Estimations of Fe^0/−1–N₂ interaction energies of iron(0)-dicarbene and its reduced analogue by EDA-NOCV analyses: crucial steps in dinitrogen activation under mild conditions

Abstract

Metal complexes containing low valence iron atoms are often experimentally observed to bind with the dinitrogen (N₂) molecule. This phenomenon has attracted the attention of industrialists, chemists and bio-chemists since these N₂-bonded iron complexes can produce ammonia under suitable chemical or electrochemical conditions. The higher binding affinity of the Fe-atom towards N₂ is a bit ‘mysterious’ compared to that of the other first row transition metal atoms. Fine powders of α-Fe⁰ are even part of industrial ammonia production (Haber–Bosch process) which operates at high temperature and high pressure. Herein, we report the EDA-NOCV analyses of the previously reported dinitrogen-bonded neutral molecular complex (cAAC^R)₂Fe⁰–N₂ (1) and mono-anionic complex (cAAC^R)₂Fe⁻¹–N₂ (2) to give deeper insight of the Fe–N₂ interacting orbitals and corresponding pairwise intrinsic interaction energies (cAAC^R = cyclic alkyl(amino) carbene; R = Dipp or Me). The Fe⁰ atom of 1 prefers to accept electron densities from N₂ via σ-donation while the comparatively electron rich Fe⁻¹ centre of 2 donates electron densities to N₂ via π-backdonation. However, major stability due to the formation of an Fe–N₂ bond arises due to Fe → N₂ π-backdonation in both 1 and 2. The cAAC^R ligands act as a charge reservoir around the Fe centre. The electron densities drift away from cAAC ligands during the binding of N₂ molecules mostly via π-backdonation. EDA-NOCV analysis suggests that N₂ is a stronger π-acceptor rather than a σ-donor.

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Introduction

Different forms of energy can be argued as the ingredients of life.¹ Energy, life and information are linked to each other.² Nitrogen is one of the most common and most essential elements for the sustainability of living organisms, plants and animals. The earth's atmosphere is mostly dominated (78%) by dinitrogen gas (N₂) and yet most of the living organisms, plants and animals cannot directly utilize it according to their needs.³ This is due to the extreme inertness and non-polar nature of kinetically stable N₂ molecules. The reduction of N₂ to ammonia (NH₃) and/or to other forms of N-containing compounds such as amino acids, nucleoside, nucleotides and most importantly peptides are keys to the existence of life on earth.⁴ Thermodynamically, reduction of areal N₂ to relatively more stable NH₃ is exothermic (−46 kJ mol⁻¹ at 298 K). However, the binding of N₂ and followed by activation of the N≡N bond is challenging to chemists and bio-chemists. Interestingly, a few microorganisms in the nature have found a way to solve the problem⁵ providing around hundred twenty megatons of nitrogen source per year by nitrogen fixation. It is associated with some leguminous plants, like clover, beans, peas, alfalfa, lentils and lupins.⁶ The enzyme called nitrogenase possesses a bimetallic inorganic core V/Mo–Fe₇S₉C¹⁻ (co-factor) which is responsible for N₂ binding in the reduced state.^7,8 It catalytically produces ammonia via reductive protonation either by ‘distal’ or ‘alternative’ pathways with the loss of hydrogen gas during this process.^7,8 The exact nature and mode of the dinitrogen binding and activation have not yet fully clear. N-containing nutrients are essential for the human race on the earth. Humans adopted domestic cultivation as early as 10 000 BC.⁹ Fertilizers are now-a-days a must for effective cultivation. More than a century ago, Haber originally utilized an osmium catalyst under high temperature and pressure to produce 125 mL of NH₃ per hour.¹⁰ In the following years Bosch and Mittasch developed efficient Fe₃O₄/FeO/α-Fe⁰ catalyst with high surface area for industrial production of twenty tonnes of NH₃ per day in the next year at BASF company.^10,11 The catalytic efficiency of iron is further promoted with K₂O, CaO, SiO₂, and Al₂O₃. At present global annual production rate of ammonia is 174 million tonnes.¹² The actual Mittasch's catalyst (Fe₃O₄/FeO/α-Fe⁰) (Scheme 1) in Haber–Bosch catalytic cycle is the outer surface (α-Fe⁰) of very reactive Fe₃O₄/FeO/α-Fe⁰ particles having a body centre cubic (bcc) structure with two singly-occupied d_z² and d_x²−y² orbitals which do not participate in multicentre delocalized bonding with its neighbouring Fe⁰ atoms.¹³

Scheme 1 Illustration of H₂ and N₂ adsorption, dissociation and formation of NH₃ in famous Haber–Bosch process showing α-Fe⁰ active catalytic surface.

To obtain a favourable thermodynamic driving force for the reaction between N₂ and H₂ the industrial process is designed to occur at high pressure (Scheme 1). In 2007 Gerhard Ertl has been awarded the Nobel Prize in chemistry for his captivating decades long works on fundamental processes at the gas–solid interface involving Fe⁰–N₂ adsorption on the α-Fe⁰ surface of Fe₃O₄/FeO/α-Fe⁰ catalyst. His work on ‘Interaction of nitrogen with iron surfaces’ clarified the long-standing confusion in Haber–Bosch process.¹⁴ It has been found that N≡N bond dissociates on pure Fe-surfaces forming Fe₄N atomic-bilayer just above room temperature. He also explained the role of promoter K₂O in Haber–Bosch ammonia synthesis process employing photoelectron spectroscopy and other experimental techniques. The pre-adsorbed potassium on the Fe-surface removes energy barrier of dissociative nitrogen chemisorption of N₂ molecule.¹⁵ The overall yield of NH₃ in Haber–Bosch industrial process is 97% when the unreacted gases are recycled again and again.¹⁰ However, at present this process consumes ∼2% of the total global energy supply. Additionally, it produces large amounts of greenhouse gases.¹⁶ Alternative synthetic methods which will produce NH₃ in a much greener way are highly desired.^17–41 Low valence and/or low valent metal complexes^{17–33,37–41} and low coordinate boron–carbene^34–36 compounds are found to bind N₂ which can be activated to obtain NH₃ or N₂H₄ under milder conditions.^17–41 The reductive protonation of bonded N₂ of these complexes can lead to the formation of either NH₃ or N₂H₄ or even a mixture of both. Formation of ammonia is more common due to its higher thermodynamic stability over hydrazine. It has been stated that π-backdonation from metal to N₂ (M → N₂) are very pivotal for the weakening of strong N≡N bond. Higher the electron densities on metal atom, higher is the π-backdonation from metal to N₂ (Scheme 2). However, there is no report on the estimation of M–N₂ interaction energies in a stable/isolable complex showing the extent of π-backdonation from M → N₂ and σ-donation from N₂ → M (M = transition metal; Scheme 2).⁴² The energy decomposition analysis-natural orbital for chemical valence (EDA-NOCV)⁴³ analysis is a very powerful tool that can be employed for the estimation of intrinsic interaction energy (ΔE_int) and pairwise orbital interaction energy (ΔE_orb(n)). The triple bond of the free dinitrogen (N₂) molecule is extremely strong. EDA-NOCV analysis of free N₂ revealed that 30% of the total interaction energy between two N-atoms is only contributed by electrostatic energy (ΔE_elstat). The remaining 70% is orbital interaction energy (ΔE_orb) which is due to the covalent character of triple bond of N₂ with zero dipole moment.^43,44 The Pauli repulsion energy (ΔE_Pauli) between two interacting N-atoms is quite high due to repulsion between the electron clouds with similar spins (N–N = 1.102 Å). The Wiberg bond order has been computed to be 3.03. The orbital interaction energy (ΔE_orb) is actually due to the covalent interactions in both σ (3σ_g⁺) + π (1π_u) bonds. The former is 65.6% while the latter is nearly half (34.4%) of the former. They together (σ + π) give total orbital interaction energy (ΔE_orb).^43,44 Point to be noted that degenerate π*-orbitals (1π_g) of N₂, which are composed of p_x and p_y atomic orbitals, are high lying in energies (1π_g; LUMO). The LUMO+1 is σ* orbital (3σ_u⁺) and HOMO is N–N σ orbital (3σ_g⁺) of N₂.^43,44

Scheme 2 End-on interactions between the orbitals metal (M) and N₂.

Several metal complexes with low valence iron atoms containing coordinated N₂ have been synthesized, isolated and characterized by X-ray single crystal structure determination.^{18–21,27–33,40,41} Additionally, they have been studied by different spectroscopic methods to shed light on their electronic structures. NBO calculations have been carried out to correlate the N–N bond lengths with those of experimentally obtained values to give emphasis on weakening of N–N bond due to M → N₂ backdonation.^{18–21,27–33,40,41} However, there is till now no report⁴² on the exact nature of the M–N₂ bonds and on their corresponding interaction energies (M = Fe and other transition metal) of stable/isolable dinitrogen bonded metal complexes. Herein, we report on the DFT, NBO, QTAIM calculations and EDA-NOCV analysis of previously reported dinitrogen-bonded (cAAC^R)₂Fe⁰–N₂ (1) and (cAAC^R)₂Fe⁻¹–N₂ (2) complexes⁴¹ to give a deeper insight into the nature of M–N₂ bonds and corresponding pairwise interaction energies (cAAC^R = cyclic alkyl(amino) carbene; R = Dipp⁴¹ or Me for our theoretical studies). The role of non-innocent cAAC ligands has also been discussed here.

Results and discussion

The spin of each Fe-atom of ferromagnetic α-iron metal is S = 1.¹⁰ The spin ground state of (cAAC^Dipp)₂Fe⁰ has been confirmed to be S = 1 by EPR and ⁵⁷Fe Mössbauer spectroscopy by Peters et al.⁴⁵ Additionally, they have experimentally shown⁴¹ (by UV/vis spectroscopy) that the N₂ binds to (cAAC)₂Fe⁰ in end-on fashion. This N₂ binding at Fe-centre is highly temperature sensitive (<−80 °C).⁴¹ Experimentally the authors have isolated the elusive anionic (cAAC^Dipp)₂Fe⁻¹–N₂ species by reducing in situ formed precursor (cAAC^Dipp)₂Fe⁰–N₂ (1′) with KC₈ in the presence of 18-crown-6 ether below −95 °C with the chemical composition of [(cAAC^Dipp)₂Fe(N₂)][K(18-crown-6)] (2′) (Scheme 3). The latter species (2′) has a ground state S = ½ confirmed by solution EPR measurements.⁴¹ This anionic complex has further been shown to catalytically produce NH₃ below −95 °C. The reduction of dinitrogen to ammonia takes place upon treatment with N₂, KC₈ and HBAr^F₄·2Et₂O in ether medium. Only a little has been reported about their (1′–2′) aspects of chemical bonding.⁴¹

Scheme 3 Representative Fe–N₂ containing iron complexes.^{17,18,38,40,41,45}

We have modelled and optimized (L)₂Fe⁰–N₂ as neutral (1; L = cAAC^Me) and anionic complexes (2; L = cAAC^Me) stabilized by cAAC^Me ligands to shed light on the bonding and stability of spectroscopically observed elusive neutral (cAAC^Dipp)₂Fe⁰–N₂ (1′; cAAC^Dipp) and crystallographically characterized [(cAAC^Dipp)₂Fe⁻¹(N₂)][K(18-crown-6)] complexes (2′) reported by Jonas Peters and co-workers. The Fe–N bond distance of [(cAAC^Dipp)₂Fe(N₂)][K(18-crown-6)] is 1.777 Å while the N–N bond length of the bonded N₂ is 1.035(4) Å which is slightly shorter than that of the free N₂ (1.102 Å) molecule. X-ray crystallography of the complex 2′ revealed that Fe-centre adopted a distorted trigonal planar coordination geometry.⁴¹

The modelled neutral (cAAC^Me)₂Fe–N₂ complex (1) has been optimized in singlet (Fig. S1†), triplet (Fig. 1) and quintet electronic states (Fig. S1†). The calculations at BP86-D3(BJ)/Def2TZVPP level of theory in the gas phase suggest that triplet state is more stable by 11.53 and 20 kcal mol⁻¹ over singlet and quintet states, respectively. The N–C–C–N torsion angle of 37.7° in complex 1 suggests that the two cAAC ligands are relatively perpendicular to each other, while the C–Fe–C bond angle of 149.3° shows that the geometry is lightly bent compared to that of (cAAC)₂Fe⁰ containing a two coordinate Fe⁰ atom with C_cAAC–Fe–C_cAAC bond angle of 169.52(5)°.⁴⁵ The Fe–N and N–N bond lengths of the simplified complex 1 are 1.801 Å and 1.140 Å respectively (with Me-group on N-atom of cAAC ligand). The two cAAC ligands are almost equidistant from the central Fe atom with a minor difference (Fig. 1). In contrast to the Fe–Mo cofactor (FeMoco) of nitrogenase enzyme,^7,8 the two coordinate (cAAC)₂Fe can bind to N₂ even in resting condition below −80° ⁴¹ or in other words without the external supply of electrons.

Fig. 1 Optimized geometries of complex 1 in triplet state (s = 1) and mono-anionic complex 2 in doublet state (s = 1/2) at BP86-D3(BJ)/Def2-TZVPP level.

Upon reduction, the geometry becomes more bent in complex 2 as indicated by the C_cAAC–Fe–C_cAAC bond angle of 117.4° (Fig. 1). This differs from the C–Fe–C bond angle (140.8°) of experimentally isolated [(cAAC^Dipp)₂Fe(N₂)][K(18-crown-6)] (2′) due to to the steric effects of two cAAC^Dipp ligands. We can reason the reduction in C–Fe–C bond angle in the modelled complex to the presence of less bulky substituents on cAAC ligand which reduces the steric repulsion. This reduction in C–Fe–C bond angle also slightly lower the C–Fe bond lengths in complex 2 compared to that of the reported structure. The Fe–N bond distance of modelled complex 2 (1.782 Å) correlated well with the reported value of 1.777 Å (2′). The geometrical parameters calculated at BP86-D3(BJ)/Def2TZVPP level agrees well with the experimental values with no major discrepancies. However, we have also performed geometry optimization of complexes 1 and 2 at the TPSS-D3(BJ)/Def2TZVPP and PW6B95-D3/Def2TZVPP level to compare and support the results. While the Fe–N bond lengths of complexes 1 and 2 calculated at TPSS-D3(BJ) level are 1.808 Å, 1.782 Å respectively (Fig. S1†), the calculated N–N bond lengths are 1.136 and 1.149 Å (Fig. S1†). The geometrical parameters calculated at TPSS-D3(BJ) match well with the results of the BP86-D3(BJ) level. However, the Fe–N bond lengths (1.899 and 1.864 Å) calculated at PW6B95-D3 level (Fig. S1†) differ significantly with those calculated at TPSS-D3(BJ), BP86-D3(BJ) and also experimental values. The calculated C–Fe–C bond angle of complex 2 at TPSS-D3(BJ) is also acute (120.7°), supporting the reason for the difference from the experimental bond angle as mentioned above. The N–C–C–N torsion angle of 145.1° indicates that the two carbene ligands are slightly more trans to each other in complex 2. The coordination geometries of Fe-centres reveal that both complexes 1 and 2 possess a distorted trigonal planar geometry as indicated by Σ_angle of 359.8° and 359.9° respectively and are in agreement with the reported structure (2′).⁴¹ The longer C–N bond lengths of 1.343–1.345 Å in complex 1 and 1.397–1.407 Å in complex 2 than that of 1.315(3) Å in free carbene, indicate spin delocalization onto ligands (C_cAAC ← Fe).⁴⁶ The dissociation of (cAAC^Me)₂Fe–N₂ bond [(cAAC^Me)₂Fe–N₂ → (cAAC^Me)₂Fe + N₂] in complex 1 and 2 is slightly endothermic (ΔG²⁹⁸ = 18.9–29.6 kcal mol⁻¹) and the energy of dissociation is 30.1–40.26 kcal mol⁻¹ (bond enthalpy) respectively. The electron affinity of 1 is 13.74 kcal mol⁻¹.

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–N bond. The Wiberg bond index (WBI) of 0.82 (1), 0.92 (2) for Fe–N bond and 2.53 (1), 2.43 (2) for N–N bond of 1 and 2, respectively (Table 1). The Fe–N and N–N bond orders are consistent with the Fe–N and N–N bond lengths of both the complexes. The N–N bond orders (BO; 2.53 (1), 2.43 (2)) of N₂ in complexes 1 and 2 are significantly smaller than those of free N₂ molecule (BO = 3.03). This indicates the weakening of the N–N bond via π-backdonation after the binding of N₂ with Fe-centres which is crucial for the activation of N₂. Previous temperature dependent UV/vis studies showed that N₂ binding at Fe⁰ centre could only happen below −80 °C.⁴¹ The computational results show that the spin density of the Fe–N bond with an electron occupancy of 0.99 is mostly concentrated on N-atom (80.6%) for complex 1. The calculation does not show bond occupancy for the Fe–N bond of complex 2. The C_cAAC–Fe bonds of complex 1 and 2 show two occupancies representing σ- and π-interactions with spin density mostly concentrated on C_cAAC (62.9–71.5%) for σ-interactions and Fe (68.4–75.3%) for π-interactions (Table 1). The natural charge distribution of (cAAC^Me)₂Fe⁰ shows a negative charge on cAAC ligands and a positive charge on the Fe-atom suggesting π-backdonation (Fe → N₂) is stronger than σ-donation (N₂ → Fe). Upon binding to N₂, the cAAC ligands develop a positive charge and the Fe-center of 1 shows an increase in positive charge as well, while the N₂ ligand accumulates a negative charge, suggesting N₂ is stronger π-acceptor than a σ-donor. This indicates that the charge transfer occurs in the direction cAAC → Fe → N₂. It is well known that cAAC is a non-innocent ligand.^46b,c It can control the charge flow and distribute the electron densities distributions based on the electronic situations and or requirement. Whereas the negative charge on cAAC, Fe and N₂ of complex 2 suggests the delocalization of one electron-charge upon reduction of 1. The α-SOMO and α-SOMO−1 of complex 1 represent the two unpaired electrons residing in d_xy and d_x²−y² of the triplet state. The α-SOMO−1 shows π-interaction of d_x²y² orbital of Fe and lone pair on cAAC ligand with π_x-orbital of N₂, while α-SOMO−2 indicates π-interaction of d_yz orbital of Fe-atom with π_y-orbital of N₂ (Fig. S2†). Whereas α-SOMO of complex 2 represents an unpaired electron in d_xz orbital of Fe showing small amount of interaction with π_x orbital of N₂. The α-SOMO−1, α-SOMO−2 and α-SOMO−3 indicate the interaction of d_x²−y², d_z² and d_yz orbitals of Fe with π_x and π_y orbital of N₂ (Fig. S3†). The QTAIM analysis shows a bond path (Fig. S4†) and considerable electron density ρ(r) along the Fe–N bond path in both complexes 1 and 2 (Table 2). Little increase in ρ(r) along Fe–N and C_cAAC–Fe bond paths in complex 2 corroborates the delocalization of electron density and agrees with the charge distribution from NBO analysis. The ellipticity (ε_BCP = λ₁/λ₂ − 1) is a measure of bond order and in general, the ε_BCP of a single and triple bond is close to zero because of cylindrical contours of electron density ρ, while for double bond the value is greater than zero.⁴⁷ This is due to the asymmetric distribution of electron density ρ perpendicular to the bond path for a double bond. The ellipticity (ε) values of 0.248 and 0.383 for the Fe–N bond of complexes 1 and 2 suggests the possible multiple bond character.

Table 1 NBO results of the (cAAC)₂Fe–N₂ bonds of complexes 1 and 2 at the BP86-D3(BJ)/def2-TZVPP level of theory. Occupation number ON, polarization and hybridization of the (cAAC)₂Fe–N₂ bonds and partial charges q

Complex	Bond	ON	Polarization and hybridization (%)		WBI	qFe	qN2	qcAAC
1	Fe–N	0.99	Fe: 19.4 s(21.3),p(19.4),d(59.3)	N: 80.6 s(58.4), p(41.6)	0.82	0.440	−0.122	0.144
	C–Fe	0.96	Fe: 28.5 s(20.0), p(13.8), d(66.2)	C: 71.5 s(41.8), p(58.2)	0.84
		0.91	Fe: 75.3 s(0.0), p(4.7), d(95.3)	C: 24.7 s(0.8), p(99.2)
2	Fe–N	—	—	—	0.92	−0.223	−0.275	−0.510
	C–Fe	0.97	Fe: 37.1 s(20.6), p(8.3), d(71.1)	C: 62.9 s(45.3), p(54.7)	1.09
		0.90	Fe: 68.4 s(0.8), p(7.5), d(91.7)	C: 31.6 s(0.2), p(99.8)
(cAAC)2Fe	C–Fe	0.91	Fe: 14.6 s(42.5), p(50.0), d(7.5)	C: 85.4 s(39.5), p(60.5)	0.88	0.245	—	−0.244
		0.90	Fe: 98.9 s(0.4), p(0.2), d(99.4)	C: 1.1 s(5.6), p(94.4)

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Table 2 AIM results of the (cAAC)₂Fe–N₂ bonds of complex 1 and anionic complex 2 at the BP86-D3(BJ)/Def2-TZVPP level of theory. (The values are in a.u.)

Bond	ρ(r)	∇^2ρ(r)	H(r)	V(r)	G(r)	εBCP
Fe–N(1)	0.131	0.796	−0.039	−0.277	0.238	0.248
C–Fe(1)	0.124	0.342	−0.056	−0.196	0.140	0.318
Fe–N(2)	0.139	0.793	−0.046	−0.290	0.244	0.383
C–Fe(2)	0.142	0.376	−0.072	−0.237	0.165	0.107

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The EDA-NOCV method⁴⁸ 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 geometries.⁴⁸ To give the best bonding description of Fe–N bond by EDA-NOCV method, we have considered neutral (cAAC^Me)₂Fe fragment in electronic triplet state and neutral N₂ fragment in electronic singlet state (1Σ_g⁺) for complex 1 and mono-anionic [(cAAC^Me)₂Fe]⁻ fragment in electronic doublet state and neutral N₂ fragment in electronic singlet state (1Σ_g⁺) for complex 2 (Table 3). The instantaneous interaction (ΔE_int) demonstrates the strength of the bond and ΔE_int for Fe⁰-complex 1 (87.9 kcal mol⁻¹) is significantly higher than that of Fe⁻¹-complex 2 (63.8 kcal mol⁻¹). This lowering of instantaneous interaction is favourable as the reduced Fe⁻¹-complex 2 is the active species in the catalytic conversion of N₂ → NH₃ in the presence of strong proton donor. Note that the instantaneous interactions in 1 and 2 are moderately higher than their bond dissociation energies and the difference can be attributed to the preparative energy. The preparative energies emanate 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. The orbital (covalent) interactions marginally dominate the total attractive interactions in both complexes 1 (57.9%) and 2 (53.2%). The Fe–N bond of 1 is slightly more covalent in nature than that of 2. The electrostatic interactions contribute 40.2–45% and dispersion contribution provide 1.8–1.9% to the total attractive interactions (Table 3). We optimized complex 1 in diethyl ether solvent (see ref. 41) using the CPCM solvation model and performed an EDA-NOCV calculation to check the effect of the solvent on the bond strength (ΔE_int). Interestingly, the results show that the effect of solvent is minimal and showed imperceptible differences in the bonding parameters like intrinsic interactions (87.5 kcal mol⁻¹) and orbital interactions (−159.7 kcal mol⁻¹) compared to that of the gas phase (87.9 and 161 kcal mol⁻¹) (Table S1†).

Table 3 The EDA-NOCV results at the BP86-D3(BJ)/TZ2P level of (cAAC)₂Fe–N₂ bonds of complexes 1 and 2 using neutral (cAAC)₂Fe in electronic triplet state and neutral N₂ fragment electronic singlet state as interacting fragments for complex 1 and singly charged [(cAAC)₂Fe]⁻in electronic doublet state and neutral N₂ fragment electronic singlet state as interacting fragments for complex 2. Energies are in kcal mol⁻¹

Energy	Interaction	(cAAC)2Fe (T) + [N2] (S); (1)	[(cAAC)2Fe]^− (D) + [N2] (S); (2)
a The values in the parentheses show the contribution to the total attractive interaction ΔEelstat + ΔEorb + ΔEdisp.b The values in parentheses show the contribution to the total orbital interaction ΔEorb.
ΔEint		−87.9	−63.8
ΔEPauli		190.2	164.1
ΔEdisp^a		−5.2 (1.9%)	−4.1 (1.8%)
ΔEelstat^a		−111.9 (40.2%)	−102.4 (45.0%)
ΔEorb^a		−161.0 (57.9%)	−121.4 (53.2%)
ΔEorb(1)^b	(cAAC)2Fe ← N2 σ-donation	−61.4 (38.1%)
	(cAAC)2Fe → N2 π-backdonation		−39.4 (32.4%)
ΔEorb(2)^b	(cAAC)2Fe → N2 π-backdonation	−53.6 (33.3%)	−34.0 (28.0%)
ΔEorb(3)^b	(cAAC)2Fe → N2 π-backdonation	−33.2 (20.6%)	−25.2 (20.8%)
ΔEorb(4)^b	(cAAC)2Fe ← N2 σ-donation	−7.5 (4.6%)	−14.7 (12.1%)
ΔEorb(rest)^b		−5.3 (3.3%)	−8.1 (6.7%)

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The total orbital interactions can further be broken down into pairwise contributions which can shed light on the type of interactions (Table 3). The deformation densities and the associated molecular orbitals provide insight into the direction of charge flow as shown in Fig. 2 and 3. The first orbital term (ΔE_orb1) of complex 1 represents the σ-electron donation (Fe ← N₂) from HOMO (3σ_g⁺) of N₂ into vacant d-type anti-bonding orbital (LUMO; mixture of p_z orbitals of C_cAAC and d-orbital of Fe⁰ of 1) of (cAAC)₂Fe⁰ along with the slight charge transfer from d_xz orbital (HOMO−2) of Fe and contributes 38% of the total orbital interactions. The deformation densities of Fig. 2 (top, left) show charge flow from red region on N₂ to blue region on (cAAC)₂Fe⁰. The second and third orbital terms (ΔE_orb2–3) designates π-backdonations (Fe → N₂) from hybrid d_z²–d_{x² y²} orbital (HOMO) of Fe into vacant degenerate π* orbital LUMO (1π_g) of N₂ and partly into SOMO (d_yz) of Fe center and from d_xz orbital (HOMO−1) of Fe into vacant degenerate π* orbital LUMO′ of N₂ in second and third orbital terms respectively. The π-backdonations together contribute 53.9% to the total orbital interactions (Table 3). The weaker fourth orbital term (4.6%) is due to σ-electron donation (Fe ← N₂) from HOMO−2 (2σ_u⁺) of N₂ into vacant d-type orbital (LUMO) of Fe and the two Fe ← N₂ σ electron donations (ΔE_orb1, ΔE_orb4) together contribute 42.6% (Fig. 2) of 1. Table 3 shows that the Fe⁰ → N₂ π-backdonation (ΔE_orb2–3) in 1 is nearly 10% higher than σ-donation (ΔE_orb1,4). The fluctuations of electron clouds on cAAC ligands during the formation of σ- and π-bonds as expected since cAAC is known as both σ-donor and π-acceptor.⁴⁶

Fig. 2 The shape of the deformation densities Δρ_(1)–(4) that correspond to ΔE_orb(1)–(4), and the associated MOs of (cAAC)₂Fe–N₂ (1) and the fragments orbitals of (cAAC)₂Fe in triplet state and N₂ in the singlet state at the BP86-D3(BJ)/TZ2P level. Isosurface values of 0.003 au for Δρ_(1–4). The eigenvalues |ν_n| give the size of the charge migration in e. The direction of the charge flow of the deformation densities is red → blue. Energies are in kcal mol⁻¹.

Fig. 3 The shape of the deformation densities Δρ_(1)–(4) that correspond to ΔE_orb(1)–(4), and the associated MOs of [((cAAC)₂Fe)N₂]⁻ (2) and the fragments orbitals of [(cAAC)₂Fe]⁻ in doublet 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_n| give the size of the charge migration in e. The direction of the charge flow of the deformation densities is red → blue. Energies are in kcal mol⁻¹.

In contrast, the first three orbital terms (ΔE_orb1–3) of complex 2 represent π-electron backdonations (Fe → N₂). While the first orbital term (ΔE_orb1) comes from the π-electron backdonation from d_z² orbital (HOMO) of Fe⁻¹ into degenerate vacant π(p_y)* orbital (LUMO′) of N₂, the second orbital term (ΔE_orb2) is due to π-backdonation from d_x²_y² orbital (HOMO-2) into vacant degenerate π* orbital (LUMO) (1π_g) of N₂. The third orbital term (ΔE_orb3) is due to π-backdonation from d_yz orbital (HOMO−1) of Fe⁻¹ into vacant degenerate π* orbital LUMO′ of N₂. The three π-backdonations together contribute 81.2% of the total orbital contributions. The fourth orbital term (ΔE_orb4) represents the σ electron donation (Fe ← N₂) from HOMO (3σ_g⁺) of N₂ into vacant d-type orbital (LUMO) of Fe and contributes 12.1% to the total orbital interactions (Fig. 3). It is to be observed that due to the mixing of orbitals of cAAC ligand, the shapes of d orbitals of Fe are slightly deformed and can be seen from the associated molecular orbitals of [(cAAC^Me)₂Fe] fragment in Fig. 2 and 3. The mixing of the p_z-orbital of cAAC ligands with d-orbitals of Fe-centre of 1 is much higher than that of 2.

Overall, Fe → N₂ π-backdonations are stronger than Fe ← N₂ σ-donations in both complexes 1 and 2. The percentage of Fe → N₂ π-backdonation in 2 is nearly one and half times higher than that of 1 and Fe ← N₂ σ-donation in 2 is over nearly four times lower than that of 1. A close look at the deformation densities (Fig. 2 and 3) in 1–2 suggests that electronic effect of cAAC ligands is much lower in 2 than in 1 during the formations of σ- and π-bonds. The matrix isolated triplet M(N₂)₈ (M = Ca, Sr, Ba) species are also mainly stabilized by [M(d_π)] → (N₂)₈ π-backdonation.⁴² The EDA-NOCV results, in particular, the σ-donation and π-backdonations and the ellipticity values of QTAIM agrees well with each other and ascertain the speculation of the authors that “the ability of [(CAAC)₂Fe]/[(CAAC)₂Fe(N₂)] to perform nitrogen fixation may arise from the relative flexibility of the system, which is capable of switching between two- and three-coordinate geometries, and allows the formation of highly covalent Fe–N₂ multiple-bond interactions”.⁴¹

In conclusion, although a plethora of iron complexes are shown to bind N₂ molecules in past. The nature of the bonding interactions between Fe-centre and N₂ molecule has not been studied by EDA-NOCV. This study for the first time has provided a quantitative and detailed illustration orbital interactions to shed light on the engrossing Fe–N₂ bond. The bonding interactions between (L)₂Feⁿ (n = 0, −1) and N₂ fragments of two low coordinate and low valence Fe-complexes have been studied by DFT, NBO, QTAIM and EDA-NOCV analyses which revealed that Fe → N₂ π-backdonations are major interactions for efficient N₂ binding. However, the N₂ → Fe σ-donation contributions is not negligible in both the complexes. Fe⁰ center of (L)₂Fe⁰ of 1 is a better σ-acceptor than Fe⁻¹ of 2 while Fe⁻¹ center of (L)₂Fe⁻¹ of 2 is a much stronger π-backdonor due to its richness of electron densities in the latter. The Fe–N₂ interaction energy of 1 is significantly higher than that of 2. These two Fe-complexes are an unprecedented set of complexes among the N₂-bonded Fe-complexes^{18–21,27–33,40,41} which have been studied by EDA-NOCV calculations. The role of cAAC has been clearly shown by the deformation densities during N₂ binding at Fe-centre (charge flow from red → blue). Our EDA-NOCV analysis will help the synthetic chemists to have much clearer view/understanding on the bonding interactions of captivating Fe–N₂ bond and design a superior metal-complex for efficient N₂ binding in their future studies.

Computational methods

Geometry optimizations and vibrational frequencies calculations of (cAAC)₂Fe–N₂ as neutral (1) and anionic complexes (2) in singlet, doublet, triplet and quintet electronic states has been carried out at the BP86-D3(BJ)/Def2TZVPP, for triplet and doublet states additionally at the TPSS-D3(BJ)/Def2TZVPP and PW6B95-D3/Def2TZVPP level⁴⁹ in gas phase. The absence of imaginary frequencies assures the minima on potential energy surface. We have also optimized complex 1 in diethyl ether solvent using CPCM solvation model.⁴⁹ All the calculations have been performed using Gaussian 16 program package.⁵⁰ NBO⁵¹ calculations have been performed using NBO 6.0 (ref. 52) program to evaluate partial charges, Wiberg bond indices (WBI)⁵³ and natural bond orbitals. The nature of Fe–N₂ bonds in complexes 1 and 2 were analyzed by energy decomposition analysis (EDA)⁵⁴ coupled with natural orbital for chemical valence (NOCV)⁵⁵ using ADF 2018.105 program package.⁵⁶ EDA-NOCV calculations were carried out at the BP86-D3(BJ)/TZ2P⁵⁷ level using the geometries optimized at BP86-D3(BJ)/def2-TZVPP level. EDA-NOCV method involves the decomposition of the intrinsic interaction energy (ΔE_int) between two fragments into four energy components as follows:

ΔE_int = ΔE_elstat + ΔE_Pauli + ΔE_orb + ΔE_disp, (1)

where the electrostatic ΔE_elstat term is originated from the quasi-classical electrostatic interaction between the unperturbed charge distributions of the prepared fragments, the Pauli repulsion ΔE_Pauli is the energy change associated with the transformation from the superposition of the unperturbed electron densities of the isolated fragments to the wavefunction, which properly obeys the Pauli principle through explicit anti-symmetrisation and renormalization of the production of the wavefunction. Dispersion interaction, ΔE_disp is also obtained as we used D3(BJ). The orbital term ΔE_orb comes from the mixing of orbitals, charge transfer and polarization between the isolated fragments. This can be further divided into contributions from each irreducible representation of the point group of the interacting system as follows:

The combined EDA-NOCV method is able to partition the total orbital interactions into pairwise contributions of the orbital interactions which is important in providing a complete picture of the bonding. The charge deformation Δρ_k(r), which comes from the mixing of the orbital pairs ψ_k(r) and ψ_−k(r) of the interacting fragments, gives the magnitude and the shape of the charge flow due to the orbital interactions (eqn (3)), and the associated orbital energy ΔE_orb presents the amount of orbital energy coming from such interaction (eqn (4)).

Readers are further referred to the recent reviews articles to know more about the EDA-NOCV method and its applications.⁴⁸

Conflicts of interest

Authors do not have any conflict of interest.

Acknowledgements

We thank Prof. Gernot Frenking and Prof. K. M. S for providing computational facilities. S. M. also thank Dr S. Pan. S. M. thanks CSIR for SRF. K. C. M thanks SERB for the ECR grant (ECR/2016/000890) and IIT madras for seed grant.

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Footnote

† Electronic supplementary information (ESI) available: Tables, figures, QTAIM, and optimized coordinates. See DOI: 10.1039/d1ra08348a

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