexes. The decrease in N–N bond order (BO) of N2 in complexes 1 and 2 compared to that of free N2 (BO = 3.03) indicates the weakening of the N–N bond after complexation with metal, which is crucial for the activation of N2. The α-SOMO and α-SOMO–1 of complex 1 represent the two unpaired electrons residing in d and d of the triplet state (Figure S2), whereas α-SOMO, α-SOMO–1, and α-SOMO–2 of complex 2 represent the three unpaired electrons residing in d, d, and d of the quartet state (Figure S3). The unpaired electrons show some interaction with the p orbitals of N2. The remaining d-orbitals of both complexes 1 and 2 represent π-interactions with the p orbitals of the dinitrogen.

Table 1

Partial Charges on Fe, N2, and S2 Atoms of Complexes 1, 2-quartet and Their Precursors at the BP86/Def2-TZVPP Level of Theory

molecule	qFe	qN2	qS2/N2	CPh
complex 1	–0.158	–0.24	–0.194	–0.271
[S2Fe]2–	0.016		–0.350	–0.315
complex 2-quartet	+0.340	–0.26	–0.939	–0.256
[(NacNac)C6H5)Fe]−	+0.477		–1.07	–0.372

The AIM analysis shows solid paths (Figure S4) indicating the chemical bond between the Fe and N atoms. The electron density ρ(r) at the bond critical point (BCP) reflects the type of interaction and in turn the strength of the bond. The considerable electron densities of 0.132 and 0.126 au (Table S1), which are in between 0.1 and 0.2 au,[38] indicate that Fe–N bond is stronger than weak closed-shell interactions like ionic or van der Walls, and weaker than electron sharing (covalent) interactions. Complex 1 shows a slightly higher electron density ρ(r) than that of complex 2 and is consistent with the Fe–N2 bond lengths. Another factor that determines the type of interactions is the balanced ratio of positive kinetic electron energy density (G(r)) and negative potential electron energy density (V(r)), given as −G(r)/V(r). A ratio greater than 1.0 indicates noncovalent interactions and that less than 0.5 indicates covalent interactions, and the value in between 0.5 and 1 represents a partial covalent character.[38] Complexes 1 and 2-quartet show −G(r)/V(r) ratios of 0.857 and 0.843 (Table S1), respectively, which demonstrate the partial covalent character of the Fe–N2 bond. The negative total energy density values (H(r)) also support the partial covalent character of the Fe–N2 bond. The ellipticity values are a measure of the bond order, and the ellipticity values of 0.06 and 0.11 of complexes 1 and 2-quartet indicate a partial multiple bond character.

Table provides the EDA-NOCV results of the Fe–N bond of complexes 1 and 2-quartet calculated using dianionic [(S)2Fe]2– in electronic triplet state and neutral N2 fragment electronic singlet state as interacting fragments for complex 1, and monoanionic [(NacNac)(C6H5)Fe]− in electronic quartet state, doublet state, and neutral N2 fragment electronic singlet state as interacting fragments for 2-quartet (Scheme ). A careful examination of the molecular orbitals from NBO analysis helped in identifying the orbitals with unpaired electrons (Figures S2 and S3). The instantaneous interaction (ΔEint) indicates the intrinsic strength of the bond. Complexes 1 and 2-quartet show almost similar instantaneous interaction (−76.7, −76.9 kcal mol–1), albeit the slightly higher Pauli repulsion (8 kcal mol–1) in 2-quartet, while the intrinsic strength of complex 2-doublet is further reduced, probably owing to higher Pauli repulsion. In addition, a higher electrostatic contribution (Table ) arises from the difference in geometry. Note that the instantaneous interactions in 1 and 2-quartet are reasonably higher than the bond dissociation energies, and the difference can be attributed to the preparative energy. The preparative energies originate from the modifications in the geometry of the fragments from their equilibrium structure to the geometry in the compound, and also from the electronic excitation to a reference state.

Table 2

EDA-NOCV Results at the BP86-D3(BJ)/TZ2P Level of Fe–N2 Bonds of Complexes 1, 2-quartet, and 2-doublet Using Dianionic [(S)2Fe]2– in Electronic Triplet State and Neutral N2 Fragment Electronic Singlet State as Interacting Fragments for Complex 1 and Monoanionic [(NacNac)(C6H5)Fe]− in Electronic Quartet, Doublet States, and Neutral N2 Fragment Electronic Singlet State as Interacting Fragments for Complex 2-quartet and 2-doublet, Respectivelya

energy	interaction	[(S)2Fe]2– (T) + [N2] (S) (1)	[(NacNac)(C6H5)Fe]− (Q) + [N2] (S) (2-quartet)	[(NacNac)(C6H5)Fe]− (D) + [N2] (S) (2-doublet)
ΔEint		–76.7	–76.9	–61.3
ΔEPauli		158.3	165.3	181.8
ΔEdispb		–6.4 (2.7%)	–4.5 (1.9%)	–5.3 (2.2%)
ΔEelstatb		–91.6 (39.0%)	–90.2 (37.2%)	–110.0 (45.2%)
ΔEorbb		–136.9 (58.3%)	–147.5 (60.9%)	–127.8 (52.6%)
ΔEorb(1)c	(L)Fe → N2 π backdonation	–53.3 (38.9%)	–70.2 (47.6%)	–67.1 (52.5%)
ΔEorb(2)c	(L)Fe → N2 π backdonation	–41.7 (30.5%)	–41.9 (28.4%)	–36.5 (28.6%)
ΔEorb(3)c	(L)Fe ← N2 σ  backdonation	–30.7 (22.4%)	–23.0 (15.6%)	–17.4 (13.6%)
ΔEorb(4)c	(L)Fe ← N2 σ  backdonation		–7.1 (4.8%)
ΔEorb(rest)c		–11.2 (8.2%)	–5.3 (3.6%)	–6.8 (5.3%)

Energies are in kcal mol–1.

The values in the parentheses show the contribution to the total attractive interaction ΔEelstat + ΔEorb + ΔEdisp.

The values in parentheses show the contribution to the total orbital interaction ΔEorb.

Scheme 5

Schematic Representations of the Fragments with Corresponding Multiplicities Considered for the EDA-NOCV Calculation

The orbital (covalent) interactions are predominant and contribute 52.6–60.9% to the total attractive interactions in complexes 1, 2-quartet and 2-doublet, while the electrostatic interactions contribute 37.2–45.2% and the dispersion contributes 1.9–2.7% to the total attractive interactions (Table ). The higher orbital contributions indicate the covalent nature of the Fe–N bond. The pairwise interactions, resulting from the breakdown of the total orbital interactions, provide further insight into the type of interactions. Table illustrates three pairwise contributions (ΔEorb(1–3)) for complex 1 and four pairwise contributions (ΔEorb(1–4)) for 2-quartet. The largest orbital stabilization (ΔEorb(1)) comes from the Fe → N2 π electron backdonation followed by another Fe → N2 π backdonation (ΔEorb(2)) and Fe ← N2 σ electron donation (ΔEorb(3)) in complexes 1 and 2-quartet (Scheme ). Additionally, 2-quartet shows another weak Fe ← N2 σ electron donation (ΔEorb(4)). The stronger Fe → N2 π backdonations contribute 69.4–76% to the orbital interactions in both complexes 1 and 2-quartet and agree well with the charge distributions from the NBO analysis, whereas Fe ← N2 σ electron donations contribute 20.4–22.4% and equate well with the bonding analysis of M–N bonds in matrix isolated M(N2)8 (M = Ca, Sr, Ba) complexes, where M–N bonds are dominated by M(dπ) → (N2) π backdonations from metal orbitals.[37a,39]

Scheme 6

σ-Donation and π-Backdonation in Complexes 1 and 2-quartet

See Figures and 3 and Table to obtain a quantitative idea about the strengths of each bonding interaction.

Figure 2

Shape of the deformation densities Δρ(1)–(3) that correspond to ΔEorb(1)–(3), and the associated MOs of [(S)2Fe)N2]2– (1) and the fragment orbitals of [(S)2Fe]2– in triplet state and N2 in the singlet state at the BP86-D3(BJ)/TZ2P level. Isosurface values of 0.003 au for Δρ(1–3). The eigenvalues |ν| give the size of the charge migration in e. The direction of the charge flow of the deformation densities is red → blue.

Figure 3

Shape of the deformation densities Δρ(1)–(4) that correspond to ΔEorb(1)–(4), and the associated MOs of [(NacNac)(C6H5)Fe)N2]− (2-quartet) and the fragment orbitals of [(NacNac)(C6H5)Fe]− in quartet state and N2 in the singlet state at the BP86-D3(BJ)/TZ2P level. Isosurface values of 0.003 au for Δρ(1–4). The eigenvalues |ν| give the size of the charge migration in e. The direction of the charge flow of the deformation densities is red → blue.

The corresponding deformation densities Δρ(1–3/4) associated with ΔEorb(1–3/4) shown in Figures 2 and 3 reveal that the first Fe → N2 π backdonation Δρ(1) is from HOMO (1) and HOMO–1 (2-quartet) (d) orbitals of Fe into the vacant degenerate π* orbital LUMO (1πg) of N2, whereas the second Fe → N2 π backdonation Δρ(2) is from HOMO–1 (1) and HOMO (2-quartet) (d) orbitals of Fe into the vacant degenerate π* orbital LUMO′ (1πg′) of N2 (Scheme ). The third deformation density Δρ(3) represents the Fe ← N2 σ electron donation from HOMO (3σg+; filled bonding σ2s* with the same phase (+, +)) of N2, along with the slight polarization (hybridization) within the fragment from d orbital (SOMO–1/SOMO–2) of Fe into the vacant LUMO+6 and LUMO+1 orbitals of Fe in complexes 1 and 2-quartet, respectively. Besides the three major deformation densities, complex 2-quartet shows another weak deformation density Δρ(4), which is similar in shape to Δρ(3), but the electron donation is from HOMO–2 (2σu+; filled antibonding σ2s* with opposite phase (+, −)) of N2 (Figure ; Scheme , top), which might have led to deviation of the Fe–N–N angle (174°) from 180°. Complex 2-doublet shows three pairwise contributions, which reveal stronger Fe → N2 π backdonations and slightly weaker Fe ← N2 σ donation (Table ) compared to that of the complex 2-quartet. The deformation densities of the complex 2-doublet can be seen in Figure S5.

The aromaticity of the benzene/phenyl ring in complexes 1 and 2-quartet, their precursor complexes, and ligands has been measured by calculating the magnetic NICS, introduced by Schleyer et al.,[40] using the gauge-independent atomic orbital (GIAO) approach at BP86/def2-TZVPP level on the geometries optimized at BP86-D3(BJ)/def2-TZVPP level. The NICS method is considered as a popular probe of aromaticity due to its ability to describe the aromaticity, antiaromaticity, and non-aromaticity of ring systems both qualitatively and quantitatively.[41] The NICS values calculated at the geometric centers of the ring are termed as NICS(0) and is considered as a measure of the σ + π electron delocalization, whereas the values calculated at 1 Å above the plane of the ring are designated as NICS(1), which represents π-electron delocalization.[42]

Negative NICS values specify aromaticity and positive NICS values indicate antiaromaticity, while values close to zero represent non-aromaticity. A close inspection of the NICS values from Table shows that the aromaticity of the dithiolate (S2)− ligand decreases on coordinating to iron and then again increases upon interacting with N2 in complex 1. The reduction in the aromaticity on coordinating to metal is comparable to that of metallabenzynes.[43]

Table 3

NICS(0/1) Results of 1, 2-quartet, and 2-doublet and Their Precursors at the BP86/Def2TZVPP Level

compound	NICS(0)	NICS(1)
S2 ligand	–6.49	–7.92
[S2Fe]2–	–2.29	–1.72
complex 1	–8.03	–5.89
[(NacNac)C6H5)Fe]−	–4.79	–7.98
complex 2-quartet	–5.47	–8.63
complex 2-doublet	–5.02	–8.03

On similar lines, the precursor of complex 2-quartet shows an increase in aromaticity after binding to N2. The decrease in the aromaticity of the fragments [S2Fe]− and [(NacNac)C6H5)Fe]− (Table ) can be attributed to the backdonation from Fe into the π* orbital of the aromatic carbon as expected. Olefins are often seen to form a π-complex with the transition metals. The donor–acceptor type bonds between metal-atom and olefins are speculated. However, after binding to N2 the Fe → N2 π-backdonation increases, which eventually changes the direction of charge flow from C → Fe → N2 as shown by NBO calculations. Additionally, the slight increase in Fe–C bond length (0.06 Å) after binding to N2 supports the change in the direction of charge flow. This triggers the increase in aromaticity in complexes 1 and 2-quartet as shown in Table . Scheme shows the location of NICS(0) and NICS(1) in the molecules represented in Table . The NBO pictures (Figure ) of 1 and 2-quartet (right) showed the orbital interactions between the d-orbitals of Fe atoms and the π-orbital of benzene/phenyl ring (double-headed arrow). It is known that aromatic rings will possess a diamagnetic ring current, while the antiaromatic and paramagnetic species will induce a paramagnetic ring current under applied magnetic field. The true picture of the aromaticity of the benzene/phenyl ring of these two complexes could be even more complex than it appears. The bottom point is that Fe-aromatic-ring interactions are somehow related to the N2 (π-accepting ligand) binding similar to the (benzene)–M(CO)–CO.

Scheme 7

Schematic Representation of NICS(0) and NICS(1) in the Molecules Represented in Table

Pink point for NICS(0): a point in the plane of the C6 ring. Blue point for NICS(1): a point in the plane above/below the plane of the ring.

Figure 4

NBOs of complex 1 (left) and 2-quartet (right) showing the orbital interactions between Fe and the π-orbital of the benzene/phenyl ring (double-headed arrow).

Summary and Conclusion

In conclusion, we have reported the EDA-NOCV and NICS analyses of dithiolate-Fe0-N2 (1) and L-FeI(N2)(Ph) (2), which can be regarded as model complexes with relevance to the nitrogen-fixing FeMoco cofactor of the nitrogenase enzyme. The quantum mechanical calculations on 2 with smaller substitutions suggest that B (with bulkier substituents on N atoms of L) is more likely to have a quartet ground state than a doublet state. The calculations suggested the endothermic dissociation of Fe–N2 bond [(L)Fe0/I–N2 → (L)Fe0/I + N2] in complexes 1–2. NBO calculations indicate the direction of charge flow from metal to dinitrogen [(L) → Fe → N2], which rationalizes the activation N≡N bond. The EDA-NOCV analysis shows higher orbital contributions, indicating a higher covalent character than the ionic character of the Fe–N2 bond. The pairwise orbital interactions suggest that the combination of two π-backdonations [(d)Fe → (π*)N2] is much stronger than σ-donation [(σ1s/2s)N2 → (d)Fe], which has been schematically represented in Schemes and and pictorially/quantitatively displayed in Figures and 3/Table . The ΔEint values of the Fe–N2 bonds of these two complexes are in the range of 76–77 kcal mol–1. Additionally, NICS calculations suggest that the Fe(0/I) → C(π*; aromatic ring) π-backdonations are significantly stronger before N2 binding (Table ). The computed σ- and π-aromaticities corresponding to 1–2-quartet are significantly lower after dinitrogen binding due to the flow of electron densities from the Fe centers to N2. However, the complexes 1 and 2-quartet differ in the magnitude of σ- and π-aromaticities due to the difference in the position of the Fe atom and also oxidation state.