Nitrogen Reduction to Ammonia on a Biomimetic Mononuclear Iron Centre: Insights into the Nitrogenase Enzyme

Abstract Nitrogenases catalyse nitrogen fixation to ammonia on a multinuclear Fe‐Mo centre, but their mechanism and particularly the order of proton and electron transfer processes that happen during the catalytic cycle is still unresolved. Recently, a unique biomimetic mononuclear iron model was developed using tris(phosphine)borate (TPB) ligands that was shown to convert N2 into NH3. Herein, we present a computational study on the [(TPB)FeN2]− complex and describe its conversion into ammonia through the addition of electrons and protons. In particular, we tested the consecutive proton transfer on only the distal nitrogen atom or alternated protonation of the distal/proximal nitrogen. It is found that the lowest energy pathway is consecutive addition of three protons to the same site, which forms ammonia and an iron‐nitrido complex. In addition, the proton transfer step of complexes with the metal in various oxidation and spin states were tested and show that the pK a values of biomimetic mononuclear nitrogenase intermediates vary little with iron oxidation states. As such, the model gives several possible NH3 formation pathways depending on the order of electron/proton transfer, and all should be physically accessible in the natural system. These results may have implications for enzymatic nitrogenases and give insight into the catalytic properties of mononuclear iron centres.


Introduction
Nitrogenases are vital enzymes for life on Planet Earth and catalyse the conversion of N 2 from the atmosphere into ammonia:o ne of the building blocks of biological molecules. [1] The active site of nitrogenase is still controversial, but it is now accepted to contain an iron-molybdenumc luster (FeMoco) with seven iron atoms and one terminal molybdenum atom with all metal atoms bridgedb yn ine sulfur atoms. The inner atom of the FeMoco clusterh as long remainedu ncharacterised but recent experimental evidenceh as implicated it to be ac arbon atom, although its function remains unclear. [2] Nitrogenase catalyses the overall reduction of N 2 to two NH 3 molecules by using eight protons and eight electrons that are delivered throughaproton-transfer channel and electron-transfer machineries, respectively. [3] The exact position of the nitrogenb ind-ing to the FeMoco cluster is unknown and its catalytic mechanism remains am ystery;t herefore, extensive spectroscopic, kinetics ande lectrochemical studies have been performed to obtain insights into the intricated etailso ft he mechanism. [4] Detailed computational studies tested possible mechanismsa s well as the coordinatione nvironment and the function of the centralc arbon of the FeMoco cluster. [5,6] However, as the reaction process on the FeMoco clusteri sf ast, there remain many controversies relatedt ot he mechanism and particularly to the order of proton and electron transfer.A saresult, model complexesh ave been developed to gain insight into these chemical processes.
Thus, to understand the structural and functional features of enzymea ctive sites, biomimeticm odels are often developed that mimic the reactivec entre;t hat is, the metal with its ligand coordination features, but these are then studied in solution. [7] Specific biomimetic modelso fn itrogenase have been designeda nd developed to gain insight into the nitrogen fixation process and the features of the reaction complex needed for efficient turnover. [8] In particular, studies focused on the synthesis and characterisation of mononuclear iron and manganeses ystems with nitride and/or imido bound. [9,10] In one such biomimetic model complex, the Peters group used a mononuclear iron system and found evidence of nitrogen reductiont oa mmonia. [11] As such, this would be one of the few synthetic mononuclear iron complexes known to be able to reduce nitrogen to ammonia through the addition of external protons and electrons in analogy to the FeMoco cluster of nitrogenase. Scheme 1d isplays the mononuclear iron centre with tris(phosphine)borane (TPB) and N 2 bound, [(TPB)FeN 2 ] À , 1.B yu sing electron paramagnetic resonance (EPR), Mçssbauer and extendedX -ray absorption fine structure (EXAFS) spectroscopy,s everal nitrogen-based intermediates were trapped and characterised including ad oubly protonated hydrazido complex. [11a] The authors studied the proton transfer reactions with (Et 2 O) 2 H + as an acid in tetrahydrofuran solvent.
Currently,l ittle is knowno nt he proton-and electron-transfer processes in nitrogenases and particularly lacking is the order in which these processes happen.T he same is true for the synthetic mononuclear models hown in Scheme 1. Te chnically,t he first three protont ransfers can take place consecutively on the terminal nitrogen atom of N 2 (the distal Na tom, N d ), so that it can split off an ammonia molecule and leave an iron-nitrido complex. Scheme 2d escribes the possible reaction mechanisms that were studied in this work starting from the reactantc omplex 1.T he first step considers single proton transfer to either the distal nitrogen (via TS1 d )o rt he proximal nitrogen atom (via TS1 p )t of ormt he singly-protonated species 2 d and 2 p ,r espectively.T he next proton transfer onto 2 d gives an [FeNHNH] (3 dp )o r[ FeNNH 2 ]( 3 dd )c omplex via transition states TS2 p or TS2 d .P roton transfer towards 3 dp and 3 dd can give the ammonia complex 4 ddd or the [FeNHNH 2 ]c omplex 4 dpd and their mechanistic pathways were studied here as well. Thus, we consider consecutive proton transfer as well as an alternating proton transfer,i nw hich the first proton is donated to the distal nitrogen atom, the second proton to the proximal nitrogen atom (N p ), the third proton to the distal nitrogen atom again, etc.
In addition, each proton-transfer step can be followed by electron transfer directly.C learly,t he mechanism of nitrogen reduction to ammonia on an onheme iron centre can take place through many possible reactionp athways. To gain insight into the mechanism of ammonia production from N 2 on am ononuclear iron centre, we performed ac omputational study,w hich may have further relevance to the mechanism of nitrogenase enzymes. Our comprehensive DFT study on the proton-and electron-transfer mechanisms for reduction of N 2 to ammonia considers al arge variety of possible processes rangingf rom consecutive proton transfer to alternating proton/electron transfer steps.T hese studies give valuable insight into the nitrogen fixation reactionusing the mononuclear iron model from Scheme 1. We show that, technically,atriple protont ransfer without electron donation can lead to the release of ammonia;h owever,l ower energy pathways are found when one or more electrons are donated into the chemical system.A ss uch, it appears that the catalytic centrew ill not necessarily need an electron after each protona bstraction, but if it happenst he overall nitrogen fixation process will be more efficient.

Results and Discussion
The study presented in this work startedf rom the [(TPB)FeN 2 ] À complex shown in Scheme 1a nd Scheme 2. At the UB3LYP/ BS2//UB3LYP/BS1 + ZPE (zero-pointe nergy) level of theory, the doublet spin state is the ground state, whereas the quartet and sextet spin states are higherl ying by 4.3 and 23.9 kcal mol À1 ,respectively.Geometrically, the doublet and quartet spin states have al inear Fe-N-Ng roup, whereas it is bent( by 1378) in the sextets pin state. Although we calculated the lowest three spin states for each structure, we will focus on the lowest lying one in the main paper only;t he results covering all other spin states are depositedi nt he Supporting Information.

Consecutive protonation pattern
We first considered the mechanism of three consecutive proton-transfer reactions starting from the iron-dinitrogen complex 1 in the absence of ar eduction partner and with (Et 2 O) 2 H + as the proton source, see Scheme 2. In particular,w e calculated the [(TPB)FeN p (H) x N d (H) y ] À1 + x + y complexes with x = 0-3 and y = 0-3 andassume that only proton transfer reactions take place. We considered complexes with the distal as well as proximal nitrogen atom protonated.H owever,t he structures with av alue of x > y,t hat is, more protons bound to the proximal nitrogen than to the distal nitrogen atom, either failed to converge or,d uring the geometry optimisation,w ere reoriented in such aw ay that the nitrogen atom with the most number of protons became the terminal nitrogen atom (N d ). Therefore, the [(TPB)FeN p (H)N d ] 0 structure (2 p )i su nstable and its geometry optimisation gave [(TBP)FeNNH] 0 (2 d )i nstead. Consequently,t he first proton transfer can only take place on the distal nitrogen atom. Structure 2 d has close lying doublet and quartet spin state structures (within1 kcal mol À1 )a nd hence will react through two-state reactivity on competing doublet andq uartet spin surfaces, similart ow hat was seen for mononuclear iron(IV)-oxo complexes with heme and nonheme ligand environments. [12,13] In the next step of the catalytic cycle, we attempted to protonate 2 d and located two local minima, namely [(TPB)FeN p (H)N d (H)] + (3 dp )a nd [(TPB)FeN p N d H 2 ] + (3 dd ), whereby the latter is 2.9 kcal mol À1 lower in energy than the former in the quartet spin state.
We then calculated the driving force forp rotont ransfer from (Et 2 O) 2 H + from 2 2 d leadingt ot hese structures using isolated speciesa ccording to reactions 1a nd 2a nd find valueso f DE + ZPE = À14.6 kcal mol À1 for Equation (1) and À12.5 kcal mol À1 forEquation (2). Based on these driving forces, therefore, terminal protonation of the diazenide group will be preferred over proximal protonation, but only by af ew kcal mol À1 .C onsequently,t he kinetics for both pathways was considered here.
In the final proton-transfer step in Scheme 2(top), we investigated addition of at hird proton to the distaln itrogen atom, which forms ammonia and immediatelyb reaks the NÀNb ond to form 4 ddd .T he ground state of 4 ddd is the quartet spin state in analogy to iron(IV)-tosylimido complexes calculated previously. [14] Higher in energy than the quartet spin ground state are the sextet spin state (by 4.5 kcal mol À1 )a nd the doublet spin state by 30.7 kcal mol À1 .T he final dissociation of ammonia from the 4 4 ddd complex only costs 5.4 kcal mol À1 at the DE + ZPE level of theoryt hrough the breakingo ft he hydrogen bond between ammonia and the iron(IV)-nitrido group.W e also testedt he proximal protonation of 3 dd (as will be discussed in the next section) and found it to be similar in energy.
Subsequently,w ei nvestigated the kineticso ft he protontransfer reactions displayed in Scheme 2. Accordingly,wecreated modelso fs tructures, 1, 2 d , 3 dd , 3 dp and 4 ddd ,a nd included a proton source as used in Ref. [11a],t hat is, (Et 2 O) 2 H + ,t ot he complex. The structures with (Et 2 O) 2 H + included in the model are labelledw ith RC in subscript after the name and have the same spin state ordering and relative energies as the isolated structures. Thus, Figure 1g ives the energy landscapea nd structures of lowenergy proton-transfer transition states for the consecutive protont ransfert o1 in the absence of an electron donor.F or each of the individual reactantc omplex structures, that is, 1 RC , 2 d,RC , 3 dd,RC , 3 dp,RC and 4 ddd,RC ,o nt he doublet, quarteta nd sextet spin states ag eometry scan for proton transfer was performed, whereby one degree of freedom (the reactionc oordinate) was fixed and all other geometric degrees of freedom minimised. The maximao ft hese geometry scans were subjected to atransition state search and gave us the proton-transfer transition states for each of the reaction steps. Thus, 2,4,6 TS1 d are the transition states for the protont ransfer from (Et 2 O) 2 H + to 2,4,6 1 at the distal nitrogena tom.
The first pathway investigated relatest ot he protont ransfer from (Et 2 O) 2 H + to [(TPB)FeN 2 ] À to give the [(TPB)FeNNH] and two diethyl ether molecules. Optimised geometries starting from the end point of the geometry scans originating from 2,4,6 1 RC resemble the 2,4,6 2 d optimised structures (see Supporting Information, Figure S3) and confirmt he pathway from 1 to 2 d . Subsequently,w et ook the 2,4,6 2 d structures and added the proton donor group (Et 2 O) 2 H + and optimised 2,4,6 2 d,RC .T hereafter,t he proton-transfer pathway was investigated and led to the transition states for distal protonation. The energy landscape described in Figure 1i s, therefore, based on the relative energies of the reactant complexes and the transition states with respect to 2 1.T he first proton transfer to [(TPB)FeN 2 ] À takes place on the doublet spin state via 2 TS1 d and has an energy of 4.9 kcal mol À1 ,w hich is lower in energy than the nearest quartet and sextet spin states. By contrast, optimised geometries of structures 2 implicate them to be close in energy on the doublet and quartet spin state surfaces. Consequently,d uring the lifetimeo fs tructure 2 it is likely that full equilibration will lead to am ixture of doublet and quartet spin state structures.G eometrically, 2 1 and 2 2 d structures contain very similar Fe-N and N-N distances and hence their electronic configuration is the same.
The optimised geometry of 2 TS1 d is given in Figure 1a nd is characterised with as mall imaginary frequency of i261cm À1 . This value is much lower than those typicallyf ound for hydrogen atom abstraction barriers of well over i1500 cm À1 due to a sharp and narrow peak on the potentiale nergy surface. [15] As such, the proton transfer potentiale nergy surface will be flatter with ab road barrier.M oreover, transitions tates with large imaginary frequencies generally give rate constantsw ith a large kinetic isotope effect, which is not expected in our system described here. Thus, replacement of the transferring proton in (Et 2 O) 2 H + by ad euteron may increase the barriers slightly but not by ah uge amount. [16] The donating protoni n 2 TS1 d is located at ar elativelyl arge distance of 2.02 ,w hich appearsu nusually long. However, as can be seen from the structure, 2 TS1 d reflectst he simultaneous breakingo ft he Et 2 OH + ···OEt 2 hydrogen bond and the transfer of the protont o N d .T hese two simultaneous steps prevent ac loser approach of the proton to N d .
Distal protonation of 2,4 2 d leads to 2,4 3 dd via ab arrier 2,4 TS2 d with values of 6.4 (doublet) and 5.0 (quartet) kcal mol À1 with respectt ot heir precursor local minima. These structures,s imilar to 2 TS1 d ,h ave as mall imaginary frequency of i197 (i190) cm À1 for 2 TS2 d ( 4 TS2 d ), respectively.A lso in theses tructures the transferring proton is still located atalarge distance; hence,t he structures are earlyo nt he potential energy surface. Previously, [17] early transition states were correlated with barrier heights with low energy,i na greement to what is seen in Figure1.
Formation of intermediate 3 dd from 2 d leads to significant changes in bond lengths along the FeÀNa nd NÀNi nteractions. To be specific,t he FeÀNb ond shortens to 1.718 in 2 3 dd as ar esult of increasing double bond character in the FeÀNi nteraction. At the same time, the NÀNb ond elongates to well over 1.32 and loses double bond character.Wefind the quartet spin state to be the ground state of 3 dd and 3 dp with the doublet and sextet spin states well above the quartet spin state by 17.2 and 14.7 kcal mol À1 ,r espectively.T hese results appear to contradictexperimental observations that implicated ad oublet spin ground state. [11a] However,t he doubly reduced complex (3 dd À ), which we also calculated hasadoublet spin ground state. It could very well be, therefore, that the experimentally characterised EPR spectrum may reflect the doubly reduced species instead. Further work will be necessary to establisht his.
The lowest lying transition state for protonation of 3 dd is on the quartet spin state surface with ab arrier( 4 TS3 d )o fa bout 15.0 kcal mol À1 .T herefore, the energetic barrierf or the third consecutive protonation step is considerably larger than the first two protont ransfer barriers.F urthermore, the reaction from 4 3 dd leadingt o 4 4 ddd is endothermic by 4.0 kcal mol À1 . Structurally,i ti sa kin to 4 3 dd with Fe-N and N-N distances of 1.819 and 1.325 .S imilar to the 2 TS1 d and 2, 4 TS2 d structures discussed above, the donating proton is at ar elativelyl arge distance from N d of well over 2 and has as malli maginary frequency of i148 cm À1 .A fter passingt he proton transfer transition states 2,4,6 TS3 d ,t he geometry scans fall to complex 4 ddd , which is an iron-nitrido with aw eakly bound ammonia molecule. This complex dissociates ammonia to form the final products.
In summary,t he calculations shown in Figure 1i mplicate easy and fast triple protonation of the distal nitrogen atom from [(TPB)FeN 2 ] À in ah ighly exothermic reactionp athway. Therefore, triple protonation without electrond onation is a feasible process for this mononuclear nonheme iron complex. It may very well be, therefore, that in the multinuclear FeMoco cluster,b inding of N 2 can also be followed by triplep rotonation without electron transfer.H owever,r eductions teps could speed up the process and hence we investigatedt hat possibility.

Alternating proton transfer pattern
As noted above, we failed to optimise 2,4,6 2 p ;h owever, we did succeed in optimising the structures of 2,4,6 3 dp and 2,4,6 4 dpd (see the Supporting Information, Figures S10 and S17). We therefore decided to investigate the protont ransfer pathways leading to these intermediates. Unfortunately,i na nalogy to the problem associated with locating 2 TS1 p ,w ea lso failed the geometry optimisationso f 2,4,6 TS2 p ,w here the protond uring the geometry optimisationsm oved to the distal nitrogena tom in-stead. These transition states, therefore, mustb ec onsiderably higheri ne nergy than those leading to 2,4,6 TS2 d .
The final alternative pathway considered was proximal protonation from [(TPB)FeNNH 2 ] + (3 dd )( Figure 2a). Ab arrier height (via 4 TS3 p )o fo nly 15.1 kcal mol À1 was found for this process, which is only 0.1 kcal mol À1 higheri ne nergy than distal protonation. Consequently, 4 3 dd can react through either distal or proximal nitrogen protonation with almost equal barriers and hence probabilities. Structurally,t he transition states for proximal and distal protonation of 4 3 dd are very similar.

Proton transfer pathways of reduced complexes
In the nitrogenase enzymea sw ell as in biomimetic model complexes,t he nitrogen reduction to ammonia is accomplished with multiple electron-transfer steps;h owever,t he order of the proton-and electron-transfer steps remains unclear.I np articular,i ti sv ery well possible that the enzyme is designedi ns uch aw ay that the proton-ande lectron-transfer steps are alternated. The above resultso nt he mononuclear iron complex 1 show an energetically feasible pathway for ammonia synthesis without reductions teps. To test whether the proton transfer ability is enhanced by reduction of the metal centre, we calculated the proton transfer driving forces of some of the reduced complexes and, particularly,t he protonation of 2,4,6 3 dd + and its one-electron and two-electron reduced forms, designated 1,3,5 3 dd 0 and 2,4,6 3 dd À ,w here we now give the overall chargeo ft he complexi ns uperscript after the label. In addition, we investigated the distal protonation from 2,4,6 3 dp + and its one-and two-electron reduced forms;t hat is, 1,3,5 3 dp 0 and 2,4,6 3 dp À .T able 1s ummarises the obtained results for the proton transfer from 3 dd and 3 dp with overall charge Q = 1, 0o r À1.
As follows from the data shown in Ta ble1,u pon reduction of the complex, the thirdp roton transfer becomes energetically more exothermic for all cases and especially ah igh exothermicity of the reactioni sf ound for the system with charge of Q = À1. The barrier heights also generally decrease upon changingt he chargeo ft he complex from Q = 1t oQ = 0t o Q = À1. The trend is seen for both examples;t hat is, distal protonation of 3 dd as well as 3 dp .I np articular,t he barrierh eight for distal protonation of 3 dd drops from 15.0 kcal mol À1 for the non-reduced system,t hat is, the one shown in Figure 1, to 4.4 kcal mol À1 after double reduction.I na ddition, the driving force for the reaction increases steeply and is more exothermic for the doubly reduced system. Distal protonation of the [FeNHNH] system shows similart rends with larger exothermicity of the protont ransfer reactiona nd lower barrierh eights. These studies implicate that although triple protonation is a feasible process withoutt he addition of external electrons, the overall reaction efficiency can be improved by adding electrons to the system.M ost probably,t he alternating addition of protons and electrons will be the energeticallyf avourablep rocess for nitrogen fixation. However,i nt he absence of available electron donors, the reaction can still proceed through sequential protonation, albeit considerably slower.

Thermochemical cycles
To shed more light on the possible reaction pathwaysf or electron-and proton-transfer,w ec alculated individual reactions startingf rom 2 1 for alternating and consecutive proton and electron transfer;the results are shown in Figure3.T ocalculate the proton-transfer energies, we used either the H 3 O + /H 2 O couple or the (Et 2 O) 2 H + /2Et 2 Oc ouple to balance the reaction. However,t he H 3 O + /H 2 Oc ouple just shifts the relative free energies of protont ransfer and makes all reaction pathways much more exergonic. As such, proton transfer will be av ery fast process in aw ater solution.U sing the (Et 2 O) 2 H + /2Et 2 O couple the proton transfers are all exergonic but by am ild amount,w hich means these reactions teps will be kinetically slower and individual intermediates may be trapped accordingly,i na greement with the experimentalo bservations. Nevertheless, the proton transfert rends are the same regardless of the proton donor and the effect is only systematic. Figure 3s tarts from 2 2 d 0 andt he proton transfer pathways are given from left to right and the electron transfer from top to bottom.T hus, proton transfer to form 4 3 dd + is exergonicb y DG = À32.8 kcal mol À1 with (Et 2 O) 2 H + as ap rotons ource, whereas electron transfer to give 3 2 d À releases DG = À51.2 kcal mol À1 .A ss uch, electron transfer is energetically favoured over protont ransfer in ad iethyl ether solution.T he protont ransfer energies between 2 1 À and 2 2 d 0 using (Et 2 O) 2 H + as proton source matchest he value from Figure 1e xcellently and so does the proton-transfer energy to give 4 3 dd + .O verall, the three consecutive proton-transfers teps from 2 1 À are all exergonic and hence possible at room temperature. However,t he proton-transfer steps are energetically the most favourable from complexes with an overall charge of Q = À1; that is, 2 1 À , 3 2 d À and 2 3 dd À .M ost probablyt he overall charge of À1g ives these complexes high pK a values and make them react fast with externalp rotons. This meanst hat alternating proton and electron transfer should give the most energeticallyf avourable reactionp rocess for conversion of N 2 into ammonia and an iron-nitrido complex.
On the other hand, the energetically most favourable reduction steps will be those where ap ositively charged complex is reduced to an eutralo ne;t hat is, 4 3 dd + and 5 4 ddd + ,w hich release DG ET = À80.9 and À96.0 kcal mol À1 ,r espectively.T herefore, the nitrogen fixation reaction is possible through many different reaction pathways of protona nd electron donations. We find at hermodynamic viable process of triple proton transfer without electron donation as well as ones where triple proton transfer is coupled to one or two electron transfers.

Electronicchanges during the reaction mechanism
To understand the electronic changes during the proton-transfer reaction, we analysed the electronic configurations and orbitald escriptionso fc omplexes 1, 2 d , 3 dd and 4 ddd in detail. Figure 4d isplays the high-lying occupied and low-lying virtual orbitals of 2 d and av alence bond descriptiono ft he electronic configurations of 2 1 and 2,4 2 d .T hese valence bond descriptions highlight the molecular orbitals that are formed andb roken in each step and the formal charge distributions on the atoms. In particular, in the valence bond drawings, electrons are represented by ad ot, and al ine between two dots gives am olecular orbitalo ccupied by two electrons. In the past we used these assessments to explain regioselectivities of reaction mechanisms and the origins of bifurcation processes and explained experimental reactivity trends. [18] The key valence orbitals are determined by the 3d atomico rbitals on the metal that interact with neighbouring atoms. Thus, the low-lying p* xy orbitali san on-bonding orbital in the plane of the phosphorus atoms and has as hape seen before for nonheme iron complexes. [13,19] Ad egenerate set of orbitals for the interactions of the metal with the two nitrogen atoms leads to as et of bonding (p xz /p yz ,n ot showni nF igure 4) and antibonding (p* xz and p* yz )o rbitals that cover the Fe, N d and N p atoms. In blue, we give the four electrons that occupy the p xz and p* xz orbitals and in purple those for the p yz and p* yz orbitals. Even in the reactant complex 2 1 there is considerable mixingo ft he iron and N 2 p-type orbitals and, consequently,a lso charget ransfer from nitrogen to metal. In the reactant complex the p* xz and p* yz orbitals are doubly occupied and, as ar esult,t he FeÀNb ond length is short and corresponds to af ormal single bond with a distance of 1.805 .T he atomic3 d z2 orbital of iron is involved in ab ondingo rbital with the 2p z on boron to form the s* z2 orbital, which also gives considerable charge transfer from iron to boron of Q = À0.42 and ar elativelys hort FeÀBd istance of 2.397 .T he highest lying 3d orbital on iron is singly occupied (s* x2-y2 )a nd gives 2 1 an overall orbital occupation of p* xy 2 p* xz 2 p* yz 2 s* z2 2 s* x2-y2 1 and af ormal 3d 9 configuration. The valence bond structure, therefore, gives eight electrons along the FeÀ Nb ond, representing the occupation of the p xz 2 p* xz 2 p yz 2 p* yz 2 orbitals. TheFe ÀBinteraction is formally as ingle bond through occupationo ft he s* z2 orbital with two electrons (shown in green in the valence bond drawing), whereas the unpaired electron in s* x2-y2 is given in red. Upon protonation of the terminaln itrogen atom, as in 2,4 2, the degeneracy of the p* xz /p* yz couple is lost. Specifically,t he 2p y orbitalo nt he terminal nitrogen atom splits off from the molecular p yz /p* yz interaction and forms a s NH bond with the 1s orbitalo ft he incoming proton. Electronically,t he two electrons that form the s NH orbital both originate from the transfer of one electron from the p* xz and p* yz orbitals into s NH .A sa result of this, the quartet spin state drops in energya nd becomes the most favourable configuration, with orbitalo ccupation s NH 2 p* xy 2 p* xz 1 p* yz 1 s* z2 2 s* x2-y2 1 .T he loss of p* xz /p* yz electrons in 2 d leads to elongation of the NÀNd istance to 1.25 in both the quartet andd oublet spin states. However,t he FeÀ Bi nteraction stays intact at ad istance of 2.405 (2.534) in 4 2 d ( 2 2 d ), respectively,d ue to the still doubly occupied s* z2 orbital.
The second proton transfer from 2,4 2 d to form 4 3 dd is electronically depicted in Figure 5. In 4 3 dd the N=Nd ouble bond is broken and charged ensity migrates from nitrogen to iron strengthening the FeÀN p bond. As ac onsequence of strengthening of the FeÀNb ond, the FeÀBb ond is weakenedo r broken and the s* z2 orbital converts into an atomico rbital. It is seen that the FeÀBd istance elongates to well over 3 in both structures 3 and 4.A tt he same time, one electron from s* z2 is Figure 3. UB3LYP/BS2//UB3LYP/BS1 calculated thermochemical cycles for proton (horizontal)and electron(vertical)transfer from 2 1 with free energies (DG)in kcal mol À1 .V alues in square bracketsr efer to data with (Et 2 O) 2 H + /2Et 2 Oasp roton transferc ouple, while outside parenthesis is data for the H 3 O + /H 2 Ocouple. promoted into the p* yz orbital to get the overall orbital occupation p* xy 2 p* xz 1 p* yz 2 s* z2 1 s* x2-y2 1 .I nt he final proton transfer to the terminal nitrogen atom, an ammonia molecule is formed andt he FeÀNd istance reduces to 1.688 ,b ut the electronic configurationstays the same.

Conclusions
We present as eries of density functional theory calculations on the electron-and proton-transferp rocesses in am ononuclear iron modelo fn itrogenase.W ec alculate barrierh eights for protont ransfer in the absence of an electron donor and show af easible processw ith three consecutive proton transfer barriers in an overall exothermic process. Protonation is favoured on the distal nitrogen atom so that triple protontransfer forms one ammonia molecule and an iron-nitrido complex. Te sts on proximal protonation find barriers that are higher in energy due to stereochemical interactions and shieldingo ft he proximal site. We finally tested protont ransfer from complexes with different overall chargea nd show that the energetically favourable process is consecutive proton and electron transfer. However, alternative pathways are energetically accessible and cannotb er uled out. The calculations point out that proton and electron transfer do not necessarily need to happenc onsecutively because the energetics are also favourable for multiple proton transfer withoute lectron transfer.A ss uch, multiple pathways for the formation of ammonia from molecular nitrogen are possible, which give the enzyme sufficient flexibility to operate under low acid or low reduction conditions.

Experimental Section
All computational studies presented here used density functional theory methods as implemented in the Gaussian 09 program package, [20] and extensively benchmarked and calibrated against experimental data. [21] These calculations on nonheme iron complexes reproduced experimental rate constants and Hammett trends well. Our model was based on the [(TBP)FeN 2 ] À structure as described by Peters et al., [11a] and the mechanisms for proton transfer were studied with protonated diethyl ether dimer,( Et 2 O) 2 H + .A st he overall charge of our chemical system ranges from À1t o+ 2w e did full geometry optimisations with as olvent model included; namely,t he polarised continuum model (CPCM), [22] with dielectric constant mimicking tetrahydrofuran, which was the experimentally used solvent. Initial geometry optimisations, frequencies and geometry scans were performed using the hybrid density functional method UB3LYP [23] in combination with basis set BS1:L ACVP basis set with electron core potential on iron and 6-31G on the rest of the atoms. [24] Energetics were improved by single-point calculations with basis set BS2:t riple-z LACV3P + basis set with electron core potential on iron and 6-311 + G* on the rest of the atoms. All energies reported in this work are DE + ZPE data with energies at BS2 and zero point corrections with BS1.
To test the accuracy of our optimisation algorithm, we repeated the geometry optimisations of local minima and some of the transition states using tight convergence criteria in Gaussian. In none of these cases;h owever,d id the energy change by more than 10 À6 hartrees and neither did the optimised geometries change significantly.T he reproducibility of the calculations was investigated by reoptimising the proton-transfer reaction from 2 1 to 2 2 with the PBE0 density functional method. [25] As follows (see the Supporting Information, Figure S17), the structure and relative energies are very similar to those found with B3LYP and therefore the project was finished with B3LYP only.