COMPARATIVE ASSESSMENT OF THE COMPOSITION AND CHARGE STATE OF NITROGENASE FeMo-COFACTOR

Abstract

A significant limitation in our understanding of the molecular mechanism of biological nitrogen fixation is the uncertain composition of the FeMo-cofactor (FeMo-co) of nitrogenase. In this study we present a systematic, density functional theory-based evaluation of spin coupling schemes, iron oxidation states, ligand protonation states, and interstitial ligand composition using a wide range of experimental criteria. The employed functionals and basis sets were validated with molecular orbital information from X-ray absorption spectroscopic data of relevant iron-sulfur clusters. Independently from the employed level of theory, the electronic structure with the greatest number of antiferromagnetic interactions corresponds to the lowest energy state for a given charge and oxidation state distribution of the iron ions. The relative spin state energies of resting and oxidized FeMo-co already allowed the exclusion of certain iron oxidation state distributions and interstitial ligand compositions. Geometry optimized FeMo-co structures of several models further eliminated additional states and compositions, while reduction potentials indicated a strong preference for the most likely charge state of FeMo-co. Mössbauer and ENDOR parameter calculations were found to be remarkably dependent on the employed training set, density functional and basis set. Overall, we found that a more oxidized [Mo^IV-2Fe^II-5Fe^III-9S²⁻-C⁴⁻] composition with a hydroxyl-protonated homocitrate ligand satisfies all of the available experimental criteria, and is thus favored over the currently preferred composition of [Mo^IV-4Fe^II-3Fe^III-9S²⁻-N³⁻] from the literature.

1. Introduction

Biological nitrogen fixation is catalyzed by the two-component nitrogenase metalloenzyme.¹ The catalytically active [M-7Fe-9S] cluster of nitrogenase is present in three forms distinguished by its composition, where M is Mo, V or Fe. The Mo-containing nitrogenase is the most active and the most studied, and thus is the focus of this research. A significant limitation in understanding the molecular basis of biological nitrogen fixation is the lack of electronic structural and compositional knowledge of the catalytically active iron-molybdenum-sulfur cluster cofactor, FeMo-co. FeMo-co has been identified as a [Mo-7Fe-9S-X] cluster from the nearly atomic resolution ($1.16\acute{\mathrm{Å}}$) crystal structure of the MoFe protein of nitrogenase.² While the composition of the central ligand (X) could not be unambiguously established experimentally, the crystallographic analysis of the resolution-dependent electron-density profile and the interaction of nitrogenase with dinitrogen and ammonia suggested that X is likely N. The two neighboring elements also fit well the experimental electron density profiles. In FeMo-co, these atoms would correspond to carbido (C⁴⁻), nitrido (N³⁻), or oxo (O²⁻) ligands. Other 10 electron ions as alternative ligands, such as B⁵⁻, F⁻, Na⁺, or Mg²⁺ can likely be excluded due to charge incompatibility (see below) or limited biochemical availability (B⁵⁻, F⁻). The Cys275 and His442 residues at the terminal Fe and Mo, respectively, and a non-protein ligand, homocitrate, complete the FeMo-co inner sphere coordination environment.

The MoFe-protein has been isolated with three forms of FeMo-co: resting or native (FeMo-co^N), one-electron reduced (FeMo-co^Red) and one-electron oxidized (FeMo-co^Ox).³ Electron nuclear double resonance (ENDOR) data suggest the Mo center is diamagnetic with a formally +IV (4d²) oxidation state in the resting form.⁴ X-ray absorption spectroscopic (XAS) measurements further support the presence of Mo^IV oxidation state in all three forms.^{5, 6} FeMo-co^N shows a characteristic S_t = 3/2 EPR signal, while the reduced form is EPR silent with integer spin, S_t ≥ 1. The oxidized form is diamagnetic as observed at 4 K,^7-9 but a low lying excited S_t ≥ 1 state is populated between 240 and 320 K.¹⁰ The reduction potential for the FeMo-co^Ox/FeMo-co^N couple has been determined to be −42 mV,¹¹ while the second reduction step for FeMo-co^N/FeMo-co^Red has only been estimated to be −465 mV.³

FeMo-co can be extracted (exFeMo-co) into N-methyl formamide (NMF) solution with the homocitrate ligand remaining coordinated, a deprotonated solvent anion (NMF⁻) substituting the negatively charged thiolate of Cys275, and a neutral NMF molecule replacing the imidazole of His442.¹² A cation binding study indicated that exFeMo-co^Ox has an overall charge of −2.¹³ With a plausible assumption that the protonation state of homocitrate is the same in the protein-bound and extracted form, the charge of FeMo-co^Ox can be considered to be the same as the exFeMo-co^Ox. Thus, the charge of FeMo-co^N can be assigned to −3, which provides a criterion for evaluating the formal oxidation states of the unknown Fe centers. Moreover, the S_t = 3/2 resting form and a diamagnetic Mo^IV center limit the formal Fe oxidation states to 6Fe^II-1Fe^III, 4Fe^II-3Fe^III, 2Fe^II-5Fe^III, and a 7Fe^III state that is unlikely due to the required Fe^IV site in the oxidized form within a sulfide coordination environment. ⁵⁷Fe ENDOR experiments led to the suggestion of the 6Fe^II-1Fe^III assignment for the CO-bound FeMo-co,¹⁴ while Mössbauer isomer shifts were more consistent with the 4Fe^II-3Fe^III state for the resting form.¹⁵ An electrochemical study of exFeMo-co linked the above Mössbauer and ENDOR assignments by implying that the CO-bound form is more consistent with a 2-electron reduced form relative to the resting state.¹²

Earlier computational studies employing density functional theory (DFT) have also favored the 4Fe^II-3Fe^III oxidation state for the resting form. Vrajmasu et al. calculated Mössbauer isomer shifts for all possible Fe oxidation states and X = C⁴⁻, N³⁻, and O²⁻; only the [4Fe^II-3Fe^III-N³⁻], [4Fe^II-3Fe^III-C⁴⁻], and [2Fe^II-5Fe^III-N³⁻] oxidation state assignments were consistent with experiments.¹⁶ An indication for the interconnectedness of the formal oxidation states of the Fe centers and the nature of the interstitial ligand was already found by Lovell et al., who initially obtained computational results preferring the 6Fe^II-1Fe^III state using an early FeMo-co model without the presence of an interstitial atom.¹⁷ However, inclusion of an anionic central ligand gave better agreement between the calculated and experimental Mössbauer isomer shifts for the [4Fe^II-3Fe^III-N³⁻] state than that of [6Fe^II-1Fe^III-N³⁻].¹⁸ Furthermore, structural optimizations favored the 4Fe^II-3Fe^III state with either N³⁻ or C⁴⁻ while disfavoring O²⁻. The calculated reduction potentials indicated that [4Fe^II-3Fe^III-N³⁻] was the most likely oxidation state and composition. Notably, the results for the [2Fe^II-5Fe^III-N³⁻] state/composition was not reported. By comparing HOMO energies of FeMo-co and Fe-S clusters, Dance found preference for [4Fe^II-3Fe^III-N³⁻], or [4Fe^II-3Fe^III-C⁴⁻] with a protonated μ²-sulfide or Fe site.^{19, 20} Comparison of the three lowest energy spin states showed that [2Fe^II-5Fe^III-N³⁻] had an S_t = 3/2 ground state, consistent with experiment, while [4Fe^II-3Fe^III-N³⁻] had an S_t = 5/2 ground state. The S_t = 3/2 state was found to be about 20 kJ/mol higher for the latter. By contrast, using non-collinear spin calculations, Shimpl et al. reported S_t = 3/2 to be the ground state for [4Fe^II-3Fe^III-N³⁻], while the ground states for [2Fe^II-5Fe^III-N³⁻] and [6Fe^II-1Fe^III-N³⁻] were S_t = 1/2 and S_t = 0.24, respectively, with the optimized [4Fe^II-3Fe^III-N³⁻] giving the best agreement with experiment.²¹ In summary, previous computational work favors the [4Fe^II-3Fe^III-N³⁻] state, although other states and compositions could not be unequivocally ruled out.

It is important to note that density functional theory calculations can be greatly influenced by the nature of exchange and correlation functionals, the amount of mixing of exact exchange, the completeness of employed basis sets, and the level of truncation of the employed computational model. In addition, due to the presence of high spin Fe centers within weak-field ligand environments, the method of describing ferro- and antiferromagnetic interactions is critical. Mössbauer¹⁵ and ENDOR²² measurements indicate four parallel spins and three antiparallel to the majority spin (spin-up or α) direction. While theoretically not exact,²³ a commonly used practical method to treat spin coupling interaction within the formalism of DFT is the broken symmetry (BS) approach.²⁴ For FeMo-co^N, Noodleman defined 10 major BS spin-coupling patterns¹⁷ with numerous alternative spin-configurations. In addition to the challenge of obtaining and maintaining the correct spin state, the lowest energy BS state was found to depend on the chemical composition of the computational model and the employed density functional.²⁵ As discussed below, the atomic coordinates of computational models are also critical, particularly when the coordinates are based on a protein crystal structure with modest resolution. Furthermore, the protonation states of coordinated residues and ligands are often unknown, even for a close to atomic resolution protein structure. The protonation state of the homocitrate ligand is a key aspect that has not yet been systematically evaluated. This is important, since as a charged ligand, the homocitrate contributes to the overall charge of FeMo-co. Furthermore, the protonation state can also affect the bonding interactions around the Mo center and thus have implications for a proposed mechanism in which homocitrate becomes monodentate, opening up a coordination site for N₂.²⁶ 2 The deprotonated homocitrate ligand with a charge of −4 (or a truncated version with a charge of −2) has been chosen for many theoretical studies,^{18, 20, 27, 28} while some assume a −3 charge for the complete ligand.^{14, 16} An earlier computational work already suggested the possibility that the coordinated hydroxyl oxygen is protonated in the resting form.²⁹ Others proposed that protonation of the coordinated carboxylate group may be the first step of the catalytic mechanism.^{26, 30}

In this study we carried out a comprehensive evaluation of a comprehensive compilation of experimental data with respect to spin coupling schemes, spin state energies, iron oxidation states, compositions of the interstitial atom, protonation states of the coordinated groups of the homocitrate ligand, reduction potentials, isomer shifts, quadrupole splittings and hyperfine coupling parameters. Based on a series of structural, energetic, electronic, and magnetic criteria, we can rule out certain compositions and oxidation states, and we find that only the [Mo^IV-2Fe^II-5Fe^III-9S²⁻-C⁴⁻]⁺ composition with hydroxyl-protonated homocitrate ligand (HC³⁻) is favored consistently for FeMo-co^N.

2. Computational Details

The computational model of FeMo-co (Figure 1) was based on the highest resolution ($1.16\acute{\mathrm{Å}}$) crystal structure of the MoFe protein available to date from Azotobacter vinelandii (PDB ID 1M1N)². The ligands Cys275, His442, and homocitrate were truncated to methylthiolate, imidazole, and glycolate, respectively. We consider glycolate to be an acceptable computational model of homocitrate for evaluating the electronic and geometric structures of FeMo-co due to the limited role of the omitted distal carboxylate arms of homocitrate in polarization of the FeMo-co electron density similarly to weakly bound, solvated counter ions. The majority of this work (see below for exceptions) was carried out using Gaussian03 Rev. E.01³¹ employing the gradient-corrected Becke88³² exchange and Perdew86³³ correlation functionals (BP86) and the Stuttgart-Dresden effective core potentials and valence basis set (SDD-VTZ(d))^34-36 for all atoms, with additional polarization functions for Fe³⁷, Mo³⁷ and S³⁸. This choice was rigorously validated for [4Fe-4S] clusters in a previous work,³⁹ and to ensure consistency, representative calculations (see below) were also carried out with hybrid functionals such as B3LYP⁴⁰, B(5HF)P86⁴¹ and/or a larger basis set (6-311+G(d))⁴². Isomer shifts, quadrupole splittings and the hyperfine coupling constant for interstitial ligand X were calculated using ADF2009^43-45 at the BP86/STO-TZP level, with an integration accuracy of 5. The Conductor like Screening Model (COSMO)^46-49 with ε = 30 was used to approximate the polar environments of the complexes in the isomer shift training set, while the less polar constant, ε = 10, was used to approximate the dielectric environment of the protein matrix around FeMo-co. The spin coupling calculations were all carried out using the oxidation state assignment and composition [4Fe^II-3Fe^III-N³⁻] on the experimental FeMo-co structure for in vacuo computational models. Notably, gas phase calculations for models with −4 or greater negative overall charge showed unreasonable spin densities; thus, these highly charged models were embedded in a polarizable continuum model (PCM)^50-52 with ε = 10. Relative energies of spin states calculated using PCM were within 2 kJ/mol of corresponding energy differences from gas phase calculations. However, for consistency, all geometry optimizations were performed in the presence of PCM. Optimizations at the computationally more expensive B(5HF)P86/6-311+G(d) level resulted in geometric structural deviations of only 0.01 Å relative to BP86/SDD-VTZ(d). This is similar to previously determined experimental vs. calculated structural differences of less than 0.03 Å (RMS value) for the model system, [Fe₄S₄(SEt)₄]²⁻ at B(5HF)P86/6-311+G(d) level.³⁹

Figure 1.

Computational model of FeMo-co based on the $1.16\acute{\mathrm{Å}}$ crystal structure of the MoFe protein from Azotobacter vinelandii (PDB ID 1M1N)².

Ferro- and antiferromagnetic spin coupling schemes were obtained using the broken symmetry (BS)²⁴ approach.⁵³ The initial localized spin states were constructed by the ionic fragment approach.³⁹ For example, the FeMo-co^Ox state has been described in the literature as diamagnetic (S_t = 0).^7-9 Thus, the initial electronic structure was constructed from Fe^II (m_s = ±2) and Fe^III (m_s = ±5/2) centers to result in an M_s = 0 state, where the total number of spin up (α) and spin down (β) electrons was equal. Consistently we use the S_t and M_s spin quantum numbers to differentiate among the pure spin states and the calculated broken symmetry (BS) spin states. The initial ionic electronic structure was allowed to relax to the broken-symmetry solution. The order of Fe^II and Fe^III centers in the ionic fragments had no effect on the converged broken-symmetry state. Pure antiferromagnetically coupled spin states were considered for reduction potential calculations by using a spin projection procedure⁵⁴ based on the Heisenberg Hamiltonian with FeMo-co modeled as a two spin-system. This approach is conceptually incorrect due to the presence of 7 paramagnetic centers; however, this can be considered as a first order approximation due to the formal topology of FeMo-co being composed of a [Mo-3Fe-3S] and a [4Fe-3S] clusters that are coupled through three bridging sulfide and the central ligands. With this simplified model, there is a linear relationship between energies and expectation values of the spin operator (<S²>), which was determined from the broken symmetry and the pure ferromagnetically coupled (maximal S_t) state. Then the energy of the pure ground spin state was obtained using the known <S²>-value (e.g., 15/4 for an S_t = 3/2 state). A more rigorous approach to spin projection,⁵⁵ in which the Hamiltonian included coupling between the individual Fe sites, was carried out for [4Fe^II-3Fe^III-N³⁻], and the projected ground state energy only deviates by 4 kJ/mol between the two approaches (see Section 3.2). Double exchange⁵⁶ effects were not included in the spin state analysis due to technical limitations. These are the subject of ongoing work, as an extensive treatment adds substantial complexity, even to two-center systems, such as [2Fe-2S] clusters.⁵⁷ A recent work considered double exchange interactions for a multinuclear spin system on top of the Heisenberg exchange and an effective Coulomb intercenter repulsion;⁵⁸ however, due to computational limitations the size of the system was limited to six Fe.

In order to evaluate the adequacy of the selected level of theory, the comparison of experimental⁵⁹ and calculated sulfur 3p orbital characters (S(3p)) of metal-sulfide bonds was carried out. Sulfur K-edge X-ray absorption spectroscopic measurements⁵⁹ for a prototypical model complex of [Fe₄S₄(SEt)₄]²⁻ define a total of 1.23 and 0.41 e donation from the bridging sulfides and thiolate sulfurs to the irons. The theoretical sulfur covalency values were derived from the difference between the S(3p) atomic populations of the covalent electronic structure and the theoretical ionic limit of six electrons. S(3p) characters were obtained from the Natural Population Analysis (NPA)⁶⁰ with a minimal valence set, where S(3d), Fe(4s, 4p), Mo(5p) and higher orbitals were treated as part of the Rydberg atomic orbital set. The BP86/SDD-VTZ(d) level gives 1.19 and 0.40 e S(3p) character for the Fe-sulfide and Fe-thiolate bonds that already well approximate the experimental values. Employing a larger all-electron basis set (6-311+G(d)) and an experimentally validated hybrid functional, B(5HF)P86,⁴¹ improve only slightly this agreement to 1.22 and 0.42 e. A detailed analysis of errors in calculated parameters for the same model system has already been published.³⁹

To determine reduction potentials that include contributions from solvation effects, free energy changes (ΔG°_reduction) were calculated⁶¹ according to the following equations:

$$\Delta {G^{\circ }}_{\text{reduction}}=\Delta {G^{\circ }}_{\text{solute}}+\Delta \Delta {G^{\circ }}_{\text{solvation}}$$ (1)

$$\Delta {G^{\circ }}_{\text{solute}}=\Delta {{\epsilon }_{\mathrm{SCF}}}^{\mathrm{s}.\mathrm{p}.}+\Delta {\mathrm{ZPE}}_{\text{solute},\mathrm{corr}}+\Delta {H^{\circ }}_{\text{solute},\mathrm{corr}}-T\Delta {S^{\circ }}_{\text{solute},\mathrm{corr}}$$ (2)

$$\Delta \Delta {G^{\circ }}_{\text{solvation}}=\Delta \Delta G_{\text{electrostatic}}+\Delta \Delta G_{\text{nonelectrostatic}}$$ (3)

where Δε_SCF^s.p. is the difference in the gas phase spin projected (indicated by the superscript ‘s.p.’) ground state electronic energy of the PCM-optimized reduced and oxidized forms. The enthalpy, entropy and zero-point energy (ZPE) corrections were calculated as changes between the reduced and oxidized forms of the solute; ΔG_{electrostatic} refers to the electrostatic solute-solvent interactions; and ΔG_{nonelectrostatic} refers to the non-electrostatic cavitation, dispersion and repulsion energies of solvent-solvent interactions. Overall, in this approach we take into account both inner and outer sphere relaxation effects including the geometric relaxations upon solvation. The standard one-electron reduction potentials (n = 1) were then calculated using the Nernst equation:

$$\Delta {G^{\circ }}_{\text{reduction}}=-nF{E}^{\circ }$$ (4)

where F is the Faraday constant, 23.06 kcal mol⁻¹ V⁻¹. A −4.43 eV correction was applied as a reference for the absolute reduction potential of the normal hydrogen electrode (NHE).¹¹ The use of only gas phase optimized structures and exclusion of the corrections due to geometric changes upon solvation can introduce a considerable 60 mV error.⁶² With the above approach, the gas phase optimizations actually can be omitted, since each contribution mentioned in Equations (1)-(3) can be derived from PCM-optimized structures and related energy analysis.

Mössbauer quadrupole splittings, ΔE_Q, were calculated from the electric field gradient tensors (V) in a coordinate system where V_zz ≥ V_xx ≥ V_yy, using Eq. (5), where e is the elementary charge, Q is the nuclear quadrupole moment of ⁵⁷Fe (0.158 barn)⁶³ and η is the asymmetry parameter (∣V_xx-V_yy)/V_zz∣.

$$\Delta E_{\mathrm{Q}}=\frac{1}{2}eQ{V}_{zz}\sqrt{1+\frac{{\eta }^2}{3}}$$ (5)

Hyperfine coupling constants (HFCC) depend critically on the spin-polarized electron density at the nucleus (ρ_s(0)), which is difficult to calculate accurately for transition metal systems.⁶⁴ For multinuclear complexes, magnetic interactions and the use of the BS approach further complicate the calculations. Neese et al. have developed a method based on the Heisenberg Hamiltonian,⁶⁵ which derives scaling factors for calculated HFCCs at transition metal centers. However, a recent study of the [6Fe-6S] catalytic cluster of [FeFe]-hydrogenase demonstrates that even with the scaling factors the absolute accuracy of calculated HFCCs is low, although the ratios of HFCCs can be qualitatively useful.⁶⁶ In this work we employ a semi-empirical method developed by Mouesca et al.,^{67, 68} which avoids calculation of the problematic ρ_s(0) values. The procedure has previously been used to analyze spin coupling in FeMo-co¹⁷ and the P-cluster⁶⁷ of nitrogenase.

The isotropic contributions to the observed HFCCs (a_i^exp) for Fe sites in a spin coupled system are proportional to the projections (K_i) of the local site spins (S_i) onto the total spin. Thus, the hyperfine parameters (a_i^calc) were determined using the following equation:

$$a_i^{\mathrm{calc}}=K_i(\mid {\rho }_s({\mathrm{Fe}}_i)\mid ∕2S_i)a_i^{\text{ionic}}$$ (6)

In Equation (6), the spin densities, ρ_s(Fe_i), scale the empirically derived⁶⁸ intrinsic Fe site parameters, a_i^ionic, which are −34.0 MHz, −32.5 MHz, and −31.0 MHz for Fe²⁺, Fe^2.5+ and Fe³⁺ with S_i = 2, 9/4 and 5/2, respectively. K_i factors (see Table S12) were calculated according to Eq. (7) developed by Noodleman and coworkers.^{17, 25}

$$K_i=\langle {\mathit{S}}_i\cdot {\mathit{S}}_t\rangle ∕\langle {\mathit{S}}_t\cdot {\mathit{S}}_t\rangle$$ (7)

Calculations of hyperfine couplings for X = ¹⁴N or ¹³C were also performed according to Eq. (8) by Noodleman and coworkers,²⁵ where a_iso^BS(X) values were obtained from the broken symmetry calculation and scaled by the P_x factors 0.40, 0.46 and 0.51 for the 6Fe^II-1Fe^III, 4Fe^II-3Fe^III and 2Fe^II-5Fe^III oxidation state distributions, respectively.

$$a_{\mathrm{iso}}\left(\mathrm{X}\right)=\frac{1}{6}\sum _{i=2,3\dots 7}(\mid K_i∕S_i\mid S_t)a_{\mathrm{iso}}^{\mathrm{BS}}\left(\mathrm{X}\right)=P_{\mathrm{x}}{a}_{\mathrm{iso}}^{\mathrm{BS}}\left(\mathrm{X}\right)$$ (8)

Due to the local symmetry of the central 6 Fe belt and the bridging sulfide ligands, we considered the same hyperfine coupling interaction between the Fe and the interstitial atom, X. The electron density at X takes into account the individual effects of the neighboring Fe sites, and the projection of the calculated hyperfine coupling of X onto the total spin S_t = 3/2 takes into account the individual projection coefficients and spin of each Fe site.

The ⁵⁷Fe isomer shifts (δ) from Mössbauer spectroscopy are directly proportional to the electron density at the nuclei, ρ(0). Calculated ρ(0) values are dependent on the employed functional and basis set;⁶⁹ thus, to calculate the ⁵⁷Fe isomer shifts for FeMo-co, the relationship between ρ(0) and δ was obtained for a training set, which is composed of [Fe-S] and [Mo-Fe-S] clusters of various charge and spin states. The calculated and experimental values were fit to Eq. (9), where a constant, A (in e a₀⁻³), was chosen to reduce the magnitude of ρ(0) (in e a₀⁻³), and the fit parameters are α (in e⁻¹ a₀³ mm s⁻¹) and C (in mm s⁻¹).

$$\delta =\alpha \left(\rho \right(0)-A)+C$$ (9)

3. Results and Discussion

3.1 Evaluation of Broken-Symmetry Spin Coupling Schemes

Assuming weak-field ligand environments from the thiolate and sulfide ligands, the formally Fe^III and Fe^II centers adopt high-spin S = 5/2 and 2 states, respectively. The total spin (S_t = 3/2) of FeMo-co^N is a result of ferro- and antiferromagnetic coupling between the Fe centers, of which four have parallel and three have antiparallel (4+3) spin orientations according to the interpretations of ENDOR²² and Mössbauer¹⁵ data. When FeMo-co’s electronic structure is treated with broken symmetry (BS) formalism, a given charge and oxidation state distribution with high-spin Fe centers can have 35 nonequivalent BS states with M_s = 3/2 that are also consistent with the above-mentioned experimental 4+3 spin orientation. These states can be divided into 10 groups based on the number of antiferromagnetically coupled Fe pairs. The first type is bridged by two sulfides, and the second bridged by one sulfide and X (see representative states in Figure 2A).¹⁷ The former is exclusive to pairs that include the terminal Fe. There is a third type of Fe pair, which is bridged by only X. In order to build up a reference base for a priori choosing the lowest energy spin state, we evaluated all 35 spin states (see Table S1). We also evaluated the dependence of the relative energies of spin coupling states on the applied functional (BP86 vs. B3LYP) and basis set (SDD-VTZ(d) vs. 6-311+G(d)).

Figure 2.

Relative energies of the 35 individual spin states to the lowest energy state, BS7, plotted against (A) the number of sulfide bridged antiferromagnetically coupled Fe pairs and (B) the total number of antiferromagnetic interactions with N_Fe-S-Fe and N_Fe-X-Fe given in parentheses for each group of BS states. Spin distributions (A, inset) show representative examples from each group used in calculations with various functionals and basis sets (C). The nomenclature for the BS states was adapted from Ref. 17. Numerical results are available as supporting information.

Figure 2 summarizes the results obtained for the relative energies of various spin-coupling schemes of [4Fe^II-3Fe^III-N³⁻].⁷⁰ The results in Figure 2A display a trend of lower energy with increasing numbers of sulfide-bridged antiferromagnetically coupled pairs of Fe centers (N_Fe-S-Fe) at the BP86/SDD-VTZ(d) level. Representative individual coupling schemes within each of the 10 major groups are depicted in the inset of Figure 2A. Notably, the BS2 state is strikingly (>25 kJ/mol) lower in energy than the BS9 and BS5 states, even though they all have the same N_Fe-S-Fe (6). This is because BS2 has an additional six X-bridged antiferromagnetically coupled Fe pairs (N_Fe-X-Fe), while BS9 and BS5 have four. Similarly, BS4 and BS10 are almost equivalent in energy to BS8 and BS6 because the former ones have more N_Fe-S-Fe (8 vs. 7), but less N_Fe-X-Fe (4 vs. 6). Thus, the primary factor affecting the stability of BS states is the number of individual M-L-M antiferromagnetic interactions (2N_Fe-S-Fe + N_Fe-X-Fe), as shown in Figure 2B.

Figure 2C shows a representative state for each number of antiferromagnetically coupled Fe pairs calculated at the different levels of theory (see Table S2 for numerical results). Although the overall trend is the same in each case, there is a notable functional dependence for the order of higher lying states in Figure 2C. With the pure DFT (GGA) functional, BP86, the lowest energy spin state other than BS7 in Figure 2C is BS6, consistent with the findings of Noodleman and coworkers,²⁵ who examined the same representative states using a GGA functional, PW91. However, we find that using the popular hybrid functional, B3LYP, BS10 is lower in energy than BS6. Most importantly, the ground state for each evaluated level of theory is BS7, and the overall trend is the same. A similar trend was also observed by Noodleman and coworkers using an early FeMo-co model without the interstitial atom, although BS6 was found to be the ground state.¹⁷ With X = N³⁻ and a change in functional, they found BS7 to be the ground state for X = N³⁻,²⁵ in agreement with results from Blöchl and coworkers,²¹ who used a different theoretical approach. Additionally, ESEEM and ENDOR measurements indicate that if X = N or C the hyperfine coupling to X is weak, which, as shown by DFT, favors a spin state with symmetric spins in the central ‘6Fe-belt’, such as BS7.²⁵

Within BS7, the oxidation states 6Fe^II-1Fe^III, 4Fe^II-3Fe^III and 2Fe^II-5Fe^III can be described by several formal distributions that all satisfy M_s = 3/2. Three such distributions are given for the 2Fe^II-5Fe^III state in Figure 3. Although the formal subcluster M_s values vary, due to delocalization, calculations converge to a single electronic structure (Figure 3, far right). Thus, the cluster oxidation state, M_s value and spin coupling scheme are enough to uniquely describe an electronic structure, without specifying the specific oxidation state distribution.

Figure 3.

Three of the formal oxidation state distributions for the 2Fe^II-5Fe^III state, with subcluster M_s values indicated below. Calculated spin densities ρ_s(Fe) for [2Fe^II-5Fe^III-N³⁻] are given on the right.

3.2 Spin State Dependence on Oxidation States and Compositions for FeMo-co^N and FeMo-co^Ox

A commonly considered criterion for evaluating the likeliness of a given oxidation state and composition for FeMo-co is that the ground spin state must be consistent with the experimentally observed S_t = 3/2. It is important to realize that the consideration of only weak-field, high spin Fe^II and Fe^III centers limits the possible oxidation states of the resting form to 6Fe^II-1Fe^III, 4Fe^II-3Fe^III 2Fe^II-5Fe^III, and 7Fe^III, all of which can access the S_t = 3/2 state. The 7Fe^III state is unlikely, as discussed in the introduction, and was not considered here. In order to assess the ground and excited spin states, the energies of S_t = 5/2 and 1/2 states for each oxidation state with X = C⁴⁻, N³⁻ or O²⁻ were compared to S_t = 3/2 using the lowest energy BS7 spin coupling scheme with high spin Fe^III and Fe^II centers at atomic coordinates derived from the crystal structure². Due to the limitation of the BS approach, only the M_s value is defined in the FeMo-co calculations.⁵³

The relative spin state energies presented in this section have been calculated by assuming that the BS7 state with a given M_s value best represents the spin state of corresponding S_t, i.e., the S_t = 3/2 state is modeled by an M_s = 3/2 BS state. To estimate the validity of this assumption we have considered the Heisenberg spin Hamiltonian. As a first order approximation, FeMo-co can be considered as a two spin system, where a single exchange coupling constant, J, couples the [4Fe-3S] subcluster to the [Mo-3Fe-3S] subcluster. With this model, the spin projected⁵⁴ ground state is −22 kJ/mol lower in energy than the ground BS state for [4Fe^II-3Fe^III-N³⁻], and excited spin states are similarly corrected by about −20 kJ/mol. Thus the two-spin model will not effect the relative ordering of the ground and the closest BS state energies. As an improvement to the single J model, the coupling of all 7 spin sites with 18 J constants was carried out using the Yamaguchi generalized spin projection method,⁵⁵ and spin state energies were obtained by diagonalizing a sizeable Hamiltonian.⁷¹ For [4Fe^II-3Fe^III-N³⁻] oxidation/composition the resulting ground state remains S_t = 3/2 and it is 18 kJ/mol lower in energy than the M_s = 3/2 BS7 state. The lowest energy S_t = 1/2 and S_t = 5/2 states lie about 5 kJ/mol above the ground S_t = 3/2 state. Overall, the BS and the Heisenberg approaches both give qualitatively correct results with respect to the experimental S_t = 3/2 ground state, and the same relative ordering of excited states. Furthermore, from a through analysis of the eigenvectors of the Heisenberg Hamiltonian we find that the BS7 state with high spin Fe centers and a particular M_s value (±3/2, for example) has the highest weighing (11%) among all of the more than 10000 BS states in the lowest energy pure spin state with a corresponding S_t value (3/2, accordingly).

In contrast to other work,^{19, 21} Figure 4A shows that M_s = 3/2 is the lowest lying BS state regardless of the oxidation state and composition. The preferred 4Fe^II-3Fe^III assignment has a large energy gap (> 30 kJ/mol) between the ground and excited spin states; this becomes considerably less (~10 kJ/mol) for 6Fe^II-1Fe^III and 2Fe^II-5Fe^III. Overall, an M_s = 3/2 ground state does not allow for discriminating between compositions, charges, or formal oxidation states (for numerical results see Table S3).

Figure 4.

Relative energies of (A) the M_s = 1/2 (dotted gray line) and 5/2 BS states (dotted black line) to the M_s = 3/2 ground BS state (solid black line) of FeMo-co^N, and the M_s = 1 (dotted gray line) and 2 BS states (dotted black line) relative to the M_s = 0 BS state (solid black line) of FeMo-co^Ox using the experimental crystal structure (B) and optimized geometries (C). Numerical results are available as supporting information.

The oxidized form of FeMo-co (FeMo-co^Ox) has an even electron S_t = 0 ground spin state according to Mössbauer^{7, 8} and MCD⁹ measurements, providing another means of evaluating oxidation state and composition. The energies of three spin states, M_s = 0, 1, or 2, were calculated for the 5Fe^II-2Fe^III, 3Fe^II-4Fe^III and 1Fe^II-6Fe^III oxidation states, which are the corresponding one-electron oxidized forms of 6Fe^II-1Fe^III, 4Fe^II-3Fe^III, and 2Fe^II-5Fe^III (with an S_t = 3/2 ground state), respectively. As shown in Figure 4B, when using the FeMo-co^N crystal structure for oxidized calculations, no combination of Fe centers and interstitial atom has an M_s = 0 ground state. Importantly, using structurally optimized FeMo-co^Ox models, we find that the M_s = 0 state becomes the ground spin state for 1Fe^II-6Fe^III (Figure 4C) with a low lying M_s = 1 state (~3 kJ/mol), showing a close agreement with experiment¹⁰. For 3Fe^II-4Fe^III and 5Fe^II-2Fe^III, geometry optimized structures show the same experimentally inconsistent high energy M_s = 0 state as in Figure 4B (for numerical results see Table S4). However, if the 3Fe^II-4Fe^III state is considered to be the reduced form of 2Fe^II-5Fe^III, rather than the oxidized form of 4Fe^II-3Fe^III, then the results are consistent with the S_t ≥ 1 state shown by experiment. Independently from the composition of the interstitial atom, these results indicate a strong preference for the 1Fe^II-6Fe^III oxidation state assignment for FeMo-co^Ox, which in turn corresponds to 2Fe^II-5Fe^III for the resting FeMo-co^N form.

3.3 Geometric Differences with Various Oxidation States and Compositions

As shown for the relative energies of FeMo-co^Ox spin states, electronic structure is intimately linked to geometric structure. Comparison of the interatomic distances in selected optimized FeMo-co^N structures to those in the nearly atomic resolution (1.16 Å) crystal structure² and Extended X-ray Absorption Fine Structure analyses^{6, 72} can provide another criterion for evaluating different compositions, charges and iron oxidation state distributions, as these properties are expected to affect the overall size of the cluster and the Fe-X bond lengths. Table 1 compares the structural optimization results for the FeMo-co^N form in the most probable states, [2Fe^II-5Fe^III-N³⁻], [2Fe^II-5Fe^III-C⁴⁻], [4Fe^II-3Fe^III-O²⁻], [4Fe^II-3Fe^III-N³⁻], and [4Fe^II-3Fe^III-C⁴⁻], with experimental metric data. The optimized structure of the [2Fe^II-5Fe^III-O²⁻] state is not reported here due to cluster dissociation. The results for the [6Fe^II-1Fe^III-N³⁻] state are shown in Table S5, but this is unlikely relevant due to its highly reduced state. Looking at the S(Cys)-Fe through Fe^(Fe)…Fe^(Fe) distances, the 2Fe^II-5Fe^III structures are generally contracted by up to 0.07 Å relative to the crystal structure, while the 4Fe^II-3Fe^III structures are expanded up to 0.07 Å. Notable exceptions are the Fe^(Fe)…Fe^(Fe) distances in [4Fe^II-3Fe^III-O²⁻], which are 0.14 Å expanded. The Fe^(Fe)…Fe^(Fe) distances are expected to be among the most sensitive to the composition of X, along with the Fe^(Fe)-X, Fe^(Fe)…Fe^(Mo), Fe^{(Mo) …}Fe^(Mo) and Fe^(Mo)-X distances. For X = O²⁻, these distances are 0.10 Å – 0.16 Å expanded relative to the crystal structure compared to deviations of −0.02 Å – 0.06 Å for X = N³⁻ and C⁴⁻. The stronger donation from the higher charged and less electronegative N³⁻ or C⁴⁻ interstitial atoms seems to be necessary to maintain short distances between X and the Fe centers.⁷³ Similar to previous studies,^{18, 25, 74} we find that O²⁻ is likely not the interstitial atom based on geometric criteria. At this level of experimental information and theoretical treatment, the differences between the structures with N³⁻ versus C⁴⁻ are too small (less than 0.03 Å) to be able to unambiguously rule out either composition.

Table 1.

Interatomic distances in optimized FeMo-co^N for selected oxidation states. Experimental distances are given for the average of four FeMo-co structures from the crystal structure² along with those from two EXAFS studies.^{6, 72} Superscripts (Fe) and (Mo) refer to the [4Fe-3S] and [Mo-3Fe-3S] subclusters, respectively; (b) denotes the bridging sulfides. HC(O_hydroxyl) refers to the deprotonated (O⁻) or protonated (OH) hydroxyl group of the homocitrate ligand.

	calculated distances (Å)									experiment
	2FeII-5FeIII-X				4FeII-3FeIII-X					Ref. 2, 6, 72
X =	C4−		N3−		C4−		N3−		O2−
HC(Ohydroxyl)	O−	OH	O−	OH	O−	OH	O−	OH	O−
S(Cys)-Fe	2.22	2.20	2.20	2.18	2.30	2.28	2.27	2.26	2.25	2.27
Fe-S(Fe)	2.26	2.25	2.25	2.25	2.32	2.32	2.31	2.31	2.32	2.28
Fe…Fe(Fe)	2.63	2.62	2.63	2.63	2.73	2.72	2.73	2.72	2.73	2.66
S(Fe)-Fe(Fe)	2.28	2.27	2.28	2.27	2.32	2.31	2.31	2.30	2.30	2.27
Fe(Fe)-S(b)	2.19	2.19	2.19	2.19	2.24	2.23	2.23	2.23	2.22	2.23
Fe(Fe)…Fe(Fe)	2.65	2.64	2.69	2.68	2.66	2.65	2.67	2.67	2.80	2.65
Fe(Fe)-X	2.01	2.00	2.03	2.03	2.01	2.00	2.01	2.01	2.10	1.98
Fe(Fe)…Fe(Mo)	2.59	2.57	2.58	2.57	2.62	2.61	2.62	2.61	2.76	2.59
Fe(Mo)…Fe(Mo)	2.66	2.66	2.68	2.68	2.61	2.60	2.63	2.63	2.74	2.61
Fe(Mo)-S(b)	2.20	2.19	2.20	2.18	2.24	2.22	2.23	2.21	2.23	2.22
Fe(Mo)-X	2.00	2.00	2.00	2.00	2.01	2.00	2.02	2.01	2.12	2.02
Fe(Mo)…Mo	2.76	2.72	2.78	2.74	2.74	2.70	2.75	2.71	2.76	2.69
S(Mo)-Fe(Mo)	2.28	2.28	2.29	2.29	2.29	2.28	2.29	2.28	2.28	2.23
S(Mo)-Mo	2.40	2.37	2.40	2.37	2.39	2.37	2.40	2.38	2.41	2.35
Mo-N(His)	2.25	2.22	2.24	2.21	2.26	2.24	2.26	2.22	2.24	2.30
Mo-Ocarboxyl	2.12	2.11	2.10	2.08	2.16	2.16	2.14	2.13	2.11	2.18
Mo-Ohydroxyl	2.01	2.22	1.98	2.20	2.05	2.26	2.03	2.23	2.01	2.20
avg. Mo-O/N	2.13	2.19	2.11	2.16	2.16	2.22	2.14	2.19	2.12	2.23
Fe…Mo	7.02	6.94	7.02	6.95	7.17	7.11	7.17	7.10	7.22	7.00
avg. error	−0.01	−0.02	−0.01	−0.01	0.02	0.02	0.02	0.02	0.05
RMS dev.	0.06	0.04	0.07	0.05	0.06	0.04	0.07	0.04	0.11
core avg. error	0.01	0.00	0.02	0.01	0.03	0.02	0.03	0.02	0.07
core RMS dev.	0.04	0.03	0.05	0.04	0.04	0.03	0.04	0.03	0.09

In the [Mo-3Fe-3S] subcluster there are modest contractions and expansions of 0.02 Å in the Fe^(Mo)-S^(b) bond length for the 2Fe^II-5Fe^III and the 4Fe^II-3Fe^III structures, respectively. These trends reverse for the Fe^(Mo)…Fe^(Mo) distances, which are about 0.05 Å longer in 2Fe^II-5Fe^III than in the 4Fe^II-3Fe^III structures or crystal structure. The remaining distances in the Mo-containing subcluster (Fe^(Mo)…Mo, S^(Mo)-Fe^(Mo), and S^(Mo)-Mo) are 0.04 Å to 0.09 Å expanded relative to the experimental structures regardless of the composition and oxidation state. The core metrics without the terminal ligand distances have acceptably low overall RMS deviations of 0.04 Å – 0.05 Å for FeMo-co^N relative to the experimental structures; however, the [Mo-3Fe-3S] subcluster expands in 4Fe^II-3Fe^III and 2Fe^II-5Fe^III, while the [4Fe-3S] subcluster expands in 4Fe^II-3Fe^III structure, but contracts in 2Fe^II-5Fe^III. The end-to-end distance of FeMo-co (Fe^…Mo) shows a large difference. In 4Fe^II-3Fe^III, the longest dimension of the cluster is at least 0.17 Å expanded, while in 2Fe^II-5Fe^III, this distance deviates by only 0.01 Å from the experimental value of 7.00 Å. The significance of the 0.17 Å expansion may be limited by considering the percent difference from 7.00 Å, yet the preference of the Mo^IV-2Fe^II-5Fe^III assignment for FeMo-co^N cannot be ignored, since the magnitude of this deviation is considerable larger than the uncertainty in the crystallographic coordinates at 1.16 Å resolution.

As proposed earlier,^{2, 18} we also considered protonated interstitial ligands, such as HN²⁻, HC³⁻ and H₂C²⁻ ions, for the 2Fe^II-5Fe^III oxidation state. When X = HC³⁻, the Fe centers closest to the H atom on the interstitial ligand are repelled, resulting in overall expansion of the cluster. The average and RMS deviations are very similar (0.11 Å) to those observed for X = O²⁻ composition. The expansion is more extreme with HN²⁻ and H₂C²⁻ due to considerably reduced e donation to the Fe centers and, in the case of H₂C²⁻, the larger size. On the basis of these structural findings, we can rule out protonated interstitial ligands as filling the central cavity of FeMo-co.

3.4 The Protonation State of the Homocitrate Ligand

A large deviation of 0.15-0.22 Å from the experimental structure is found between the Mo center and the O_hydroxyl group of the homocitrate ligand (Table 1 - columns marked with OH for the homocitrate hydroxyl group, HC(O_hydroxyl), vs. experimental values). This is an important difference, because the protonation state of this ligand can significantly affect the electronic structure and thus the redox and coordinative properties of the Mo site. Due to lack of a strong secondary coordination sphere effect involving this hydroxyl group, the long experimental Mo-O_hydroxyl bond indicates that the hydroxyl arm of the homocitrate is likely protonated. To test the correlated effects of ligand protonation and coordination geometry, a set of structural optimizations was carried out for the [2Fe^II-5Fe^III-N³⁻] state in which either the uncoordinated δ-N of imidazole was deprotonated (imidazolato ligand) or the glycolate ligand was protonated at the proximal carboxyl oxygen, the distal carboxyl oxygen or the hydroxyl oxygen. The variations in the Mo^…Fe and Mo-L distances are summarized in Table 2. The presence of an imidazolato ligand results in a slight increase of the Mo-O bond lengths; however, the Mo-N bond length becomes unreasonably short (2.17 Å) relative to the experimental values of 2.30 Å (crystallography) and 2.29 Å (EXAFS). Protonation of either oxygen atoms of the carboxyl group results in an expanded Mo-O_carboxyl bond (2.26 and 2.24 Å) without significantly improving the Mo-O_hydroxyl bond length (2.01 Å). However, the hydroxyl-protonated model, Mo-O_hydroxyl, shows excellent agreement with the crystallographic data (both 2.20 Å). Furthermore, the Mo^…Fe and Mo-S distances decrease by 0.03-0.04 Å to 2.74 and 2.37 Å, respectively, which are closer to the crystallographic values (2.69 and 2.34 Å) than in the deprotonated form. As expected, the conjugate Mo-O_carboxyl and Mo-N(His) bonds to the Mo-O_hydroxyl bond decrease by 0.02-0.03 Å to compensate for the decreased donation from O_hydroxyl to the Mo center compared to the deprotonated model. However, this decreases the level of agreement in these bond lengths relative to the crystal structure to 0.10 and 0.09 Å, respectively. Overall, the improved Mo^…Fe/Mo-S distances and the good agreement in the Mo-O_hydroxyl bond length favor the O_hydroxyl-protonated homocitrate ligand model with an RMS deviation of $0.06\acute{\mathrm{Å}}$ compared to $0.12\acute{\mathrm{Å}}$ without protonation relative to the crystal structure. We rationalize the disagreement in other Mo-ligand bond lengths by the absence of second sphere coordination sphere interactions in our computational model, such as a network of hydrogen bonded water molecules around the coordinated short carboxyl arm of the homocitrate^{29, 75-77} and the εN of His442.

Table 2.

Effect of homocitrate and imidazole ligand protonation states on the optimized Mo^…Fe and Mo-L distances (Å) in the [2Fe^II-5Fe^III-N³⁻] state. O_carboxyl^(d) and O_carboxyl^(p) represent protonation at the distal and proximal O_carboxyl center, respectively. The RMS deviations are given relative to the crystal structure.

homocitrate imidazole	deprotonated protonated	deprotonated deprotonated	HOcarboxyl(d) protonated	HOcarboxyl(p) protonated	HOhydroxyl protonated	XRD Ref. 2	EXAFS Ref. 6	EXAFS Ref. 72
Mo…Fe(Mo)	2.78	2.80	2.77	2.77	2.74	2.69	2.70	2.68
Mo…S(Mo)	2.40	2.41	2.38	2.38	2.37	2.34	2.37	2.34
Mo-N(His)	2.24	2.17	2.23	2.23	2.21	2.30	2.21a	2.29
Mo-Ocarboxyl	2.10	2.12	2.26	2.24	2.08	2.18	2.21a	2.14
Mo-Ohydroxyl	1.98	1.98	1.99	2.01	2.20	2.20	2.21a	2.31
Avg. Mo-O/N	2.11	2.09	2.16	2.16	2.16	2.22	2.21	2.25
RMS dev.	0.12	0.13	0.11	0.10	0.06

^aMo-O/N distances were reported only as an average, due to inherent difficulty in distinguishing between light atoms.

Using the O_hydroxyl-protonated state, the best agreement with experimental data is achieved for the [2Fe^II-5Fe^III-C⁴⁻], [4Fe^II-3Fe^III-N³⁻], and [4Fe^II-3Fe^III-C⁴⁻] states (Table 1 - columns HC = OH). For 2Fe^II-5Fe^III, the X = C⁴⁻ model is more consistent with the experimental structures than X = N³⁻ in nearly all tabulated dimensions, and the RMS deviations for the core distances slightly improve from $0.04\acute{\mathrm{Å}}$ to $0.03\acute{\mathrm{Å}}$ upon protonation. At the same time, the [2Fe^II-5Fe^III-N³⁻] state cannot be definitively eliminated based on the interatomic distances alone. Comparing the best structures obtained with protonated homocitrate ligand, the [2Fe^II-5Fe^III-C⁴⁻] model is somewhat contracted relative to the crystal structure, with an average deviation of $-0.02\acute{\mathrm{Å}}$, while the 4Fe^II-3Fe^III oxidation state models are slightly expanded, with an average deviation of $0.02\acute{\mathrm{Å}}$; however, the overall RMS deviations are the same. To avoid overlooking compositions and oxidation states due to fortuitous error cancellation, we evaluated the possibility of X = O²⁻ with the protonated model, but the RMS deviation for the core distances remains too high ($0.09\acute{\mathrm{Å}}$), with considerable deviations in the Fe^(Fe)-X ($0.13\acute{\mathrm{Å}}$) and Fe^(Fe)…Fe^(Mo) ($0.16\acute{\mathrm{Å}}$) distances. Also, the results for the O_hydroxyl-protonated 6Fe^II-1Fe^III-N³⁻ state (see Table S5) show unreasonable large geometric differences relative to the experimental structure.

3.5 Reduction Potentials

Reduction potentials were considered as energetic criteria for evaluating the oxidation state and composition of FeMo-co. The reduction potential of the FeMo-co^Ox/FeMo-co^N pair was calculated for the 2Fe^II-5Fe^III, 4Fe^II-3Fe^III and 6Fe^II-1Fe^III states with C⁴⁻, N³⁻, or O²⁻, covering a large range of charges (from −5 to −1 for our model), in addition to two of the O_hydroxyl-protonated models favored in the structural studies described above. For FeMo-co^Ox, we used the spin states shown in this work to be lowest in energy: M_s = 0 for 1Fe^II-6Fe^III, and M_s = 1 for 3Fe^II-4Fe^III and 5Fe^II-2Fe^III. The ligand protonation state is assumed to be unchanged during the reduction process, and this is supported by an EXAFS study showing a 0.03 Å increase in the average Mo-O/N distance upon reduction,⁷⁸ which is also reproduced in our calculations.

Table 3 summarizes the calculated reduction potentials along with a decomposition analysis according to Eqs. (1)-(3). The reduction potentials for the models with deprotonated homocitrate range from −2.68 V to +0.59 V for the most and least negatively charged states, [6Fe^II-1Fe^III-N³⁻]⁵⁻ and [2Fe^II-5Fe^III-N³⁻]⁻, respectively, while the experimental value lies between these extremes at −0.042 V.¹¹ Examining the intermediately charged states, the [4Fe^II-3Fe^III-N³⁻]³⁻ is still too negatively charged (Ε°°= −0.83 V), but [2Fe^II-5Fe^III-C⁴⁻]²⁻ gives Ε° = 0.00 V, which is close to the experimental value. However, as discussed above, models with protonated O_hydroxyl groups (denoted with +H) need to be considered. Thus, by evaluating protonated models we find that the reduction potentials for [4Fe^II-3Fe^III-N³⁻+H]²⁻ and [2Fe^II-5Fe^III-C⁴⁻+H]⁻ are −0.34 V and 0.38 V, respectively, nearly equidistant from the experimental value in opposite directions, and both can be considered as favored by this criterion.

Table 3.

Reduction potentials (in V) relative to the standard hydrogen electrode (SHE). Column “s.p.” indicates the spin projection correction using the two spin system model. The contributions under ΔG°_solute reflect the difference between the zero-point energy (ZPE), enthalpy and entropy corrections to the reduced and oxidized solvated species as a result of structural optimizations. Reduction potentials were calculated from Δε_SCF^s.p., ΔG°_solute and ΔΔG°_solvation, as described in Eqs. (1)-(3). The models labeled “+H” are the O_hydroxyl-protonated models. All numbers are given in V.

model	gas phasea			solute corrections				Δ Δ G ° solv		Ε° vs. SHE
	Δ ε SCF	s.p.	Δ ε SCFs.p.	ΔZPE	Δ H °	T Δ S °	Δ G °	Δ Δ Gelec	Δ Δ Gnon
[6FeII-1FeIII-N3−]5−	−6.37							8.14	−0.02	−2.68
[4FeII-3FeIII-C4−]4−	−4.96							7.79	−0.02	−1.62
[4FeII-3FeIII-C4−+H]3−	−2.81							6.07	−0.03	−1.19
[4FeII-3FeIII-N3−]3−	−2.33			−0.01	0.00	0.04	−0.04	6.00	−0.03	−0.83
[4FeII-3FeIII-N3−+H]2−	0.30	−0.02	0.28	−0.02	−0.02	−0.09	0.05	3.78	−0.02	−0.34
[4FeII-3FeIII-O2−]2−	0.77			−0.01	15 -0.04	−0.13	0.08	3.58	−0.04	−0.05
[4FeII-3FeIII-O2−+H]1−	3.45			−0.01	−0.02	−0.06	0.03	1.31	−0.04	0.31
[2FeII-5FeIII-C4−]2−	0.68	−0.03	0.65	0.06	−0.03	−0.12	0.15	3.66	−0.03	0.00
[2FeII-5FeIII-C4−+H]1−	3.46	−0.04	3.43	0.04	0.00	−0.03	0.07	1.34	−0.03	0.38
[2FeII-5FeIII-N3−]1−	3.81	−0.03	3.77	0.04	0.03	0.06	0.01	1.25	−0.01	0.59
experiment (Ref. 11)										−0.042

^aIn vacuo electronic energy (⟨Ψ(0) ∣ Ĥ ∣ Ψ(0)⟩)⁵⁰ with PCM-optimized geometry.

Although reduction potentials alone do not rule out either of the O_hydroxyl-protonated models, they exhibit a general trend that allows for the elimination of models on the basis of overall cluster charge. For example, we can readily rule out the [2Fe^II-5Fe^III-N³⁻+H] state for FeMo-co^N, because its neutral total charge would render its reduction potential even more positive than that of [2Fe^II-5Fe^III-N³⁻]⁻ (0.59 V) and [2Fe^II-5Fe^III-C⁴⁻+H]⁻ (0.38 V). The calculated reduction potentials indicate the overall charge of the truncated FeMo-co^N model is likely −2 or −1. Considering the −3 charge of the full homocitrate ligand compared to −1 for the glycolate with protonated hydroxyl groups in both, we expect the overall charge of FeMo-co^N to be −4 or −3. Previous work indicated the charge of exFeMo-co^Ox is −2,¹³ corresponding to a total charge of −3 for FeMo-co^N (−1 for our model). Thus, these charge considerations show a preference for the 2Fe^II-5Fe^III oxidation state distribution with X = C⁴⁻ and protonated homocitrate.

By analyzing each component of the reduction potential calculations, we find that the major contributions are from the ionization potential (Δε_SCF or Δε_SCF^s.p.) and the electronic solute-solvent interactions (ΔΔG_elec). Corrections accounting for differences in protein-embedded structures upon reducing FeMo-co (ΔG°_{solute corrections}) improve the reduction potential by up to 150 mV,⁷⁹ while spin projection (s.p. – using two spin projection method) and non-electrostatic solute-solvent interactions (ΔΔG_non) each account for less than 40 mV. While none of these corrections are negligible, the first approximation of using the SCF energies (Δε_SCF + ΔΔG_{electrostatic}) to calculate the reduction potential results in an error of only 10 mV for the [2Fe^II-5Fe^III-C⁴⁻+H] state and even less for the [4Fe^II-3Fe^III-N³⁻+H] state due to error cancellations. However, this cancellation is not universal, since we find a larger error in certain cases (e.g., 90 mV for the [2Fe^II-5Fe^III-C⁴⁻] model). Importantly, the overall conclusions derived from reduction potential calculations remain the same regardless of how the reduction potentials are calculated.

3.6 Spectroscopic Properties

In addition to composition, geometric structure, and relative energies of spin and oxidation states, we also examined the electronic structural information from Mössbauer and ENDOR spectroscopic measurements. These have been used in literature as dominant criteria to differentiate among various proposals for the structure and composition of FeMo-co, since they are highly sensitive to oxidation state, ligand environment, and geometric structure.⁸⁰ We find that the calculated Mössbauer isomer shifts, quadrupole splittings, and ENDOR hyperfine coupling constants are greatly affected by the composition of the experimental training set, and the employed level of theory.

3.6.1. Mössbauer Isomer Shifts

The currently accepted process of calculating Mössbauer isomer shifts requires the derivation of an empirical relationship between calculated electron density values at the nucleus (ρ(0)) and experimental isomer shifts for a set of model compounds at a given level of theory. For our training set we have employed a variety of [Fe-S] and [Mo-Fe-S] clusters that are the closest models for the coordination environment of the Fe centers in FeMo-co. Since most of the published isomer shifts for the training set are for solid state samples (see Tables S6 and S7), it was most appropriate to use the crystallographic structures in the calculations (see Table S6 method 1), yielding a best fit to Eq. (9) of δ = −0.620 e⁻¹ a₀³ mm s⁻¹ (ρ(0) – 11833 e a₀⁻³) + 0.563 mm s⁻¹ (Figure S1A) with a standard deviation of 0.06 mm s⁻¹. From this equation, the isomer shifts were derived using the calculated average ρ(0) of the Fe centers in FeMo-co in the structurally optimized 2Fe^II-5Fe^III, 4Fe^II-3Fe^III and 6Fe^II-1Fe^III states with C⁴⁻ or N³⁻.

As shown by the δ₁ values in Table 4 (see Table S8 for individual site δ values), isomer shift decreases by an average of 0.13 mm s⁻¹ with oxidation along the series from 6Fe^II-1Fe^III to 4Fe^II-3Fe^III to 2Fe^II-5Fe^III with X = N³⁻. Interestingly, the isomer shift decreases by about 0.05 mm s⁻¹ in going from X = N³⁻ to C⁴⁻ due to an increase in ρ(0), which is, in turn, likely caused by increased overlap with the Fe(4s) as discussed by Neese⁸¹ for a series of Fe halides. The average isomer shift of the [2Fe^II-5Fe^III-N³⁻] state (0.41 mm s⁻¹) agrees best with the experimental¹⁵ value of 0.41 mm s⁻¹, followed by the [4Fe^II-3Fe^III-C⁴⁻+H] state (0.45 mm s⁻¹). Notably none of these states and compositions were shown above to be favored by other criteria. As with the reduction potentials, the average isomer shift of the most likely hydroxyl-protonated states, [2Fe^II-5Fe^III-C⁴⁻+H] and [4Fe^II-3Fe^III-N³⁻+H], lie nearly equidistant from the experimental value, at 0.32 mm s⁻¹ and 0.51 mm s⁻¹, respectively.

Table 4.

Mulliken spin densities (∣ρ_s^(Fe)∣), quadrupole splittings (∣ΔE_Q∣) and isomer shifts (δ) averaged over the Fe sites; hyperfine couplings of Fe (a^test) and X (a(X)); and RMS deviations of the individual site hyperfine couplings (a_i) for a series of oxidation states and compositions, where +H indicates O_hydroxyl-protonated models.

level of theory	model	δ1 (mm s−1)a	δ2 (mm s−1)a	δ3 (mm s−1)a	∣ρs(Fe)∣	∣ΔEQ∣ (mm s−1)	atest (MHz)	RMS dev. ai(MHz)	a(X) (MHz)
BP86b	2FeII-5FeIII-N3−	0.41	0.29c	0.45	2.92	1.13	−25.1	4.2	1.1
	4FeII-3FeIII-N3−	0.53	0.38c	0.54	3.06	1.03	−27.3	5.6	−0.3
	6FeII-1FeIII-N3−	0.68	0.52c	0.66	2.98	0.95	−29.6	5.0	−0.3
	2FeII-5FeIII-C4−	0.35	0.24c	0.40	2.73	0.90	−24.3	3.5	3.7
	4FeII-3FeIII-C4−	0.48	0.34c	0.50	2.89	0.94	−25.1	4.7	−0.7
	4FeII-3FeIII-O2−	d		d	3.27	d	−29.5	6.8	d
	2FeII-5FeIII-C4−+H	0.32	0.22	0.38	2.68	0.86	−23.8	3.3	2.7
	4FeII-3FeIII-C4−+H	0.45	0.32c	0.48	2.85	0.93	−24.4	4.5	−1.0
	4FeII-3FeIII-N3−+H	0.51	0.45	0.52	3.03	0.97	−27.0	5.5	−0.4
B3LYPb	2FeII-5FeIII-C4−+H				3.42	1.16	−25.4	5.9	6.1
	4FeII-3FeIII-N3−+H				3.50	1.43	−31.8	8.0	−0.7
B(5HF)P86/ 6-311+G(d)	2FeII-5FeIII-C4−+H				2.44		−24.1	2.7
	4FeII-3FeIII-N3−+H				2.77		−25.1	4.5
	Exp	0.41e		0.41e		0.69e	−17.9e		< 0.07f

^aSubscripts refer to the methods employing a training data set with (1) crystal structures, (2) BP86/STO-TZP optimized structures, or (3) crystal structures without outliers.

^bSDD-VTZ(d) basis set for ∣ρ_s(Fe)∣ and a^test; STO-TZP for ∣ΔE_Q∣, a(X) and δ.

^cEstimated based on range of δ for [2Fe^II-5Fe^III-C⁴⁻+H].

^dCalculations did not converge.

^eRef. 15

^fRef. 25

Alternatively, the training set structures can be optimized in order to use the minimum energy structure for the employed computational method, as often preferred.^{16, 63, 82} The best fit for the set of optimized structures (see Table S6 method 2) is δ = −0.744 e⁻¹ a₀³ mm s⁻¹ (ρ(0) – 11833 e a₀⁻³) + 0.593 mm s⁻¹ (Figure S1B), with a standard deviation of 0.04 mm s⁻¹. This fit appears to be significantly different than the previous fit; however, the effect on the calculated average isomer shift of FeMo-co is only 0.01 mm s⁻¹ on average over the eight listed states. For consistency, the FeMo-co structure should also be optimized at the BP86/all-electron STO-TZP level as used for the training set. With the optimized structures, the average isomer shifts of the [2Fe^II-5Fe^III-C⁴⁻+H] and [4Fe^II-3Fe^III-N³⁻+H] states are 0.22 mm s⁻¹ and 0.45 mm s⁻¹, respectively; thus, the latter state is favored with this method.

Importantly, a significant drawback of the isomer shift fitting procedure is the dependence on the choice of model compounds for the training set. The slopes of α = −0.620 e⁻¹ a₀³ mm s⁻¹ or −0.744 e⁻¹ a₀³ mm s⁻¹ from method 1 and method 2 above, respectively, are steeper than the published values ranging between −0.3 and −0.5 e⁻¹ a₀³ mm s⁻¹.^{16, 18, 83} We note that the two models with the largest deviation from the correlation line in Figure S1A are [Fe(S₂-o-Xyl)₂]⁻ and [Fe₂S₂(S₂-o-Xyl)₂]²⁻, and their experimental isomer shifts of 0.13 mm s⁻¹ and 0.17 mm s⁻¹, respectively,^{84, 85} are much lower than values typically used for [Fe^III-S] complexes in training sets (for example Refs. 16, 17, 83). Rao and Holm used 0.28 mm s⁻¹ as the lowest isomer shift for an [Fe^III-S] complex in their evaluation of the linear relationship between isomer shifts and oxidation state.⁸⁶ Notably, their fit predicts 0.40 mm s⁻¹ for the 2Fe^II-5Fe^III oxidation state and 0.51 mm s⁻¹ for 4Fe^II-3Fe^III. Thus, if we remove these outliers (see Table S6 method 3), the new correlation line is described by δ = −0.491 e⁻¹ a₀³ mm s⁻¹ (ρ(0) – 11833 e a₀⁻³) + 0.568 mm s⁻¹ (Figure S1C), with a standard deviation of 0.04 mm s⁻¹, and the slope is more consistent with the aforementioned published values. With this method, the average isomer shifts of the [2Fe^II-5Fe^III-C⁴⁻+H] and [4Fe^II-3Fe^III-N³⁻+H] states become 0.38 mm s⁻¹ and 0.52 mm s⁻¹ (δ₃ values in Table 4), respectively, favoring the former.

The three described methods produce significantly different sets of data, resulting in a large error bar for the calculated isomer shifts. For example, the isomer shifts of the [2Fe^II-5Fe^III-C⁴⁻+H] state were calculated within a range of 0.16 mm s⁻¹. The second method yields the smallest isomer shifts. In order to estimate the δ₂ values for other states not explicitly calculated, we can subtract 0.16 mm s⁻¹ from the maximum calculated isomer shift for each state, producing an assumed lower limit for δ₂ (see Table 4), because the range used is much larger than that observed for [4Fe^II-3Fe^III-C⁴⁻+H] (0.07 mm s⁻¹). Then, after taking into account the standard deviations of each method (e.g., δ₃ values carry an error bar of 0.04 mm s⁻¹), we find that all evaluated states except [6Fe^II-1Fe^III-N³⁻] have theoretical isomer shifts around the experimental value. We can consider the third method to be the most appropriate due to the exclusion of training set complexes with unusually low isomer shifts. Furthermore, the third method uses structures optimized with our standard, previously validated procedure, and is thus expected to be more accurate than the second method. Thus, the δ₃ values can be considered as a stringent criterion for selecting only the 2Fe^II-5Fe^III oxidation state with C⁴⁻ or N³⁻ central ligands as preferred assignments, with or without protonated homocitrate ligand.

3.6.2 Mössbauer Quadrupole Splitting

First, we carried out of an evaluation of the calculated Mössbauer quadrupole splitting parameters (ΔE_Q) using the same training set as for the isomer shift calculations (see above). The absolute values of ΔE_Q for the selected Fe sites are found to have an RMS deviation of 0.31 mm s⁻¹ from the experiment when using crystallographic coordinates, and 0.32 mm s⁻¹ for the corresponding optimized structures (see Table S6), which is a typical level of accuracy.^{63, 80, 83} The calculated ΔE_Q values for the 2Fe^II-5Fe^III, 4Fe^II-3Fe^III and 6Fe^II-1Fe^III states with C⁴⁻ or N³⁻ are presented in Table 4 (see Table S9 for individual site ΔE_Q values). The sign of ΔE_Q is difficult to calculate reliably,⁸⁷ and thus not surprisingly, none of the oxidation states or compositions match the experimental distribution of six negative and one positive ΔE_Q in our calculations. To facilitate comparison of the theoretical and experimental quadrupole splitting values, we take the mean of ∣ΔE_Q∣ over the Fe sites and find a range of 0.86 mm s⁻¹ ([2Fe^II-5Fe^III-C⁴⁻]+H) to 1.13 mm s⁻¹ ([2Fe^II-5Fe^III-N³⁻]) for the various states. These are all overestimated relative to the experimental value of 0.69 mm s⁻¹, although considering the error bar of 0.32 mm s⁻¹, all tested states except the deprotonated [2Fe^II-5Fe^III-N³⁻] and [4Fe^II-3Fe^III-N³⁻] give results consistent with experiment, indicating the difficulty of distinguishing between states by this criterion.

The lowest four calculated mean ∣ΔE_Q∣ values are attributed to states with X = C⁴⁻ and the highest four to those with X = N³⁻, while there is no obvious correlation with oxidation state. However, there is a strong correspondence between the ordering of states by increasing mean absolute Fe spin density (∣ρ_s(Fe)∣) and increasing ∣ΔE_Q∣ with only one exception (2Fe^II-5Fe^III-N³⁻, see Table S10 for individual site ρ_s(Fe) values). This correlation indicates that the dominant factors affecting spin densities including bond covalency and the employed level of theory also strongly influence ΔE_Q values. Indeed, a change in functional that increases Fe spin density also increases the ∣ΔE_Q∣ values for the two most favored states from the compositional, structural and energetic considerations, [2Fe^II-5Fe^III-C⁴⁻+H] and [4Fe^II-3Fe^III-N³⁻+H], from 0.86 mm s⁻¹ and 0.97 mm s⁻¹ (BP86) to 1.16 mm s⁻¹ and 1.43 mm s⁻¹ (B3LYP). The [2Fe^II-5Fe^III-C⁴⁻+H] state is consistently the closest to the experiment, but the accuracy of these calculations, as demonstrated with the training set, is not high enough to give strong preference to this state.

3.6.3 Hyperfine Couplings

Due to the limitations for describing accurate hyperfine couplings of transition metal nuclei from ab initio calculations, the ⁵⁷Fe hyperfine coupling constants (a_i^calc) were determined through a semi-empirical procedure (see Methods Section) as previously applied by Noodleman et al. ²⁵ for the [4Fe^II-3Fe^III-N³⁻] state. We extended these calculations to the 2Fe^II-5Fe^III, 4Fe^II-3Fe^III and 6Fe^II-1Fe^III states with C⁴⁻, N³⁻, or O²⁻. The resulting a_i^calc values (see Table S11) are summed over the seven Fe sites to give a^test, a straightforward parameter introduced by Mouesca et al.⁶⁸ for comparison with experimental data. The results in Table 4 show that the a^test value of the [2Fe^II-5Fe^III-C⁴⁻+H] state (−23.8 MHz) is closest to that of the Mössbauer experiment (−17.9 MHz),¹⁵ while the [4Fe^II-3Fe^III-O²⁻] (−29.5 MHz) and [6Fe^II-1Fe^III-N³⁻] (−29.6 MHz) states have the largest deviations. Although the spin projection coefficients, K_i, are dependent on the oxidation state assignments of each iron site (see Table S12), spin densities are the dominant factors contributing to differences in a^test in this series. As with the quadrupole splittings, there is a nearly perfect correspondence between the ordering of FeMo-co states arranged by a^test values from least to most negative, and the ordering by increasing ∣ρ_s(Fe)∣, with the only exception being the [6Fe^II-1Fe^III-N³⁻] state, which has an intermediate ∣ρ_s(Fe)∣. Due to the reliance on atomic spin density values, the a^test values are highly dependent on the employed functional and basis set. In addition to the BP86/SDD-VTZ(d) level of theory used for the series, the [2Fe^II-5Fe^III-C⁴⁻+H] and [4Fe^II-3Fe^III-N³⁻+H] states were evaluated with B3LYP/SDD-VTZ(d) and B(5HF)P86/6-311+G(d), which has been found previously³⁹ to be excellent for [Fe-S] cluster spin densities. With B3LYP/SDD-VTZ(d), a^test becomes more negative for both states and the difference between them increases from −3.1 MHz to −6.4 MHz, while with B(5HF)P86/6-311+G(d), the gap decreases to −0.9 MHz. Despite strong computational method dependence, the [2Fe^II-5Fe^III-C⁴⁻+H] state consistently has the closest a^test to experiment.

As a further analysis of the hyperfine couplings, and to avoid possible error cancellation caused by the summation of positive and negative values in determining a^test, the RMS deviation of the individual site a_i^calc values were also compared (Table 4). Since the specific Fe site corresponding to an experimental a_i is unknown, the RMS deviations were calculated by ordering the a_i values numerically. Here, again, the [2Fe^II-5Fe^III-C⁴⁻+H] state has the smallest RMS deviation of 3.3 MHz, compared to 5.5 MHz for [4Fe^II-3Fe^III-C⁴⁻+H], and the largest value of 6.8 MHz for [4Fe^II-3Fe^III-O²⁻]. The ordering of states is generally the same as for a^test with some minor rearrangements. With B3LYP the RMS deviations increase by about 2.5 MHz, while with B(5HF)P86/6-311+G(d) the results improve, yielding 2.7 MHz for [2Fe^II-5Fe^III-C⁴⁻+H]. Overall, the hyperfine coupling calculations favor both protonation states of [2Fe^II-5Fe^III-C⁴⁻]. Since the error is difficult to estimate, other states cannot be excluded based on this criteria alone.

Advanced EPR methods, such as ENDOR and ESEEM techniques, are ideal for detecting weakly coupled spin systems, such as an interstitial atom within the central 6Fe belt in the BS7 state (see Section 3.1 for description). On the basis of the lack of a central ¹³C, or ^14/15N atom signal it was suggested that if the interstitial ligand X is C⁴⁻ or N³⁻ then the a_iso(¹³C) or a_iso(¹⁴N) coupling constants must be less than 0.05-0.1 MHz or 0.03-0.07 MHz, respectively.²⁵ Table 4 shows the calculated a_iso(X) values for the same series of FeMo-co states used for the Mössbauer parameters. In each state a_iso(X) is higher than the experimental detection limit with the lowest absolute value of 0.3 MHz for the [4Fe^II-3Fe^III-N³⁻] and [6Fe^II-1Fe^III-N³⁻] states. The dependence on the computational method is strong, since switching from BP86 to B3LYP functional approximately doubles a_iso(X). Thus, we conclude that the required level of accuracy to reproduce a very small hyperfine coupling for X is out of reach with current DFT functionals, even when employing a level of theory calibrated to experimental metal-ligand bonding information.

4. Conclusions

In this work, we applied broken symmetry DFT calculations with spectroscopically (XAS) calibrated functionals and saturated basis sets to provide a comprehensive evaluation of the available experimental information about the electronic, geometric, energetic, and magnetic properties of the protein-bound nitrogenase FeMo-co. We found that the relative energies of spin coupling schemes are dominantly governed by the number of antiferromagnetic interactions, including those mediated by the interstitial ligand (X). The ground state spin coupling scheme, BS7, has the maximum number of antiferromagnetic M-S/X-M interactions. Using the BS7 spin coupling scheme, we calculated the ground spin state for oxidized and resting FeMo-co, geometric structures, reduction potentials, and Mössbauer and hyperfine parameters for the oxidation states 6Fe^II-1Fe^III, 4Fe^II-3Fe^III, and 2Fe^II-5Fe^III assuming the presence of weak-field ligand environment at the Fe centers with 10-electron interstitial ligands C⁴⁻, N³⁻, and O²⁻.

Table 5 summarizes the preferred oxidation states for the iron centers and compositions for the interstitial atom based on independent experimental criteria and homocitrate protonation states. The findings for each criterion follow:

Table 5.

Magnetic, electronic, geometric, and energetic preference for oxidation states of the iron centers and composition of the interstitial ligand. HC(O⁻_hydroxyl) and HC(HO_hydroxyl) indicate the deprotonated and protonated states of homocitrate, respectively.

criterion	oxidation state	interstitial atom
		HC(O−hydroxyl)	HC(HOhydroxyl)
resting St = 3/2	no preference	no preference	no preferencea
oxidized St = 0	MoIV-2FeII-5FeIII	C4−, N3−	C4−a, N3−a
geometry	MoIV-2FeII-5FeIII	C4−, N3−	C4−
	MoIV-4FeII-3FeIII		C4−, N3−
charge	MoIV-2FeII-5FeIII	N3−	C4−
	MoIV-4FeII-3FeIII		O2−
reduction potential	MoIV-2FeII-5FeIII	C4−	C4−
	MoIV-4FeII-3FeIII	O2−	N3−, O2−
isomer shift (all)	MoIV-2FeII-5FeIII	C4−, N3−	C4−, N3−b
	MoIV-4FeII-3FeIII	C4−, N3−	C4−, N3−
isomer shift (δ3)	MoIV-2FeII-5FeIII	C4−, N3−	C4−, N3−b
quadrupole splitting	MoIV-2FeII-5FeIII	C4−	C4−
	MoIV-4FeII-3FeIII	C4−	C4−, N3−
	MoIV-6FeII-1FeIII	N3−	N3−b
Fe hyperfine coupling	MoIV-2FeII-5FeIII	C4−	C4−
X hyperfine coupling	no preference	no preference	no preference

^aEstimated based on results for deprotonated models. The S_t = 0 and 1 states of [2Fe^II-5Fe^III-C⁴⁻+H] were tested and the results were consistent with the deprotonated case.

^b[2Fe^II-5Fe^III-N³⁻+H] and [6Fe^II-1Fe^III-N³⁻+H] results estimated.

(1) We are not able to rule out any possibilities based on the ground spin state of resting FeMo-co, as each is consistent with the experimental S_t = 3/2 state.

(2) However, only the 2Fe^II-5Fe^III oxidation state is consistent with the S_t = 0 ground oxidized form.

(3) The optimized geometries with deprotonated homocitrate favor the 2Fe^II-5Fe^III states with C⁴⁻ or N³⁻, while strongly disfavoring O²⁻ and protonated forms of the central ions due to an unreasonable expansion of the central ‘6Fe-belt’ relative to the crystal structure. Contrary to what is expected based on size, a highly charged, larger interstitial atom with lower electronegativity is preferred over a smaller, more electronegative ion to maintain the cluster core geometry. The optimized FeMo-co^N structures consistently show that the Mo-O_hydroxyl bond length is far too short (0.14 to 0.21 Å) relative to its experimental value for all oxidation states and compositions. This discrepancy was eliminated by protonating the coordinated O_hydroxyl group. With the O_hydroxyl-protonated model, the [2Fe^II-5Fe^III-C⁴⁻+H], [4Fe^II-3Fe^III-C⁴⁻+H] and [4Fe^II-3Fe^III-N³⁻+H] states show the closest agreement with the experimental structures.

(4) The [2Fe^II-5Fe^III-C⁴⁻+H] state is preferred based on the experimentally consistent −2 charge in the FeMo-co^Ox or exFeMo-co^Ox form.

(5) The states with the most reasonable reduction potentials for FeMo-co^Ox/FeMo-co^N all carry a total charge of −1 or −2. It is important to emphasize that a solely reduction potential-based evaluation of composition can be misleading, since the reduction potential for the [4Fe^II-3Fe^III-O²⁻] state with −2 total charge only deviates 10 mV from experiment, despite significant disagreement in other criteria. Alternative models such as [4Fe^II-3Fe^III-N³⁻+H] with a protonated bridging sulfide ligand are also expected to have favorable reduction potentials based on the overall charge despite the already reported¹⁸ cluster expansion. The reduction potentials of [2Fe^II-5Fe^III-C⁴⁻+H] (0.38 V) and [4Fe^II-3Fe^III-N³⁻+H] (−0.34 V) are the closest to the experimental value of −0.042 V.

(6) Mössbauer isomer shift calculations are strongly dependent on the employed training set composition and structural optimization state, but with our favored method only the 2Fe^II-5Fe^III states with C⁴⁻ or N³⁻ yield experimentally consistent values.

(7) The quadrupole splittings are closest to experiment with [2Fe^II-5Fe^III-C⁴⁻+H], but the large error bars overlap the experimental value for nearly all tested states.

(8) Current DFT methods does not have the required accuracy for calculating unambiguously hyperfine couplings in a multinuclear, delocalized mixed-valence, spin-coupled system, such as FeMo-co. Nevertheless, the 2Fe^II-5Fe^III oxidation state with C⁴⁻ has ⁵⁷Fe hyperfine couplings is the least inconsistent with experiment with respect to both a^test and RMS deviation of the individual site parameters, a_i.

(9) The hyperfine coupling for the central ligand X is larger than the limits set by experiment, regardless of composition and oxidation state, likely due to the aforementioned limited accuracy.

In conclusion, only [2Fe^II-5Fe^III-C⁴⁻+H] is consistently favored, and we consider it to be the most likely oxidation state and composition. The [4Fe^II-3Fe^III-N³⁻+H] state is the second best, as it passed the structural (with only the protonated homocitrate) and reduction potential criteria; however, it failed with respect to the relative energies of oxidized spin states, the overall charge, the isomer shifts and the hyperfine parameters. The more oxidized electronic state, the protonation state of the homocitrate, and the presence of a carbide central ligand open up exciting further directions in investigating the molecular mechanism of biological nitrogen fixation and the biosynthesis of the FeMo-cofactor of nitrogenase.