Electron Redistribution within the Nitrogenase Active Site FeMo-Cofactor During Reductive Elimination of H2 to Achieve N≡N Triple-Bond Activation

Terminal Hydride Complex of High-Spin Mn

The iron-molybdenum cofactor of nitrogenase (FeMoco) catalyzes fixation of N2 via Fe hydride intermediates. Our understanding of these species has relied heavily on the characterization of well-defined 3d metal hydride complexes, which serve as putative spectroscopic models. Although the Fe ions in FeMoco, a weak-field cluster, are expected to adopt locally high-spin Fe2+/3+ configurations, synthetically accessible hydride complexes featuring d5 or d6 electron counts are almost exclusively low-spin. We report herein the isolation of a terminal hydride complex of four-coordinate, high-spin (d5; S = 5/2) Mn2+. Electron paramagnetic resonance and electron-nuclear double resonance studies reveal an unusually large degree of spin density on the hydrido ligand. In light of the isoelectronic relationship between Mn2+ and Fe3+, our results are expected to inform our understanding of the valence electronic structures of reactive hydride intermediates derived from FeMoco.

Computational Model Study of the Experimentally Suggested Mechanism for Nitrogenase

The mechanism for N2 activation in the E4 state of nitrogenase was investigated by model calculations. In the experimentally suggested mechanism, the E4 state is obtained after four reductions to the ground state. In a recent theoretical study, results for a different mechanism have been found in excellent agreement with available Electron Paramagnetic Resonance (EPR) experiments for E4. The two hydrides in E4 leave as H2 concertedly with the binding of N2. The mechanism suggested differs from the experimentally suggested one by a requirement for four activation steps prior to catalysis. In the present study, the experimentally suggested mechanism is studied using the same methods as those used in the previous study on the theoretical mechanism. The computed results make it very unlikely that a structure obtained after four reductions from the ground state has two hydrides, and the experimentally suggested mechanism does therefore not agree with the EPR experiments for E4. Another structure with only one hydride is here suggested to be the one that has been observed to bind N2 after only four reductions of the ground state.

Drug Design in the Exascale Era: A Perspective from Massively Parallel QM/MM Simulations

The initial phases of drug discovery - in silico drug design - could benefit from first principle Quantum Mechanics/Molecular Mechanics (QM/MM) molecular dynamics (MD) simulations in explicit solvent, yet many applications are currently limited by the short time scales that this approach can cover. Developing scalable first principle QM/MM MD interfaces fully exploiting current exascale machines - so far an unmet and crucial goal - will help overcome this problem, opening the way to the study of the thermodynamics and kinetics of ligand binding to protein with first principle accuracy. Here, taking two relevant case studies involving the interactions of ligands with rather large enzymes, we showcase the use of our recently developed massively scalable Multiscale Modeling in Computational Chemistry (MiMiC) QM/MM framework (currently using DFT to describe the QM region) to investigate reactions and ligand binding in enzymes of pharmacological relevance. We also demonstrate for the first time strong scaling of MiMiC-QM/MM MD simulations with parallel efficiency of ∼70% up to >80,000 cores. Thus, among many others, the MiMiC interface represents a promising candidate toward exascale applications by combining machine learning with statistical mechanics based algorithms tailored for exascale supercomputers.

Connecting the geometric and electronic structures of the nitrogenase iron-molybdenum cofactor through site-selective 57Fe labelling

Understanding the chemical bonding in the catalytic cofactor of the Mo nitrogenase (FeMo-co) is foundational for building a mechanistic picture of biological nitrogen fixation. A persistent obstacle towards this goal has been that the 57Fe-based spectroscopic data-although rich with information-combines responses from all seven Fe sites, and it has therefore not been possible to map individual spectroscopic responses to specific sites in the three-dimensional structure. Here we have addressed this challenge by incorporating 57Fe into a single site of FeMo-co. Spectroscopic analysis of the resting state informed on the local electronic structure of the terminal Fe1 site, including its oxidation state and spin orientation, and, in turn, on the spin-coupling scheme for the entire cluster. The oxidized resting state and the first intermediate in nitrogen fixation were also characterized, and comparisons with the resting state provided molecular-level insights into the redox chemistry of FeMo-co.

Dynamic effects on ligand field from rapid hydride motion in an iron(ii) dimer with an S = 3 ground state

Hydride complexes are important in catalysis and in iron-sulfur enzymes like nitrogenase, but the impact of hydride mobility on local iron spin states has been underexplored. We describe studies of a dimeric diiron(ii) hydride complex using X-ray and neutron crystallography, Mössbauer spectroscopy, magnetism, DFT, and ab initio calculations, which give insight into the dynamics and the electronic structure brought about by the hydrides. The two iron sites in the dimer have differing square-planar (intermediate-spin) and tetrahedral (high-spin) iron geometries, which are distinguished only by the hydride positions. These are strongly coupled to give an S total = 3 ground state with substantial magnetic anisotropy, and the merits of both localized and delocalized spin models are discussed. The dynamic nature of the sites is dependent on crystal packing, as shown by changes during a phase transformation that occurs near 160 K. The change in dynamics of the hydride motion leads to insight into its influence on the electronic structure. The accumulated data indicate that the two sites can trade geometries by rotating the hydrides, at a rate that is rapid above the phase transition temperature but slow below it. This small movement of the hydrides causes large changes in the ligand field because they are strong-field ligands. This suggests that hydrides could be useful in catalysis not only due to their reactivity, but also due to their ability to rapidly modulate the local electronic structure and spin states at metal sites.

Terminal N2 Dissociation in [(PNN)Fe(N2 )]2 (μ-N2 ) Leads to Local Spin-State Changes and Augmented Bridging N2 Activation

Nitrogen fixation at iron centres is a fundamental catalytic step for N₂ utilisation, relevant to biological (nitrogenase) and industrial (Haber-Bosch) processes. This step is coupled with important electronic structure changes which are currently poorly understood. We show here for the first time that terminal dinitrogen dissociation from iron complexes that coordinate N₂ in a terminal and bridging fashion leaves the Fe-N₂ -Fe unit intact but significantly enhances the degree of N₂ activation (Δν≈180 cm^-1 , Raman spectroscopy) through charge redistribution. The transformation proceeds with local spin state change at the iron centre (S= 1 / 2 ${{ 1/2 }}$ →S=³ /₂ ). Further dissociation of the bridging N₂ can be induced under thermolytic conditions, triggering a disproportionation reaction, from which the tetrahedral (PNN)₂ Fe could be isolated. This work shows that dinitrogen activation can be induced in the absence of external chemical stimuli such as reducing agents or Lewis acids.

13C ENDOR Characterization of the Central Carbon within the Nitrogenase Catalytic Cofactor Indicates That the CFe6 Core Is a Stabilizing "Heart of Steel"

Substrates and inhibitors of Mo-dependent nitrogenase bind and react at Fe ions of the active-site FeMo-cofactor [7Fe-9S-C-Mo-homocitrate] contained within the MoFe protein α-subunit. The cofactor contains a CFe6 core, a carbon centered within a trigonal prism of six Fe, whose role in catalysis is unknown. Targeted 13C labeling of the carbon enables electron-nuclear double resonance (ENDOR) spectroscopy to sensitively monitor the electronic properties of the Fe-C bonds and the spin-coupling scheme adopted by the FeMo-cofactor metal ions. This report compares 13CFe6 ENDOR measurements for (i) the wild-type protein resting state (E0; α-Val70) to those of (ii) α-Ile70, (iii) α-Ala70-substituted proteins; (iv) crystallographically characterized CO-inhibited "hi-CO" state; (v) E4(4H) Janus intermediate, activated for N2 binding/reduction by accumulation of 4[e-/H+]; (vi) E4(2H)* state containing a doubly reduced FeMo-cofactor without Fe-bound substrates; and (vii) propargyl alcohol reduction intermediate having allyl alcohol bound as a ferracycle to FeMo-cofactor Fe6. All states examined, both S = 1/2 and 3/2 exhibited near-zero 13C isotropic hyperfine coupling constants, Ca = [-1.3 ↔ +2.7] MHz. Density functional theory computations and natural bond orbital analysis of the Fe-C bonds show that this occurs because a (3 spin-up/3 spin-down) spin-exchange configuration of CFe6 Fe-ion spins produces cancellation of large spin-transfers to carbon in each Fe-C bond. Previous X-ray diffraction and DFT both indicate that trigonal-prismatic geometry around carbon is maintained with high precision in all these states. The persistent structure and Fe-C bonding of the CFe6 core indicate that it does not provide a functionally dynamic (hemilabile) "beating heart"─instead it acts as "a heart of steel", stabilizing the structure of the FeMo-cofactor-active site during nitrogenase catalysis.

How the Bioinspired Fe2Mo6S8 Chevrel Breaks Electrocatalytic Nitrogen Reduction Scaling Relations

The nitrogen reduction reaction (NRR) is a renewable alternative to the energy- and CO₂-intensive Haber-Bosch NH₃ synthesis process but is severely limited by the low activity and selectivity of studied electrocatalysts. The Chevrel phase Fe₂Mo₆S₈ has a surface Fe-S-Mo coordination environment that mimics the nitrogenase FeMo-cofactor and was recently shown to provide state-of-the-art activity and selectivity for NRR. Here, we elucidate the previously unknown NRR mechanism on Fe₂Mo₆S₈ via grand-canonical density functional theory (GC-DFT) that realistically models solvated and biased surfaces. Fe sites of Fe₂Mo₆S₈ selectively stabilize the key *NNH intermediate via a narrow band of free-atom-like surface d-states that selectively hybridize with p-states of *NNH, which results in Fe sites breaking NRR scaling relationships. These sharp d-states arise from an Fe-S bond dissociation during N₂ adsorption that mimics the mechanism of the nitrogenase FeMo-cofactor. Furthermore, we developed a new GC-DFT-based approach for calculating transition states as a function of bias (GC-NEB) and applied it to produce a microkinetic model for NRR at Fe₂Mo₆S₈ that predicts high activity and selectivity, in close agreement with experiments. Our results suggest new design principles that may identify effective NRR electrocatalysts that minimize the barriers for *N₂ protonation and *NH₃ desorption and that may be broadly applied to the rational discovery of stable, multinary electrocatalysts for other reactions where narrow bands of surface d-states can be tuned to selectively stabilize key reaction intermediates and guide selectivity toward a target product. Furthermore, our results highlight the importance of using GC-DFT and GC-NEB to accurately model electrocatalytic reactions.

Review on the QM/MM Methodologies and Their Application to Metalloproteins

The multiscaling quantum mechanics/molecular mechanics (QM/MM) approach was introduced in 1976, while the extensive acceptance of this methodology started in the 1990s. The combination of QM/MM approach with molecular dynamics (MD) simulation, otherwise known as the QM/MM/MD approach, is a powerful and promising tool for the investigation of chemical reactions’ mechanism of complex molecular systems, drug delivery, properties of molecular devices, organic electronics, etc. In the present review, the main methodologies in the multiscaling approaches, i.e., density functional theory (DFT), semiempirical methodologies (SE), MD simulations, MM, and their new advances are discussed in short. Then, a review on calculations and reactions on metalloproteins is presented, where particular attention is given to nitrogenase that catalyzes the conversion of atmospheric nitrogen molecules N₂ into NH₃ through the process known as nitrogen fixation and the FeMo-cofactor.

Thermodynamically Favourable States in the Reaction of Nitrogenase without Dissociation of any Sulfide Ligand

We have used combined quantum mechanical and molecular mechanical (QM/MM) calculations to study the reaction mechanism of nitrogenase, assuming that none of the sulfide ligands dissociates. To avoid the problem that there is no consensus regarding the structure and protonation of the E₄ state, we start from a state where N₂ is bound to the cluster and is protonated to N₂H₂, after dissociation of H₂. We show that the reaction follows an alternating mechanism with HNNH (possibly protonated to HNNH₂) and H₂NNH₂ as intermediates and the two NH₃ products dissociate at the E₇ and E₈ levels. For all intermediates, coordination to Fe6 is preferred, but for the E₄ and E₈ intermediates, binding to Fe2 is competitive. For the E₄, E₅ and E₇ intermediates we find that the substrate may abstract a proton from the hydroxy group of the homocitrate ligand of the FeMo cluster, thereby forming HNNH₂, H₂NNH₂ and NH₃ intermediates. This may explain why homocitrate is a mandatory component of nitrogenase. All steps in the suggested reaction mechanism are thermodynamically favourable compared to protonation of the nearby His‐195 group and in all cases, protonation of the NE2 atom of the latter group is preferred.

A Mechanism for Nitrogenase Including Loss of a Sulfide

Nitrogenase is the only enzyme in nature that can fix N₂ from the air. The active cofactor of the leading form of this enzyme contains seven irons and one molybdenum connected by sulfide bridges. In several recent experimental studies, it has been suggested that the cofactor is very flexible, and might lose one of its sulfides during catalysis. In this study, the possible loss of a sulfide has been investigated by model calculations. In previous studies, we have shown that there should be four activation steps before catalysis starts, and this study is based on that finding. It was found here that, after the four reductions in the activation steps, a sulfide will become very loosely bound and can be released in a quite exergonic step with a low barrier. The binding of N₂ has no part in that release. In our previous studies, we suggested that the central carbide should be protonated three times after the four activation steps. With the new finding, there will instead be a loss of a sulfide, as the barrier for the loss is much lower than the ones for protonating the carbide. Still, it is suggested here that the carbide will be protonated anyway, but only with one proton, in the E₃ to E₄ step. A very complicated transition state for H₂ formation involving a large structural change was obtained. The combined step, with a loss of H₂ and binding of N₂ , is calculated to be endergonic by +2.3 kcal mol^-1 ; this is in excellent agreement with experiments in which an easily reversible step has been found.

Comparisons of bond valences and distances for CO- and N2-bound clusters of FeMo-cofactors

By comparisons of N2 and isoelectronic substrate CO bound FeMo-cofactors (FeMo-cos) in nitrogenases, we have used a classical bond valence method to calculate the oxidation states of the iron and molybdenum atoms in FeMo-cos.

Quantitative Account of the Bonding Properties of a Rubredoxin Model Complex [Fe(SCH3)4]q, q = -2, -1, +2, +3

Iron-sulfur clusters play important roles in biology as parts of electron-transfer chains and catalytic cofactors. Here, we report a detailed computational analysis of a structural model of the simplest natural iron-sulfur cluster of rubredoxin and its cationic counterparts. Specifically, we investigated adiabatic reduction energies, dissociation energies, and bonding properties of the low-lying electronic states of the complexes [Fe(SCH₃)₄]^2-/1-/2+/3+ using multireference (CASSCF, MRCISD), and coupled cluster [CCSD(T)] methodologies. We show that the nature of the Fe-S chemical bond and the magnitude of the ionization potentials in the anionic and cationic [Fe(SCH₃)₄] complexes offer a physical rationale for the relative stabilization, structure, and speciation of these complexes. Anionic and cationic complexes present different types of chemical bonds: prevalently ionic in [Fe(SCH₃)₄]^2-/1- complexes and covalent in [Fe(SCH₃)₄]^2+/3+ complexes. The ionic bonds result in an energy gain for the transition [Fe(SCH₃)₄]^2- → [Fe(SCH₃)₄]^- (i.e., Fe^II → Fe^III) of 1.5 eV, while the covalent bonds result in an energy loss for the transition [Fe(SCH₃)₄]²⁺ → [Fe(SCH₃)₄]³⁺ of 16.6 eV, almost half of the ionization potential of Fe²⁺. The ionic versus covalent bond character influences the Fe-S bond strength and length, that is, ionic Fe-S bonds are longer than covalent ones by about 0.2 Å (for Fe^II) and 0.04 Å (for Fe^II). Finally, the average Fe-S heterolytic bond strength is 6.7 eV (Fe^II) and 14.6 eV (Fe^III) at the RCCSD(T) level of theory.

Dinitrogen binding and activation at a molybdenum-iron-sulfur cluster

The Fe-S clusters of nitrogenases carry out the life-sustaining conversion of N₂ to NH₃. Although progress continues to be made in modelling the structural features of nitrogenase cofactors, no synthetic Fe-S cluster has been shown to form a well-defined coordination complex with N₂. Here we report that embedding an [MoFe₃S₄] cluster in a protective ligand environment enables N₂ binding at Fe. The bridging [MoFe₃S₄]₂(μ-η¹:η¹-N₂) complex thus prepared features a substantially weakened N-N bond despite the relatively high formal oxidation states of the metal centres. Substitution of one of the [MoFe₃S₄] cubanes with an electropositive Ti metalloradical induces additional charge transfer to the N₂ ligand with generation of Fe-N multiple-bond character. Structural and spectroscopic analyses demonstrate that N₂ activation is accompanied by shortened Fe-S distances and charge transfer from each Fe site, including those not directly bound to N₂. These findings indicate that covalent interactions within the cluster play a critical role in N₂ binding and activation.

On the Use of Normalized Metrics for Density Sensitivity Analysis in DFT

In the past years, there has been a discussion about how the errors in density functional theory might be related to errors in the self-consistent densities obtained from different density functional approximations. This, in turn, brings up the discussion about the different ways in which we can measure such errors and develop metrics that assess the sensitivity of calculated energies to changes in the density. It is important to realize that there cannot be a unique metric in order to look at this density sensitivity, simultaneously needing size-extensive and size-intensive metrics. In this study, we report two metrics that are widely applicable to any density functional approximation. We also show how they can be used to classify different chemical systems of interest with respect to their sensitivity to small variations in the density.