Dihydrogen Catalysis: A Degradation Mechanism for N2-Fixation

Article pubs.acs.org/JPCA

Dihydrogen Catalysis: A Degradation Mechanism for N2‑Fixation Intermediates Rubik Asatryan,*,†,‡ Joseph W. Bozzelli,‡ and Eli Ruckenstein† †

Department of Chemical and Biological Engineering, State University of New York, Buffalo, New York 14260, United States Department of Chemistry and Environmental Science, New Jersey Institute of Technology, Newark, New Jersey 07102, United States

‡

S Supporting Information *

ABSTRACT: Molecular hydrogen plays multiple roles in activation of nitrogen. Among others, it inhibits the overall process of N2-reduction catalyzed by nitrogenase enzyme. The H2-assisted dehydrogenation and the H-atom transfer reactions (called dihydrogen catalysis, DHC) are suggested as possible mechanisms for the degradation and removal of potential intermediates formed during the reduction of nitrogen. Several iron-organic model reactions associated with the core stereospecific reaction (cis-N2H2 + H2 → N2 + H2 + H2) are examined using a comprehensive density functional theory and ab initio analysis of the corresponding potential energy surfaces. A variety of energetically feasible decomposition pathways are identified for the DHC-oxidation of ironbound [NxHy]-species. A liberated diazene intermediate (HNNH) is suggested to interact in situ with two proximal hydridic H-atoms of an activated (hydrided) Fe-catalyst to produce N2 and H2 with a low or even no activation barrier. The majority of identified pathways are shown to be highly sensitive to the electronic environment and spin configuration of metallocomplexes. The H2-assisted transport of a single H-atom from a bound [NxHy] moiety to either the proximal or distal (Fe, S or N) active centers of a catalyst provides an alternative degradation (interconversion) mechanism for the relevant intermediates. The two types of molecular hydrogen-assisted reactions highlighted above, namely, the H2-assisted dehydrogenation and the transport of H-atoms, suggest theoretical interpretations for the observed H2-inhibition of N2 activation and HD formation (in the presence of D2). The DHC reactions of various [NxHy] moieties are expected to play significant roles in the industrial high-pressure hydrodenitrification and other catalytic processes involving the metabolism of molecular hydrogen.

1. INTRODUCTION

substrates of nitrogenase enzyme and key intermediates in heterogeneous catalysis of dinitrogen and dihydrogen,2−8 has the low activation barrier of 22.5 kcal mol−1 (ΔG‡ = 28.7 kcal mol−1):

In the process of developing a comprehensive potential energy surface (PES) for hydrazine (N2H4), in order to evaluate the chemical activation reactions of amidogen radicals (•NH2), a stereoselective reaction channel (eq 1a) has been previously identified at the CCSD(T)/CBS and CBS-QB3 levels of theory involving the gas-phase decomposition of cis-diazene (N2H2).1 This pathway (Figure 1), associated with the most significant

H 2 + cis‐N2H 2 ↔ N2 + H 2 + H 2

(1a)

The H2-assisted reaction 1a can be considered as dihydrogen catalysis (DHC) where the initial hydrogen molecule is regenerated in the products. This constitutes an elementary model for the synchronous double H-atom transfer reactions of a H-donor (cis-diazene) to a D2 molecule (eq 1b).

D2 + cis‐N2H 2 → 2DH + N2

(1b)

Here, the D-notation for hydrogen is employed to distinguish two types of hydrogen atoms. However, reaction Figure 1. Transition state for gas-phase reaction 1a.1 An attacking dihydrogen molecule (H2 on the left-hand side of eq 1a) initiates the decomposition of cis-N2H2 into N2 and 2H2. © 2012 American Chemical Society

Received: April 17, 2012 Revised: October 18, 2012 Published: October 24, 2012 11618

dx.doi.org/10.1021/jp303692v | J. Phys. Chem. A 2012, 116, 11618−11642

The Journal of Physical Chemistry A

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relevant for a variety of organometallic and heterogeneous processes involving the metabolism of molecular hydrogen,18 such as hydrogen storage,18a high-pressure catalytic hydroprocessing,18b and catalytic activation of carbon monoxide, which also constitutes a substrate of nitrogenase enzyme,2−8 and its hydrogenation provides a model reaction in heterogeneous catalysis.6,18c,d The concept of dihydrogen catalysis is now receiving more general recognition (particularly in organometallic catalysis).16,17,18e−g Quite recently, it has been shown that the molecular hydrogen reversibly catalyzes formation of C−H and N−H bonds in aminopyridinate ligated iridium complexes.18e 1.1. Activation of N2. The fixation of N2, generally considered as its reduction to NH3, has been studied over several decades; however, the detailed molecular mechanism and conversion pathways remain open issues.2−12,20−28 The NN bond is exceptionally strong (ca. 225 kcal mol−1), and the first step in the activation of this triple bond is extremely unfavorable despite the overall 22 kcal mol−1 exothermicity of the ammonia synthesis. Recent theoretical calculations at the G2M(MP2)//MP2/6-31G** level suggest13 that the lowest barrier for the association of H2 with N2 to form iso-diazene is 125.4 kcal mol−1, in agreement with the value of 124.3 kcal mol−1 obtained via the multiconfigurational MRCI+Q/ AVQZ//MCSCF/AVQZ method.29 The extremely high barrier makes the direct reaction between N2 and H2 very unlikely; therefore, chain-reactions were considered as the dominant mechanism for the high-temperature hydrogenation of nitrogen.13 A strong contrast exists between the conventional and the biological N2-activation processes. Very high pressures and temperatures (200 atm and 500 °C) and Fe- or Ru-based catalysts are employed to hydrogenate nitrogen in the industrial Haber−Bosch process, which is believed to proceed via an initial dissociative adsorption of reagents on the catalyst surface.30 In contrast, the activation of N2 in biological media occurs under ambient conditions stimulated by an enzyme, the nitrogenase. Nitrogenase is composed of a molybdenum−iron protein involving the reaction active center (FeMo-co cofactor) and a Fe-protein containing the [Fe4S4] cluster that acts as a one electron reducing agent.3,43 The active site of the iron−molybdenum cofactor (Fe7MoS9X), schematically illustrated in Figure 2, contains two incomplete cubane clusters Fe4S3 and MoFe3S3 (with a missing μ3S vertex in each of the polyhedra) bridged by three μ2-sulfide ligands. The Fe7MoS9X core is linked to the protein through its terminal Fe1 (tetrahedral coordination) and Mo (octahedral coordination) metal atoms. The six inner iron atoms (Fe2 to Fe7) form an approximate trigonal prism waist, which gives rise to an unusual distorted trigonal-planar coordination for the central iron atoms. The interstitial Xatom, a fourth possible coordination center for each of the central Fe-atoms, has been found quite recently to be a carbon atom (carbide) based on Fe X-ray fluorescence spectroscopy,69a,b and a mechanism has been suggested for its insertion into the FeMo-co.69c Mutation experiments involving two amino acids of the first noncovalently bonded coordination sphere of FeMo-co led to the conclusion that α-Val-70 residue serves as a gatekeeper for the substrate arrival to the Fe2−Fe3− Fe7−Fe6 face of the central prism, whereas the α-His-195, which is hydrogen bonded to a μ2S atom, constitutes an agent for proton delivery to the active site of FeMo-co.2 The α-Arg-

1b can be considered also as an isotopic scheme, which explains the HD formation observed during the nitrogenase catalyzed reduction of nitrogen in the presence of molecular deuterium.9−12 Such a simple process has been earlier hypothesized by Burgess et al.11 to explain the H2-inhibition of N2-fixation and HD formation processes, and later examined theoretically by Durrant using the MP4/6-31+(2d,p)//MP2/631G(d) method (vide infra).12 A similar reaction barrier involving the iso-diazene isomer has also been calculated by Hwang and Mebel.13 The reverse N2-activation reaction (eq 1a) exhibits a barrier of only 76 kcal mol−1 (ΔG‡ = 85.5 kcal mol−1), which is significantly lower (by almost 50 kcal mol−1) than the analogous bimolecular nitrogen fixation reaction (ca. 125 kcal mol−1).13 However, the reverse reaction is termolecular (N2 + H2 + H2 → H2 + cis-N2H2) with low probability to occur in the gas-phase in ambient conditions. The reaction may occur only at very high pressures.14 However, it is expected to be feasible when the molecular hydrogen is activated on a heterosurface. Reaction 1a is similar to the degenerate termolecular hydrogen-atom exchange reaction that proceeds via a H6hexagonal transition state and hence is allowed by the Woodward−Hoffmann rules, in contrast to the symmetry forbidden H4-reaction scheme.15 Theoretical aspects of such reactions have been addressed elsewhere along with a comprehensive analysis of the pertinent literature.16 Two major DHC mechanisms are distinguished: (a) mediated by H2 dehydrogenation reaction, analogous to eq 1a , which produces the reductive elimination of a hydrogen molecule, and (b) molecular hydrogen-assisted H-atom transport (HAT), which produces a proximal or a distal (remote) H-atom transfer (eq 2).

D2 + HY∼X ↔ DH + Y∼XD

(2)

where X and Y virtually can be any atoms. The HAT mechanism, introduced in a previous paper and tested for various organic and organometallic systems,16 has recently been proven to be valid also for a pure inorganic system, the H2-reduction of alumina-supported monomeric vanadium-oxide species.17 In this article, we examine various new pathways for molecular hydrogen assisted reactions under the general term of dihydrogen catalysis (DHC, with a somewhat broader meaning of the term catalysis). We provide detailed discussions on processes pertinent to the degradation of potential intermediates of enzymatic (nitrogenase) and other relevant catalytic processes involving dinitrogen and dihydrogen. All conclusions are based on a comprehensive analysis of the respective potential energy surfaces using various density functional theories and ab initio theoretical protocols. Dihydrogen catalysis is a kinetic process that combines the general features of dihydrogen-bond,19,41c,d,61a transition metal (TM)-hydride, and dihydrogen complex19a,41a,b,e,61a,66a formation processes. The transition state of DHC can be formally regarded as a dihydrogen bond (named by Crabtree and coworkers for a bond between a hydrogen-bond acceptor and a conventional proton donor19b) mediated by molecular hydrogen (see, e.g., scheme to eq 1b). Therefore, the DHCmechanisms developed in this article are expected to be 11619



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molecular level constitutes an intriguing issue.35 It was examined particularly for a bioinspired system using the redox potentials and pKas of oxomanganese complexes calculated at the B3LYP/cc-pVTZ-(f) level of theory.35a Nitrogenase also reduces some other substrates, such as C2H2, HCN, and N2O to the final products C2H4, CH4 + NH3, and N2 + H2O, respectively. Hydrogen does not form during the enzymatic reduction of acetylene, and C2H2 is stereospecifically converted to cis-C2H2D2 in the presence of D2O.3 Various [NxHy] intermediates were considered and identified for N2 activation.2,8,24a,c The formation of a coordinated ∼N NH moiety is commonly believed to provide the first hydrogenation step. There are two options for further hydrogen (H+/e−) addition, denoted by Hoffman and co-workers as (i) distal (based on the Chatt cycle,26,33 further developed by Schrock27), which involves the sequential addition of H-atoms to a single N-atom prior to N−N bond cleavage, after the third hydrogenation, and (ii) alternating pathway, which considers alternate addition of H-atoms to the two (distal and proximal) N-atoms before N−N bond cleavage occurs after the fifth hydrogenation step (Scheme 1).2

Figure 2. Schematic core of molybdenum−iron cofactor (FeMoco) of nitrogenase enzyme (Fe7MoS9X cluster) using crystallographic labels.43 The Fe2−Fe3−Fe7−Fe6 reactive face for the substrate coordination (circled) has been identified by the mutation analysis of covalently nonbonded two amino acids: α-V70 as a substrate gatekeeper and αH195 as an agent for proton delivery.2 Highlighted μ2S-bridged dimer and single-iron moieties have been effectively used in various theoretical models.10,19,20,22,24,25b

Scheme 1. Distal (Top) and Alternating (Bottom) Pathways for Reduction of Nitrogen;2 the Alternating Pathway Is Further Developed in a Recent Paper of Hoffman and Coworkers2e

96 residue also being H-bonded to a bridged sulfur atom can be considered as another source of protons.24b However, the repetitive proton delivery is suggested to occur through a waterchain terminating at the HOH 679, which is 4.0 A from the nearby μ3S (Figure 2). The N2 conversion on nitrogenase is considered to occur as follows: N2 + (6 + 2x)H+ + (6 + 2x)e− → 2NH3 + x H 2

(3)

where x varies between 1.0 and 7.5, depending on the type of enzyme; for the most significant FeMo-enzyme, it is unity, whereas the all-iron nitrogenase produces the highest amount of hydrogen.2−7,31 Thorneley and Lowe developed a kinetic model for ammonia synthesis formulated in terms of En states, where n indicates the number of electrons delivered to the MoFe protein during their formation relative to the resting state E0.31 Each electron accepted by the MoFe protein is accompanied by a proton. During catalysis, the Fe-protein ([4Fe-4S] cluster) delivers one electron at a time driven by the binding and hydrolysis of two MgATP within the protein, which constitutes the rate limiting step.2−6 According to a quite recent view (deficit-spending model2b), the slower step is the intramolecular electron transfer from a P-cluster ([8Fe-7S]) to the active site [7Fe-9S-X-Mohomocitrate] both located within the MoFe protein. N2 is irreversibly activated after three to four electrons are accumulated, whereas only two electrons are required for the activation of alkyne reduction.2c,d Nitrogen is further reduced to [NxHy] intermediates, one of the identified intermediates being hydrazine (N2H4). The highly reactive diazene, which also constitutes a substrate for nitrogenase, could not be detected.8,11a The degradation mechanism of diazene at the molecular level as well as the sequence of reduction and protonation steps are still controversial.33b,34 The periodic density functional theory (DFT) calculations of Kästner and Blöchl suggested that each electron transfer is accompanied by a proton transfer to FeMo-co.25 Assuming that the protonationreduction steps are tightly coupled, the hydrogen build-up is usually modeled as a single hydrogen atom addition.2,20−22,24,25 The theoretical modeling of proton coupled electron transfer at

The second step H-addition of two distinct mechanisms occurs to a proximal or a distal nitrogen atom generating either ∼=N−NH2 or ∼NHNH isomer species, respectively. Both pathways eventually lead to the formation and elimination of two NH3 molecules.2 Following the Thorneley−Lowe kinetic scheme,31 the degree and type of hydrogenation of FeMo-co with H atoms and possibly H2 molecules are key variables, and the degradation and removal of any of intermediates from the chain of reactions would suppress the overall activation process.2c,d Significant progress has been made recently in the theoretical modeling of nitrogenase structure and reactivity, yet many features of this intricate system remain unknown.4,6,12,20−25 Only the theoretical results directly related to the present study will be discussed in what follows. The role of molecular hydrogen is much less studied and still quite controversial. H2 is known to be a specific, competitive inhibitor of nitrogenase and also a side product of proton reduction by nitrogenase.2−8 This inhibition of N2 reduction by H2 indicates a unique relationship between dihydrogen and dinitrogen. Most N2 fixing bacteria contain the hydrogenase enzyme, which recycles the excess hydrogen. They oxidize H2 back to H2O and couple this reaction to ATP formation.42 1.2. Multiple Functions of Dihydrogen. The diversity of nitrogenase interactions with molecular hydrogen is associated with the distinct roles of proton chemistry and enzyme 11620



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chemistry of H2 and D2.3,6,9−12,31−33 The following types of interactions are distinguished: (A) In the absence of other substrates, the protons are reduced to dihydrogen that can be fully suppressed by most other substrates. This process is known as general hydrogen evolution.3,37−40 (B) Molecular hydrogen is always produced during N2 turnover (when nitrogenase reduces N2 to NH3) as a side product (eq 3), commonly referred to as obligatory hydrogen evolution (OHE).40 (C) H2 is a competitive inhibitor of N2 turnover (competes with nitrogen for an active site of nitrogenase),39 but of no other substrate, except diazene (N2H2).8 There is no H2-inhibition when the enzyme reduces hydrazine (N2H4), which is another relevant substrate-intermediate of N2 reduction by nitrogenase.2,3 (D) The HD exchange reaction further connects N2 and H2 to nitrogenase.9−12,37−40 The molecular hydrogen evolved in the course of OHE also contains HD when D2 is added to the N2 gas-phase, as observed by Burris and co-workers.9 The conversion of D2 to HD occurs in the presence of N2, and of no other substrate, and requires one electron per HD formed, as resulted from biochemical balance studies.11 This is in contrast to the hydrogenase-like D2/H+ exchange that requires no electrons.10a,11a The exchange mechanism is ruled out for nitrogenase based on a much slower rate of T+ incorporation (from T2) into the aqueous phase (less than 2.4% of the rate of HD production in a parallel reaction under D2).11a Electrons appearing as HD are diverted exclusively from NH3 formation, and therefore, concomitant H2-evolution is not affected (cf. eq 3). Bulen proposed to consider HD formation and H2inhibition as different manifestations of the same molecular process.11b,37,39 More recent experiments on the N2/H2(D2) chemistry of modified FeMo-proteins by Newton and co-workers reopened the question of the nature of the required reduced-nitrogen intermediates to explain the dichotomy between the H2-inhibition and HD-formation processes.32a (E) There is another, less studied reaction for the production of H2 by nitrogenase described by Liang and Burris that releases a burst of H2 when the nitrogenase activity is initiated.38b,c This is a singular fast reaction that occurs after the components of nitrogenase are mixed, followed by the slower, steady-state production of H2. The H2 burst is considered to be a noncatalytic event resulting from a single activation process. According to the above-mentioned Lowe−Thorneley kinetic scheme,31 H2 is obligatory released when N2 binds to the cluster, and displaces the bound H2, thus accounting for the fixed stoichiometry. It has been proposed2 that E3H3 (three electrons/protons are transferred to the enzyme, vide supra) is a metal hydride species represented by E3H2(H), which is activated via protonation by an adjacent amino acid side chain. H2-evolution is thought to occur via the reaction of a hydride ligand with a proton bound to the amino acid (see also ref 40c). The formation of mono-, di-, and trihydridic intermediates are also suggested to play a key role.11a,26b Computational models demonstrated that OHE occurs when the H2-elimination becomes energetically viable during the successive protonation/reduction (PR) of the coordinated

nitrogen.6,21a,22,23 Different models suggested different sources and types of hydrogen atoms to be eliminated. Siegbahn and co-workers, for instance, suggested to consider H-atoms attached to bridged sulfur ligands as potential candidates in obligatory H2 formation.20 In the Rod−Nørskov model, the molecular hydrogen is simply eliminated from the cleavage of Fe−H and S−H bonds,21a whereas the H2-elimination mechanism developed by McKee combines the Fe−H and X−H bonds (X being an interstitial atom, N, or C) in an opencage model.22 A comprehensive mechanistic model of the hydrogen chemistry of the active site of nitrogenase was developed by Dance. 6a The coordination of different combinations of H and H2 on the two types of S and Fe atoms of FeMo-co (endo- and exo-positions) have been characterized. According to this model, the accumulation of Hatoms (e− + H+) on FeMo-co starts from a water chain to one of the μ3-S atoms. The generation of Fe−H2 complexes has been shown to have different reaction profiles of the Hmovements. In addition, an intriguing allosteric influence of the coordination of one Fe on the structural and dynamic aspects of another Fe has been revealed, which is consonant with the earlier reports of Siegbahn and co-workers concerning the favorable coordination of N2 to an iron atom when an adjacent sulfur center is protonated.20 The results of Dance6 may serve as an excellent basis for further development of DHC mechanisms presented in the current article. Yet, dihydrogen catalysis reactions involve more complicated hydrogen chemistry stemmed from the synchronous processes discussed in the next sections. Overall, despite the significant progress in the area of nitrogenase reactivity, the atomistic explanation of H2inhibition and HD-formation reactions remains controversial. The central point of the controversy constitutes the chemical nature of the species involved in these processes.32,12 Some features are best described in terms of HD formation mediated by a partially reduced N2 intermediate40 such as diazene,11a whereas others fit in the metal (mono-, di-, and tri-) hydridic intermediates formation, relevant to the Lowe−Thorneley scheme.9,11a,26,31 In diazene mechanism, initially proposed by Burris and coworkers9 and further developed by Burgess and co-workers,11 diazene is considered as a mediator in HD formation: N2ase + N2 + 2H+ + 2e− → N2ase[N2H 2]

The enzyme bound N2H2 decomposes and leaves behind a N2bound enzyme when attacked by D2: N2ase[N2H 2] + D2 → N2ase[N2](or N2ase + N2) + 2HD

In Durrant’s theoretical N2-activation model, both a reduced N2 species and a metal hydride as intermediate are invoked.12 However, the diazene mechanism has been ruled out because of the high activation barrier of 69 kcal mol−1. The HD formation has been suggested to explain by scrambling of H2 with a hydridic H-atom located at the same Mo-center, assuming the facile formation of the mixed hydrogen-hydride complex MoH(D2). The approximate barrier for such a scrambling has been estimated to be 23 kcal mol−1.12 In the current article, among a variety of novel pathways, we have explored also a similar pathway for the decomposition of a bound diazene coordinated to an iron center resulting in a much lower barrier of activation, which makes this mechanism rather competitive. The above-described data indicates an intricate and not yet completely clarified mechanism for the interaction of molecular 11621



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maintain the unusual, yet typical for nitrogenase, trigonal Sligated iron centers (section 3.2.4, Scheme 4). Two iron centers are connected via μ2S or μ3S bridges. Such a binuclear model, alone or in combination with Mo,25b has been used in modeling N2 reduction by nitrogenase.20−22 A more hypothetical Fe3model (Scheme 5) is tested to demonstrate the validity and feasibility of molecular hydrogen mediated reactions between far-away reaction centers, which otherwise could not react directly due to steric and distance constraints. Some general mechanistic implications are discussed in section 4, followed by the main conclusions in section 5. The results of a detailed comparative analysis of the selected DHC reactions by DFT and ab initio methods are presented in the Appendix.

hydrogen with nitrogenase during N2 activation. The DHC mechanism developed in the current article proposes several protocols based on elementary reactions, which generate either two or one HD molecules per attacking gas-phase D2 molecule. The first type of reaction has the same stoichiometric parameters as the above experimental models of HD formation. It implies the consumption of two electrons (one electron per HD), in line with the main conclusion from almost all experimental models.8,11,37 The DHC mechanism also suggests the formation of one HD molecule resulting only in the redistribution of electrons (alteration of the oxidation numbers of TM ions). There are also options for D2 to form prereaction dihydrogen complexes or generate various prereaction van der Waals complexes (involving N2H2 or other substrates and extraligands) before a cyclic DHC reaction occurs. The present article is designed to demonstrate various features of the H2-catalysis (pathways) in the degradation of intermediates of nitrogen reduction (coordinated and free [NxHy]-species). The removal of significant intermediates is assumed to suppress the overall N2-reduction, providing a theoretical explanation for the experimentally observed inhibition of nitrogenase function by molecular hydrogen as well as the HD formation from D2. The main goal of the current article is to examine the relevance of the DHC mechanism, rather than the detailed modeling of the nitrogenase functions, which is currently in progress. It is obvious that the natural FeMo-co operates in a cooperative effort of all seven sulfur-ligated Fe and one Mo atoms, yet many mono- and bimetallic biomimetics were successfully synthesized to activate N 2 (vide infra).10,26−28,33,44−46,74a The interstitial nitride or carbide moiety (suggested recently to be a carbon atom69a,b) also plays a decisive role in the alteration of the oxidation state and electronic environment of transition metal atoms. Recognizing that iron is involved in a variety of enzymatic and heterogeneous catalytic processes,2−7,26−28,42 we have examined various heterogeneous DHC models based on Fe-organic complexes. Several straightforward six-membered ring transition state DHC models are first examined. They involve the Me2FeH2 metallocomplex, which is a donor of hydrogen atoms provided by the Me2Fe bare-complex (section 3.1, Figure 3). Then, two main scenarios involving free and bound diazene intermediates combined with a bare iron-sulfide (HnS)2Fe cluster (as the simplest model of the nitrogenase active center20−22,24) are considered. Scenario I involves the interaction of a free N2H2/ N2D2 molecule (released into solution or loosely bound) with a donor of hydridic hydrogen atoms (HS)2FeH2 and its decomposition into elemental nitrogen and hydrogen with concomitant formation of H2/HD (section 3.2.1, Scheme 1). Scenario II examines the attack of a molecular hydrogen (D2) on a bound diazene moiety of (HnS)2FeN2H2 resulting again in the formation of elemental gas-products (section 3.2.2.1). As an alternative to Scenario II, several reaction pathways involving a transition metal in an extended ring transition state (endocyclic TS) with fairly low activation barriers are also developed (section 3.2.2.2). A distinct dihydrogen catalysis pathway for degradation of nonhydridic intermediates, based on the H2mediated H-atom transport mechanism (HAT), is further described in section 3.2.3. The DHC mechanism is also applied to other intermediates than diazene (various surface bound ∼[NxHy] systems) using more complex and biorelevant binuclear models, which

2. METHODOLOGY AND COMPUTATIONAL DETAILS The near-degeneracy effects due to the formation of d-bonds, the strong dynamical correlation effects from the tightly packed electrons of the d shell, and the non-negligible relativistic effects are the main constraints (highlighted particularly by Siegbahn52), which produce difficulties in the theoretical treatment of transition metal systems. Single reference wave function methods encounter most difficulties, and a multireference based theory with a large active space and an extended basis set is needed to properly describe the d-bonds of such systems. Even though the DFT methods are single reference methods, they better account for static and dynamic correlation effects.35,53−63 In this regard, three well tested DFT functionals (hybrid B3LYP and B3PW91, and a nonhybrid BP86) along with a correlated MP2 ab initio method are employed in this article to investigate the dihydrogen catalysis reactions. The initial calculations were performed at the B3LYP hybrid DFT level47 using the Dunning−Hay double-ζ basis set48a and the Los Alamos effective core potential (ECP) for Fe (the scalar relativistic LanL2DZ basis set),48b as implemented in Gaussian03.49 To evaluate the basis set and ECP effects on the energy profiles of reactions, the full electron triple-ζ 6-311++G(2d,2p) basis set was employed including diffuse functions to account for long distance interactions, and polarization functions to treat properly the flexible angular charge distributions for the key reactions. The SDD basis involving the Dresden/Stuttgart pseudopotential for iron atoms50 was also utilized for comparison. In SDD basis set, 10-electron core of Fe atoms were replaced by a scalar relativistic ECP using the 6s5p3d1f basis set (MDF10). Even though the extended 6-311+G(2d,2p) basis set has been proven to be effective for the first row TM,51 including the modeling of nitrogenase,20 we have augmented further this basis set with additional diffuse functions on hydrogen atoms to increase its flexibility in treating the DHC reactions, which involve multihydrogen interactions in TS. The B3LYP method combines the nonlocal Hartree−Fock exchange functional along with the corrective terms for the density gradient developed by Becke47a with the LYP correlation functional of Lee et al.47b recommended by a group of Gaussian coauthors (see also the Appendix).47c This method was well tested, particularly by thermochemical and transition state calculations, similar to those used in the current article.20,35,53−55,60b However, the individual DFT methods, including the B3LYP method, are known to have some limitations in evaluating the absolute values of formation enthalpies of organic molecules and metallocomplexes when atomization energy based approaches are used,56c,57,58 in contrast to those based on isodesmic reaction procedures, as 11622



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stressed earlier in a detailed analysis.57 Nevertheless, the B3LYP functional is quite suitable for elaboration of mechanisms and relative energy values.53,54,57−60 Quite recently, Simón and Goodman re-evaluated DFT functionals and found that the B3LYP functional is still suitable for transition state calculations of practically important systems.53 The performance of B3LYP functional for 13 metal−ligand bond lengths, including the Fe− S bond, was ranked fifth in the test of 42 functionals, as noted by Truhlar and co-workers.55 This functional in conjunction with the full electron 6-311+G(2d,2p) and the LanL2DZ basis sets have been successfully used by Siegbahn and co-workers for a nitrogenase modeling involving the di-iron and truncated cluster (neutral and negatively charged) calculations.20 It is worth noting that the B3LYP method provided reasonable energies for simple TM complexes, which usually are in highspin states in their ground states.63b This is important for the current study where various spin state PES are explored. In addition, the best results have been obtained for Fe, Zn, and Co compounds linked to H, F, O, and S ligands,63b which constitutes basic atomic combinations of concern to us (Fe with H and S as ligands). A set of stationary points have been calculated using the pure GGA BP8663a and the hybrid B3PW91 functionals.47a,56a The BP86 functional has been chosen because of its good performance in a variety of organometallic systems,63b−d whereas the hybrid GGA functional B3PW91 has been proven to provide suitable results in predicting the oxidative addition of H2 to Fe(CO)4 and other Fe(0) compounds.38b,55 B3PW91 is also known to be successful in more correlated systems such as metals and small-gap semiconductors and, importantly, in evaluating systems with different spin-multiplicities.56c,62 A detailed account of comparative results is presented in the Appendix. We note that DHC barriers calculated at B3LYP and B3PW91 hybrid functional levels appear to be remarkably close to each other, but they differ somewhat from those provided by the pure GGA BP86 and MP2 methods. The MP2 method is costly and has convergence problems, as often stressed in the literature on metallocomplexes.59c,64 The energy barriers calculated in this article, denoted ΔE‡, are based on the electronic energies corrected for the zeropoint vibration energies calculated at the same level of theory. The initial calculations were performed using the B3LYP/ LanL2DZ method, which is cost-effective, convergent, and yet fairly consistent. The significant reaction profiles were recalculated using the all-electron and SDD basis sets for comparison. All results presented in this article are at the B3LYP/LanL2DZ level unless otherwise specified. The stationary points have been determined by vibrational analysis (the TS modes are sketched in the relevant figures for clarity). The intrinsic reaction coordinate (IRC) procedure is employed to identify the connectivity between the stationary points across the PES. The final scanning point structures were fully optimized to ensure that a reaction through the saddle point leads to the proper reactants and products. The effect of an ultrafine grid is considered in the B3LYP calculations for typical reactions with no noticeable improvements in results (being only twice as much time-consuming), in agreement with the results of Simón and Goodman.53 The effect of basis set superposition error (BSSE) was not included. It has been found only to be of the order of ∼1 kcal mol−1 for simple TM complexes.63d 2.1. Model Selection. The main goal of the current study is to elaborate general DHC pathways on the basis of detailed

analyses of the respective potential energy surfaces. Small model reactions are computationally less demanding and allow exploring in more detail the intricate multidimensional PES. Various low-spin (spinless, S = 0) and higher-spin (S = 1, 2, 4, and 5) neutral and ionic reaction systems were examined using iron-based model clusters. The initial focus of this article is the reaction of diazene with the straightforward single-iron tetrahedral catalyst (CH3)2FeH2 as the source of two hydridic hydrogen atoms employed previously.1,16 Such a simple metallocomplex model involves the preactivated Fe(IV) and Fe(III) iron centers in neutral and anionic systems, respectively. These by no means are models for nitrogenase but were selected merely to examine various Feclusters and to identify general trends in DHC reactions. However, such systems are widely involved in the development of relevant biomimetics. In a recent study by Peters and coworkers,46a a methyl ligated iron system serves as a basic compound in the synthesis of a new class of iron-complexes, which contains, essential for nitrogenase, the S−Fe−N2 linkage supported by a hydridic ligand. The protonation of a methyl ligated center results in the loss of methane followed by binding of N2. Methyl ligated systems are of particular interest in hydrocarbon reactions mediated by iron-based catalysts.70 Fe(CH3)2+, H−Fe+−C2H5, and (H2)Fe(C2H4)+ ions are wellknown intermediates in the C−H and C−C bond activation reactions.65 They can serve as models for dihydrogen-todihydride transformation mechanisms.19a,41a,66a Methyl ligands may also contribute to the understanding of agostic (C−H− metal, three-center) stabilizing interactions.66b We note that H-atoms are strong-field ligands when coordinated to an iron center, and together with the σ-donor effects of methyl groups, they generally provide low-spin configurations of complexes. In contrast, the simplest FeH2 hydride, and the supercomplex FeH2(H2)3 trapped in a laserablated experiment,66c prefer quintet and triplet electronic configurations, respectively. These results justify the additional focus on the effect of multiplicity of iron complexes on the DHC-performance. To model various features of biorelevant catalytic active sites, the (weak-field) sulfide ligated systems are considered, initially based on a simple (HS)2Fe skeleton. This system is well tested in literature, particularly in the modeling of N2-coordination to nitrogenase.12,20,21a The Fe-atom in the neutral (HS)2Fe has a formal oxidation state of +2 with the highest spin multiplicity of 5 (S = 4/2). An iron center bearing additional hydridic atoms may have various oxidation states dependent on the local charge distribution and ligand environment. Various combinations of (−S−), (HS−), and (H2S−) groups representing the sulfide, thiolate, and thioether ligands, respectively, were used to construct different formal oxidation number iron atoms.20 The DHC mechanism implicates different coordination features and spin configurations. For single-Fe models, we considered a low-spin singlet (S = 0) and higher-spin triplet and quintet spin states. The following mononuclear systems are in particular considered (see Tables 1 and 2 and other complexes specified in the text): [Fe(SH)2 (N2H 2)] [Fe(SH 2)2 (N2H 2)] [Fe(SH)2 (N2H3)] 11623

Q = 0; S = 0, 1, 2 Q = + 2; S = 0 and S = 1 Q = + 1; S = 0 and Q = 0; S = 1/2



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Figure 3. Transition state structures of selected singlet state DHC reactions (eqs 4−6) involving the interaction of a straightforward catalyst (Me)2FeH2 with (a) two hydrogen molecules and (b) diazene (cis-N2H2) and (c) methylenimine (H2CNH) intermediates.

[Fe(SH)3 (N2H 2)]

Q = + 1; S = 0, 2

[Fe(CH3)2 (N2H 2)]

Q = 0; S = 0, 1

[FeH(SH)2 (NNH)]

Q = 0; S = 0, 1, 2

[FeH(SH)(SH 2)(NNH)] [Fe(SH 2)2 (NNH)]

The transition metal hydride (Me)2FeH2 serves as a dihydrogen donor H2-catalyst (DHC) in the following set of reactions:

Q = 0; S = 0, 2

(5)

The formal oxidation state of iron ions in the initial complexes is +4, which is reduced to +2 in products as a result of DHC-mediated reductive elimination of H2 (the net removal of two hydridic H-atoms) with the regeneration of the hydridic active centers (Scheme 2) Scheme 2. Reductive Elimination of Dihydrogen

The Fe(IV) oxidation state is primarily considered here to maintain the overall cluster neutrality. However, the +3 oxidation number arises when a negative charge is placed on the cluster (vide infra). Fe(III) is more relevant to the common understanding of the charge distribution in nitrogenase, which is currently under active debate. The uncertainty comes from different interpretations of the lowest energy states in the resting and redox states. According to the common view,24 seven iron centers in the resting state of nitrogenase are distributed as 4Fe2+3Fe3+, whereas a recent alternative suggests that the 2Fe2+5Fe3+ allocation better satisfies the available experimental data.60a It should be, however, emphasized that an iron ion in a higher oxidation state may well operate in an activated state of a catalyst (particularly, nitrogenase) when an undercoordinated iron center becomes stabilized by interacting with a π-acceptor or σ-donor extra ligand with an appropriate energy of their redox orbitals. The Fe(IV) oxidation state can be assigned to intermediates of numerous processes.44−46 The high oxidation state iron complexes with terminal nitrido ligands have been well characterized spectroscopically.45b−e,46b,c Some nitrides of transition metals, that decompose with acids to form ammonia, are known for several decades to form in solutions when a TMcomplex interacts with a strong reducing agent.27,28 Femediated Chatt-cycle for the reduction of N2 to NH3 involves the sequential hydrogenation of a distal and proximal nitrogen atoms of an end-on coordinated N2 resulting in the conversion of Fe(I) to Fe(IV) and vice versa.3,26,46b In this case, the nitrido

[H(H 2S)Fe(μ2 SH)2 Fe(SH)NNH] (S = 1/2 and 3/2)

[(H 2S)Fe(μ2 S, μ2 SH)Fe(SH 2)NNH] (S = 0)

H(H 2S)Fe(μ2 S)2 Fe(SH 2)NHNH 2 and [(H 2S)Fe (μ2 S)2 Fe(SH 2)N2H 2]

Me2FeH 2 + cis‐N2H 2 = Me2Fe + H 2 + H 2 + N2

(6)

Several complexes relevant to the nitrogenase binuclear models (tested in the literature20,21b,22,60b) involving μ2S- and μ3S-bridged complexes of various spin-multiplicities, such as the complexes [(H2S)Fe(μ2S)2Fe(SH2)N2] and [H(H2S)Fe(μ 2 S) 2 Fe(SH 2 )NNH], were examined to obtain more quantitative and validated results. The highest molecular spin of 10/2 in these complexes is distributed unequally between two iron centers (S = 5/2 and S = 3/2 for the Fe-centers linked to the H and HNN ligands, respectively) with two remaining unpaired electrons located on the μ2S -bridging atoms (Figure 9). The following binuclear electroneutral complexes were also examined (Scheme 4):

and [(H 2S)Fe(μ2 S)2 Fe(SH 2)N2]

(4)

Me2FeH 2 + CH 2NH = Me2Fe + H 2 + H 2 + HCN

Q = 0; S = 0, 1

and [(H 2S)Fe(μ2 SH)2 Fe(SH)N2]

Me2FeH 2 + H 2 + H 2 = Me2Fe + H 2 + H 2 + H 2

(S = 0 and 1 )

In addition, a neutral spinless three-iron center model was employed to demonstrate the possibility of DHC reactions between otherwise inaccessible remote active centers. The reagent and the product are correspondingly represented by the complexes [H(HS)Fe(μ2S,μ2SH)Fe(μ2S,μ2SH)Fe(SH)NNH] and [(HS)Fe(μ2S,μ2SH)Fe(μ2S,μ2SH)Fe(SH)N2] (Scheme 5).

3. RESULTS AND DISCUSSION 3.1. DHC on the Straightforward Model Catalyst (Me)2FeH2. Figure 3 illustrates three transition states involving the organometallic complex Me2FeH2 as donor of hydrogen atoms with features similar to those encountered in the gasphase reaction 1a. These TS have been determined on singlet PES for reactions with diazene (HNNH) and methylenimine (CH2NH), which are intermediates in the reduction of N2 and HCN substrates, respectively,2−6 as well as for the plain DHC reaction with two hydrogen molecules. 11624



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complex >Fe4+N bearing an iron(IV) serves as a key intermediate. Such a scenario has been pointed out by Schrock for a Mo-centered system,27 assuming that a single-iron site can accommodate electronically distinct π-acidic N2 and π-basic nitride (N3−) and imide (NH2−) ligands.46b The feasibility of N2 fixation via a single-site Fe(I)/Fe(IV) cycle has been demonstrated recently by Peters and co-workers based on the terminal iron(IV) nitride species. A diamagnetic Fe(IV) trihydride system [PhBPiPr3]Fe(H3)(PMe3) has been thoroughly characterized.46b It is well established also that Fe(IV) plays the main role in various bio-oxidation processes via the formation of ferryl intermediates >Fe4+O.67,68 In addition, a variety of stable high oxidation state synthetic iron compounds were also explored.46c Inspired by unprecedented formal three-coordinate near planar geometry of the six μ3S-bridged iron atoms in the FeMoco cluster (cf. Figure 2), several mononuclear Fe-complexes with tripodal S-ligands in various oxidation states of the iron atoms, such as [Fe4+Cl(PS3)] complex and derivatives, have recently been synthesized and characterized.45b On the basis of the above discussion, various single iron DHC models with similar electronic environments are developed in the current article described in section 3.2. The dihydrogen catalysis of the [FeN2H2(HS)3] complex is an example of such processes (see Table 1). We note that Fe(IV) provides a required oxidation state for a binuclear iron site of the intermediate X of class I ribonucleotide reductase, being linked to two μ-oxo bridged oxygen ligands.46d It serves also in the di-iron(IV) core of the intermediate Q of the soluble methane monooxygenase proposed by Xue et al.46e In the similar binuclear models examined by us in section 3.2.4, the μ2-sulfur bridges are employed instead of the oxygen ones. 3.1.1. Decomposition of Diazene (N2H2). Three diazene (diimide) isomers exist: trans-N2H2, cis-N2H2, and iso-diazene (aminonitrene), NNH2. The most stable is the trans-diazene (formation enthalpies at 298 K are 49.1, 54.1, and 73.3 kcal mol −1 , respectively, calculated at CCSD(T)/CBS+ZPE (CCSD(T)/aug-cc-pVTZ level of theory, as we reported previously1). The main focus of the current article is the cisisomer (the term diazene is referred to cis-N2H2 throughout the current article, unless otherwise specified), which appears to be the most important isomer in considered stereoselective DHC reactions. Note that trans-diazene along with iso-diazene also obey general DHC rules, as detailed elsewhere.16 However, such reactions involve more strained smaller size transition states (one H atom remains off-cycle in H2-assisted H-atom transfer reaction of trans-diazene to iso-diazene, while isodiazene undergoes H2-assisted H2-elimination reaction via a 5membered ring TS that includes a terminal N-atom), and the processes require higher barriers of activation. 3.1.1.1. Reaction 5. As expected, the barrier height for the catalytic decomposition of cis-N2H2 on a methyl ligated cluster Me2FeH2 (eq 5) is fairly low, 10.6 kcal mol−1, calculated at the all-electron B3LYP/6-311++G(2d,2p) level compared to the 26.4 kcal mol−1 value for the gas-phase reaction 1a obtained previously at the CCSD(T)/CBS+ZPE(CCSD(T)/aug-ccpVTZ ab initio level1 (see Table A1 of the Appendix for more details and comparisons). In overall, the utilization of LanL2DZ basis set, which employs an effective core potential (ECP) for the inner electrons of the iron atoms and a double-ξ quality Huzinaga−

Dunning basis set for the remaining the atoms, predicts a 6.1 kcal mol−1 activation barrier for the organometallic reaction 5. Remarkably, the hybrid B3PW91 method applied to this reaction predicts a barrier, which is almost identical to that obtained by the B3LYP method combined either with the LanL2DZ or the 6-311++G(2d,2p) basis sets (viz., 6.1 and 10.9 kcal mol−1 versus 6.1 and 10.7 kcal mol−1, respectively). However, the results based on the SDD basis set are in this particular case consonant with the all-electron values (10.4 and 10.8 kcal mol−1, respectively). The BP86 values are significantly lower for both basis sets employed, as for the simple gas-phase reaction (eq 1-A, Appendix 1). The MP2/6-311++G(2d,2p) method predicts a reaction profile consistent with DFT, but the barrier appears to be substantially lower at 1.3 kcal mol−1. Interestingly, the barrier height of 25.3 kcal mol−1 predicted by MP2 method for the simple gas-phase reaction is in good agreement with both hybrid DFTs as well as the benchmark CCSD(T)/CBS (26.4 kcal mol−1) and composite CBS-QB3 (22.5 kcal mol−1) values.1 We note also that, the barrier for the all-hydrogen reaction (eq 4) is quite high (ΔE‡ = 59.8 kcal mol−1). The reverse reaction barrier is lower by 9.1 kcal mol−1. The solvent (H2O) effect is almost negligible as results from B3LYP(IEF-PCM)/ LanL2DZ calculations (the barrier is reduced only by 0.5 kcal mol−1; see Supporting Information). All these indicate a low ability of TS to become stabilized either by a ligand or by a solvent environment, in contrast to reactions 5 and 6, which involve more electronegative reactive centers. The endothermicity of reaction 4 is in contrast with the majority of DHC reactions considered in this article, which are mostly exothermic, except for the cationic counterpart of reaction 8 discussed in section 3.2.2 (see Figure 5). More specific ligand environments reduce the barrier dramatically (see also ref 16). The transformation of H2CNH intermediate back to the HCN substrate of nitrogenase proceeds, for instance, much easier via a polarized transition state (ΔE‡ = 25.1 kcal mol−1). 3.1.1.2. Anionic Reaction 5b. A periodic DFT study of Red and Nørskov21a follows that the coordination of an extra-ligand (e.g., CO) to a central sulfur of the FeMo-co cluster becomes much stronger when a negative charge is placed on such a cluster. This is in-line with the proposal of Lee, Hales, and Hoffman7 and a suggestion of Noodleman and co-workers that the active site of nitrogenase is negatively charged in its relevant oxidation state.24b Therefore, it is important to know whether the DHC reaction mechanism is affected by ionization. The four-coordinate iron center in the negatively charged [(Me)2FeH2]− reagent of reaction 5b is in a +3 formal oxidation state, more relevant to nitrogenase. During a typical reductive (H2-assisted) hydrogen elimination, it is oxidized to Fe(I). [(Me)2 Fe3 +H 2]− + cis‐N2H 2 = [Me2Fe1 +]− + H 2 + H 2 + N2

(5b)

Calculations demonstrated that the anionic reaction maintains the general features of the DHC reaction 5. However, it occurs much easier than its neutral counterpart, even though the neutral reaction involves a higher-energy reagent bearing Fe(IV). In addition, a prereaction van der Waals complex is formed at the entrance channel of PES, which is significantly more stable than the isolated reactants (by about 22 kcal mol−1 at the B3LYP/LanL2DZ level). Then, a small barrier arises (1.8 11625



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and 3.1 kcal mol−1 at B3LYP/LanL2DZ and B3PW91/ LanL2DZ levels, respectively) leading to the same gas-phase simple products plus an anionic bare catalyst Me2Fe−. These initial results clearly demonstrate that the local charge distribution may substantially modify the DHC reaction profile retaining, however, the general mechanistic features (see also section 3.2.2). We note that none of the methyl ligated straightforward models intended to mimic the nitrogenase functions; they have been examined merely for the better understanding of the mechanisms of DHC reactions. However, similar reactions may well occur in various catalytic processes involving hydrocarbons and Fe-based compounds.70 3.2. DHC on Thiolate and Thioether Ligated Models. Inorganic sulfide (−S−) as well as thiolate (−S−R) and thioether (R−S−R) ligands attached to an iron and other TMatoms are widespread in biology. Such moieties are also present in nitrogenase.43 To explore the mechanism of DHC reactions generated on S-containing complexes, various mono-, bi-, and trinuclear models were developed. First, a mononuclear (HS)2Fe structure was employed (the methyl ligands in the model were replaced with SH-groups). Despite the simplicity, such a model has been successfully used in literature to examine the general trends in the reduction of nitrogen to ammonia.20−22 These π-donating, weak-field ligands typically generate high-spin complexes possessing long Fe−L bonds, which are also relevant to nitrogenase.46,71 On the basis of ligand field considerations (weak-field sulfide donor set, with a coordination number less than five), it is commonly considered that the iron centers of the FeMo-co cofactor (MoFe7S9X cluster) possess their high-spin configurations.2−8,23 They are coupled ferromagnetically forming a low-spin complex with many localized singly occupied orbitals.24 To treat such a spinpolarized system, a DFT method called “broken symmetry plus approximate spin-projection” (BS-DFT) has been developed, which places α- and β-electron densities in different special regions and generates mixed spin-symmetry states with lower space-symmetry (broken symmetry).24a A detailed comparison of BS and high-spin approaches, applied to the hydrogenation reaction of (HS)2Fe to (H2S)2Fe, has been performed by McKee using the B3LYP/6-311G(d,p)/ECP(Fe, SDD) density functional theory.22 Despite geometry changes, the calculated energy differences appear to be close for both the high-spin and the broken symmetry solutions.22 It was concluded that the high-spin systems constitute an adequate model to represent the mechanism of a reaction on a cluster with low overall spin but with local high-spin configurations. Such an approach, employed also in the current work, allows reducing the severe SCF-convergence problems, leaving, however, uncertain the possible change of the multiplicity for different parts of the PES dependent on the degree of coupling of the iron atoms with their oxidation states.22a There are numerous possible [NxHy] species coordinated to a single-iron center, which can be considered at every stage of N2-reduction. A new class of model compounds containing a S−Fe−N2 linkage of the trigonal bipyramidal local symmetry has recently been synthesized by Peters and co-workers.46 Mononuclear and binuclear iron complexes possess both N2 and sulfur ligands in the immediate iron coordination sphere of iron atoms featuring the S−Fe−N2 linkage in nitrogenase. The addition of a hydride donor moiety further increases the reactivity of iron centers. Computationally less demanding small models allow elucidating different aspects of nitrogenase

structure and reactivity.20,21b,44−46,74 In this section, various mononuclear models were constructed involving reactions between FeSnHm complexes with N2H2-cis and other substrates, as well as reactions of dihydrogen with coordinated [NxHy] intermediates. Several pathways were calculated for the degradation of bound diazene to examine whether the DHC mechanism is relevant to the inhibition of N2-reduction by molecular hydrogen (see introduction). Two possible submechanisms (scenario) were particularly analyzed. Scenario I corresponds to the interaction of a free (liberated or loosely coordinated) N2H2 with the hydridic (HS)2FeH2 center of a metallocomplex leading to diazene degradation (destruction) and formation of N2 and H2. The attack of molecular hydrogen on N2H2 group coordinated to the bare-catalyst (HS) 2 Fe, viz., the (HS)2FeN2H2 complex constitutes Scenario II, which also produces gas-phase H2 molecules via a hydrogen-assisted dehydrogenation of coordinated [NxHy]. The generated N2 remains weakly bound to the catalyst, hence representing the initial stage of N2-activation.31 3.2.1. Decomposition of Diazene on (HnS)2FeH2 Hydridic Catalyst. Four different pathways were identified fulfilling Scenario I, which lead to the destruction of a diazene (denoted in eq 7 and Scheme 3 as cis-N2D2 for clarity) back to the elemental gas products: (HS)2 FeH 2 + cis‐N2D2 = (HS)2 Fe + N2 + 2HD

(7a)

(H 2S)2 FeH 2 + cis‐N2D2 = (HS)(H 2S)FeH + N2 + 2HD (7b)

Scheme 3. Four Types of Diazene (N2D2) Degradation Reactions Mediated by a Model Hydridic Catalyst (HnS)2FeH2, Scenario Ia

a

Dotted lines indicate reaction coordinates in TS calculated at B3LYP/6-311++G(2d,2p) all-electron level. Reactions 7a and 7b generate two H2 molecules similar to the gas-phase reaction (1), whereas 7c and 7d singular pathways produce only one HD molecule. 11626



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Figure 4. DHC reaction profiles (in kcal mol−1) for decomposition of cis-diazene on a hydridic catalyst (HS)2FeH2 calculated at the B3LYP/6-311+ +G(2d,2p) level. The low-spin (right-hand side pathway) process is described in Scheme 3 (eq 7a). The high-spin reaction (left-hand side pathway) generates open-shell products with a HN2• radical fragment being only a component of the intermolecular complex, not a noninnocent ligand.

spin multiplicity of the metallocomplex cluster. Notably, the transition state of the triplet state DHC model is located significantly lower than its low-spin counterpart. The decomposition of diazene on a spin-less hydridic metallocomplex occurs through an activation barrier (albeit only of 5 kcal mol−1 height), whereas the high-spin state reactions proceed spontaneously via a small barrier and a shallow prereaction complex, located below the entrance channel of PES. In addition, the high-spin transition state converges to a different type of product involving open-shell HN2•. The eliminated hydrogen molecule is trapped as a ligand attached to the iron center of an intermolecular complex (Figure 4). The open-shell HNN group could be a noninnocent ligand75 if linked to the metal as it occurs in some complexes considered below (see, e.g., Figures 6−9). However, being coordinated only to ligands via two H-bonds (NH···SH and HNN···HH), the HN2• radical is not a ligand but a component of the intermolecular complex. The natural bond orbital (NBO) population analysis reveals that the spin densities in these TS are redistributed to the ligand atomic centers as a result of ligand-bonding and backbonding interactions. The polarization of bonds occurs as in the simple gas-phase model TS (eq 1a). The two hydridic H-atoms at the iron centers carry some negative natural charges (qH =

(H 2S)2 FeH 2 + cis‐N2D2 = (H 2S)2 FeHD + N2 + HD (7c)

(H 2S)(HS)FeH 2 + cis‐N2D2 = (HDS)(H 2S)Fe + N2 + HD

(7d)

DHC provides a scavenger mechanism for the possible removal of the free diazene (liberated, dissociated from the cofactor into the solution), which is known to accumulate in certain biological media,8a,77 and other [NxHy]-intermediate species mediated by the hydridic hydrogen centers of the catalyst (nitrogenase). There are experimental evidence, based particularly on the ENDOR-analysis, regarding the presence of such hydridic moieties.2 A strong coupling of two H atoms has been obtained in nitrogenase at an intermediate state of its turnover cycle.2c,36 The cis-diazene reaction with the model hydridic clusters (HnS)2FeH2 occurs with remarkably low or even no activation barriers (see Figure 4 for the corresponding low- and high-spin energy profiles). Consistent with the described above general scheme of heterogeneous DHC-reactions, all pathways generate molecular hydrogen. The mechanistic details are sensitive to the ligand environment (the oxidation state of the iron center) and the 11627



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Figure 5. DHC decomposition profile (in kcal mol−1) for dihydrogen (D2)-mediated exocyclic reaction of cis-diazene moiety of the (H2S)2FeN2H2 cluster containing two thioether (protonated at SH) ligands similar to reaction 8.

−0.11e and −0.07e), whereas the N−H bonds are considerably polarized; the protic hydrogen atoms are charged positively (qH = +0.17e and +0.23e) in the low-spin state. In contrast, the Fe−H bonds become more polarized in higher-spin state TS because of the higher ligand-bonding and back-bonding interactions and the accumulation of more positive charges on the iron center and hydridic atoms. Thus, the catalytic decomposition of diazene by a pair of surface hydridic atoms (strongly coupled hydrogen atoms2,36) is kinetically feasible, and a DHC process may well inhibit the N2-reduction of nitrogenase provided that a loosely bound or released into the solution diazene plays a functional role in the overall activation of N2. The absence of diazene in nitrogenase experiments, in contrast to the experimentally detected hydrazine, provides support for such an assumption. As a matter of fact, hydrazine does not undergo DHC catalysis (at least, we failed to localize a TS similar to that for diazene). Note that a free diazene may also undergo rapid disproportionation, if accumulated, to give N2 and hydrazine. Four distinct mechanisms have been identified, which fulfill the requirements of Scenario I. They occur with different activation energies (Scheme 3). Pathways 7a and 7b are typical DHC reactions involving two hydrogen atoms from a catalyst and lead to the generation of two H2 molecules. However, the combination of the hydrogen atoms of diazene with a hydridic (at the electropositive Fe) and a protic (at the electronegative S) hydrogen atom in reaction 7b maintains the oxidation state of the iron center unchanged. In the two other reactions 7c and 7d, one of the hydrogen atoms of cis-N2H2 interacts directly with either an iron or a sulfur atom of the complex. Again, the barriers are reduced when the polarity of TS increases (cf. Scheme 3). Notably, both reactions 7c and 7d produce only one HD molecule. In summary, all explored reactions are quite plausible and may easily occur under mild conditions, as expected for processes involving the reactive diazene. However, they may end up with different products when different spin state PES are considered. The most feasible pathways are those with open-shell systems via reactions 7c and 7d, which occur on quintet and doublet PES, respectively. The 5-membered TS ring reaction 7c requires ca. 2.8 kcal mol−1 activation energy,

which is about half the barrier for the 7a and 7b reactions (5.1 and 6.1 kcal mol−1, respectively). The last two reactions have double H-contacts with a catalyst center being characterized by a fragment {(Fe−H)2···(H−N)2}; see Scheme 3. The energy barrier for the doublet electronic state mono Hcontact reaction 7d is negative; ΔE‡ = −5.2 kcal mol−1 at the B3LYP/6-311++G(2d,2p) all-electron level. The activation enthalpy of this process (calculated at 298 K) is at the level of the entrance channel of PES, whereas the room temperature Gibbs activation free energy is significantly higher ΔG‡ = 5.3 kcal mol−1. We note that reactions 7a, 7b, and 7d lead to the formation of different adduct-complexes, whereas reaction 7c with a mono H-contact {FeH···HNNH···Fe} transition state regenerates the same organometallic compound (H2S)2FeH2 (provided that the isotopic content of hydrogen atoms remains unchanged) and serves as a conventional catalyst (Scheme 3). As indicated above, the important role of the bridging sulfides has been emphasized in the literature using a simplified computational models of nitrogenase.20,21b,22,25b This is in line with reactions 7a and 7d with an interplay between Fe and S centers. Additional calculations were performed for these systems to compare the results obtained by different methods. All DFT results appear to be close to those presented in the previous sections and, for this reason, they are not presented here. Note only that the MP2/LanL2DZ ab initio method for the particular H2-elimination reaction 7b, which involves both Fe−H and S−H centers, predicts an activation barrier fairly close to that predicted by DFT (5.7 kcal mol−1 vs 6.1 kcal mol−1). Thus, according to Scenario I, a hydrogen-donor metallocomplex can easily catalyze the degradation of a free or loosely bound diazene and eliminate this key intermediate from the reaction chain (medium) and, as a consequence, inhibit the overall turnover cycle of nitrogenase. 3.2.2. Degradation of [NxHy]-Ligated Intermediates by Molecular Hydrogen. 3.2.2.1. Exocyclic DHC. Whereas the actual contribution of a free diazene in the chain of nitrogenase intermediates has yet to be evaluated, a variety of coordinated [NxHy]-species were well identified in a variety of experimental 11628



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Table 1. Dihydrogen Catalysis (Exocyclic) for Degradation of η1-Bound cis-Diazene Intermediates

multiplicity (SH)2-ligands 1 (S = 0) 3 (S = 2/2) 5 (S = 4/2) (SH2)2-ligands 1 (S = 0) 3 (S = 2/2) (SH)2-ligandsf 1 (S = 0) 2 (S = 1/2) (SH)3-ligands 1 (S = 0) 5 (S = 4/2) (CH3)2-ligands 1 (S = 0) 3 (S = 2/2)

total charge 0 0 0 +2 0 +1 0 +1 +1 0 0

q(Np); q(Nd)a

Fe/spin

q(Fe)a

q(Hp); q(Hd)a

ΔE‡b (kcal mol−1)

Fe(II) complexes, reaction 8 −0.25; −0.08 0 +0.64 +0.16 ;+0.18 40.3 (38.2)e −0.33; −0.08 2.47 +0.81 +0.16; +0.18 38.3 (36.2)e −0.32; −0.04 3.59 +1.10 +0.17; +0.17 34.3 (31.3)e Fe(II) complexes (extra H+/H• at S atoms; cf., Figure 5) −0.33; +0.04 0 +1.13 +0.13; +0.21 29.5 TS-ring shifted to Fe (see Table 2) Fe(IV) and Fe(III) complexes (extra H+/H• at Ndistal atom) −0.21; −0.29 0 +0.67 +0.14; +0.15 64.0 −0.33; −0.41 2.35 +0.73 +0.14; +0.16 69.2 Fe(IV) complexes −0.22; +0.02 0 +0.22 +0.08; +0.09 45.5 −0.34; +0.01 3.50 +1.10 +0.15; +0.19 41.6 Fe(II) complexes −0.21; −0.15 0 +0.62 +0.15; +0.19 40.9 −0.46; −0.18 2.80 +1.10 +0.13; +0.18 38.6

ν1c (cm−1)

Θd (deg)

−1995.5 −1992.4 −1983.7

115.9 158.5 110.8

−1676.2

101.0g

−1582.9 −1868.2

157.5 160.5

−1848.8 −1893.4

103.7g 119.5

−2040.3 −1963.2

98.7g 162.9

a

Natural charges on Fe, distal and proximal N, and attached protic H atoms. bZero-point energy corrected reaction barriers. cImaginary frequencies for TS. dTrigonal wide angle at the Fe-center. eAll-electron B3LYP/6-311++G(2d,2p) results are in parentheses (the entire data are at B3LYP/ LanL2DZ level). fProtonation/hydrogenation at the distal nitrogen atom produces [−NHNH2] moiety. gH-bonding between sulfide and the proximal nitrogen atom.

studies based mainly on detailed spectroscopic analyses.2 Therefore, two new types of dihydrogen mediated reactions, which occur via exocyclic, and endocyclic transition states, respectively, have been identified and characterized (Scenario II). The first set of reactions (eq 8) involves a TS-ring moiety located in the exo-position to the Fe-center of the main cluster (see Figure 5 and Table 1). The attack of molecular hydrogen on a coordinated N2H2 moiety requires the significant potential barrier of 34.3 kcal mol−1 for the high-spin quintet state reaction (the singlet state barrier is 40.3 kcal mol−1) at the B3LYP/LanL2DZ level of theory. (HS)2 FeN2H 2 + H 2 = (HS)2 FeN2 + 2H 2

All trigonal centers in the TS of reaction 8 are nearly planar. A small out-of-plane (trigonal-pyramidal) character is present in the singlet TS of the neutral SH-ligated structure. The sum of angles at Fe-center is 328°, which decreases to 312° when SHgroups are replaced with methyl ligands. An improvement of the model catalyst via the addition of an ancillary ligand (which is not directly included in the active center of the reaction), or by replacing the existing ones, is expected to alter the reaction profiles. As noted above, the addition of an H-atom to a bridging sulfur in the nitrogenase models resulted in a significant increase in the binding energy of N2 to the iron centers.20 For this reason, additional calculations were performed to clarify the effect of complementary ligation on the barrier height. The DHC reactions involving methyl-ligated clusters behave in the same way as reaction 8. Table 1 shows, surprisingly, that there is almost no ligand effect on the relative energy of TS when sulfide groups (week field ligands) are replaced by CH3 (a strong-field, σ-donor) ligands. The barriers on singlet and triplet surfaces exhibit only small increases (less than 1 kcal mol−1): 40.9 and 38.6 kcal mol−1 vs 40.3 and 38.3 kcal mol−1, respectively. The protonation (addition of H+) or hydrogenation (addition of an H• radical/H+ + e−) of a distal N-atom, which generates a more advanced (in terms of Thorneley− Lowe kinetic steps31) coordinated ∼NH−NH2 intermediate, increases the barriers to 64.0 and 69.2 kcal mol−1 (for the protonated and hydrogenated systems, respectively). In contrast, the protonation of both (HS−) ligands (Q = +2, S = 0) to form two thioether (H2S−) groups decreases the barrier dramatically, more than a factor of 2, to 29.5 kcal mol−1 (Figure 5). These results are in qualitative agreement with the

(8)

The reverse reaction barriers are considerably higher, 60.2 and 62.8 kcal mol−1 for the quintet and singlet states, respectively. These reaction profiles are much less sensitive to the spin configuration of the initial complex than the free diazene degradation reactions on a hydridic catalyst surface (Scenario I, Scheme 3 and Figure 4). We note that the allelectron B3LYP/6-311++G(2d,2p) results for all three spinstate PES are quite consistent (lower by only ∼2−3 kcal mol−1) to those obtained using LanL2DZ basis set, which employs a core effective potential for the iron atoms and takes into account some relativistic and spin−orbit coupling effects via parametrization (see Table 1). The unpaired electron-densities on the iron centers in the high-spin configurations is about 3.5e, which is comparable to that calculated by McKee for a neutral and a cationic dimer of HFeSH using both the high-spin (S = 10/2) and broken symmetry approaches.22 11629



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Table 2. Dihydrogen Catalysis (Endocyclic) for Degradation of Hydridic η1-NNH Intermediatesa

multiplicity (SH)2-ligands 1 (S = 0) 3 (S = 2/2) 5 (S = 4/2) (SH2)(SH)-ligands 1 (S = 0) 5 (S = 4/2) (SH2)2-ligands 1 (S = 0) 3 (S = 2/2)

total charge 0 0 0 0 0 0 0

q(Np); q(Nd)b

Fe/spin

q(Fe)b

q(Hh); q(Hd)b

Fe(IV) complexes, reaction 9; cf., Scheme 4 and Figure 6 −0.08; −0.14 0 +0.38 −0.04; +0.26 −0.23; −0.16 3.20 +0.89 −0.21; +0.27 −0.21; −0.14 3.39 + +1.00 −0.18; +0.32 Fe(II) complexes, reaction 10; cf., Figure 8 HAT-mechanism HAT-mechanism Fe(II) complexes, reaction 9f; cf., Scheme 4 −0.29; −0.21 0 +0.31 −0.14;+0.17 −0.34; −0.26 2.64 +0.56 −0.23;+0.21

ΔE‡c (kcal mol−1)

ν1d (cm−1)

Φe (deg)

26.2 15.2 9.7

−1938.5 −1590.0 −968.7

90.0 88.0 78.9

28.3 18.9

−1649.8 −1467.6

33.0 24.5

−1779.3 −1785.4

104.3 94.9

a

B3LYP/LanL2DZ level. bNatural charges on iron, proximal (Np) and distal (Nd), and H-atoms attached to Fe (hydridic) and Nd (protic) centers. Zero-point energy corrected reaction barriers. dImaginary frequencies for TS. eH−Fe−N reactive angle. fSee Table A1 for higher level calculation results.

c

theoretical results of Dance6a and Siegbahn and co-workers20 who demonstrated an increased activation of molecular nitrogen coordinated to an iron center of a model nitrogenase when the S-center is hydrogenated. As seen from Table 1, the barriers for Fe(II) oxidation state complexes are relatively low, whereas higher oxidation state complexes provide higher barriers. Certain electronic parameters of TS (d-AO populations, effective charges) correlate well with the barrier heights. The decrease of the Mulliken effective charges on proximal Hatoms, q(Hp), is seen to correlate with ΔE‡, whereas the corresponding q(Hd) for distal atoms remain almost identical (Table 1). In overall, the barrier is lower when a higher positive charge is located on an iron center. As shown in Figure 5, the concurrent protonation of both sulfhydryl ligands of (HS)2FeN2H2 not only reduces the barrier (vide supra) but also changes drastically the thermochemistry of processes. The reaction becomes endothermic (by 6.3 kcal mol−1) in contrast to its neutral counterpart reaction 8 and all DHC reactions considered in this article, with the exception of the all-hydrogen reaction 4, discussed in section 3.1, which is also endothermic. Thus, the ligand protonation (double cation formation) thermodynamically stimulates the reverse reaction, which is a termolecular process. This is rather intriguing since the exothermic reverse reaction constitutes a nitrogen fixation process, which, according to these results, may occur under some circumstances. In summary, a typical intermediate of nitrogenase represented by a bound diazene cluster undergoes degradation by a dihydrogen molecule (D2) in all considered above processes with concomitant formation of two HD molecules generating weakly N2 bound complexes. The iron cluster is further reduced if N2 departs from the product complex. 3.2.2.2. Endocyclic DHC (TS-Ring Expansion to the Iron Center). The stabilization of the six-membered ring transition states (Figures 1 and 3−5) can be achieved by polarizing the TS chemical bonds. It can be accomplished by promoting the formation of hydridic H-centers instead of protic ones or by

replacing the attached reactive or ancillary ligands. However, the DHC mechanism becomes energetically more feasible when the vacant d-orbitals of a transition metal are directly involved in the TS-ring. One can see from Table 2 that such a ring expansion provides a new type of DHC reaction pathways (eq 9), with a significantly reduced barrier of activation. (HS)2 Fe(H)NNH + D2 = (HS)2 FeN2 + 2HD

(9)

Figure 6 illustrates such an expansion of the transition state ring to the Fe-center. The switch to a larger (seven membered) ring-TS implies changing the formal oxidation number of the iron ion in the reagent complex from +2 to +4, as opposed to the above-described exocyclic reaction 8. The respective data regarding the exo- and endocyclic reactions are listed at the top of Tables 1 and 2 for comparison. Thus, a switch from Fe(II) to Fe(IV), in this particular case, significantly reduces the barriers of DHC reactions. According to B3LYP/6-311++G(2d,2p) calculations, a singlet state DHC process via 7-membered ring-TS provides an activation barrier of 24.4 kcal mol−1 (vs 26.2 kcal mol−1 at the B3LYP/LanL2DZ level, Table2). The process occurs much easier when the spin-multiplicity is increased (Table 2). For instance, the quintet high-spin state reaction barrier is reduced to as low as ΔE‡ = 6.1 kcal mol−1 (9.7 kcal mol−1 at B3LYP/ LanL2DZ level) compared to its exocyclic counterpart of 31.3 kcal mol−1, calculated at the same all-electron level (Table1, values in parentheses). The results for the DHC reaction 9 of both singlet and quintet spin-states using various calculation protocols are detailed in Table A1 and further discussed in the Appendix. The participation of spin-inversion in the rate-determining steps, known as the multistate reactivity (MSR), is believed to be a key feature in organometallic chemistry of ironcomplexes.65e Obviously, the spin-crossing can dramatically affect the DHC reaction mechanisms and rate constants. As expected from Hund’s rules and confirmed by calculations, the high-spin systems (including the correspond11630



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Figure 6. Quintet state DHC reaction profile for degradation of partially reduced intermediate (HS)2Fe(H)N2H with a switch of the TS-ring to the iron center (energies in kcal mol−1). Molecular hydrogen (D2) mediates a feasible pathway to the formation of the original N2-complex, (HS)2Fe− N2, and the concomitant formation of 2HD molecules (eq 9). Schematic drawing illustrates the net reaction and Mulliken spin-densities of corresponding centers. The reagent is described as a resonance hybrid of two structures, the contribution of the structure containing NNH-radical moiety (a noninnocent ligand75) being more significant.

involving thioether ligands. The enhanced oxidation of an inring Fe-atom changes more efficiently the transition state energy. The iron center in the product of the reductive H2elimination reaction 9 is expected to possess a +2 oxidation number when the dinitrogen is loosely bound but remains virtually undistorted (RFeN = 2.224 Å, ΔRNN = 0.0005 Å, and ΔνNN = 26.5 cm−1 as compared to the isolated N2 calculated at the B3LYP/6-311++G(2d,2p) level of theory; RNN =1.0915 Å vs experimental 1.0977 Å for isolated N2). This is in accord with Holland’s interpretation developed to characterize the formal oxidation states of the end-on/side-on coordinated N2systems.34 It is based on Badger’s nonlinear correlation equation, which connects the bond lengths and the stretching frequencies of NN bonds in a series of complexes. According to Mulliken population analysis, there are three unpaired electrons with α-spin localized on d-orbitals of the high-spin iron. Since the molecular spin-state is a quintet, another unpaired electron has to be present. It is indeed present but is partly localized on the HNN-ligand. This

ing transition states) are generally more stable than the lowspin ones. The intrinsic reactivity of complexes emerges from different spin configurations, thus providing a multistate reactivity. Spin-crossing can diminish the barriers (in some cases even make them disappear) as one can see in Figure 4, which describes the DHC degradation of the N 2 H 2 intermediate. The quintet state reagent of the endocyclic DHC reaction (Figure.6) is more stable by 12.7 kcal mol−1 compared to its singlet-state counterpart. The difference is even larger for the corresponding transition states (the difference being as high as 29.3 kcal mol−1 in the favor of the high-spin state). Hence, one can conclude that the spin-crossing stimulates this type of reaction.76 In contrast to 6-membered ring TS reactions where the barrier is almost unchanged when a thiolate (−SH) ligand is replaced by a thioether one (−SH2), the barriers are quite different for 7-membered ring TS reactions, which involve a transition metal (Figure 6). The barriers are larger for systems 11631



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Scheme 4. DHC Reaction Models for Degradation (Oxidation) of [NNH]-Bound Intermediates (Scenario II) with Concomitant Formation of Two HD Molecules; Oxidation Numbers on Iron Centers Are Formalized Regarding the Spin-Less Complexes

3.2.2.3. Oxidation of More Complex Intermediates. As indicated above (see also the introduction), a variety of [NxHy]species other than diazene (N2H2) can be formed as fixationrelevant intermediates in the catalytic cycle of nitrogenase.2,3,5,8 All such species (e.g., coordinated ∼NNH, ∼NNH2, ∼NHNH2, and others) can serve as potential H-atom donors when attacked by an external H2. We have identified several DHC pathways involving some of these intermediates. In section 3.2.2.1, we already mentioned one of them, viz., the reaction of coordinated N2H3 intermediate, whose degradation requires a high barrier of activation. Figure 7 illustrates the degradation of another intermediate, the double hydrogenated distal nitrogen atom −NNH2 moiety with a fairly low barrier of activation (ΔE‡ = 29.1 kcal mol−1), producing a complex possessing a noninnocent open-shell ligand NNH. 3.2.3. Degradation of Nonhydridic Intermediates via H2Assisted H-Atom Transport (HAT). Figure 8 illustrates a second major DHC mechanism applied to the degradation of a nonhydridic intermediate (HS)Fe(SH2)NNH. The attacking dihydrogen (D2) here serves as a transporter of a terminal hydrogen atom (bound to NN as a diazenido-complex) to the iron center (eq 10), as it occurs in typical HAT-reactions introduced earlier.16

suggests that the HNN group can be considered a noninnocent ligand,75 which has a resonance-hybrid structure. The classical structure possesses +4 oxidation state iron center versus Fe3+ in the hybrid structure (see schematic drawing in Figure 6). In the endocyclic N2H2-mediated TS rings (Table 1), both atoms of the attacking H2-molecule are linked to the protic Hatoms attached to the electronegative N-atoms. The switching from a 6-membered ring TS to a seven membered one occurs through a hydridic atom, which incorporates the attractive electrostatic interactions in TS, thus stabilizing the ring and reducing the barrier (cf., data in Tables 1 and 2). The barrier decreases also because of the formation of a less strained (lower energy) 7-membered ring-TS (Figure6). The atomic charges and barrier heights are inversely related in this group of transition states. In contrast to the 6-membered ring DHC reactions described in previous sections, the effective charges of distal H-atoms in extended ring systems q(Hd) varies significantly. An inverse relationship is seen between q(Hd) and the corresponding barrier heights, ΔE‡. A similar correlation holds for the corresponding q(Fe), thus confirming the conclusion that a higher positive charge on an iron center increases the hydridic character of proximal H-atoms thus stabilizing the cyclic structure of TS and reducing the barrier height (Table 2). 11632



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Figure 7. Quintet state DHC model for degradation of intensely reduced N2 intermediate [NNH2] bound to an iron-hydride active center, H(H2S)Fe(SH)NNH2 (energies in kcal mol−1). Oxidation by dihydrogen (D2) produces a less-reduced diazenido complex, (H2S)Fe(SH)NNH, and concomitantly forms two HD molecules. Schematic drawing illustrates the net reaction producing a resonance-hybrid complex containing a noninnocent ligand,75 the NNH radical moiety (cf., Mulliken spin-densities of corresponding centers).

provide a relevant first-step intermediate of N2-reduction by nitrogenase. Two iron centers are linked through, typical for nitrogenase, μ2S-bridges (cf., Figure 2). The iron ions have typical distorted trigonal-coordination, which offers lower formal oxidation numbers. The interplay of the attached thioether (H2S−) and thiolate (HS−) groups changes the oxidation state of the corresponding center, as in the mononuclear reaction 9 described above. The initial complex can be regarded as a partially reduced dinitrogen intermediate bearing a −NNH moiety, which is bound to a Fe(III)-center in low-spin state (oxidation number assignment is more complicated for high-spin systems as is illustrated in Figure 9, vide infra). The second identical iron center is occupied by a hydridic H-atom. Molecular hydrogen (D2) mediates the elimination of these two H-atoms leading to the formation of a weakly N2-bound adduct, (H2S)Fe(μ2S)2Fe(SH2)N2, with the concomitant formation of two HD molecules (eq 11a, Scheme 4). Each iron center undergoes reduction to Fe2+.

(HS)Fe(SH 2)NNH + D2 = D(HS)Fe(SH 2)N2 + HD (10)

Destruction of the HNN-group in this particular case concurrently generates a hydridic ligand, which is attached to the iron center. The reaction occurs again via cyclic TS (Figure 8). However, the ring-size of transition state is lowered by one constituent atom compared to the corresponding H2-assisted H2-elimination reaction. Importantly, the process produces only one H2 (HD) molecule. The initial oxidation state of the iron center remains unchanged during reaction (Fe2+). A weak linkage occurs between the newly generated N2-moiety and the iron center of the product (ΔRNN < 0.001 Å). We note that reaction 10 is not an electron consuming process as it occurs in discussed above reductive elimination processes, but rather leads to the redistribution of the electron density, which may change the oxidation numbers of TM in polynuclear processes. The barriers of HAT-reactions are fairly little dependent on model details (see Table 2). 3.2.4. DHC Reactions on Polynuclear Clusters. Figure 9 illustrates the energy profile of the high-spin degradation reaction of −NNH group involved in the H(SH2)Fe(μ2S)2Fe(SH2)NNH binuclear complex. Such a model is believed to

H(H 2S)Fe(μ2 S)2 Fe(SH 2)NNH + D2 → (H 2S)Fe(μ2 S)2 Fe(SH 2)N2 + 2HD 11633

(11a)



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Figure 8. Molecular hydrogen (D2) assisted H-transport mechanism (HAT) for degradation of nonhydridic (HS)Fe(SH2)NNH intermediate bearing an [NNH] open-shell moiety (cf., Figure 7) bound to an iron center (quintet state). The schematic drawing illustrates the net reaction involving a resonance-hybrid reagent bearing a noninnocent NNH radical group (the corresponding Mulliken spin-densities are provided).

The Mulliken population analysis of the equilibrium structures of the high-spin reaction 11a suggests considering one of the ligands in the reagent-complex as a noninnocent ligand.75 The schematic drawing in Figure 9 describes the reagent as a resonance hybrid of two structures, with little contribution of the classical one due to the high degree of localization of an unpaired-electron on the NNH-group (∑ρ = 0.85 e−). Almost eight unpaired electrons are distributed between the two iron centers (ρFe = 3.78 e− and 3.52 e− for the Fe-atoms bearing H- and NNH-groups, respectively). The remaining unpaired electrons are equally localized on the μ2Sbridging atoms (ρS = 0.78 e−). These open-shell sulfur atoms can be probably described as partially noninnocent ligands, and this suggests the assignment of (II) and (I) oxidation states to the two iron centers (Figure 9). The binuclear model for DHC degradation of ∼NNH moiety (eq 11a) predicts a somewhat lower barrier compared to that of a single Fe one (e.g., the singlet state barriers are 23.2 vs 26.2 kcal mol−1, respectively). The barrier for the high-spin state (S = 10/2) reaction is even lower, 19.2 kcal mol−1 at B3LYP and 18.4 kcal mol−1 at B3PW91 density functional levels in conjunction with the same ECP basis set. Taking into account that the double bridged Fe2S2 and MoFeS2 moieties of FeMo-co (highlighted by ellipses in Figure 2) are in fact tricoordinated systems, two doublet and one quartet state model reactions were additionally developed involving the μ3S-linkages (eq 11b, Scheme4) relevant to nitrogenase. We found that the activation barriers are fairly

H(H 2S)Fe(μ2 SH)2 Fe(SH)NNH + D2 → (H 2S)Fe(μ2 SH)2 Fe(SH)N2 + 2HD

(11b)

(H 2S)Fe(μ2 S, μ2 SH)Fe(SH 2)NNH + D2 → (H 2S)Fe(μ2 S)2 Fe(SH 2)N2 + 2HD

(11c)

H(H 2S)Fe(μ2 S)2 Fe(SH 2)NHNH 2 + D2 → (H 2S)Fe(μ2 S)2 Fe(SH 2)N2H 2 + 2HD

(11d)

A DHC reductive H2-elimination has the same stoichiometric parameters as those assumed in the above mentioned experimental models of HD formation (the overall generation of two HD molecules or the consumption of one electron per HD molecule) and provides a possible HD-formation pathway. The formal oxidation number of the iron center bearing the newly generated nitrogen moiety in low-spin state is again +2 since N2 remains nearly undistorted and electroneutral (ΔRNN < 0.001 Å, ΔνNN = 26.1 cm−1) as compared to the isolated dinitrogen, whereas the Fe−N2 distance is as large as 2.223 Å. One shall note that the structure of the singlet state product of DHC degradation differs somewhat from that of the highspin state, in agreement with the corresponding single Femodel results. The NN bond in the singlet state structure has a noticeable double bond character (ΔRNN = 0.011 Å, ΔνNN = 135.2 cm−1, and RFeN = 1.804 Å), being covalently bound to the iron center. 11634



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Figure 9. Binuclear DHC model for degradation of H(H2S)Fe(μ2S)2Fe(SH2)NNH high-spin complex as a mimic intermediate of N2-reduction (energies in kcal mol−1). Partially reduced [NNH]-group and a hydridic H-atom are bound to different Fe(II) centers. Molecular hydrogen (D2) regenerates a weakly bound N2-adduct, (H2S)Fe(μ2S)2Fe(SH2)N2, with concomitant formation of two HD molecules. The schematic drawing illustrates the net reaction and localization of unpaired electrons from Mulliken population analysis. The formal oxidation states of the metals are determined based on two open-shell bridging sulfur atoms, which are best described as partially noninnocent ligands that formally provide only half an electron to each of the iron centers.

Scheme 5. Hypothetical Trinuclear DHC Model Involving Interaction of Remote Iron Centers (11-Membered Transition State) with Concomitant Formation of Two HD Molecules

close (ΔE‡ = 23.5 and 26.9 kcal mol−1 for S = 1/2 and 3/2, respectively). DHC reactions may also occur between coordinated to an iron center NNH group and a protic center attached to a μ2Sbridge (eq 11c, Scheme 4). However, this process requires the higher activation barrier of 34.3 kcal mol−1. The 11d set of reactions represents a more general tentative mechanism for the degradation of another type [NxHy]-species. See, for instance, the degradation reaction of −NNH2 moiety promoted by a single-iron model catalyst (Figure 7) with ΔE‡ = 29.1 kcal mol−1, discussed above. Obviously, the H-atoms may undergo also direct H2elimination reactions under proper steric conditions. The

calculated most favorable barriers are lower than those for the analogous DHC reactions. The singlet state reaction barrier is 14.2 vs 23.2 kcal mol−1 (eq 11a) calculated at the same B3LYP/ LanL2DZ level. However, it should be emphasized that the direct H2-elimination process requires substantial skeletal deformations and, obviously, that it is not allowed for reactions between more distant and conformationally hindered centers. Instead, a flexible hydrogen molecule (D2) facilitates such a remote interaction for both the H2-assisted H2-elimination and the H-atom transport processes. To demonstrate such a scenario, a tentative trinuclear model of DHC reaction was developed (eq 12, Scheme 5). 11635



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in HD formation. Bazhenova and Shilov argued against this mechanism for thermodynamic reasons due to the instability of the free diazene.28 Indeed, the enthalpies of formation of diazene isomers are fairly high (49.1, 54.1, and 73.3 kcal mol−1 at 298 K, for trans-N2H2, cis-N2H2, and iso-diazene (aminonitrene), HNN2, respectively, calculated at CCSD(T)/CBS +ZPE (CCSD(T)/aug-cc-pVTZ level of theory, as reported earlier).1 However, one should take into account that the free and the complex-bound N2H2 behave differently and that diazene is considerably stabilized by metal coordination, as shown by Sellmann and co-workers.10 The DHC mechanism, which is developed in the current contribution, is based on direct quantum chemical calculations of PES and provides detailed analysis of the diazene mechanism for HD formation. Durrant has examined a mechanism similar to pathway (I) considering the degradation of a bound Mo−N2H2 intermediate by H2 to N2 (bound to Mo) plus 2H2.12 The geometries of the stationary points have been calculated at MP2/6-31G(d) level followed by the single-point energy calculations at MP4/6-31+(2d,p) level. Despite the overall exothermicity (−4 kcal mol−1), this route has been found kinetically not viable (high activation barrier of 69 kcal mol−1). For the alternative Fe-centered reaction, we have identified a number of transition states with activation barriers ranging from 29.5 kcal mol−1 to as high as 69.2 kcal mol−1 (see Table 1 and section 3.2.2) with the last value comparable to that reported by Durrant for the Mo−N2H2 reaction. As repeatedly emphasized above, the barrier of pathway (I), as well as of all pathways identified in this article, are highly sensitive to the electronic environment of TM (oxidation state, spin multiplicity, and the overall charge of a cluster). It is reasonable to expect that the value reported by Durrant for the Mo-centered reaction can also be modified by model variations. Even though we have obtained much lower barriers for the activation of such processes, a precise lower limit for a Fe-centered reaction is yet to be determined by further model improvements. Mechanism (II) involves the degradation of a dissociated into solution N2H2 intermediate on a hydridic center of a catalyst. As expected for the highly reactive diazene, this reaction proceeds very fast and is dependent on model details. The high-spin reactions occur instantly (section 3.2.1). Note that pathways (I) and (II) are compatible with the experimental two electron consumption scheme discussed above11a with the allocation of one electron per HD molecule. The important issue in the mechanism (II) is the feasibility of the release of a diazene from the reaction area into the solution. From Durrant’s data that employed a truncated FeMo-co model, such a process requires about 44 kcal mol−1 energy when Mo is considered as the active center. The two remaining reaction schemes, (III) and (IV), are concerned with the partially reduced species from the N2fixation processes. They involve the interaction of molecular hydrogen (D2) with diazenido [−NNH] intermediate, a protonated (hydrogenated) form of N2. The first protonation step is the most unfavorable, and yet, it is the most important one in the overall activation of nitrogen (see introduction), and the degradation of this intermediate will certainly suppress NH3 formation. Pathway (IV) provides the unique option of shifting back this partially reduced intermediate toward the preceding state in the Lowe−Thorneley kinetic scheme, viz., to the formation of unreduced-coordinated N2 (eq 10). This process generates simultaneously a novel hydridic center. The particular

H(HS)Fe(μ2 S, μ2 SH)Fe(μ2 S, μ2 SH)Fe(SH)NNH + D2 → (HS)Fe(μ2 S, μ2 SH)Fe(μ2 S, μ2 SH)Fe(SH)N2 + 2HD

(12)

Despite the additional geometrical constraints, the barrier appears to be comparable to that of the binuclear DHC reaction on a singlet state PES (22.2 vs 26.2 kcal mol−1, respectively). Importantly, the general reaction features also remain completely the same. The somewhat lower barrier in the extended trinuclear model can be particularly explained by the formation of a less strained TS-ring (containing as much as 11 members!). Ongoing studies are based on Fe4-clusters involving an interstitial carbide moiety and a truncated FeMo-co core cluster (Fe8S9X). The initial results indicate that the above conclusions remain valid.

4. MECHANISTIC IMPLICATIONS (CONNECTIONS TO NITROGENASE) At least four reaction mechanisms developed in the current contribution can be linked to the interactions of molecular hydrogen and nitrogen with nitrogenase. Among them, the H2inhibition and HD formation processes have been highlighted in the introduction. The selected interaction schemes presented below include the most controversial intermediate diazene (N2H2) and the first reduction adduct diazenido intermediate [−N2H] (see section 3 for additional options): I. Mediated by dihydrogen (D2) oxidation of a partially reduced (bound) diazene intermediate Fen[N2H 2] + D2 → Fen − 2[N2] + 2HD

II. Degradation of a liberated (dissociated into solution) diazene intermediate on a hydridic center of an activated cluster Fen[2H] + cis‐N2D2 → Fen − 2 + N2 + 2HD

III. Mediated by dihydrogen (D2) concomitant oxidation of a hydridic and partially reduced diazenido [−N2H] moiety of an intermediate Fen[N2H, H] + D2 → Fen − 2[N2] + 2HD

IV. Mediated by dihydrogen (D2) conversion (destruction) of a partially reduced (bound-N2H) intermediate to a corresponding metal hydride (or a novel protic center, e.g., at the S-atom of either the sulfide or thiolate groups) and a bound-N2 Fen[N2H] + D2 → Fen[H, N2] + HD Any of these processes can inhibit the overall reduction of N2 to NH3 by removing a significant intermediate from the reaction chain; they can form HD when D2 is applied. However, they differ mainly in reaction products and the consequences related to the consumption and redistribution of electrons (variation of the oxidation numbers of the metals). The diazene mechanism (I) has been initially proposed by Burris and co-workers,9a and further developed by both experimental11 and theoretical contributions.12a This mechanism considers that the key intermediate diazene is a mediator 11636



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barrier for such a process is 18.9 kcal mol−1 (see Figure 8; section 3.2.4).

may suppress the turnover cycle of N2-activation by nitrogenase. The majority of identified pathways is sensitive to the electronic environment and spin configuration of the reaction complexes. The intrinsic reactivity of complexes emerging from different spin configurations suggest a multistate reactivity, which constitutes a characteristic feature of iron complexes.65e Spin-crossing can diminish the barriers as exemplified, for instance, in Figure 4, regarding the degradation of N2H2. The ligand environment, type, location, and number of relevant transition metal atoms, combined with the electron supply channels, are key parameters for switching and regulating the DHC processes dependent on charges and multiplicities on active centers. The developed mechanisms may guide experimentalists in interpretation of various interactions of molecular hydrogen with nitrogenase, summarized in the introduction (section 1.2). The interstitial X-atom alterations (C or N), additional metal−metal bonding formation, and changes in TM-oxidation states can modify the electronic structure of the active center (FeMo-co) and stabilize different local spin states and hence change the mechanism of molecular hydrogen mediated processes. For certain substrates, this easily occurs when a transition-metal is switched. It would explain, for instance, why the substitution of Mo(4d55s1) in FeMo-co by V(3d35s2) creates a different behavior in N2- and CO-coordination (activation) and H2inhibition,3,7 as it was also argued quite recently.72 Dihydrogen catalysis and remote transfer of H-atoms supported by molecular hydrogen16,17,18e−g is believed to open a variety of new pathways relevant to a number of industrially significant processes, such as high-pressure hydroprocessing (hydro-denitrification, hydro-desulfurization, and hydro-deoxygenation),18b activation of CO,18c,d hydrogenassisted selective catalytic reduction,73 and hydrogen storage.18a

(HS)Fe(SH 2)NNH + D2 = (HS)DFe(SH 2)N2 + HD (13)

The H2-mediated H-atom transport reaction constitutes an interconversion between a hydridic and a protic H-atom. Note that HAT may also occur between two protic H-atoms (e.g., −N2H and −S centers) to form −N2 and −SH moieties, as noted earlier for simple models.16 Notably, this process does not consume extra electrons to generate HD, but provides a redistribution of electrons accompanied with the change in the oxidation states of the metal centers. If the initial activation of N2 occurs with the simultaneous (or sequential) formation of a hydridic center (there is also the option for σ-bond metathesis of H212), the generated adduct may undergo degradation via mechanism (III) to give two HD molecules (section 3.2.2.2; Tables 2 and A1, and Figures 6 and 7) with the net utilization of two electrons. The barriers range from 9.7 to 33.0 kcal mol−1 (Table 2) with the lowest value for the reaction of a Fe(IV) single-iron high-spin (quintet) model, and a medium value 19.2 kcal mol−1 for the high-spin binuclear model transformation Fe(II) → Fe(I) (Scheme 4, eq 14). (HS)Fe(SH 2)NNH + D2 = (HS)DFe(SH 2)N2 + HD (14)

The solvent environment is expected to influence significantly the mechanism of enzymatic reactions. To evaluate if a solvent and the surrounding protein environment (more precisely, its general polarity) can decisively change the DHC reaction profiles, we recalculated two reaction mechanisms (eqs 4 and 14) using the Integral Equation Formalism based Polarized Continuum Model (IEF-PCM) implemented in Gaussian09.49b The results are presented in the Supporting Information. Overall, the results are fairly consistent. Supplementary Figure S2 provides essentially the same profile for reaction 14 as for its gas-phase counterpart (Figure 9). However, the barrier is increased somewhat from 23.2 to 27.5 kcal mol−1on S = 0 PES. The solvent-influenced singlet state TS structure appears to be more compact at the peripheries; the R(Fe−N) distance is particularly decreased by 0.058 Å. Importantly, the intermetallic Fe−Fe distance is increased substantially to the more realistic 3.252 Å compared to 2.549 Å in the gas-phase TS. In turn, the high-spin TS is very loose and tends to collapse within the computational procedure employed. Obviously, there is of certain interest to examine the effect of solvent on more intricate DHC processes.

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APPENDIX. COMPARATIVE ANALYSIS OF METHODS AND BASIS SETS EMPLOYED Three typical DHC reactions have been selected for a comparative analysis on validating the density functional and ab initio methods and basis sets employed in this article (Anotations are used for clarity). H 2 + cis‐N2D2 = N2 + 2HD

(1-A)

(Me)2 FeH 2 + cis‐N2D2 = Me2Fe + N2 + 2HD

(5-A)

(HS)2 Fe(H)NNH + D2 = (HS)2 FeN2 + 2HD

(9-A)

The activation energies for reaction 9-A for a singlet and a quintet electronic state PESand two singlet state reactions, namely, the simplest gas-phase reaction 1-A and the straightforward (methyl ligated) reaction 5-A, are listed in Table A1. Reaction 9-A produces the degradation of a hydridic intermediate (HS)2Fe(H)NNH leading to the formation of two HD molecules. Such a scenario involving the net utilization of two electrons has been suggested in various experimental models to explain the inhibition of N2-fixation by molecular hydrogen (vide supra).3,39 Reactions 1-A and 5-A achieve the decomposition of the liberated diazene. Organometallic reactions were selected as typical DHC processes; they involve iron ions in the TS-rings (the corresponding structures and energetic profiles are illustrated in Figures 3b and 6). The potential energy surface for selected reactions was a priori expected to be more sensitive to the

5. CONCLUSIONS An organometallic dihydrogen catalysis (DHC) is proposed to explain the inhibiting role of H2 and HD formation (in the presence of D2) observed in the reduction of nitrogen. The DHC mechanism involves dehydrogenation and/or H-atom transport processes assisted by molecular hydrogen, which occur via cyclic transition states. A detailed analysis of various potential energy surfaces using DFT and ab initio methods indicates the diversity of H2-mediated reactions, which can be employed by Nature in regulating the enzymatic processes. A variety of energetically feasible decomposition pathways involving the free diazene and iron-bound [NxHy]-species are particularly identified for the DHC oxidation of key intermediates and substrates of nitrogenase enzyme, which 11637



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Table A1. Activation Energies (ΔE‡) of Selected DHC Reactionsa Calculated at Different DFT and ab Initio Levels (in kcal mol−1) method CCSD(T)/CBSb1 CBS-QB31 B3LYP/6-311++G(2d,2p) B3LYP/SDD B3LYP/LanL2DZd B3PW91/6-311++G(2d,2p) B3PW91/SDD B3PW91/LanL2DZ BP86/6-311++G(2d,2p) BP86/SDD BP86/LanL2DZ MP2/6-311++G(2d,2p) MP2/LanL2DZ MP4/6-31+G(2d,p)// MP2/6-31G(d)

S=0

24.4 26.7 26.3 24.1 27.9 27.6 22.6 26.3 26.6 e e

Rxn 9-A

Rxn 5-A

S = 4/2

S=0

6.1 8.1 9.7 4.9 7.4 9.4 3.5 4.7 3.4 e e

Rxn 1-A

10.7 10.8 6.1 10.9 10.4 6.1 e 8.8f 6.5f 1.3 g

E XC = E X LSDA + a0(E X exact − E X LSDA ) + a x ΔEx B88 + EC VWN + ac(ΔEC LYP − ΔEC VWN)

c

To avoid double counting, the local part (ΔECVWN) has been subtracted from ΔECLYP. In contrast to the gradient-corrected PW91functional,56a the LYP has originally been designed to predict the properties of He atom, which constitutes a better example of a highly non-uniform electron density in molecules than the uniform electron-gas based PW91. Hence, the B3LYP method (eq A2) is generally expected to be more suitable for molecular reactions, whereas the B3PW91 method is more appropriate for free electron-like systems.47c Whereas the B3LYP method underestimates the dissociation energies of some transition metal−ligand bonds (M−L) in small diatomic molecules, the pure GGA functionals, such as BP86, tend to overestimate them due to different accuracies in the energies of the open-shell products.63 As shown by Jensen and co-workers, these opposite systematic errors are of comparable magnitudes.63b,c,b For this reason, we also employed the BP86 method63a for comparison. The B3LYP method somewhat underestimates dispersion interactions in TM hydride- and dihydrogen bonding.61a However, the distance-dependent H-bonding interactions are mostly dominated by the electrostatic interactions rather than dispersion corrections, as shown by David Sherrill and coworkers.61b As seen from Table A1, the activation energies calculated at different levels for three selected DHC processes are in general agreement with each other regardless of the structural differences and the type of TS. However, the qualitative trends are somewhat different and dependent on the employed methods and basis sets. In overall, the two hybrid density functional methods (B3LYP and B3PW91), in conjunction with all-electron and two ECP-based basis sets predict results consistent and close to each other, as already emphasized in the text of this article. The MP2 ab initio method encounters difficulties in SCFconvergence for the more intricate reaction 9-A, which involves a delocalized [NNH] moiety linked to the iron center (Figure 6), whereas the pure GGA BP86 functional predicts consistently lower barriers for all reactions considered here, except for the singlet state reaction 9-A (first column, Table A1) for which the BP86 data are in good agreement with both hybrid functionals combined with any of the basis sets employed. The barrier underestimation by BP86 functional is clearly seen if one compares the barrier heights of the simple gas-phase reaction 1-A with the benchmark value of 26.4 kcal mol−1 calculated at CCSD(T)/ CBS+ZPE(CCSD(T)/aug-cc-pVTZ and the 22.5 kcal mol−1 calculated at CBS-QB3 composite levels, reported previously and included in Table A1 for comparison.1 For the simplest reaction, all methods including the MP2 predict comparable results. We note that the BP86 functional underestimates the activation energies for the highspin quintet state reaction 9-A for all basis sets employed, most likely because of the over-stabilization of cyclic-TS systems in high-spin reactions. The pure GGA functional overestimates the stability of combined systems in the straightforward reaction 5-A, which involves interaction of Me2FeH2 catalyst with the diazene via two N−H···H−H bonds (Figure 3b). We note that a prereaction van der Waals complex is formed for this singlet state reaction. Yet, the relative barrier heights calculated from

S=0 26.4 22.6 21.1 22.6 22.6 19.4 21.8 21.8 12.3 14.0 13.4 19.7 25.3 25.6h12

a

The energy profile for quintet state reaction 9-A and transition states for the straightforward reaction 5-A and simplest gas-phase reaction 1A are illustrated in Figures 6, 3b, and 1, respectively. bZPE energies are calculated at the CCSD(T)/aug-cc-pVTZ level (ref 1). cDunning/ Huzinaga valence double-ξ basis is used for nonmetal atoms in methods employing ECP for Fe. dIllustrated in Figure 5. eFailed to converge. fRelative to a prereaction complex. gFailed to converge; ΔE‡ at the MP2/6-31G(d,p) level is 3.3 kcal mol−1 . hIncluding zero-point vibration energies (ref 12).

method/basis set combination (different treatment of the effect of partially filled electronic d-shells of Fe-centers and ligands). The iron centers bear a +4 formal oxidation number in the reagent complexes, which reduced to +2 for both Me2Fe and loosely bound (HS)2FeN2 products of reactions 5-A and 9-A. The end-on coordinated nitrogen in eq 9 (Figure 6) has a collinear structure because of the effective π-backbonding interactions of the iron d-orbitals with the π*-orbitals of N2. Methods

Three well tested DFT methods, namely, two hybrid (B3LYP and B3PW91) and the pure BP86 generalized gradient approximation (GGA) functionals, were used to explore the above DHC reactions. The B3PW91 method corresponds to the original hybrid scheme suggested by Beck.47a It involves the Kohn−Sham orbital based Hartree−Fock exchange energy (EXexact), the uniform electron gas exchange-correlation energy (EXLSDA), the Beck-1988 gradient correction for exchange (ΔEXB88), and the Perdew and Wang-1991 gradient correction for the correlation (ΔECPW91). E XC = E X LSDA + a0(E X exact − E X LSDA ) + a x ΔEx B88 + acΔEC PW91

(A2)

(A1)

The three coefficients a0, ax, ac are empirical parameters originally derived as 0.2, 0.72, and 0.81, respectively.47a The coefficients, as well as the scheme itself, have been later modified to be applicable to diverse systems.47d A group of Gaussian co-authors suggested to replace ΔECPW91 by the Lee− Yang−Parr correlation functional (ΔECLYP)47b giving birth to the most popular B3LYP method:47c 11638



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the simple Pople basis set 6-31G(d,p) performs in some cases better than the much larger ones due to the inherited errors cancellation.16,59d The MP2 method in conjunction with the same triple-ξ basis set augmented by diffuse and polarization functions underestimates the gas-phase (eq A1) barrier consonant with the B3PW91 predictions (19.7 and 19.4 kcal mol−1, respectively) compared to the benchmark CCSD(T)/ CBS value of 26.4 kcal mol−1 (or even 22.5 kcal mol−1 value at the CBS-QB3 composite level of theory) reported earlier.1 However, B3LYP functional predicts the value 21.1 kcal mol−1, which is closer to the benchmark ab initio and the composite level results (see Table 1A). Surprisingly, the utilization of a less extended valence double-ξ quality Dunning/Huzinaga basis for N and H atoms in the gas-phase reaction 1-A leads to even much closer results to those of CCSD(T)/CBS for all methods considered, including the MP2 ones. Note that the MP2/LanL2DZ wavefunction method was discussed in section 3.2.1 regarding the H2-elimination reaction 7b, which involves both Fe−H and S−H centers and predicts results comparable to that of DFT (5.7 vs. 6.1 kcal mol−1), whereas the all-electron MP2/6-311++(2d,2p) calculations failed to converge in this case.

the corresponding vdW-complexes are close to data predicted by other methods (within 1−2 kcal mol−1). Remarkably, the hybrid B3PW91 method predicts a barrier for reaction 5-A, which is almost identical to the B3LYP results when either LanL2DZ or 6-311++G(2d,2p) basis sets are used (6.1 and 10.9 kcal mol−1 versus 6.1 and 10.6 kcal mol−1, respectively). However, the B3PW1 results for a high-spin reaction 9-A are somewhat lower than those predicted by B3LYP combined with SDD and all-electron basis sets, but they are much closer at the LanL2DZ level (9.4 vs. 9.7 kcal mol−1, respectively). The barrier predicted by BP86/LanL2DZ for a quintet state reaction 9-A is somewhat out of picture, being by 1.4 kcal mol−1 lower than the SDD barrier, and even lower than the all-electron barrier, as opposed to B3LYP and B3PW1 results. Basis Sets

Overall, an augmented by diffuse and polarization functions allelectron triple-ξ basis set 6-311++G(2d,2p) produces somewhat lower barriers within the same DFT and ab initio methods than two other basis sets, which involve the effective core potentials (ECP) for TM, viz., the LanL2DZ (Los Alamos ECP for iron and sulfur atoms with the Dunning/Huzinaga valence double-ζ basis for other atoms48) and SDD (Dresden/Stuttgart ECP for iron and sulfur atoms50 and Dunning/Huzinaga full double-ζ basis for other atoms48a), except for reaction 5-A. As seen from Table A1, the SDD and the all-electron basis sets predict closer results for this reaction compared to LanL2DZ (ca. 4−5 kcal mol−1 differences for B3LYP and B3PW91 functional data). Apparently, the full double-ξ quality basis D95 employed in standard SDD basis set is comparable to the allelectron triple-ξ basis set in this particular system involving the first row C and N atoms, in contrast to the LanL2DZ basis, which uses a valence double-ξ basis for carbon atoms (D95 V). However, it turns out to be less important for the singlet state HS-ligated systems (eq 9-A), where the SDD results are almost identical to those predicted by LanL2DZ and consistently (by about 2-4 kcal mol−1) higher than those calculated at the allelectron level (Table A1). Perhaps, the ECP approach for Satoms in both cases plays a decisive role in the calculated energy of TS. The inner electrons of iron atoms in both basis sets are treated via the effective core potentials and indirectly include some relativistic and spin-orbit coupling effects via parameterization. A similar trend (a small decrease in the barrier height produced by the all-electron basis set) remains valid also for the exocyclic reaction 8, discussed in section 3.2.2. In this case, the TS-ring does not contain a transition metal; it combines only NN, two N−H, and three H−H bonds in a cyclic TS (Figure 5). As follows from Table 1, the barriers for this reaction at the B3LYP/LanL2DZ level are consistently higher by ∼2−3 kcal mol−1 for both singlet and quintet state PES. The MP2 method encounters SCF convergence difficulties for the straightforward reaction 5-A when the simpler LanL2DZ basis set including ECP for iron atoms is employed, whereas the utilization of all-electron 6-311++G(2d,2p) basis set predicts a structure consistent with DFT transition state but a lower barrier of 1.3 kcal mol−1 as opposed to the gas-phase value of 25.3 kcal mol−1, which is in good agreement with other results, including the CCSD(T)/CBS benchmark value (26.4 kcal mol−1).1 The poor performance of MP2 for organometallic systems with smaller basis sets is in agreement with literature data.64 Interestingly, more limited-basis MP2/6-31G(d,p) calculations provide higher and closer to other data value of 3.3 kcal mol−1. There are several indications in literature that

Summary

(a) The two hybrid density functionals B3LYP and B3PW91 are more consistent in predicting different types of transition states and provide results closer to each other compared to the pure GGA BP86 and MP2 ab initio methods. They are also computationally less demanding and converge easier in the calculation of intricate DHC systems. (b) The BP86 pure GGA functional consistently underestimates the barrier height for all considered in this section reactions in conjunction with any of the basis sets employed, except for the singlet state reaction 9-A combined with the ECP-based basis sets (LanL2DZ and SDD). (c) The MP2 results are less adequate for organometallic systems. They are more costly and converge with higher difficulty than the DFT calculations, in agreement with literature data. (d) The basis set effects are important for certain types of DHC reactions. For the straightforward reaction 5-A, the LanL2DZ basis set substantially underestimates the barrier for any of the DFT functionals, including BP86. However, it is well suited for biorelevant sulfur-ligated systems, such as reaction 9-A, in both spin-states, as well as for the simple gas-phase reaction 1-A. Perhaps, the valence double-ζ Huzinaga−Dunning basis set employed in standard LanL2DZ basis set for the carbon atoms of methyl ligands is less appropriate for the correct location and the relative energy of TS reaction 5-A when compared to all-electron triple-ζ and full-electron double-ζ (SDD) basis sets. However, the effect of fullelectron vs ECP treatments for sulfur atoms (SDD vs LanL2DZ) appears to be comparable, as follows from the almost perfect agreement regarding the reaction 9-A at all DFT levels. (e) Augmented with diffuse and polarization functions, 6311++G(2p,2d) all-electron triple-ζ basis set somewhat underestimates the barrier when compared to LanL2DZ and SDD basis sets for reaction 9-A, for both singlet and quintet states. This might be due to the spin−orbit 11639



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5992−5998. (e) Dance, I. Dalton Trans. 2012, 41, 4859−4865. (f) Dance, I. Dalton Trans. 2012, 39, 2772−2983. (7) (a) Lee, H.; Hales, B. J.; Hoffman, B. M. J. Am. Chem. Soc. 1997, 119, 11395−11400. (b) Lee, H.; Cameron, L. M.; Hales, B. J.; Hoffman, B. M. J. Am. Chem. Soc. 1997, 119, 10121−10126. (8) (a) Barney, B. M.; McClead, J.; Lukoyanov, D.; Laryukhin, M.; Tang, T.-C.; Dean, D. R.; Hoffman, B. M.; Seefeldt, L. C. Biochemistry 2007, 46, 6784−6794. (b) Barney, B. M.; Lukoyanov, D.; Igarashi, R. Y.; Laryukhin, M.; Yang, T. C.; Dean, D. R.; Hoffman, B. M.; Seefeldt, L. C. Biochemistry 2009, 48, 9094−9102. (e) Barney, B. M.; Yang, T.C.; Igarashi, R. Y.; Dos Santos, P. C.; Laryukhin, M.; Lee, H.-I.; Hoffman, B. M.; Dean, D. R.; Seefeldt, L. C. J. Am. Chem. Soc. 2005, 127, 14960−14961. (9) Hoch, G. E.; Schneider, K. C.; Burris, R. H. Biochim. Biophys. Acta 1960, 37, 273−279. (10) (a) Sellmann, D.; Fürsattel, A.; Sutter, J. Coord. Chem. Rev. 2000, 200−202, 545−561. (b) Lehnert, N.; Wiesler, B. E.; Tuczek, F.; Henninge, A.; Sellmann, D. J. Am. Chem. Soc. 1997, 119, 8869−8878. (c) Sellmann, D.; Fürsattel, A. Angew. Chem., Int. Ed. 1999, 38, 2023. (11) (a) Burgess, B. K.; Wherland, S.; Newton, W. E.; Stiefel, E. I. Biochemistry 1981, 20, 5140−5146. (b) Stiefel, E. I.; Newton, W. E.; Watt, G. D.; Hadfield, K. L.; Bulen, W. A. Adv. Chem. 1977, 162, 353− 388. (12) (a) Durrant, M. C. Biochemistry 2002, 41, 13934−13945. (b) Durrant, M. C. Biochemistry 2002, 41, 13946−13955. (13) Hwang, D.-Y.; Mebel, A. M. J. Phys. Chem. A 2003, 107, 2865− 2374. (14) Higher-order many-body forces occur between H2 molecules at much higher pressures: Ree, F. H.; Bender, C. F. Phys. Rev. Lett. 1974, 32, 85. The increased molecular overlap leads to symmetry breaking, which makes possible charge-transfer states between adjacent H2 molecules: Hemley, R. J.; Soos, Z. G.; Hanfland, M.; Mao, H.-K. Nature 1994, 384. The presence of nitrogen can perhaps augment these processes due to the high polarizability of NN triple bond, especially when assisted by an active center on a hetero-surface. (15) (a) Woodward, R. B.; Hoffmann, R. The Conservation of Orbital Symmetry; Verlag Chemie: Weinheim, Germany, 1970. (b) Dixon, D. A.; Stevens, R. M.; Herschbach, D. A. Faraday Discuss. Chem. Soc. 1977, 62, 110−126. (c) Jiao, H.; Schleyer, P. v. R.; Glukhovtsev, M. N. J. Phys. Chem. 1996, 110, 12299−12304. (d) Zhong, G.; Chan, B.; Radom, L. J. Am. Chem. Soc. 2007, 129, 924−933. (e) Shaik, S. S.; Hiberty, P. C.; Ohanessian, G.; Lefour, J.-M. J. Phys. Chem. 1988, 92, 5086−5094. (16) Asatryan, R. Chem. Phys. Lett. 2010, 498, 263−269. (17) Kim, H.; Ferguson, G. A.; Cheng, L.; Zygmunt, S. A.; Stair, P. C.; Curtiss, L. A. J. Phys. Chem. C 2012, 116, 2927−2932. (18) (a) Hu, Y. H.; Ruckenstein, E. Ind. Eng. Chem. Res. 2008, 47, 48−50. (b) Girgis, M. J.; Gates, B. C. Ind. Eng. Chem. Res. 1991, 30, 2021−2058. (c) Halachev, T.; Ruckenstein, E. Surf. Sci. 1982, 122, 422−432. (d) Bartholomew, C. H. In New Trends in CO Activation; Guczi, L., Eds.; Elsevier: Budapest, Hungary, 1991, 158−214. (e) Valpuesta, J. E. V.; Rendon, N.; Lopez-Serrano, J.; Poveda, M. L.; Sanchez, L.; Alvarez, E.; Carmona, E. Angew. Chem., Int. Ed. 2012, 51, 7555−7557. (f) Asatryan R.; Bozzelli J. W. Dihydrogen Mediated Hydrogen Transfer Reactions. Fall Tech. Meeting, Eastern States Sec. Combust. Inst., October 2009, College Park, MD. (g) Asatryan, R.; Bozzelli, J. W. Hydrogen-Catalysis Phenomenon As an Option in Biological Fixation of N2: A Theoretical View, 238th ACS National Meeting, Washington, DC, August 2009. (19) (a) Crabtree, R. H. The Organometallic Chemistry of the Transition Metals, 5th ed.; John Wiley & Sons: Hoboken, NJ, 2009. (b) Richardson, T. B.; deGala, S.; Crabtree, R. H.; Siegbahn, P. E. M. J. Am. Chem. Soc. 1995, 117, 12875−12876. (c) Crabtree, R. H.; Siegbahn, P. E. M.; Eisenstein, O.; Rheingold, A. L.; Koetzle, T. F. Acc. Chem. Res. 1996, 29, 348−354. (20) Siegbahn, P. E. M.; Westerberg, J.; Svensson, M.; Crabtree, R. H. J. Phys. Chem. B 1998, 102, 1615−1623.

coupling and relativistic effects, which are indirectly included in LanL2DZ and SDD basis sets via the ECP parametrization. A similar underestimation of all-electron results occurs when the all-electron results are compared with the complete basis set benchmark CCSD(T)/CBS results for the simplest reaction 1-A where no iron center is included. Overall, the hybrid DFT methods employed in conjunction with the SDD basis set are more reliable for calculations of larger DHC systems. Perhaps, the considered methods better account for the static correlation (partially filled valence d-shells of TM result in a number of nearly degenerate electronic states) and the dynamic correlation effect, which arises from the short-range electron−electron repulsion despite that they are single reference methods. These effects are more important for reaction 9-A in which the hydrogen part of the TS ring interacts with the iron center via a delocalized π-system of [−NN− H]-linkage.

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ASSOCIATED CONTENT

S Supporting Information *

Calculated geometries and frequencies for transition states, Figures S1 and S2 on solvent effects, and complete refs 49a and 49b. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: rubikasa@buffalo.edu. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The helpful correspondence with Dr. Brian Hales is gratefully acknowledged. We thank also all reviewers for constructive suggestions. This work was supported in part by the US army Research Office (NJIT grant) and the Ruckenstein fund (SUNY at Buffalo). We acknowledge the use of the High Performance Computing resources provided by NJIT.

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REFERENCES

(1) Asatryan, R.; Bozzelli, J. W.; da Silva, G.; Swinnen, S.; Nguyen, M. T. J. Phys. Chem. A 2010, 114, 6235−6249. (2) (a) Hoffman, B. M.; Dean, R. N.; Seefeldt, L. C. Acc. Chem. Res. 2009, 42, 609−619. (b) Seefeldt, L. C.; Hoffman, B. M.; Dean, D. R. Annu. Rev. Biochem. 2009, 78, 701−722. (c) Seefeldt, L. C.; Hoffman, B. M.; Dean, R. N. Curr. Opin. Chem. Biol. 2012, 16, 19−25. (d) Doan, P. E.; Telser, J.; Barney, B. M.; Igarashi, R. Y.; Dean, D. R.; Seefeldt, L. C.; Hoffman, B. M. J. Am. Chem. Soc. 2011, 133, 17329−17340. (e) Two catalytic sub-stages of the “alternating” pathway are additionally considered regarding the fate of two reducing equivalents that remain on FeMo-co after N2-binding called the “prompt hydrogenation” and “late transfer” pathways: Lukoyanov, D.; Yang, Z.-Y.; Barney, B. M.; Dean, D. R.; Seefeldt, L. C.; Hoffman, B. M. Proc. Natl. Acad. Sci. U.S.A. 2012, 109, 5583−5587. (3) Burgess, B. K.; Lowe, D. J. Chem. Rev. 1996, 96, 2983−3012. (4) Peters, J. W.; Szilagyi, R. K. Curr. Opin. Chem. Biol. 2006, 10, 101−108. (5) Holland, P. L. Nitrogen Fixation. In Comprehensive Coordination Chemistry II; McCleverty, J., Meyer, T. J., Eds.; Elsevier: Oxford, U.K., 2004; Vol. 8, pp 569−599. (6) (a) Dance, I. J. Am. Chem. Soc. 2005, 127, 10925−10942. (b) Dance, I. J. Am. Chem. Soc. 2007, 129, 1076−1088. (c) Dance, I. Dalton Trans. 2008, 5977−5991. (d) Dance, I. Dalton Trans. 2008, 11640



Article

(21) (a) Rod, T. H.; Nørskov, J. K. J. Am. Chem. Soc. 2000, 122, 12751−12763. (b) Machado, F. B. C.; Davidson, E. R. Theor. Chim. Acta 1995, 92, 315−326. (22) (a) McKee, M. L. J. Comput. Chem. 2007, 28, 1342−1356. (b) McKee, M. L. J. Comput. Chem. 2007, 28, 1796−1808. (23) (a) Deng, H.; Hoffmann, R. Angew. Chem., Int. Ed. 1993, 32, 1062−1064. (b) Dance, I. G. Aus. J. Chem. 1994, 47, 979−990. (c) Plass, W. J. Mol. Struct. 1994, 315, 53. (d) Dance, I. J. Biol. Inorg. Chem. 1996, 1, 581−586. (e) Stavrev, K. K.; Zerner, M. C. Chem. Eur. J. 1996, 2, 83−87. (f) Dance, I. Chem. Commun. 1997, 2, 165− 166. (d) Zhong, S.-J.; Liu, C.-W. Polyhedron 1997, 16, 653−661. (g) Stavrev, K. K.; Zerner, M. C. Theor. Chem. Acc. 1997, 96, 141−145. (h) Dance, I. Chem. Commun. 1998, 5, 523−530. (i) Stavrev, K. K.; Zerner, M. C. Int. J. Quantum Chem. 1998, 70, 1159−1168. (j) Szilagyi, R. K.; Musaev, D. G.; Morokuma, K. J. Mol. Struct. 2000, 506, 131− 146. (k) Szilagyi, R. K.; Musaev, D. G.; Morokuma, K. Inorg. Chem. 2001, 40, 766−775. (l) Durrant, M. C. Inorg. Chem. Commun. 2001, 4, 60−62. (m) Durrant, M. C. Biochem. J. 2001, 355, 569−576. (n) Barriere, F.; Pickett, C. J.; Talarmin, J. Polyhedron 2001, 20, 27−36. (o) Lovell, T.; Li, J.; Liu, T.; Case, D. A.; Noodleman, L. J. Am. Chem. Soc. 2001, 123, 12392−12410. (p) Lovell, T.; Li, J.; Case, D. A.; Noodleman, L. J. Am. Chem. Soc. 2002, 124, 4546−4547. (q) Hinnemann, B.; Nørskov, J. K. J. Am. Chem. Soc. 2003, 125, 1466−1467. (r) Cao, Z.; Zhou, Z.; Wan, H.; Zhang, Q.; Thiel, W. Inorg. Chem. 2003, 42, 6986−6988. (s) Lovell, T.; Liu, T.; Case, D. A.; Noodleman, L. J. Am. Chem. Soc. 2003, 125, 8377−8383. (t) Dance, I. Chem. Commun. 2003, 3, 324−325. (u) Vrajmasu, V.; Münck, E.; Bominaar, E. Inorg. Chem. 2003, 42, 5974−5988. (v) Hinnemann, B.; Nørskov, J. K. J. Am. Chem. Soc. 2004, 126, 3920−3927. (w) Huniar, U.; Ahlrichs, R.; Coucouvanis, D. J. Am. Chem. Soc. 2004, 126, 2588− 2601. (x) Cao, Z.; Zhou, A.; Wan, H. L.; Zhang, Q. Int. J. Quantum Chem. 2005, 103, 344−353. (y) Dance, I. J. Am. Chem. Soc. 2007, 129, 1076−1088. (z) Tuczek, F. Encycl. Inorg. Bioorg. Chem. 2011, DOI: 10.1002/9781119951438.eibc0386,pp 1−21. (24) (a) Sandala, G. M.; Noodleman, L. Methods Mol. Biol. 2011, 766, 293−312. (b) Noodleman, L.; Lovell, T.; Liu, T.; Himo, F.; Torres, R. A. Current Opinion in Chem. Biol. 2002, 6, 259−273. (c) Noodleman, L.; Lovell, T.; Han, W.-G.; Li, J.; Himo, F. Chem. Rev. 2004, 104, 459−508. (d) Lovell, T.; Case, D. A.; Noodleman, L. J. Biol. Inorg. Chem. 2002, 7, 735−749. (25) (a) Kästner, J.; Blöchl, P. E. J. Am. Chem. Soc. 2007, 129, 2998− 3006. (b) Schimpl, J.; Petrilli, H. M.; Blöchl, P. E. J. Am. Chem. Soc. 2003, 125, 15772−15778. (c) Kästner, J.; Blöchl, P. E. ChemPhysChem 2005, 6, 1724−1726. (26) (a) Chatt, J.; Dilworth, J. R.; Richards, R. L. Chem. Rev. 1978, 78, 589−625. (b) Chatt, J. In Nitrogen Fixation; Stewart, W. D. P., Gallon, J. R., Eds.; Academic Press: London, 1980; pp 1−17. (27) (a) Schrock, R. R. Acc. Chem. Res. 1997, 30, 9−16. (b) Schrock, R. R. Acc. Chem. Res. 2005, 38, 955−962. (c) Schrock, R. R. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 17087. (d) Schrock, R. R. Angew. Chem., Int. Ed. 2008, 47, 5512−5522. (28) (a) Bazhenova, T. A.; Shilov, A. E. Coord. Chem. Rev. 1995, 144, 69145. (b) Shilov, A. E. Russ. Chem. Bull. 2003, 52, 2555−2562. (29) Biczysko, M.; Poveda, L. A.; Varnandas, A. J. C. Chem. Phys. Lett. 2006, 424, 46−53. (30) Hellman, A.; Baerends, E. J.; Biczysko, M.; Bligaard, T.; Christensen, C. H.; Clary, D. C.; Dahl, S.; van Harrevelt, R.; Honkala, K.; Jonsson, H.; et al. J. Phys. Chem. B 2006, 110, 17719−17735. (31) Thorneley, R. N. F.; Lowe, D. J. Kinetics and Mechanisms of the Nitrogenase Enzyme System. In Molybdenum Enzymes; Spiro, T. G., Ed.; Wiley: New York, 1985; pp 221−284. (32) (a) Fisher, K.; Dilworth, M. J.; Newton, W. E. Biochemistry 2000, 39, 15570−15577. (b) Fisher, K.; Newton, W.; Lowe, D. Biochemistry 2001, 40, 3333−3339. (33) (a) Pickett, C. J. J. Biol. Inorg. Chem. 1996, 1, 601−606. (b) Le Gall, T.; Ibrahim, S. K.; Gormal, C. A.; Smith, B. E.; Pickett, C. J. Chem. Commun. 1999, 773−774. (34) Holland, P. L. Dalton Trans. 2010, 39, 5415−5425.

(35) (a) Wang, T.; Brudvig, G. W.; Batista, V. S. J. Chem. Theory Comput. 2010, 6, 2395−2401. (b) Warren, J. J.; Tronic, T. A.; Mayer, J. M. Chem. Rev. 2010, 110, 6961−7001. (36) (a) Lukoyanov, D.; Yang, Z.-Y.; Dean, D. R.; Seefeldt, L. C.; Hoffman, B. M. J. Am. Chem. Soc. 2010, 132, 2526−2527. (b) Lees, N. S.; McNaughton, R. L.; Gregory, W. V.; Holland, P. L.; Hoffman, B. M. J. Am. Chem. Soc. 2008, 130, 546−555. (c) Igarashi, R. Y.; Laryukhin, M.; Santos, P. C. D.; Lee, H.-I.; Dean, D. R.; Seefeldt, L. C.; Hoffman, B. M. J. Am. Chem. Soc. 2005, 127, 6231−6241. (37) Bulen, W. A. 1st International Symposium on Nitrogen Fixation (ISNF'76), Pullman, WA, 1976; pp 177−186. (38) (a) Burgess, B. K. Chem. Rev. 1990, 90, 1377−1406. (b) Burris, R. H. J. Biol. Chem. 1991, 266, 9339−9342. (c) Liang, J.; Burris, R. H. Proc. Natl. Acad. Sci. U.S.A. 1988, 85, 9446−9450. (39) Guth, J. H.; Burris, R. H. Biochemistry 1983, 22, 5111−5122. (40) (a) Hadfield, K. L.; Bulen, W. A. Biochemistry 1969, 8, 5103− 5108. (b) Bulen, W. A.; Burns, R. C.; LeComte, J. R. Proc. Natl. Acad. Sci. U.S.A. 1965, 53, 532−539. (c) Ogo, S.; Kure, B.; Nakai, H.; Watanabe, Y.; Fukuzumi, S. Appl. Organometal. Chem. 2004, 18, 589− 594. (41) (a) Kubas, G. J. Metal Dihydrogen and sigma-Bond Complexes Structure, Theory, and Reactivity; Springer: New York, 2001; p 444. (b) Bagatur'yants, A. A.; Gritsenko, O. V.; Zhidomirov, G. M. Russ. J. Phys. Chem. 1980, 54, 2993. (c) Custelcean, R.; Jackson, J. E. Chem. Rev. 2001, 201, 1963−1980. (d) Epstein, L. M.; Shubina, E. S. Coord. Chem. Rev. 2002, 231, 165−181. (e) Thauer, R. K. Eur. J. Inorg. Chem. 2011, 919−921. (42) (a) Volbeda, A.; Garcin, E.; Piras, C.; deLacey, A. L.; Fernandez, V. M.; Hatchikian, E. C.; Frey, M.; Fontecilla-Camps, J. C. J. Am. Chem. Soc. 1996, 118, 12989−12996. (b) Pavlov, M.; Siegbahn, P. E. M.; Blomberg, M. R. A.; Crabtree, R. H. J. Am. Chem. Soc. 1998, 120, 548−555. (43) (a) Einsle, O.; Tezcan, F. A.; Andrade, S. L. A.; Schmid, B.; Yoshida, M.; Howard, J. B.; Rees, D. C. Science 2002, 297, 1696−1700. (b) Howard, J. B.; Rees, D. C. Chem. Rev. 1996, 96, 2965−2982. (44) Holland, P. L. Acc. Chem. Res. 2008, 41, 905−914. (45) (a) Niemoth-Anderson, J. D.; Clark, K. A.; Adrian George, T.; Ross, C. R., II. J. Am. Chem. Soc. 2000, 122, 3977−3978. (b) Scepaniak, J. J.; Young, J. A.; Bontchev, R. P.; Smith, J. M. Angew. Chem., Int. Ed. 2009, 48, 3158−3160. (c) Vogel, C.; Heinemann, F. W.; Sutter, J.; Anthon, C.; Meyer, K. Angew. Chem., Int. Ed. 2008, 47, 2681−2684. (d) Betley, T. A.; Peters, J. C. J. Am. Chem. Soc. 2004, 126, 6252− 6254. (e) Rohde, J.-U.; Betley, T. A.; Jackson, T. A.; Saouma, C. T.; Peters, J. C.; Que, L., Jr. Inorg. Chem. 2007, 46, 5720−5726. (46) (a) Takaoka, A.; Mankad, N. P.; Peters, J. C. J. Am. Chem. Soc. 2011, 128, 4956−4957. (b) Hendrich, M. P.; Gunderson, W.; Behan, R. K.; Green, M. T.; Mehn, M. P.; Betley, T. A.; Lu, C. C.; Peters, J. C. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 17107−17112. (c) Mehn, M. P.; Peters, J. C. J. Inorg. Biochem. 2006, 100, 634−643. (d) Han, W.-G.; Liu, T.; Lovell, T.; Noodleman, L. Inorg. Chem. 2006, 45, 8533−8542. (e) Xue, G.; De Hont, R.; Münck, E.; Que, L., Jr. Nat. Chem. 2010, 2, 400−405. (47) (a) Becke, A. J. Chem. Phys. 1993, 98, 5648−5652. (b) Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B 1988, 37, 785−789. (c) Stephens, P. J.; Devlin, F. J.; Chabalowski, C.; Frisch, M. J. J. Phys. Chem. 1994, 98, 11623−11627. (d) Poater, J.; Solá, M.; Duran, M.; Roblesy, J. Phys. Chem. Chem. Phys. 2002, 4, 722−731. (48) (a) Dunning, T. H., Jr.; Hay, P. J. In Modern Theoretical Chemistry; Schaefer, H.F., III, Ed.; Plenum Press: New York, 1976; Vol. 3, pp 1−28. (b) Hay, P. J.; Wadt, W. R. J. Chem. Phys. 1985, 82, 299−310. (49) (a) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; et al. Gaussian 03, revision D.01; Gaussian, Inc.: Wallingford, CT, 2004. (b) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; et al. Gaussian 09, revision C.01; Gaussian, Inc.: Wallingford, CT, 2010. (50) Dolg, M.; Wedig, U.; Stoll, H.; Preuss, H. J. Chem. Phys. 1987, 86, 866−872. (51) Jeanvoine, Y.; Spezia, R. J. Phys. Chem. A 2009, 113, 7878−7887. (52) Siegbahn, P. E. M. Adv. Chem. Phys. 1996, 93, 1333. 11641



Article

(53) Simón, L.; Goodman, J. M. Org. Biomol. Chem. 2011, 9, 689− 700. (54) (a) Asatryan, R.; Bozzelli, J. W. Chem. Phys. Phys. Chem. 2008, 10, 1769−1780. (b) Izgorodina, E. I.; Brittain, D. R. B.; Hodgson, J. L.; Krenske, E. H.; Lin, C. Y.; Namazian, M.; Coote, M. L. J. Phys. Chem. A 2007, 111, 10754−10768. (c) Asatryan, R.; Bozzelli, J. W. J. Phys. Chem. A 2010, 114, 7693−7708. (d) Holthausen, M. C.; Fiedler, A.; Schwarz, H.; Koch, W. J. Phys. Chem. 1996, 100, 6236−6242. (e) Kolboe, S.; Svelle, S. J. Phys. Chem. Lett. 2008, 112, 6399−6400. (f) Basch, H.; Hoz, S. J. Phys. Chem. A 1997, 101, 4416−4431. (g) Siegbahn, P. E. M. J. Biol. Inorg. Chem. 2006, 11, 695−701. (55) Schultz, N. E.; Zhao, Y.; Truhlar, D. G. J. Phys. Chem. A 2005, 109, 11127−11143. (56) (a) Perdew, L. P.; Wang, Y. Phys. Rev. B 1992, 45, 13244− 13249. (b) Hirva, P.; Haukka, M.; Jakonen, M. J. Mol. Model. 2008, 14, 171−181. (c) Paier, J.; Marsman, M.; Kresse, G. J. Chem. Phys. 2007, 127, 024103. (57) Asatryan, R.; Bozzelli, J. W.; Simmie, J. M. J. Phys. Chem. A 2008, 112, 3172−3185. (58) Cundari, T. R.; Arturo Ruiz Leza, H.; Grimes, T.; Steyl, G.; Waters, A.; Wilson, A. K. Chem. Phys. Lett. 2005, 401, 58−61. (59) (a) Jensen, K. P.; Roos, B. O.; Ryde, U. J. Chem. Phys. 2007, 126, 014103. (b) Jensen, K. P.; Ryde, U. Coord. Chem. Rev. 2009, 253, 769− 778. (c) Yanagisawa, S.; Tsuneda, T.; Hirao, K. Chem. Phys. 2000, 112, 545−553. (d) Durant, J. L. Chem. Phys. Lett. 1996, 256, 595−602. (60) (a) Harris, T. V.; Szilagyi, R. K. Inorg. Chem. 2011, 50, 4811− 4824. (b) Szilagyi, R.; Winslow, M. A. J. Comput. Chem. 2006, 27, 1385−1397. (61) (a) Jacobsen, H. Chem. Phys. 2008, 345, 95−102. (b) Thanthiriwatte, K. S.; Hohenstein, E. G.; Burns, L. A.; David Sherrill, C. J. Chem. Theory Comput. 2011, 7, 88−96. (62) Harvey, J. N.; Poli, R. Dalton Trans. 2003, 4100−4106. (63) (a) Perdew, J. P. Phys. Rev. 1986, B 33, 8822−8824. (b) Kepp, K. P. J. Inorg. Biochem. 2008, 102, 87−100. (c) Kornobis, K.; Kumar, N.; Wong, B. M.; Lodowski, P.; Jaworska, M.; Andruniów, T.; Rudd, K.; Kozlowski, P. M. J. Chem. Phys. 2011, 115, 1280−1292. (d) Li, J.; Schreckenbach, G.; Ziegler, T. J. Am. Chem. Soc. 1995, 117, 486−494. (64) (a) Kang, R.; Chen, H.; Shaik, S.; Yao, J. J. Chem. Theory Comput. 2011, 7, 4002−4011. (b) Raghavachari, K.; Trucks, G. W. J. Chem. Phys. 1989, 91, 1062−1065. (65) (a) Tjelta, B. L.; Armentrout, P. B. J. Am. Chem. Soc. 1996, 118, 9652−9660. (b) Schultz, R. H.; Armentrout, P. B. J. Phys. Chem. 1992, 96, 1662−1667. (c) Musaev, D. G.; Morokuma, K. J. Chem. Phys. 1994, 101, 10697. (d) Hendrickx, M.; Clima, S. Chem. Phys. Lett. 2004, 388, 290−296. (e) Schröder, D.; Shaik, S.; Shcwarz, H. Acc. Chem. Res. 2000, 33, 139−145. (66) (a) Kubas, G. J. J. Organometallic. Chem. 2001, 635, 37−68. (b) Trage, C.; Schröder, D.; Schwarz, H. Organometallics 2003, 22, 693−707. (c) Wang, X.; Andrews, L. J. Phys. Chem. A 2009, 113, 551− 563. (67) (a) Gumiero, A.; Metacalfe, C. L.; Pearson, A. R.; Lloyd Raven, E.; Moody, P. C. E. Biol. Chem. 2011, 286, 1260−1268. (b) Groves, J. T. J. Inorg. Biochem. 2006, 100, 434−447. (68) (a) Epstein, E. F.; Bernal, I. Inorg. Chim. Acta 1977, 25, 145− 155. (b) Sellmann, D.; Geck, M.; Knoch, F.; Ritter, G.; Dengler, J. J. Am. Chem. Soc. 1991, 113, 3819−3828. (c) Cummins, C. C.; Schrock, R. R. Inorg. Chem. 1994, 33, 395−396. (d) Knof, U.; Weyhermüller, T.; Wolter, T.; Wieghardt, K.; Bill, E.; Butzlaff, C.; Trautwein, A. X. Angew. Chem., Int. Ed. 1993, 32, 1635−1638. (e) Miyamae, H.; Sato, S.; Saito, Y.; Sakai, K.; Fukuyama, M. Acta Crystallogr., Sect. B: Struct. Sci. 1977, 33, 3942−3944. (f) Collins, T. J. Acc. Chem. Res. 1994, 27, 279−285. (h) Harbron, S. K.; Higgins, S. J.; Levason, W.; Feiters, M. C.; Steel, A. T. Inorg. Chem. 1986, 25, 1789−1794. (69) (a) Lancaster, K. M.; Roemelt, M.; Ettenhuber, P.; Hu, Y.; Ribbe, M. W.; Neese, F.; Bergmann, U.; DeBeer, S. Science 2011, 332, 974−977. (b) Spatzal, T.; Aksoyoglu, M.; Zhang, L.; Andrade, S. L. A.; Schleicher, E.; Weber, S.; Rees, D. C.; Einsle, O. Science 2011, 332, 940. (c) Wiig, J. A.; Hu, Y.; Lee, C. C.; Ribbe, M. W. Science 2012, 337, 1672−1675.

(70) Schröder, D.; Schwarz, H.; Clemmer, D. E.; Chen, Y.-M.; Armentrout, P. B.; Baranov, V. I.; Bohme, D. K. Int. J. Mass. Specrom. Ion Processes 1997, 161, 175−191. (71) Lee, S. S.; Holm, R. H. Chem. Rev. 2004, 104, 1135−1158. (72) Lee, C. C.; Hu, Y.; Ribbe, M. W. Science 2010, 329, 642. (73) Korhonen, S. T.; Beale, A. M.; Newton, M. A.; Weckhuysen, B. M. J. Phys. Chem. C 2011, 115, 885−896. (74) (a) Reiher, M.; Hess, B. A. Chem.Eur. J. 2002, 8, 5332−5339. (b) Himmel, H. J.; Reiher, H. Angew. Chem., Int. Ed. 2006, 45, 6264− 6288. (h) Sprignani, J.; Franco, D.; Magistrato, A. Molecules 2011, 16, 442−465. (75) See reviews: (a) Butin, K. P.; Beloglazkina, E. K.; Zyk, N. V. Russ. Chem. Rev. 2005, 74, 531−553. (b) Blanchard, S.; Derat, E.; Desage-El Murr, M.; Fensterbank, L.; Malacria, M.; Mouriès-Mansuy, V. Eur. J. Inorg. Chem. 2012, 376−389. (76) Compared to pure DFT methods, the hybrid functionals somewhat overestimate the stability of high-spin states; see, e.g., Jacobsen, H.; Donahue, J. Inorg. Chem. 2008, 47, 10037−10045. However, the large energy splitting obtained allows one to accurately identify the relative stabilities. (77) Liao, G. L.; Palmer, G. Biochemistry 1998, 37, 15583−15593.

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