The HD Reaction of Nitrogenase: a Detailed Mechanism

Abstract Nitrogenase is the enzyme that converts N2 to NH3 under ambient conditions. The chemical mechanism of this catalysis at the active site FeMo‐co [Fe7S9CMo(homocitrate)] is unknown. An obligatory co‐product is H2, while exogenous H2 is a competitive inhibitor. Isotopic substitution using exogenous D2 revealed the N2‐dependent reaction D2+2H++2e−→2HD (the ‘HD reaction’), together with a collection of additional experimental characteristics and requirements. This paper describes a detailed mechanism for the HD reaction, developed and elaborated using density functional simulations with a 486‐atom model of the active site and surrounding protein. First D2 binds at one Fe atom (endo‐Fe6 coordination position), where it is flanked by H−Fe6 (exo position) and H−Fe2 (endo position). Then there is synchronous transfer of these two H atoms to bound D2, forming one HD bound to Fe2 and a second HD bound to Fe6. These two HD dissociate sequentially. The final phase is recovery of the two flanking H atoms. These H atoms are generated, sequentially, by translocation of a proton from the protein surface to S3B of FeMo‐co and combination with introduced electrons. The first H atom migrates from S3B to exo‐Fe6 and the second from S3B to endo‐Fe2. Reaction energies and kinetic barriers are reported for all steps. This mechanism accounts for the experimental data: (a) stoichiometry; (b) the N2‐dependence results from promotional N2 bound at exo‐Fe2; (c) different N2 binding Km for the HD reaction and the NH3 formation reaction results from involvement of two different sites; (d) inhibition by CO; (e) the non‐occurrence of 2HD→H2+D2 results from the synchronicity of the two transfers of H to D2; (f) inhibition of HD production at high pN2 is by competitive binding of N2 at endo‐Fe6; (g) the non‐leakage of D to solvent follows from the hydrophobic environment and irreversibility of proton introduction.


Introduction
Nitrogenase is the enzyme that converts unreactive atmospheric nitrogen to biologically usable ammonia. The enzyme is composed of two proteins, the MoFe protein containing the active site, and the Fe protein. While the biochemical mechanism involving association and dissociation of these proteins is quite well understood, there are many uncertainties about the catalytic coordination chemistry which enables the enzyme to reduce unreactive N 2 under remarkably mild conditions that are not yet replicated in synthetic or industrial conversions of N 2 . See references [1] for reviews. The active site of Mo-nitrogenase is an unprecedented cluster with the composition Fe 7 MoS 9 C-(homocitrate), called FeMo-co ( Figure 1a).
The chemical mechanism, that is the catalysed conversion of N 2 plus protons and electrons to NH 3 , is unknown, despite numerous investigations involving reaction kinetics, [3] mutations of amino acids surrounding the active site, [4] vibrational and spin resonance spectroscopy, [1k,5] crystal structures, [1l,2] and density functional simulations. [6] Attempts to trap intermediates under turnover conditions are thwarted because protons are an unavoidable substrate (forming H 2 ), and mixtures of transient Residue numbering is from the α-subunit of Azotobacter vinelandii, crystal structure PDB 3 U7Q. [2] Hydrogen bonds are striped. (b) Atom labels for the cluster, and identification of the potential coordination positions at Fe2 and Fe6, exo or endo relative to the FeÀ C c bond. S2B, S5A and S3A are often referred to as 'belt' atoms.
intermediates occur. [7] The stoichiometry of the reaction is eq (1), and a counting of the required individual steps -binding of N 2 , eight introductions of an electron, eight introductions of protons, breaking the NÀ N bond, six NÀ H bond formations, two dissociations of NH 3 , and one formation of H 2 -yields 27!
(1) A significant aspect of the mechanism is the involvement of H 2 and the relationship between N 2 and H 2 . H 2 is a competitive inhibitor of N 2 reduction, and, conversely, the amount of H 2 generated during turnover is controlled by the N 2 partial pressure. This relationship is embodied in the N 2 /H 2 exchange equilibria of the mechanistic framework presented by Thorneley and Lowe. [3] In 1960 it was discovered that soybean root nodules containing nitrogenase generated HD when exposed to a D 2 /N 2 atmosphere. [8] This reaction, known as the HD formation reaction, was subsequently investigated further because it reveals some of the reactivity of the enzyme involving N 2 and H 2 . The resulting experimental information is summarised in the next section.

Experimental information relating to the HD formation reaction
Background, definitions and working hypotheses Accumulated evidence, mainly from mutant-reactivity experiments [4b-d,l,17] indicates that the reaction domain is the 4FeÀ 4S face containing Fe2, Fe3, Fe6 and Fe7, and more specifically the Fe2À S2BÀ Fe6 region, because variations of Val70 and His195 have the most significant effects on reactivity. Assumptions that this domain remains intact during the catalytic cycle have been challenged in recent years, by crystal structures and reactivities of nitrogenase derivatives in which S2B (or other belt atom S3A, S5A) has been displaced into the protein by another atom or ligand, [18] and a cryo-EM structure obtained during turnover. [19] The possible lability of S2B has attracted computational investigations. [6h,20] An alternative hemilability of S2B, in which only one of the S2BÀ Fe bonds is broken during catalysis, has been explored computationally. [6b,e,20d,21] The mechanism presented here assumes that the bonds from S2B to Fe2 and Fe6 remain intact. Possible coordination positions at Fe2 and Fe6 are defined in Figure 1(b), and the intermediates to be described in the following have ligands variously at the exo-Fe2, endo-Fe2, endo-Fe6 and exo-Fe locations.
Several working hypotheses underly the development of mechanism. One is that the H atoms required for the HD reaction and for N 2 hydrogenation to NH 3 arrive at S3B as the result of serial translocation of exogenous protons along the 'proton wire', and combination with electrons from the P-cluster. [22] These H atoms migrate vectorially from S3B to atoms Fe6, S2B and Fe2 of FeMoco. [22c,23] The reducing reactions of nitrogenase involve transfer of these H atoms to substrates. [24] Another working hypothesis is that N 2 diffuses to FeMo-co along a well-defined hydrophobic pathway (Figure 2a) to the exo coordination position of Fe2, where it binds end-on. This N 2 is proposed to have an unreactive but promotional function. [25] It is outside the reaction zone between Fe2 and Fe6 and less accessible to hydrogenation, but it does expand the reaction zone by lengthening the trans Fe2À C c bond and increasing the Fe2À Fe6 separation by varying amounts up to 3.3 Å (from 2.6 Å in the resting state). The endo-Fe6 position is proposed as the binding site for the N 2 that will be subsequently hydrogenated to NH 3 , and the binding site for exogenous H 2 that competes with N 2 (Figure 2b). Therefore, the N 2 -dependent D 2 !HD reaction is proposed to use promotional N 2 at exo-Fe2, and D 2 binding at endo-Fe6. Figure 2 (a) also shows the location of the separate H 2 pathway, for ingress of D 2 and egress of HD. See Figure S1 for details of the H 2 pathway.

Computational model and procedures
The density functional computed protein model is a 486-atom extract from crystal 3U7Q, including all relevant amino acids. This is my standard model for simulations of nitrogenase reactions and reactivity.
[6d,f] Details, and the rationale for inclusion of amino acids and truncation of uninvolved sidechains, are provided in the Supporting Information. Some constraints on the protein structure are required during optimization calculations because the modelled protein is incomplete and the bonding and dispersion influences of the complete protein outside the computational model are absent. The modelled protein must also maintain flexibility sufficient to accommodate the coordination of N 2 and of H 2 , and the diffusion of these molecules to and from FeMo-co. The constraining strategy and details are provided in the Supporting Information. The charge on the [CFe 7 MoS 9 ] core of FeMo-co is À 1, in agreement with experimental and computational studies. [6d,26] Density functional (DF) calculations use the DMol methodology of Delley, [27] with accurate DNP (double numerical plus polarisation) basis sets. [27d] The gradient-corrected functional PBE [28] was used because validation tests demonstrate that when used with DMol it is more accurate than other commonly used functionals. [29] The calculations were all-electron, spin-unrestricted, with no imposed symmetry. D was calculated as H and no zero-point or thermal corrections are included. The conductor-like screening model (COSMO) [30] was used with a dielectric constant of 5. Constraints on interatomic distances used the Lagrange Multiplier Algorithm. Output spin populations are calculated by the Mulliken method. [31] Further information on the density functional procedures is provided in the Supporting Information.
The electronic states of FeMo-co and its ligated forms are described as sets of signed spin populations on the seven Fe atoms of the cluster, together with the net spin S. Labelling consists of a list of the Fe atom numbers having negative spin population, with S appended in parentheses. Relative stabilities of these electronic states are guided by the general principle that oppositely-signed pairs of adjacent Fe atoms in FeMo-co are more stable than samesigned, and that the stabilisation is proportional to the magnitude of the spin populations. Antiferromagnetism (ie weak FeÀ Fe bonding) operates in the FeMo-co cluster. Interactions between the spins at Fe2 and Fe6 are of minor importance because they are diminished by ligation (often almost to zero: see values in the Supporting Information), and additionally the Fe2À Fe6 separation is increased due to extensions of one or both FeÀ C c distances. For the same reason interactions between the Fe2 and Fe6 spins and those at Fe3, Fe4, Fe5 and Fe7 are less influential than those between these four Fe atoms. Therefore, interactions within the set Fe3, Fe4, Fe5, Fe7 on the opposite face of the Fe 6 trigonal prism are dominant, and, as shown in Figure 3, the maximum number of oppositely-signed shorter edges for this group is obtained with same-signed spins along one diagonal, Fe4À Fe7 or Fe3À Fe5. Consequently only two electronic states are expected to be more stable than all others. [25] These are the states with the Fe3À Fe5 pair negative (labelled 35), or the Fe4À Fe7 pair negative (labelled 47), and these are the states investigated in the present work.
The spin population specifications input into the DMol calculation involve only Fe1, Fe3, Fe4, Fe5 and Fe7, using the sign patterns of the 47 or 35 states, with magnitudes 3.0 for Fe1 and ca. 2.8 for the other four. The spin populations of Fe2 and Fe6 are unspecified. The spin populations on all atoms are allowed to optimize. The total spin S is initially optimised (using Fermi orbital population) and then variations of + 1 and À 1 are explored.
The procedure for mapping the topology of reaction energy surfaces and for location of transition states, previously described, [6d,32] is outlined in the Supporting Information. Trajectories from the transition state to the reactant and product states were followed to determine energy differences and ensure the continuity of the potential energy surface. For steps involving association of D 2 or dissociation of HD, the separated limit of the trajectory was taken as the place where the dissociated molecule and the metal site cease their mutual influence (assessed via geometry) and the free molecule begins to tumble and diffuse freely: this Fe-(D/H) 2 separation is 3.2 � 0.2 Å. Energies calculated from these separated positions are reported at lower precision, reflecting uncertainties in defining dissociated limits.
Atomic coordinates for all intermediates and transition states, together with spin populations at the Fe atoms, are provided in the Supporting Information. (b) A working hypothesis, in which the role of exo-Fe2À N 2 (yellow) is to expand the reaction zone (violet) between Fe2 and Fe6, thereby promoting other reactions including binding of the N 2 that is subsequently hydrogenated to NH 3 , in competition with the binding of H 2 at the same site. [25]

Results
There are four stages in the mechanism, first binding of D 2 , then synchronous double hydrogenation of D 2 to form two bound DH, then dissociation of the two HD, and finally recovery of the starting intermediate. Details are presented in Schemes 1, 2 and 3. For each step the calculated reaction dynamics are presented with triangular symbols, each of which records at its centre the electronic and spin state, with the overall reaction energy under the horizontal reaction arrow, and the barriers for the forward and backward reactions against the diagonal arrows to the transition state (TS): all energies are in kcal mol À 1 . For each intermediate the En level in the Thorneley-Lowe notation, [3] is evident from the number of added H atoms.

Association of D 2 and formation of 2HD
Referring to Scheme 1, the starting structure 1 contains promotional N 2 bound at exo-Fe2, and H atoms bound at S2B, exo-Fe6 and endo Fe2. His195 is in its protonated state, with a donor NɛH hydrogen bond to S2B. Structure 1 is at the E3 level. [3] The Fe6À Fe2 separation in 1 is 2.9-3.2 Å (depending on electronic state), and the ligand binding position, endo-Fe6, is unobstructed. D 2 binds at endo-Fe6, forming 2. The optimised total spin for 1 and 2 is S = 2. The reaction potential energies (horizontal arrows in Scheme 1) for binding of D 2 are 3 or 4 kcal mol À 1 , and reaction barriers are 12, 13 kcal mol À 1 . These numbers are combinations of the negative contribution from the formation of the Fe-D 2 bonds and the positive adaption energy required to expand the endo angle at Fe6 as D 2 binds. [6f] Scheme 1. First stages of the mechanism, showing the binding of D 2 (2) and the synchronous double hydrogenation of D 2 forming two bound HD (3). The sketches show only the essential components. The triangular symbols report electronic(S) states and calculated energies (kcal mol À 1 ): the reaction energy is on the horizontal arrow, and barrier energies are oblique to the transition state (TS).

Scheme 2.
Two routes for the sequential dissociation of two Fe-bound HD.

Chemistry-A European Journal
Research Article doi.org/10.1002/chem.202202502 Structure 2 is propitious because there are H atoms contiguous to D 2 on Fe2 and Fe6. A single transition state occurs for synchronous transfer of these two H atoms to D 2 , which splits to form two HD, one at endo-Fe2 and the other at exo-Fe6. This is the remarkable key step in the overall reaction. Figure 4 shows detail of the reactant, TS, and product structures. The reaction dynamics are very favourable, with reaction energies of À 19 kcal mol À 1 and reaction barriers 2.5 to 3.1 kcal mol À 1 .

Dissociation of 2HD
The next stage of the mechanism is sequential dissociation of the two Fe-bound HD. There are two possible sequences, dissociation first from Fe2 (3!4!6) or first from Fe6 (3!5!6). Reaction energies are reported in Scheme 2 for the 35(2) and 47(2) electronic states. All the reaction energies and kinetic barriers are feasible for both pathways.

Completion of the catalytic cycle
After completion of the conversion of D 2 to 2HD, the subsequent recovery to the starting point (1) of the catalytic

Chemistry-A European Journal
Research Article doi.org/10.1002/chem.202202502 cycle needs to be considered. This requires the introduction and placement of two H atoms. As previously described, protons are delivered to FeMo-co via the 'proton wire' from the protein surface, in conjunction with electrons delivered to FeMo-co via the P-cluster. A detailed Grotthus mechanism for this delivery of protons to S3B has been calculated, and Figure 5 shows the final intermediates in this multistep process for protonation of S3B. [32c] The starting point for the placement of each H atom in the recovery phase of the HD mechanism is therefore an H atom bonded to S3B. The next steps involve conformational changes for S3BÀ H, followed by migration of each H to Fe6 or Fe2. The conformations of S3BÀ H, are illustrated in Figure 6, with labels and transition states for interconversions, together with geometry and energy data calculated for unligated FeMo-co. [32c] When H is first generated on S3B from the water chain (A to C in Figure 5) S3BÀ H is in the 3b5 conformation. Details of the dynamics for the reconfiguration of S3BÀ H depend on the ligation status of FeMo-co and vary from those of unligated FeMo-co ( Figure 6). The reconfiguration dynamics specific to the formation of 1 are calculated and reported here.
The first H added to S3B is in the 3b5 conformation, intermediate 7 in Scheme 3. From this there is an energetically favourable pathway to 8 (3b3 conformation) and then to 9 as detailed in Scheme 3. From the S3BÀ HÀ Fe6 bridge in 9 the H atom can move towards the exo or endo positions of Fe6. The favourable pathway is to exo-Fe6À H, 10, with energy changes of À 7.4 to À 14.8 kcal mol À 1 and remarkably small kinetic barriers � 1.6 kcal mol À 1 . The alternative route from 9 towards endo-Fe6 has larger kinetic barriers and leads to an Fe6À HÀ Fe2 bridge.

Chemistry-A European Journal
Research Article doi.org/10.1002/chem.202202502 Concurrently with this bridge formation, S2BH unhooks its bond to Fe2 and eventually is more than 3.2 Å from Fe2. Unhooking of S2B from Fe2 is a general property of ligated FeMo-co, and the factors that influence it have been expounded, and the potential energy surfaces for interconversions of hooked and unhooked isomers described. [21e] In general the energy differences between hooked and unhooked isomers are < 10 kcal mol À 1 , and kinetic barriers for interconversions are up to 13 kcal mol À 1 . When S2B unhooks from Fe2 the tethering Fe6-S2B bond sterically blocks subsequent formation of exo-Fe6À H, and re-formation of 1 becomes very unfavourable because the barrier to rehooking is large. However, this negative co-influence of exo-Fe6À H and unhooking of S2BH is advantageous when exo-Fe6À H is formed first, as in intermediate 10, because exo-Fe6À H inhibits unhooking of S2BH (by steric interference), and therefore the subsequent introduction of a second H atom and its movement from S3B around Fe6 to endo-Fe2À H is unimpeded by unhooking. Therefore, in the reformation of 1 the first H moves from S3B to the exo-Fe6 position, and the second H moves to the endo-Fe position (Scheme 3).
In the sequence that generates 10 from 7 all three steps are exergonic, and the barriers are remarkably small, being 1.3, 1.9 and 1.6 kcal mol À 1 respectively in the 35(1/2) electronic state, and maximum 5.1 kcal mol À 1 in other electronic states. The second H joins S3B in conformation 3b5, 11, then moves around S3B in the opposite direction to the first, forming 12 where it bridges to Fe7. In the 47(1) electronic state there is no barrier to this exergonic shift. The next movement is around Fe6 to the endo-Fe6 position, 13. The final step for the second H is to the endo-Fe2 position, recovering structure 1. This last step occurs favourably for the 47(1) electronic state, but in the other electronic states tested the final energy well is an Fe6À HÀ Fe2 bridge rather than endo-Fe2À H. The key factor in this 13!1 step is the distance between Fe2 and Fe6, which is ca. 3.3 Å in 13 and ca. 3.1 Å in 1. To transfer H from Fe6 to Fe2 requires a closing of the gap, and the Fe6À Fe2 separation decreases to 2.8 Å in the TS for the 47(1) state. This is close to the separation in the Fe6À HÀ Fe2 bridge, ca. 2.65 Å, which is why this bridge becomes an accessible local energy well in some electronic states.

Testing against experiment
I now return to the experimental information against which the proposed mechanism must be tested. 1. The HD reaction requires N 2 . The mechanism involves 'promotional' N 2 bound end-on at exo-Fe2. Would the mechanism be feasible if this N 2 is absent, or replaced by H? Additional calculations show that when there is no exo-Fe2 ligand the Fe2À C c distance is short, ca. 1.95 Å, because it is compensating, via coordinative allosterism, [33] for the ligation of Fe6 (exo-Fe6À H and/or endo-Fe6À H 2 ) which extends Fe6À C c . This results in an unsuitable small reaction domain between Fe2 and Fe6. Also, if the exo-Fe2 position is vacant the H at endo-Fe2 (essential for the proposed mechanism) rotates to the more stable exo-Fe2 position. If H is bonded at exo-Fe2 instead of N 2 , then as D 2 binds at the endo-Fe6 position in the first step (analogous to 1!2) the H atom at endo-Fe2 moves away from D 2 and towards the exo position of Fe2. The HÀ Fe2À C c angle increases to 108°, compared with 90-94°in 2. From this position the two H atoms on Fe2 can combine to form H 2 at the exo position of Fe2 with a very small barrier of 2 kcal mol À 1 . This makes the double hydrogenation of D 2 impossible. Figure 7 illustrates the adverse movement of endo-Fe2À H towards the exo-Fe2 position when that position is void or contains H. Therefore, of the three possibilities for exo-Fe2, void or occupied by N 2 or H, only N 2 permits the double hydrogenation of D 2 , in agreement with experiment. 2. Other non-physiological substrates do not activate the HD reaction. The present mechanism has not been tested computationally with the experimental substrates nitrous oxide, azide, acetylene, cyanide, methylisonitrile or hydrazine. 3. CO inhibits the HD reaction. As part of the calculations reported above I made analogous calculations with CO bound at the exo-Fe2 position in place of N 2 . The D 2 splitting to 2HD step, analogous to 2!3, is similarly feasible with exo-Fe2À CO. It is well established from IR spectroscopy [4n,34] and ENDOR, [35] supported by calculations, [36] that CO terminally bound to FeMo-co readily converts to bridging CO. The CO analogue of 7 would be expected to convert to a Fe2À COÀ Fe6 bridged form, which would block completion of the cycle and account for the CO inhibition. The fact that CO inhibits equally the D 2 ! HD and N 2 !NH 3 pathways is explained by its facile occupation of the reaction domain between Fe2 and Fe6, blocking endo-Fe6. The proposed mechanism for the HD reaction is consistent with the inhibition by CO. 4. The HD reaction is inhibited by larger pN 2 . One of the working hypotheses is that the endo-Fe6 position is the binding site for the N 2 that subsequently will be hydrogenated to NH 3 . After the promotional N 2 is bound at exo-Fe2 a second N 2 can bind end-on at endo-Fe6. [25] Increased pN 2 would shift the competition for the endo-Fe6 location against D 2 (H 2 ) binding, and inhibit HD formation. 5. The HD reaction stoichiometry is D 2 + 2H + + 2e À !2HD. This is embodied in the proposed mechanism. 6. The HD reaction and N 2 conversion to NH 3 compete for the same electrons. In contemporary mechanistic concepts for nitrogenase the reducing agents are transferable H atoms on Fe and S atoms of FeMo-co. [6d] The HD reaction and NH 3 formation are proposed to bind the substrate at the same endo-Fe6 site and to use surrounding H atoms, in competition. 7. There is negligible formation of TOH when T 2 is used instead of D 2 . This means that intermediates in the HD reaction cannot access water or protons able to reach the protein surface. In the proposed mechanism the only Dcontaining intermediates are reactant D 2 or product HD, both bound to Fe within hydrophobic surrounds. 8. Nitrogenase turning over with N 2 and HD does not form D 2 . The proposed mechanism is not reversible because the D 2 !2HD step, 2!3, is very exergonic, with barriers of 20 to 23 kcal mol À 1 for the reverse. A reverse process 2 ! 3 which could possibly generate D 2 from 2HD, is not feasible. In the context of this experimental requirement, it is appropriate to consider an alternative but related mechanism, shown in Scheme 4, that could effect the exchange 2HD!H 2 + D 2 . Here HD is added to the vacant endo-Fe6 site, followed by H··H··D exchange on Fe6, then dissociation of H 2 to form the central intermediate (yellow highlight) with a D atom on Fe6. Repetition with a second HD yields D 2 , and completes the exchange. Here the exchange of H and HD both bonded to the same Fe has some similarities with part of the 2!3 step in the proposed mechanism. However, there is an important difference. The proposed mechanism has synchronous double hydrogenation of D 2 in 2!3, but the mechanism in Scheme 4 must have nonsynchronous steps. Another statement of this difference is that the highlighted intermediate on Scheme 4 that is essential for the 2HD!H 2 + D 2 reaction does not occur in the proposed mechanism. In this way only the proposed mechanism is consistent with the experimental observation. 9. The K m (N 2 ) for HD formation and the K m (N 2 ) for NH 3 production are apparently different. The two different processes are postulated to involve different N 2 binding steps at different Fe sites, and so different binding constants are possible, and expected. 10. and 11. Different reactivities for the 195Gln and 195Asn mutated proteins. The present results provide no insight into why 195Gln supports the HD reaction but 195Asn does not. The 195Gln side chain can form a distorted hydrogen bond from NH 2 to S2B [15]

Discussion
The strong component of this mechanism is the energetically advantageous double hydrogenation of D 2 in one step, 2!3. The reaction energy of À 19 kcal mol À 1 and small barrier of 3 kcal mol À 1 are sufficient to overcome the endergonic prior binding of D 2 . The entropy penalty for the binding of D 2 needs to be included. The relevant dissociated state is not gas phase but condensed phase, with D 2 considered to be at a diffusible position within the protein.
Here the ligand will have lost translational and rotational entropy relative to the gas phase. The relevant entropy loss on binding is not known or calculated, but can be estimated through analogy with other relevant systems. Seefeldt, Peters et al. described the structure and dynamics of a modified MoFe protein containing an acetylene molecule in a pocket near the front face of FeMo-co but not bound to it, and suggested that acetylene in the protein channel leading to its pocket has already lost most of its gas phase entropy content. [17d] Using experimental data for H 2 binding to Fe complexes, and compendia of information of the entropy of small molecules in proteins, [37] I estimated the entropy change for the binding of H 2 to FeMo-co as approximately À 6 cal mol À 1 K À 1 . [6f] This corresponds to a free energy penalty of 2 kcal mol À 1 . ΔG for 1!2 is thereby estimated to be not greater than 6 kcal mol À 1 . An advantage of the double hydrogenation of D 2 in one step is avoidance of the steps in Scheme 4. Separate calculations were made using a start structure without endo-Fe2À H, and therefore potentially able to effect single hydrogenation of D 2 but unable to achieve synchronous double hydrogenation. The binding energy for D 2 at endo-Fe6 is 4 kcal mol À 1 , and the hydrogenation energy for H + D 2 !HD + D at Fe6 is À 9 kcal mol À 1 . This shows that the binding and H transfer steps in Scheme 4 are feasible: they need to be avoided to satisfy one of the experimental constraints, and the synchronous double hydrogenation mechanism satisfies this requirement. Note that the reaction energy for this single hydrogenation (À 9 kcal mol À 1 ) is half the double hydrogenation energy of 2!3 (À 19 kcal mol À 1 ). An alternative reaction sequence in which incoming D 2 binds at an empty exo-Fe6À H position is discounted because previous calculations showed that this binding is very endergonic. [6f] The follow-up dissociations of the HD are straightforward and will benefit from the small entropic component. Completion of the cycle requires introduction of two H atoms, initially as protons at S3B coupled with electronation. These H atoms move without difficulty around S3B, first to Fe6 at the exo position and secondly towards Fe2. The least secure part of the mechanism is the last stage and the regeneration of endo-Fe2À H in 1: the complication is the nearby energy well of the H bridge between Fe6 and Fe2. An alternative pathway to endo-Fe2À H could be via S2B, and another possibility is the unhooking of S2BH from Fe2, opening the Fe2À Fe6 space. These possibilities are being simulated. Endo-Fe2À H in 1 is significant because if this position is void D 2 could bind there with favourable dynamics. [6f] Further work involves variation of the state of the His195 side chain (ie NɛH or NδH, rather than NɛH plus NδH as in the present mechanism). An unresolved question is why the Asn195 mutant, incapable of hydrogen bonding with hooked S2B, stymies the HD reaction.
This paper presents the core of a mechanism for the HD reaction, consistent with most of the experimental require-ments. The intermediates and reaction steps are closely connected with the intermediates and multiple reaction steps in the N 2 !NH 3 reaction, involving introduction of H atoms, binding of N 2 with exchange of H 2 , and H to N transfers. The results presented here inform continuing investigation of these steps, and integration of the HD and N 2 !NH 3 reaction mechanisms.