The active E4 structure of nitrogenase studied with different DFT functionals

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.

Multireference Protonation Energetics of a Dimeric Model of Nitrogenase Iron-Sulfur Clusters

Characterizing the electronic structure of the iron-sulfur clusters in nitrogenase is necessary to understand their role in the nitrogen fixation process. One challenging task is to determine the protonation state of the intermediates in the nitrogen fixing cycle. Here, we use a dimeric iron-sulfur model to study relative energies of protonation at C, S, or Fe. Using a composite method based on coupled cluster and density matrix renormalization group energetics, we converge the relative energies of four protonated configurations with respect to basis set and correlation level. We find that accurate relative energies require large basis sets as well as a proper treatment of multireference and relativistic effects. We have also tested ten density functional approximations for these systems. Most of them give large errors in their relative energies. The best performing functional in this system is B3LYP, which gives mean absolute and maximum deviations of only 10 and 13 kJ/mol with respect to our correlated wave function estimates, respectively, comparable to the uncertainty in our correlated estimates. Our work provides benchmark results for the calibration of new approximate electronic structure methods and density functionals for these problems.

The E3 state of FeMoco: one hydride, two hydrides or dihydrogen?

Hydrides are present in the reduced states of the iron-molybdenum cofactor (FeMoco) of Mo nitrogenase and are believed to play a key mechanistic role in the dinitrogen reduction reaction catalyzed by the enzyme. Two hydrides are present in the E4 state according to 1H ENDOR and there is likely a single hydride in the E2 redox state. The 2-hydride E4 state has been experimentally observed to bind N2 and it has been speculated that E3 may bind N2 as well. However, the E3 state has not been directly observed and very little is known about its molecular and electronic structure or reactivity. In recent computational studies, we have explored the energy surfaces of the E2 and E4 by QM/MM modelling, and found that the most stable hydride isomers contain bridging or partially bridging hydrides with an open protonated belt sulfide-bridge. In this work we systematically explore the energy surface of the E3 redox state, comparing single hydride and two-hydride isomers with varying coordination and bridging vs. terminal sulfhydryl groups. We also include a model featuring a triply protonated carbide. The results are only mildly dependent on the QM-region size. The three most stable E3 isomers at the r2SCAN level of theory have in common: an open belt sulfide-bridge (terminal sulfhydryl group on Fe6) and either 2 bridging hydrides (between Fe2 and Fe6), 1 bridging-1-terminal hydride (around Fe2 and Fe6) or a dihydrogen ligand bound at the Fe2 site. Analyzing the functional dependency of the results, we find that functionals previously found to predict accurate structures of spin-coupled Fe/Mo dimers and FeMoco (TPSSh, B97-D3, r2SCAN, and B3LYP*) are in generally good agreement about the stability of these 3 E3 isomers. However, B3LYP*, similar to its parent B3LYP method, predicts a triply protonated carbide isomer as the most stable isomer, an unlikely scenario in view of the lack of experimental evidence for carbide protonation occurring in reduced FeMoco states. Distinguishing further between the 3 hydride isomers is difficult and this flexible coordination nature of hydrides suggests that multiple hydride isomers could be present during experimental conditions. N2 binding was explored and resulted in geometries with 2 bridging hydrides and N2 bound to either Fe2 or Fe6 with a local low-spin state on the Fe. N2 binding is predicted to be mildly endothermic, similar to the E2 state, and it seems unlikely that the E3 state is capable of binding N2.

Critical Roles of Exchange and Superexchange Interactions in Dictating Electron Transfer and Reactivity in Metalloenzymes

Electron transfer (ET) is a fundamental process in transition-metal-dependent metalloenzymes. In these enzymes, the spin-spin interactions within the same metal center and/or between different metal sites can play a pivotal role in the catalytic cycle and reactivity. This Perspective highlights that the exchange and/or superexchange interactions can intrinsically modulate the inner-sphere and long-range electron transfer, thus controlling the mechanism and activity of metalloenzymes. For mixed-valence diiron oxygenases, the spin-regulated inner-sphere ET can be dictated by exchange interactions, leading to efficient O-O bond activations. Likewise, the spin-regulated inner-sphere ET can be enhanced by both exchange and superexchange interactions in [Fe4S4]-dependent SAM enzymes, which enable the efficient cleavage of the S─C(γ) or S─C5' bond of SAM. In addition to inner-sphere ET, superexchange interactions may modulate the long-range ET between metalloenzymes. We anticipate that the exchange and superexchange enhanced reactivity could be applicable in other important metalloenzymes, such as Photosystem II and nitrogenases.

The E2 state of FeMoco: Hydride Formation versus Fe Reduction and a Mechanism for H2 Evolution

The iron‐molybdenum cofactor (FeMoco) is responsible for dinitrogen reduction in Mo nitrogenase. Unlike the resting state, E₀, reduced states of FeMoco are much less well characterized. The E₂ state has been proposed to contain a hydride but direct spectroscopic evidence is still lacking. The E₂ state can, however, relax back the E₀ state via a H₂ side‐reaction, implying a hydride intermediate prior to H₂ formation. This E₂→E₀ pathway is one of the primary mechanisms for H₂ formation under low‐electron flux conditions. In this study we present an exploration of the energy surface of the E₂ state. Utilizing both cluster‐continuum and QM/MM calculations, we explore various classes of E₂ models: including terminal hydrides, bridging hydrides with a closed or open sulfide‐bridge, as well as models without. Importantly, we find the hemilability of a protonated belt‐sulfide to strongly influence the stability of hydrides. Surprisingly, non‐hydride models are found to be almost equally favorable as hydride models. While the cluster‐continuum calculations suggest multiple possibilities, QM/MM suggests only two models as contenders for the E₂ state. These models feature either i) a bridging hydride between Fe₂ and Fe₆ and an open sulfide‐bridge with terminal SH on Fe₆ (E₂‐hyd) or ii) a double belt‐sulfide protonated, reduced cofactor without a hydride (E₂‐nonhyd). We suggest both models as contenders for the E₂ redox state and further calculate a mechanism for H₂ evolution. The changes in electronic structure of FeMoco during the proposed redox‐state cycle, E₀→E₁→E₂→E₀, are discussed.

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.

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.

The active E4 structure of nitrogenase studied with different DFT functionals

The present study concerns the technical aspects of obtaining the energetics for the E4 state of nitrogenase, the enzyme that fixes N₂ in nature. EPR experiments have shown that the critical E4 structure that activates N₂ should contain two bridging hydrides in the FeMo-cofactor. It is furthermore in equilibrium with a structure where the two hydrides have been released and N₂ binds. These observations led to the suggestion that E4 should have two bridging hydrides and two protonated sulfides. It is important to note that the structure for E4 has not been determined, but only suggested. For a long time, no DFT study led to the suggested structure, independent of which functional was used. However, in two recent DFT studies a good agreement with the experimental suggestion was claimed to have been obtained. In one of them the TPSS functional was used. That was the first out of 11 functionals tried that led to the experimentally suggested structure. In the second of the recent DFT studies, a similar conclusion was reached using the TPSSh functional. The conclusions in the recent studies have here been studied in detail, by calculating a critical energetic value strongly implied by the same EPR experiments. Both the TPSS and TPSSh functionals have been used. The present calculations suggest that those DFT functionals would not lead to agreement with the experimental EPR results either.