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Back | Show only these items: | Structure of the FeFe-cofactor of the iron-only nitrogenase and possible mechanism for dinitrogen reduction

1
Structure of the FeFe-cofactor of the iron-only nitrogenase and possible mechanism for dinitrogen reduction

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj1

We use density functional calculations to model the FeFe-cofactor of the iron-only nitrogenase.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj2

We determine the ground state geometical and magnetic structure and show that our results are in agreement with experimental observations.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj3

We model the reactivity of the FeFeco towards hydrogen and nitrogen and compare to the FeMoco.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj4

Our results for the difference in reactivity can be linked to experimental observations.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con1

Introduction

The enzyme nitrogenase catalyzes the conversion of atmospheric nitrogen to ammonia.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac1

Although nitrogen is abundant in the air, it has to be converted to a biologically accessible form, in this case NH₃, in order to be used by plants.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac2

In nature, the conversion of N₂ to NH₃ can only be performed by a small group of diazotrophic microorganisms that contain the enzyme nitrogenase.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac3

Nitrogenase catalyzes the following reaction:¹ N₂ + 8H⁺ + 8e⁻ + 16ATP → 2NH₃ + H₂ + 16ADP + 16P_iThe most common form of nitrogenase contains an FeMo-cofactor (FeMoco), a cluster of the stoichiometry MoFe₇S₉, where the reduction of N₂ most probably takes place.²

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac4

When Mo is absent, some organisms can form alternative nitrogenases, where Mo is substituted by V or Fe.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac5

In most cases, the activity of alternative nitrogenases decreases with the sequence Mo > V > Fe.³

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac6

The Fe-only nitrogenase thus has the lowest activity.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac6

The active center of this nitrogenase is an FeFe-cofactor (FeFeco), which consists exclusively of iron and sulfur atoms.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac7

In addition to the low activity for nitrogen fixation, the Fe-only nitrogenase catalyzes an unusually high hydrogen evolution.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac8

These differences are not yet understood in terms of molecular structure, i.e. whether they arise from the replacement of Mo with Fe or from other differences in the enzyme structure.

Type: Motivation | Advantage: None | Novelty: None | ConceptID: Mot1

In the present paper, we present a detailed investigation of the FeFe-cofactor and compare it to the FeMoco.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj5

We study the FeFe-cofactor by means of extensive density functional theory (DFT) calculations and outline a possible path of nitrogen fixation at the FeFe-cofactor.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj6

Comparing the energetics of this path to a tentative one for the FeMo-cofactor⁴ leads us to suggest reasons for the differences in activity.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj7

The paper is organized as follows.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac9

We briefly review the experimental and theoretical knowledge that has been assembled about the structure and function of the Fe-only nitrogenase.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj8

Then we introduce our computational method and explain how we model the FeFe-cofactor.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj9

The results section starts with a description of the magnetic ground state of the FeFe-cofactor.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj10

Then we present results for N₂ and H₂ adsorption on the FeFeco and for the subsequent hydrogenation of adsorbed N₂.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj11

We compare these results to results for the FeMoco.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj12

The X-ray structure of the conventional Mo-containing nitrogenase has been determined by X-ray diffraction for different bacteria and with different resolutions.^5–7

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac10

From these studies and from EXAFS-studies⁸ it is known that nitrogenase consists of two proteins, the Fe protein and the MoFe protein.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac11

The Fe protein contains a ferredoxin, i.e. an Fe₄S₄ cluster, and transfers electrons to the FeMo protein along with the hydrolysis of Mg-bound ATP.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac12

The FeMo protein contains a P-cluster (Fe₈S₇) and a FeMo cofactor (MoFe₇S₉, FeMoco).

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac13

The P-cluster presumably transfers the electrons which come from the ferredoxin, on to the FeMoco, where the reduction of N₂ most probably takes place.²

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac14

The protons required for the reduction come from solution.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac15

A very recent X-ray study of the MoFe-protein revealed that the FeMoco has a central ligand in the cavity, which could be either nitrogen, oxygen or carbon.⁷

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac16

Subsequent theoretical studies by us⁹ and other researchers^10,11 have presented strong support for the central ligand to be nitrogen.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac17

It has been shown by ENDOR and ESEEM spectroscopy that the central nitrogen ligand does not exchange during turnover.¹²

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac18

For the Fe-nitrogenase, there is no crystal structure available, and thus it is not yet known, whether a central N ligand is present in the cavity as well, but this seems well possible.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac19

A recent EXAFS and Mössbauer study by Krahn et al¹³. shows that the iron and sulfur atoms most probably assume the same prismatic geometry as in the FeMo cofactor.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac20

We have carried out this study for the FeMoco structure without the central ligand and with an equivalent FeFeco structure where the Mo atom is substituted by Fe.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod1

It is clear that for both the FeMoco and the FeFeco there will be changes in structure and mechanics due to an inclusion of the central ligand.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac21

The central ligand only changes the catalytic properties of the FeMoco slightly.¹⁴

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac22

Dinitrogen adsorption and reduction on the triangular Fe atoms as suggested by⁴ is still possible with energies similar to those for the FeMoco without a central ligand.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac23

We concentrate on the difference between the FeMoco and FeFeco.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj13

This means that whereas a central ligand may change the chemical properties somewhat, this should only be a second order effect on the properties we are studying here.

Type: Hypothesis | Advantage: None | Novelty: None | ConceptID: Hyp1

Previous studies

Experimental studies

It had long been assumed that the ability to fix N₂ depends on the presence of Mo in the enzyme.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac24

This assumption had to be revised when in 1980, the first evidence for alternative nitrogenases in the bacteria A. vinelandii was presented.¹⁵

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac25

It came as a surprise when in 1988 the Fe-only nitrogenase was purified from A. vinelandii¹⁶ and was proved to neither contain Mo nor V. Apart from A. vinelandii, the Fe-only nitrogenase has been purified and characterized from R. capsulatus,^17–20 and it has been purified from R. rubrum.^21,22

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac26

The Fe-only nitrogenase is only formed if both Mo and V are absent, otherwise the conventional Mo-nitrogenase or the V-nitrogenase are expressed.^23,24

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac27

Contrary to the Mo nitrogenase, there are no X-ray studies of the structure of the Fe-only nitrogenase.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac28

Therefore, until very recently it was mainly because of genetic evidence and the conservation of important amino acids that the cofactors of the different nitrogenases were assumed to be similar.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac29

Genetic studies^25–27 showed that the important genes for nitrogen fixation in Mo-nitrogenase are also present in Fe-nitrogenase.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac30

Furthermore, it was shown for R. capsulatus that the amino acids in Mo-nitrogenase which link the functional clusters to the peptide chains, are conserved in the sequence of Fe-nitrogenase, although the two sequences only show an overall agreement of 26%.²⁸

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac31

Another indication of the similarity between the Mo-nitrogenase and the Fe-nitrogenase is that hybrid enzymes, which e.g. consist of the protein of the FeFe nitrogenase, but with a FeMo cofactor, could be produced.^{22,24,29–31}

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac32

Those enzymes were able to fix N₂, but with a much lower activity.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac32

Electron paramagnetic resonance (EPR) spectroscopy has shown that the spin ground state of the dithionite-reduced FeFe-cofactor is integer, probably S = .0^17–20

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac33

This is in contrast to the FeMoco, for which it is known from electron paramagnetic resonance (EPR) that the spin state of the FeMoco is S = 3/2 in the resting state.^32,33

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac34

In a very recent study, Krahn et al¹³. investigate the Fe-only nitrogenase from R. capsulatus using EXAFS and Mössbauer spectroscopy and obtain for the first time direct information about the structure and the coordination of the FeFe-cofactor.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac35

The study confirms by Mössbauer spectroscopy that the dithionite-reduced FeFe-cofactor is diamagnetic and therefore has an integer spin state, probably S = 0.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac36

Furthermore, the Mössbauer spectroscopy results show that the FeFe-cofactor contains eight iron atoms and thus has a stoichiometry of Fe₈S₉.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac37

By means of EXAFS, Krahn et al. obtain information about how the iron atoms are coordinated within the cluster.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac38

They find that the only possible arrangement of the iron atoms which is consistent with the EXAFS spectra is the trigonal prismatic arrangement of the FeMo cofactor.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac38

Thus, they conclude that the structure of the FeFe-cofactor probably is very similar to the one of the FeMo cofactor with the Mo atom exchanged for Fe.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac39

The kinetics of the Mo-nitrogenase have been studied extensively and the results are reviewed in refs. ^{2 and 34} The most comprehensive model for the reactivity of nitrogenase and the kinetics of nitrogen fixation is the Thorneley–Lowe model.³⁵

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac40

This model also incorporates the observation that at least one H₂ is produced per N₂ fixated, even for very high N₂ pressures up to 50 bar.³⁶

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac41

This is the reason for the stoichiometry of eqn. (1).

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac42

For the Fe-nitrogenase, however, there are only few studies of the reactivity and no model comparable to the Thorneley-Lowe model exists.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac43

There are several measurements of the activity of the Fe-only nitrogenase towards different substrates.^{3,16,19,20,37}

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac44

The most recent study is the one by Schneider et al. in 1997²⁰ and investigates both the Mo-nitrogenase and the Fe-nitrogenase of R. capsulatus.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac45

In agreement with previous studies they find that the H₂-producing activity of the Fe-nitrogenase is extraordinarily high.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac46

Furthermore, the H₂ production of the Fe-nitrogenase is much less inhibited by N₂, as the H₂ production of the Mo-nitrogenase.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac47

For the Mo-nitrogenase it is found that under very high N₂ pressure, the limiting ratio of produced H₂ and fixated N₂ is H₂/N₂ = 1, in accordance with the Thorneley–Lowe scheme.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac48

For the Fe-nitrogenase, this ratio is found to be H₂/N₂ = 7.5, which means that the reduction of N₂ competes much worse with hydrogen production than for the Mo-nitrogenase.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac49

This outstanding feature of hydrogen production might make the Fe-nitrogenase useful for technical applications in connection with hydrogen production³⁸.

Type: Motivation | Advantage: None | Novelty: None | ConceptID: Mot2

Theoretical studies

Since the crystal structure of the FeMoco was first published in 1992 there have been a number of theoretical studies of both the structure and the reactivity of the FeMoco.^{4,9–11,39–53}

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac50

For the Fe-only nitrogenase, there are only few theoretical studies, a study by Plass from 1994⁴⁰ and a recent study by Lovell et al.⁵⁴

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac51

Plass⁴⁰ studied the cofactors of the Mo-, V- and Fe-nitrogenase using the Extended Hückel method.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac52

By analyzing the frontier orbitals, he showed that the Mo and V atoms do not contribute to the respective frontier orbitals of the FeMoco and FeVco and that for the FeFeco the Fe atom at the Mo position does not contribute either.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac53

This lead Plass to suggest that the atom at the Mo position is not directly involved in the N₂ binding, but rather fine-tunes the activity of the cluster.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac54

Assuming that N₂ binds to one of the six threefold-coordinate iron atoms, Plass showed that the reduction of the N₂-binding FeFeco is much more energy-demanding than the reduction of the N₂-binding FeMoco or FeVco.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac55

Lovell et al⁵⁴. recently presented density functional theory calculations on the FeVco and on the FeFeco.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac56

They investigated the geometrical and the magnetic structure of the FeFeco and suggested a spin structure for the magnetic ground state.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac57

They also presented results for isomer shifts.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac58

In the following we compare to these results whenever possible.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj14

Model for ammonia synthesis and hydrogen release

As a starting point for our study we take the results of Rod and Nørskov,⁴ who investigated both hydrogen evolution and ammonia production on the FeMoco.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac59

Their model for H₂ evolution is shown in Fig. 1.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod2

The coupled addition of protons and electrons to the FeMoco is modeled by the addition of hydrogen atoms.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac60

The first three hydrogen atoms adsorb on the μ₂S-atoms and these adsorptions are exothermic.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac61

The most energy-demanding step is the adsorption of the fourth H on one of the triangular Fe atoms.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac62

Once this is accomplished, the next step is the transfer of one H atom from the μ₂S atom to the Fe atom, which is exothermic.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac63

The subsequent desorption of H₂ is exothermic as well.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac64

In the following we use this model in order to investigate the reactivity differences of the FeMoco and the FeFeco.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj15

The two deciding energies for this process are the adsorption energy of H on the μ₂S atoms (which has to be exothermic for the process to function) and the adsorption energy of H on a triangular Fe atom, which dominates the process.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod3

The adsorption energy of H on a triangular Fe atom depends only weakly on the number of H atoms adsorbed on the μ₂S atoms.⁴

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac65

Thus, by calculating the adsorption energies for one H atom on the different possible positions on the FeFeco, we can judge the feasibility of H₂ production on the FeFeco.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod4

The model for ammonia synthesis is shown in Fig. 2.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod5

The adsorption of N₂ on one of the triangular Fe atoms is thermoneutral.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac66

Dissociation of N₂ on the cluster is highly unfavorable and thus the N₂ gets hydrogenated.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac67

The first hydrogenation step is highly endothermic and the most energy-demanding step in the whole cycle.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac68

The subsequent hydrogenations and the release of the first NH₃ molecule are exothermic.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac69

The only endothermic step is the release of the second NH₃ molecule and one can speculate that this step is much easier in solution.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac70

One should note that an intermediate in this cycle is hydrazine (N₂H₄), which has indeed been shown to be an intermediate in the enzyme turnover.²

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac71

The two most important energies, which determine the reactivity of the FeMoco, are the adsorption energy for N₂ on a triangular Fe atom, and the energy of the first hydrogenation.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod6

100

Thus we concentrate on calculating those two energies for the FeMoco and the FeFeco in the following.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj16

101

Thus, the model for ammonia synthesis for the FeMoco from ^{ref. 4} yields that the most energy-demanding step is the first hydrogenation of adsorbed N₂.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs1

102

This is to be expected, as in the first hydrogenation step from N₂ to NNH, the nitrogen triple bond is broken, and this is the bond containing most energy.⁵⁵

Type: Result | Advantage: None | Novelty: None | ConceptID: Res1

103

This holds also for the hydrogenation of N₂ in the gas phase^45,56 and on a Ru metal surface.⁴⁷

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac72

104

Therefore, for all processes where N₂ is hydrogenated directly without dissociating, it is to be expected that the first hydrogenation step from N₂ to NNH is the most energy-demanding step.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod7

105

Using this general result, we choose to focus on calculating the first two steps, the binding of N₂ and the first reduction to NNH, as these steps determine the entire process.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod7

106

We note explicitly that we only address the thermodynamics of the processes of dihidrogen and ammonia formation and do not calculate any activation barriers.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj17

107

On the other hand, there are indications that the transfer of protons to the adsorbed N₂ is not associated with significant energy barriers.^4,57,58

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac73

108

For example, in ^{ref. 4} proton transfer was modeled with the very simple proton donors NH₄⁺ and H₃O⁺, and it was found that in this setup there is no barrier for proton transfer.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac74

109

Although the question of activation barriers certainly has to be addressed in future studies, we limit ourselves to thermodynamical considerations at present.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj18

Methods

Model of the Fe-only cofactor

110

The FeMoco with its ligands from the most recent crystal structure 1M1N⁷ is depicted in Fig. 3a (general pdb references given in ref. ⁵⁹).

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac75

111

We model the FeMoco by truncating all ligands after the first ligating atom.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod8

112

Thus we stubstitute Cys by SH, His by NH₃ and homocitrate by two OH groups.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod9

113

Our model structure of the FeMoco with a central N ligand, which we have investigated in ref. ⁹ is shown in Fig. 3b.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod10

114

The model structure for the FeMoco without a central ligand is shown in Fig. 3c.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod11

115

Structure 3b is much more symmetric and resembles the experimental structure 3a more than structure 3c.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs2

116

This is due to the higher coordination of the Fe atoms in structure 3b, which are therefore kept in a more symmetical position.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res2

117

One consequence of the higher coordination is that the structure 3b is much constrained than structure 3c and cannot distort in the same way.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs3

118

However, this has only a very small effect on the ability of the triangular Fe atoms to bind and reduce N₂.¹⁴

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac76

119

As discussed in Section 1, we perform all calculations with the FeMoco model of Fig. 3c, where there is no central ligand.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod12

120

As discussed before, there is no X-ray crystal structure of the FeFeco of the iron-only nitrogenase, however, the recent EXAFS study¹³ shows that the FeFeco most probably has the same geometry as the FeMoco with Mo substituted by Fe.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac77

121

Furthermore, the His442 and the Cys275 residues, which link the FeMoco to the peptide chain, are conserved in the Fe-only nitrogenase and the gene encoding a homocitrate synthase is also present.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac78

122

Therefore, it is reasonable to assume that the FeFeco is coordinated to Cys, His, and homocitrate in the same way as the FeMoco.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod13

123

Thus, we model the FeFeco in an analogous way as the FeMoco and the model is depicted in Fig. 3d.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod13

124

However, when minimizing the FeFeco model of Fig. 3d, in some cases one of the OH groups was unstable and tended to move closer to one of the Fe atoms on the triangle.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs4

125

This rises the question, whether the homocitrate ring might be opened at the FeFeco and only form a monodentate coordination instead of a bidentate coordination which is present in the FeMoco.

Type: Hypothesis | Advantage: None | Novelty: None | ConceptID: Hyp2

126

There are hints in the literature that opening of the homocitrate ring indeed is possible.^48,49,71,72

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac79

127

We investigate this by considering a second model for the FeFeco, where the lower Fe atom only is coordinated to NH₃ and to one OH group.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod14

128

This model is shown in Fig. 3e.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod15

129

All calculations are carried out on both models in the following.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac80

130

We emphasize that we model a charge neutral cluster and unit cell in all cases.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod16

131

We consider this the most natural choice, as a net charge would introduce long-range Coulomb forces.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod16

132

Furthermore, a large negative charge on the cluster without proper shielding from the surroundings seems problematic.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod16

133

In terms of formal oxidation states, the model with one OH group (Fig. 3e) corresponds to the oxidation states [4Fe²⁺4Fe³⁺9S²⁻], which agrees with the oxidation state assignment from the isomer shift measured in ref. .¹³

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs5

134

Our model with two OH groups corresponds to the oxidation states [3Fe²⁺5Fe³⁺9S²⁻].

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs6

135

One should be aware of that in ref. ¹³ the average oxidation state of the Fe sites was measured to be 2.5 and that the oxidation state assignment of 4Fe²⁺ and 4Fe³⁺ sites therefore is a purely formal one.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod17

136

From the iron-iron interactions and the net spin density on the Fe sites one can infer that the electrons are delocalized and that the average oxidation state is a more appropriate picture.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res3

137

In this context we remark that in⁵⁴ the FeFeco with the oxidation state assignments [6Fe²⁺2Fe³⁺9S²⁻] and [4Fe²⁺4Fe³⁺9S²⁻] have been modeled.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac81

138

Fig. 3 as well as Figs. 5, 6, 7 and 8 are prepared with Molscript⁶⁰ and Raster3D⁶¹.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod18

Calculational details

139

All calculations are carried out with the program dacapo,⁶² which uses a plane-wave expansion of the Kohn–Sham wavefunctions and the generalized gradient approximation for the exchange-correlation terms.⁶³

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod19

140

Due to the plane-wave expansion, we have to choose systems which are periodic in all three dimensions.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod20

141

Here we accomplish this by repeating a supercell containing the cluster periodically in all three dimensions including enough vacuum around the cluster for the interactions between the supercells to be neglegible.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod21

142

We use a triclinic supercell with the axes a = b = 11 Å and c = 15.4 Å and the angles α = 90°, β = 69° and γ = 120°.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod22

143

In all calculations, we include plane waves with energies up to 25 Ry.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod23

144

In order to describe the core parts of the ions, we use ultrasoft pseudopotentials,⁶⁴ except for sulfur, where we use a soft pseudopotential.⁶⁵

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod24

145

For the k-point sampling of the Brillouin zone, Γ-point sampling has been used.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod25

146

The Fermi population of the Kohn–Sham orbitals is set to k_BT = 1 kJ mol⁻¹ and Pulay mixing is applied to the resulting density.^66,67

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod26

147

We have tested that the calculations are converged with respect to the plane-wave cutoff, the size of the supercell and the number of k-points within a few kJ mol⁻¹.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod27

148

All calculations have been carried out spin-polarized.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod28

149

The magnitude of the spin density on the Fe atoms is independent of the chosen (non-zero) initial spin density.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod29

150

As exchange-correlation functional, we use the spin-dependent revised Perdew–Enzerhoff–Burke (RPBE) functional.⁶⁸

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod30

151

For N₂ adsorption on Fe surfaces, where there is experimental data available for comparison, this functional describes the adsorption energies and the activation energies very well.⁶⁹

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac82

152

As initial guess for the electron densities, sums of atomic densities or the densities of previously calculated structures are used.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod31

153

As starting structure, the coordinates of the crystal structure 3MIN⁶ are used and reasonable guesses are made for the ligands.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod32

154

For the structures without adsorbates, all degrees of freedom, that means all atoms, are relaxed, except for the Mo atom (or the Fe atom at the Mo position), which is kept fixed in order to avoid translational motion of the whole cluster.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod33

155

For the structures with adsorbates, the ligands and the Mo atom are kept fixed in the positions found for the respective structures without adsorbates, and all other atoms are allowed to relax.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod34

156

An exception is made for the adsorption of N₂ on the Mo atom (or on the Fe atom in the Mo position), where the adjacent ligands are also allowed to relax.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod35

157

This will be discussed at the appropriate place in the results section.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac83

158

All energy minimizations of ionic degrees of freedom take place according to a conjugate-gradient algorithm.⁷⁰

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod36

159

The convergence criterion for the absolute force is 0.1 eV Å⁻¹ for the structures without adsorbates and 0.2 eV Å⁻¹ for the structures with adsorbates.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod37

Results

Spin ground state and geometry

160

As a starting point for determining the spin magnetic ground state of the FeFeco, we briefly look at the FeMoco.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj19

161

The magnetic ground state of the FeMoco has a total spin of S = 3/2 and the Fe atoms are antiferromagnetically coupled.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac84

162

The magnetic configuration with the lowest energy has for example been determined by Rod and Nørskov⁴ and by Lovell et al⁵⁰. and is depicted in Fig. 4a.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac85

163

For the FeFeco it is known from experiments that the spin ground state has antiferromagnetic couplings and an integer total spin, probably S = 0.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac86

164

We have investigated numerous spin configurations both with ferromagnetic and with antiferromagnetic couplings.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj20

165

We find that two antiferromagnetic configurations lie lowest in energy and are very similar in energy.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs7

166

These two spin states A1 and A2 are shown in Fig. 4b and c.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs8

167

All other spin states which we have examined, lie significantly higher in energy (>30 kJ mol⁻¹) for both the model with one OH group and the model with two OH groups.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs9

168

Taking the spin state A1 as the energy zero, the energy difference to the spin state A2 E_A2 − E_A1 is −4 kJ mol⁻¹ for the model with two OH groups and 1 kJ mol⁻¹ for the model with one OH group.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs10

169

These energy differences between the two lowest spin states A1 and A2 are much too small to be decisive for their stability.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res4

170

However, for both models we observe that the spin states A1 and A2 are significantly more stable than all other examined spin states.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs11

171

Thus, their stability seems to be independent of the details of our model, in this case independent of whether there are one or two OH groups.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res5

172

For the spin states A1, we also considered the spin isomers, i.e. those spin structures where the spin state is rotated around the C₃ axis, which is present for the cluster if one disregards the ligands.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj21

173

We find that the spin isomers are very similar in energy.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs12

174

For the spin state A2 there are no spin isomers due to its C₃ symmetry.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs13

175

The net spin densities on the Fe atoms lie in the range of 1.7–2.9 for the FeFeco with two OH groups and 2.0–2.9 for the FeFeco with one OH group.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs14

176

These spin densities are independent of the magnitude of the chosen initial (nonzero) spin densities.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs15

177

The main difference between the two models is that the bottom Fe atom, which is coordinated to NH₃ and to the OH groups has a net spin density of 1.7 in case of two OH groups and 2.0 in case of one OH group.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs16

178

This difference gives rise to the different total spins.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res6

179

For the FeMoco, the net spin density on the Mo atom is close to zero.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs17

180

As we cannot conclude from our calculations whether A1 or A2 is the ground state spin structure (it might be possible that they indeed are both present) we carry out all further calculations and analyses on both spin structures.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con2

181

This gives the advantage that we can examine the effect of the detailed spin structure on the geometries and adsorption energies.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj22

182

The bond lengths and angles of the FeFeco for the two models and spin states are listed in Table 1, where they can be compared to the values from the recent EXAFS study.¹³

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs18

183

The values for the FeMoco are also listed for comparison.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs19

184

As the experimental values are from an EXAFS study, it makes most sense to compare the averages of all bonds of the same type (Fe–S, Fe–Fe, Fe–Fe diagonal) to the EXAFS value, since the same averaging is inherent in EXAFS.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod38

185

Generally, our geometries agree very well with the experimental values.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res7

186

The Fe–S bond lengths only vary relatively little and the average is only slightly smaller than the EXAFS value.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs20

187

For the Fe–Fe bond lengths the variations are larger and the averages are somewhat larger than the EXAFS values.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs21

188

The Fe–Fe distances over the face diagonals in our models have particularly high standard deviations, but the averages are only somewhat larger than the EXAFS values.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs22

189

The high standard deviations may well be consistent with the EXAFS data, as the peak associated with this distance looks relatively broad.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs23

190

The total height of the FeFeco (distance top Fe–bottom Fe) is about 0.2–0.4 Å larger than the EXAFS value of 6.9 Å, except for the model with one OH group and spin state A1 with a value of 7.0 Å.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs24

191

In summary, the geometry the model with one OH group and spin state A1 agrees best with the EXAFS results.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res8

192

In our calculations, the total spin of the FeFeco with two OH groups is determined to be S = 1/2, and the total spin of the FeFeco with one OH group is S = 0.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs25

193

This might give a hint that the homocitrate ring is opened and only bound to the Fe in a monodentate manner, but this might also be an artefact of our model.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res9

194

Because of this and because of the fact that the formal oxidation state of our model with 1OH group and agrees with the experimentally determined one [4Fe³⁺4Fe²⁺9S²⁻], we investigate whether an opening of the homocitrate ring is possible.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj23

195

In our model, we cannot consider the reaction of the opening of the homocitrate ring, as there is no straightforward way to model the reaction, where one OH group is cleaved.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod39

196

However, by comparing the models with one and two OH groups for FeFeco and FeMoco, we can observe a relative trend in how easily one OH group can be cleaved.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod40

197

Thus, we also have calculated a model of the FeMoco with only one OH group, where we started from the model depicted in Fig. 3 and removed one OH group (we will also need this model later for the N₂ adsorption at the Mo site).

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod41

198

The energy difference ΔE_OH = [E_tot(FeFeco,1OH) − E_tot(FeFeco, 2OH)] − [E_tot(FeMoco,1OH) − E_tot(FeMoco,2OH)]describes how costly it is to remove one OH group from the FeFeco compared to the removal from the FeMoco.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod42

199

In this equation, E_tot(FeFeco,1OH) is the total energy of the FeFeco with one OH group and E_tot(FeFeco,2OH) the total energy of the FeFeco with two OH groups; the same notation is used for the total energies of the FeMoco.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod43

200

The results for ΔE_OH are

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs26

201

ΔE_OH = −26 kJ mol⁻¹ for spin state A1

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs26

202

ΔE_OH = −31 kJ mol⁻¹ for spin state A2

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs27

203

A negative sign for ΔE_OH means that the removal of one OH group from the FeFeco requires less energy than from the FeMoco.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res10

204

Thus, dependent on the magnetic state of the FeFeco, we find that the removal of one OH group from the FeFeco requires 26–31 kJ mol⁻¹ less energy than from the FeMoco.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs28

205

Taking into account that opening of the homocitrate ring has been suggested to be feasible on the FeMoco, it should certainly be feasible on the FeFeco.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con3

206

Thus, it is relevant that we consider models with both two and one OH groups.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con4

Hydrogen adsorption

207

We first study the effect of a coupled electron and proton flow to the FeFeco.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj24

208

We model this by adding a proton/electron pair to the FeFeco in various ways.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod44

209

The investigated configurations are shown in Fig. 5 and the corresponding binding energies are listed in Table 2.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs29

210

Here and in the following, the adsorption energy is defined as the total energy of the structure with the adsorbate XA (X = FeMoco, FeFeco, A = H, N₂, N₂H) minus the sum of the total energies of the bare structure X and the adsorbate in the gas phase A, ΔE_ads = E_tot(XA) − [E_tot(X) + E_tot(A)] Thus, a negative binding energy means that adsorption of A to X is energetically favorable and occurs spontaneously, whereas a positive binding energy indicates that the complex XA is unstable and that adsorption will not happen spontaneously.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod45

211

In this section we consider the adsorption of proton/electron pairs, as in the enzyme electrons are transferred to the FeFeco from the Fe-protein and protons come from solution.^2,49

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj25

212

As reference energy, we use ½H₂ in the gas phase.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod46

213

This energy zero for hydrogen is a matter of choice, but ½H₂ as the zero point corresponds directly to the standard hydrogen electrode (SHE) and is therefore an especially practical choice.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod47

214

The actual chemical potential of the transferred electrons depends on the redox potential of the [4Fe–4S]^1+/2+ cluster pair.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod48

215

In the energy diagrams Figs. 1 and 2 as well as in Fig. 9 this corresponds to an upwards shift of the initial states, because the protons and electrons are energetically higher than ½H₂ in the gas phase.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res11

216

A proton/electron pair on the FeFeco is most stable on one of the μ₂S atoms (configuration a in Fig. 5) and this is independent of the number of OH groups or the spin state.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs30

217

This is reflected in the fact that the binding energies are negative and the smallest ones observed.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs31

218

In more detail, the proton is located on the μ₂S ligand and the electron on the cluster.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs32

219

The second stable configuration is configuration e, where an H atom is located inside the cluster, but clearly coordinated to one Fe atom from the inside.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs33

220

The stability of e depends on the number of OH groups and the spin state of the FeFeco.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs34

221

The positions b and c, where the H atom is bound by one of the triangular Fe atoms, are unstable by 35–56 kJ mol⁻¹ depending on the model, spin state and whether adsorption takes place on an Fe atom in the upper or in the lower triangle.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs35

222

The position d, where the H atom is bound to an μ₃S atom, is unfavorable as well.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs36

223

We have also calculated the energies for H adsorption on the FeMoco for the same configurations, although they already have been calculated elsewhere.^4,51

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj26

224

But by calculating the adsorption energies for the FeFeco and the FeMoco with exactly the same model, we can obtain energy differences, which are relatively precise.

Type: Object | Advantage: Yes | Novelty: New | ConceptID: Obj26

225

Although the energies for both the FeFeco and the FeMoco include some errors, as we for example do not model the environment, the difference of the adsorption energies from the FeFeco to the FeMoco should be significantly more accurate, because to a large extent, we make the same errors in modeling the FeMoco and the FeFeco.

Type: Object | Advantage: Yes | Novelty: New | ConceptID: Obj26

226

The adsorption characteristics of the FeMoco is very similar to the one of the FeFeco.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs37

227

The structure a, where the H atom binds to one of the μ₂S atoms, is clearly the most stable one followed by structure e, where the H atom is inside the cluster.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs38

228

The structures b and c with the H atom binding on one of the triangular Fe atoms are equally or slightly more unstable than their counterparts for the FeFeco.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs39

229

The same holds for structure d which is clearly unfavorable.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs40

Nitrogen adsorption

230

In this section, we study the adsorption of N₂ on the FeFeco.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj27

231

Concerning possible adsorption sites on the triangular Fe atoms, we choose to study only those positions which Rod and Nørskov⁴ found to be energetically feasible, as all other adsorption positions were at least 80 kJ mol⁻¹ higher in energy and are therefore highly unlikely for the FeFeco as well.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod49

232

In ^{ref. 4} it was found that only end-on adsorption of N₂ on a triangular Fe atom is is approximately thermoneutral and that all other positions involving the triangular Fe atoms are highly unstable.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac87

233

We investigate the binding of N₂ on the FeFeco end-on to the triangular Fe atoms in configurations a and b in Fig. 6.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj28

234

The corresponding binding energies are listed in Table 3.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs41

235

Furthermore, we consider the adsorption of N₂ at the Mo atom, which has been suggested in the literature.^48,49,73

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj29

236

For the FeMoco we remove one of the OH groups to model that the homocitrate ring is opened.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod50

237

For the FeFeco, we use the model with 1OH group.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod51

238

This configuration is depicted in Fig. 6c.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs42

239

For the FeFeco we find that N₂ adsorption end-on on one triangular Fe atom is slightly endothermic with the exception of the model with two OH groups and spin state A1, for which the adsorption on the upper triangular Fe atoms is slightly exothermic.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs43

240

The binding energies do not depend very much on the number of OH groups, the magnetic state, and on whether the adsorption takes place on a Fe atom from the upper or from the lower triangle.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res12

241

Comparing these energies with the corresponding values for the FeMoco, we notice that the energies for the FeMoco are 10–20 kJ mol⁻¹ higher, depending on the number of OH groups and the magnetic state for the FeFeco.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs44

242

This means that according to our results it should be slightly more endothermic to bind N₂ to one of the triangular Fe atoms to the FeMoco than to the FeFeco.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res13

243

The binding energy for adsorption of N₂ on the bottom Fe atom (the position of the Mo atom for the FeMoco, configuration c in Fig. 6) is quite high, 71 kJ mol⁻¹ for spin state A1 and 83 kJ mol⁻¹ for spin state A2.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs45

244

This means that although the homocitrate ring is already assumed to be opened (modeled by one OH group), the adsorption of N₂ is still highly unfavorable.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res14

245

We observe the same for the FeMoco, where we are not even able to find a stable position for N₂ where it remains bound during the minimization.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs46

246

In all cases, N₂ left the FeMoco and we just obtained the sum of the energies of the isolated FeMoco and N₂.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs47

247

Therefore, we calculate configuration c for the FeMoco with the bond length Mo–N fixed to 2.01 Å, which is the bond length of the Fe–N bond from the FeFeco in configuration c corrected for the different covalent radii of Fe and Mo (see footnotes in Table 3).

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod52

248

For this constrained system we obtain a binding energy of 63 kJ mol⁻¹, which is also quite high.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs48

249

Thus, we can conclude that for both the FeFeco and the FeMoco we do not observe binding and activation of N₂ on the lower Mo/Fe site.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con5

Hydrogenation of adsorbed N₂

250

Rod and Nørskov⁴ suggested a pathway for ammonia synthesis, where N₂ is adsorbed end-on on one of the triangular Fe atoms and then stepwise hydrogenated.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac88

251

They found that the only endothermic and therefore rate-determining step is the addition of the first H atom to the adsorbed N₂.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac89

252

Therefore, we calculate the energy of this first adsorption step on the FeFeco and FeMoco, as the energy difference of this step between the two clusters may have direct consequences for their reactivity.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj30

253

We consider hydrogenation of adsorbed N₂ on Fe atoms in both the upper and the lower triangle.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod53

254

The configurations are shown in Fig. 7 and the corresponding energies are listed in Table 4.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs49

255

Again, we notice that the energies do not depend much on the number of OH groups present, but for configuration b the energies do depend on the spin state (difference of 30 kJ mol⁻¹).

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs50

256

The hydrogenation energies for the FeMoco are higher than for the FeFeco.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs51

257

They are also higher than the one found in ^{ref. 4}, who find a value of about 80 kJ mol⁻¹.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs52

258

This can again be attributed to the different models in use, as in ^{ref. 4} a chain model of the FeMoco is considered, whereas we consider a cluster model.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res15

Discussion

Structure of the FeFeco

259

We have modeled the structure and the magnetic state of the FeFeco.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj31

260

We have found that most are magnetic couplings are indeed antiferromagnetic, as found in experiments^13,20 and they give rise to a low total spin of S = 1/2 for the model with two OH groups (Fig. 3d) or S = 0 for the model with one OH group (Fig. 3e).

Type: Result | Advantage: None | Novelty: None | ConceptID: Res16

261

This is in agreement with EPR experiments, which suggest S = 0.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res17

262

We have found two lowest-lying antiferromagnetic states A1 and A2 (Fig. 4b and c), where the energy difference between is not large enough to be decisive compared to the accuracy of our calculation.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res18

263

The two spin states A1 and A2 give rise to the same total spin on the FeFeco.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res19

264

The fact that the total spin of the FeFeco model with one OH group S = 0 agrees with the experimental EPR results, whereas the total spin of the model with two OH groups with S = 1/2 does not, might be an artefact of or model, or it might mean that the homocitrate ring indeed is opened.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con6

265

Furthermore, the formal oxidation states of the FeFeco with one OH group [4Fe³⁺4Fe²⁺9S²⁻] agrees with the Mössbauer assignment from ^{ref. 13} Therefore, it is relevant to discuss, whether the homocitrate ring indeed might be opened.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj32

266

The issue of monodentate versus bidentate coordination of the homocitrate ring for the FeMoco has been discussed in the literature.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac90

267

Experimental studies, where homocitrate was substituted, have shown that the proper functionality of the FeMoco crucially depends on the presence of homocitrate.⁷¹

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac91

268

A study by Grönberg et al⁷². has shown that if homocitrate is substituted by citrate, the reactivity of the FeMoco is altered significantly.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac92

269

Theoretically, the protonation and opening of the homocitrate ring for the FeMoco have been investigated by Szilagyi et al⁴⁸. and by Durrant.⁴⁹

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac93

270

They both find that the opening of the homocitrate ring is energetically possible and enhanced by protonation of the ring, although it does not happen spontaneously.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac94

271

The possible opening of the homocitrate ring in the FeFeco has not been investigated in detail yet.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac95

272

In our model, we cannot calculate directly the energy required to open the homocitrate ring, but only the trend from FeMoco to FeFeco.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res20

273

There, we find that opening of the homocitrate ring in the FeFeco is 26–31 kJ mol⁻¹ lower in energy than for the FeMoco.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res21

274

Thus we conclude that it might well be that for the FeFeco the homocitrate ring is opened.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con7

275

The geometrical features of the FeFeco listed in Table 1 do not depend very much on the number of OH groups and on which of the two spin ground states is present.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res22

276

Furthermore, the structural features of our models are consistent with the experimental results obtained by EXAFS.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res23

277

The structure with one OH group and spin state A1 agrees best with the experimental data.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res24

278

Comparing our results to the ones of Lovell et al.,⁵⁴ we notice that there is some agreement with respect to the magnetic ground state of the FeFeco.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res25

279

Lovell et al. find the spin state A2 (in their notation BS3) to be the lowest in energy.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac96

280

Furthermore, they find the spin state A1 (in their notation BS1) to have an energy of 45 kJ mol⁻¹ higher than the spin state A2.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac97

281

This energy difference is rather large compared to ours.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res26

282

Apart from the difference that their model is a bit larger, they also treat the magnetism slightly different in their calculations.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res27

283

Concerning the geometry of the FeFeco, both the Fe–S and Fe–Fe distances of Lovell et al. are larger or similar to our results.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res28

284

One noticable difference is that they observe the total height of the FeFeco to be significantly larger (7.87 Å) than the height of the FeMoco (7.27 Å), whereas we observe their heights to be similar (7.13 Å for the FeMoco, 6.99–7.35 Å for the FeFeco).

Type: Result | Advantage: None | Novelty: None | ConceptID: Res29

285

One should note that an increase of the height from the FeMoco to the FeFeco is not observed in experimental results, as the latest X-ray structure 1M1N for the FeMoco gives a value of 7.00 Å, and the EXAFS study for the FeFeco gives 6.92 Å¹³.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac98

Hydrogen adsorption and H₂ evolution

286

For adsorption of proton/electron pairs on the FeFeco we find that the most stable adsorption site is a μ₂S ligand (a in Fig. 5, where the adsorption is exothermic for both models and spin states.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res30

287

Another possible place for a H atom to adsorb is inside the cluster, as shown in Fig. 5 e, where the adsorption is exothermic or approximately thermoneutral.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res31

288

For thr configurations b, c and d, i.e. for adsorption on the triangular Fe atoms or on the μ₃S atoms, adsorption is endothermic, but the energies are thermodynamically accessible.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res32

289

Generally, we can conclude that the reactivity of the FeFeco does not crucially depend on the number of OH groups present or on the specific spin state.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con8

290

This means that our model should be fairly robust, because the details do not seem to influence the energies strongly.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con9

291

Furthermore, the reactivity of the FeFeco follows the same pattern as the reactivity of the FeMoco, as the order of stability of all configurations is the same, and the energy differences are not very large.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con10

292

Before we proceed with a discussion of H₂ formation on the FeFeco, we briefly compare to other studies in order to validate our approach.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj33

293

The adsorption of hydrogen on the FeFeco has not been investigated before, but for the adsorption of hydrogen on the FeMoco, several studies are available for comparison.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac99

294

Our results are similar to the ones of Rod and Nørskov,⁴ who also find that the preferred place for H binding are the μ₂S atoms.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs53

295

For H adsorption on a μ₂S atom, we find a binding energy of −30 kJ mol⁻¹, whereas Rod and Nørskov find a binding energy of −10 kJ mol⁻¹.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs54

296

For H adsorption on the Fe atoms, we find a binding energies in the range of 51 to 54 kJ mol⁻¹ depending on whether the adsorption takes place near the His-end or near the Cys-end, whereas Rod and Nørskov find a binding energy of 30 kJ mol⁻¹.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs55

297

These energy differences can be explained by the different models, as Rod and Nørskov consider an infinite chain constructed of MoFe₆S₉ units, whereas we consider the whole cluster with truncated ligands.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res33

298

However, one would expect that both models lead to the same trends, and this is indeed the case.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con11

299

The adsorption of hydrogen on the FeMoco is also studied by Lovell et al.⁵¹

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac100

300

They only list the order of stability of the different adsorption structures, but not the adsorption energies compared to ½H₂ in the gas phase.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac101

301

Therefore, we can only make a qualitative comparison of the results.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs56

302

Lovell et al. find that the most stable configuration is e in Fig. 5 (E1H1-c in their notation).

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac102

303

They find that the adsorption of H on the μ₂S atoms (configuration a, E1H1-b1/E1H1-b2/E1H1-b3 in their notation) is less favorable than configuration e.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac103

304

This disagrees with our results which predict that the adsorption of H on the μ₂S atoms is the most stable configuration of all.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res34

305

The results of Lovell et al. for the relative stability of binding of H to the trigonal Fe sites from the outside (configurations b and c) are similar to ours.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res35

306

Furthermore, Lovell et al. find the protonation of the homocitrate ring to be favorable and that they find the protonation of the Mo atom to be very unfavorable.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac104

307

This might hint at that the homocitrate ring indeed can open, but that the Mo atom is probably not involved in protonation at this stage.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac105

308

Now, we can try to take a closer look at the energy differences between the FeFeco and the FeMoco in order to find out, how H₂ indeed can be formed on the FeFeco.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj34

309

In order to limit the numerous possibilities for the FeFeco, we always consider the model and the spin state, which are most stable, in the following and thereby assume that switching between the different states is possible.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod54

310

The first general result is that the energetics of hydrogen adsorption for the FeFeco is very similar to the one for the FeMoco.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res36

311

Therefore, to discuss the consequences of our results on the differences in H₂ formation between the FeFeco and the FeMoco, we can use ^{ref. 4} as a starting point.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj35

312

It was suggested that the first three H atoms adsorb on the μ₂S atoms and that this happens very easily.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac106

313

The fourth atom then adsorbs on one of the triangular Fe atoms, which requires energy and turns out to be the rate-limiting step.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac107

314

Then H₂ forms on the Fe atom and is released, both steps are exothermic.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac108

315

From the overall similarity of the energetics of the FeFeco to the FeMoco we can infer that H₂ formation on the FeFeco is possible according to the scheme shown in Fig. 1.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res37

316

We can exclude that positions other than the ones on the μ₂S atoms and on the triangular Fe atoms are relevant for H₂ formation in this context on the following grounds, First, we note that H₂ has to be formed on a Fe atom, as sulfur cannot interact simultaneously with two H atoms.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res38

317

Furthermore, it is reasonable to assume that H₂ is formed on the outside of the cluster, as space inside the cluster is limited.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res39

318

Furthermore, configuration e in the formation of H₂ is not possible because of the central N ligand.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res40

319

The same holds for configuration d, which is unfavorable and cannot contribute to the formation of H₂.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res41

320

Thus, it seems plausible that the formation of H₂ on both the FeMoco and the FeFeco can proceed in the way suggested in .^{ref. 4}

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con12

321

The first three H atoms adsorb on the μ₂S atoms, which is energetically favorable for both the FeMoco and the FeFeco.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res42

322

The fourth H atom adsorbes on one triangular Fe atom, which requires energy for both the FeMoco and the FeFeco.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res43

323

All following steps (displacement of one H atom from a μ₂S-atom to the Fe atom, desorption of H₂) are energetically favorable for the FeMoco, and although we have not calculated them for the FeFeco, it is reasonable to assume that they are approximately equally favorable.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res44

324

Thus, the adsorption of the fourth H atom on a triangular Fe atom is the rate-limiting step and the energies of the configurations b and c determine the energetics for H₂ formation.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con13

325

As can be seen in Table 2 the energies are slightly lower or equal for the FeFeco than for the FeMoco.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res45

326

Having discussed the general scheme of H₂ formation on the FeFeco, we can now turn to more subtle aspects.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj36

327

At this point, we can further limit the possible configurations for adsorption of N₂ and H by looking at the surroundings of the FeFeco.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod55

328

The amino acids surrounding the active site are mostly conserved from the Mo-containing nitrogenase to the iron-only nitrogenase, and therefore we can consider the environment of the FeMoco.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod56

329

The FeMoco with some of the residues located close to it from the crystal structure 1M1N⁷ is shown in Fig. 8.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs57

330

One notices that the His195 residue is closely located to one Fe atom on the upper triangle, the distance of Nε (one of the N atoms in the imidazole ring) to the nearest Fe atom is only 4.1 Å and to the nearest μ₂S atom only 3.3 Å.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs58

331

Both experimental⁷⁴ and theoretical studies⁴ have suggested that the His195 residue is a possible proton donor for the FeMoco.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac109

332

As this His residue is conserved in the iron-only nitrogenase, it could also be a possible proton donor for the FeFeco.

Type: Hypothesis | Advantage: None | Novelty: None | ConceptID: Hyp3

333

This implies that we should concentrate on the results for adsorption on the Fe atoms in the upper triangle, as this is the place where interaction with the His195 residue is possible.⁷⁵

Type: Result | Advantage: None | Novelty: None | ConceptID: Res46

334

For the H adsorption this means that the energy of configuration b of Fig. 5 and Table 2 determines the formation of H₂, as the adsorption of H on a Fe atom in the upper triangle is the rate-limiting step.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res47

335

As the energy of configuration b is almost equal for the FeMoco and the FeFeco, the formation of H₂ should have very similar energetics on the two clusters.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res48

336

Thus, from this discussion we can conclude that a possible scheme for H₂ evolution on the FeFeco is the scenario depicted in Fig. 1.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con14

337

Furthermore, we have found that the energetics for H₂ formation on the FeFeco is very similar to the one on the FeMoco.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con15

Dinitrogen adsorption and hydrogenation

338

The adsorption of N₂ on the triangular Fe atoms of the FeFeco is slightly endothermic or thermoneutral, with the exception of the model with two OH groups and spin state A1, where configuration b in Fig. 6 is slightly exothermic.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res49

339

We can exclude adsorption of N₂ on the lower Fe atom (the one substituting Mo), as adsorption is clearly endothermic, even though the homocitrate ring is already opened.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res50

340

We find that the energetics for both N₂ adsorption and hydrogenation on the FeFeco is very similar to the one on the FeMoco.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res51

341

This is an interesting result, as the actual activities of the FeFeco and the FeMoco are very different.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res52

342

For a discussion of more subtle aspects of N₂ adsorption and hydrogenation on the FeFeco compared to the FeMoco, we can use results from ^{ref. 4} who modeled the influence of the His195 group in an extremely simple way.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj37

343

They placed a NH₄ molecule in the vicinity of the Fe atom where N₂ was adsorbed and observed that the cluster becomes negatively charged, while the NH₄⁺ is positively charged.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac110

344

Furthermore, they found that both the adsorption of N₂ and its hydrogenation are much more facile with this proton donor.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac111

345

They found that the structure of the FeMoco with N₂ adsorbed is stabilized by ca. 80 kJ mol⁻¹ and the structure of the FeMoco with N₂H adsorbed is stabilized by ca. 130 kJ mol⁻¹.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac112

346

For our considerations, we assume that these energy shifts are the same for the FeMoco and the FeFeco.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod57

347

This is reasonable, since their environments should be very similar.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod57

348

The energies of the N₂ adsorption and hydrogenation for both the FeFeco and the FeMoco and for both without and with these energy shifts are shown in Fig. 9.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs59

349

Our calculated energies (upper curve) show that the N₂ adsorption is a bit more energy-demanding on the FeMoco than on the FeFeco.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs60

350

For the hydrogenated structures, the one for FeMoco lies still a bit higher than FeFeco, but the difference is smaller.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs61

351

For the structures with the energy shift (lower curve), the relative positions of the FeFeco and FeMoco to each other of course have not changed, as we assumed the energy shift to be the same for them.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod58

352

But one can see that now the adsorption of N₂ is exothermic for both the FeFeco and the FeMoco and therefore should happen easily.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res53

353

Once N₂ is adsorbed, energy is needed for the hydrogenation, although this energy is less than for the values without the shift.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res54

354

Assuming that the rate-determining step for the formation of NH₃ is the first hydrogenation of the adsorbed N₂, it follows that the determining energy difference for this process should be the energy difference between the state with N₂H adsorbed and the state with N₂ adsorbed.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod59

355

In Fig. 9 this energy difference is marked as ΔE_hyd(FeMoco) for the FeMoco and ΔE_hyd(FeFeco) for the FeFeco for our calculated energies (no energy shift from proton donor, upper curve).

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod60

356

For the case with the energy shift from the proton donor (lower curve) the energy differences are termed ΔE_corr,hyd(FeMoco) for the FeMoco and ΔE_corr,hyd(FeFeco) for the FeFeco.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod61

357

The difference in performance between the FeFeco and the FeMoco should be characterized by the difference of those energy differences

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod62

358

δΔqE = ΔE_corr,hyd(FeFeco) − ΔE_corr,hyd(FeMoco)

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod63

359

=ΔE_hyd(FeFeco) − ΔE_hyd(FeMoco)

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod64

360

=(107 kJ mol⁻¹ − 5 kJ mol⁻¹) − (118 kJ mol⁻¹ − 23 kJ mol⁻¹)

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs62

361

=7 kJ mol⁻¹.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs63

362

Note, as the shifts due to the proton donor were assumed to be the same for the FeFeco and for the FeMoco, the difference δΔE is of course independent of those shifts.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res55

363

Thus δΔE should be rather accurate, also because, as we argued earlier, to a large extent we make the same errors for the FeMoco and the FeFeco in our calculations.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res56

364

The result of eqn. (5) means that the rate-determining step, the hydrogenation of the adsorbed N₂ is more energy-demanding for the FeFeco than for the FeMoco.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res57

365

This agrees with the observation that the FeFeco performs worse for the nitrogen fixation than the FeMoco.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs64

366

Thus, one general result of our calculations is that the energetics of the FeFeco for nitrogen fixation seems to be slightly less advantageous than the one of the FeMoco.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con16

367

Therefore, the measured differences in activity might at least partially arise from the substitution of Mo by Fe in the active site.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con17

368

Having drawn this general conclusion, we try to quantify the differences in activity between the FeFeco and the FeMoco.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj38

369

One of the few quantitative observations regarding the activity of the Fe-only nitrogenase is that the ratio of produced hydrogen to fixed nitrogen is H₂/N₂ = 75²⁰. while it is H₂/N₂ = 1 for the conventional nitrogenase.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac113

370

As these two results are ratios, they are to a large extent independent of the specific experimental parameters.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac114

371

For a moment, we now make the simplified assumption that this difference in the ratios arises from the difference in energies of the least stable intermetiate at the cofactors (see Fig. 9).

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod65

372

Furthermore, as we have shown that the energetics for H₂ formation are almost identical for the FeFeco and the FeMoco, we assume that the difference in the H₂/N₂ ratio arises directly from the differences in energies δΔE.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod66

373

Then they are related via an Arrhenius factor This corresponds to an energy difference of δΔE = 5 kJ mol⁻¹ at room temperature (293 K).

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs65

374

We have determined δΔE = 7 kJ mol⁻¹, which is very close.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res58

375

One should note that because of the exponential, very slight changes in the energy difference cause large changes in the nitrogen to hydrogen ratio.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res59

376

One can and should of course question our assumptions and whether the two energies agree by chance.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con18

377

Furthermore, it is clear that our model is extremely simple and that there can be energy shifts due to the environment or a possible central ligand, which are not included in our model.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con19

378

In further studies one would also have to investigate, whether the proton/electron transfers are activated and how high these possible activation barriers are.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con20

379

Nonetheless, we have shown that the properties of the FeFeco and the FeMoco are rather similar, but that slight differences are sufficient to considerably modify the reactivity.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con21

380

Therefore, we speculate that the rôle of the Mo is to optimally tune the FeMoco.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con22

381

In the case, where Mo is not available, nature uses V or Fe, which work, but with a lower reactivity.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con23

Introduction

Previous studies

Experimental studies

Theoretical studies

Model for ammonia synthesis and hydrogen release

Methods

Model of the Fe-only cofactor

Calculational details

Results

Spin ground state and geometry

Hydrogen adsorption

Nitrogen adsorption

Hydrogenation of adsorbed N2

Discussion

Structure of the FeFeco

Hydrogen adsorption and H2 evolution

Dinitrogen adsorption and hydrogenation

Hydrogenation of adsorbed N₂

Hydrogen adsorption and H₂ evolution