Unveiling full mechanistic picture of Mo-catalysed nitrogen fixation driven by SmI₂–H₂O system

Abstract

Ammonia is an essential chemical that underpins modern agriculture and industry, but the direct conversion of dinitrogen to ammonia under mild conditions remains highly challenging. To this end, molybdenum nitride complexes bearing 1,3-bis(di-tert-butylphosphinomethyl)benzimidazole-2-ylidene pincer ligands have been shown to catalyse ammonia formation from dinitrogen using samarium diiodide and water. However, the catalytic mechanism remains poorly understood owing to limited information on the key intermediates and the solution-state speciation of the samarium reductant. Here we show a full catalytic mechanism by combining mechanistic experiments and theoretical analyses. We isolate molybdenum methylimide and molybdenum methylamide complexes as stable analogues of catalytic intermediates, providing direct experimental evidence for the proposed catalytic pathway. Theoretical studies further suggest a plausible structure of the tetrahydrofuran-solvated samarium diiodide–water complex, and subsequent mechanistic analyses reveal that ammonia formation proceeds through proton-coupled electron transfer. Building on these experimental and theoretical findings, we identify the molybdenum–imide formation reaction as the most energy-demanding step. These findings provide a framework for understanding catalytic ammonia formation and inform future efforts to improve dinitrogen reduction catalysts.

Ammonia can be synthesised from dinitrogen using a mononuclear molybdenum–nitride complex with samarium diiodide as the electron source and water as the proton source, but the mechanism is not fully known. Here, the authors isolate intermediate analogues and provide experimental and theoretical evidence for the proposed catalytic pathway.

Introduction

Industrial production of ammonia (NH₃) is essential for satisfying the increasing demand for nitrogen fertilisers and the critical raw materials of valuable compounds, including pharmaceuticals and synthetic polymers^1–8. For more than one century, the Haber–Bosch process has been the mainstay of industrial NH₃ synthesis^9–11. This method effectively exploits the abundant atmospheric reserves of molecular nitrogen (N₂) as a nitrogen source for NH₃ production. However, N₂ is an inert gas necessitating severe reaction conditions (high temperature and high pressure). Moreover, NH₃ synthesis utilises hydrogen gas, which is primarily obtained from natural gas and leads to considerable CO₂ emissions^9–13. These limitations have motivated ongoing efforts towards sustainable NH₃ production methods.

In nature, nitrogen fixation is catalysed by nitrogenase enzymes, whose active site contains an iron–molybdenum cofactor (FeMoco)^14–17. Inspired by biological nitrogen fixation, researchers have investigated artificial homogeneous catalysts for nitrogen fixation, particularly those involving Fe and Mo complexes. In 2003, Schrock and co-worker reported the first catalytic conversion of N₂ to NH₃ using an Mo–dinitrogen complex with a triamidoamine ligand under ambient conditions, yielding 8 equivalents of NH₃ per Mo atom¹⁸. In 2011, we developed an Mo complex with a PNP pincer ligand (PNP = 2,6-bis(di-tert-butylphosphinomethyl)pyridine), yielding 12 equivalents of NH₃ per Mo atom^19–30. Notably, an Mo–PNP catalyst ligated with iodide produced up to 415 equivalents of NH₃ per Mo atom through an innovative reaction pathway involving direct cleavage of the N≡N triple bond³¹. This pathway contrasts with the proposed mechanism for nitrogenase, which proceeds without direct N≡N bond cleavage¹⁷. In 2013, Peters and co-workers directly converted N₂ to NH₃ over an Fe-dinitrogen complex bearing a tris(phosphine)borane ligand, yielding up to 7 equivalents of NH₃ per Fe atom^19–26. Recently, we demonstrated that an Mo complex with a PCP pincer ligand (PCP = 1,3-bis(di-tert-butylphosphinomethyl)benzimidazole-2-ylidene) enhanced the catalytic activity of nitrogen fixation, yielding 4350 equivalents of NH₃ per Mo atom^32–40. Introducing an electron-withdrawing group into the PCP ligand of the Mo complex further increased the yield to 60,000 equivalents of NH₃ per Mo atom (Fig. 1a)^41,42.

Fig. 1. Catalytic NH₃ formation via Mo complexes.

a Catalytic reduction of N₂ by reductant and proton source; b a possible catalytic mechanism of ammonia synthesis with the Mo–PCP complex.

Based on the obtained stoichiometric and catalytic reactions of Mo pincer complexes^33,41, we previously proposed the reaction mechanism shown in Fig. 1b. First, the bridging dinitrogen ligand on the dinuclear Mo complex is cleaved to form an Mo–nitride complex [Mo(N)I(PCP)]. Sequential protonation and reduction then lead to the formation of Mo–imide [Mo(NH)I(PCP)], Mo–amide [Mo(NH₂)I(PCP)], and Mo–ammine [Mo(NH₃)I(PCP)]. Finally, the ammine ligand in [Mo(NH₃)I(PCP)] is substituted with dinitrogen, releasing ammonia and regenerating the dinuclear Mo–dinitrogen complex [{MoI(PCP)}₂(μ-N₂)]. We previously isolated [Mo(N)I(PCP)] as a key reactive intermediate from the reaction of Mo triiodide complex with a reductant under N₂ atmosphere. However, other reaction intermediates, such as the corresponding [{MoI(PCP)}₂(μ-N₂)], [Mo(NH)I(PCP)], [Mo(NH₂)I(PCP)] and [Mo(NH₃)I(PCP)] complexes, have not been synthesised to date.

During the early stage of this work, we combined decamethylcobaltocene (CoCp*₂, Cp* = η⁵-C₅Me₅) as the reductant with 2,4,6-collidinium trifluoromethanesulfonate ([ColH]OTf, OTf = OSO₂CF₃) as the proton source³¹. All steps from the Mo–nitride complex to the Mo–ammine complex were considered to proceed via stepwise protonation and reduction^31,39,43. Recently, the combination of SmI₂ and H₂O as reductant and proton source, respectively, has been reported to dramatically increase the reaction rate^33,41. This enhancement is likely attributable to the formation of a SmI₂–H₂O complex that facilitates proton-coupled electron transfer (PCET) processes^39,41,44. The applicability of the SmI₂/H₂O system has been observed not only for Mo–PCP complexes but also for molybdenum complexes bearing PNP ligands and simple monodentate and bidentate phosphines as auxiliary ligands, suggesting that this combination is not limited to a specific class of catalysts^34,45. However, the structure of the SmI₂–H₂O complex in solution remains unknown, inhibiting theoretical calculations of the reaction kinetics^46–53.

To better understand the reaction pathway of Mo–catalysed ammonia formation with combined SmI₂ and H₂O, we experimentally isolated and characterised Mo–imide and Mo–amide complex analogues bearing a PCP-type pincer ligand as key reactive intermediates, and theoretically investigated an entire pathway of the catalytic reaction between the Mo complexes and a proposed SmI₂–H₂O complex.

Results and discussion

Experimental elucidation of the catalytic reaction mechanism

Starting from the Mo–nitride (Mo≡N) complex [Mo(N)I(PCP)] (1), we propose that NH₃ forms via Mo–imide (Mo=NH) and Mo–amide (Mo–NH₂) intermediates, leading to the Mo–ammine (Mo–NH₃) complex (Fig. 1b). We first attempted the synthesis of an Mo–imide complex reacting the Mo‒nitride complex 1 with proton sources such as [ColH]OTf. However, unfortunately, the corresponding Mo–imide complex could not be isolated because of its instability (Fig. 2a). To elucidate the reaction pathway from the Mo–nitride to the Mo–ammine complex, we next replaced the protonation of 1 with methylation, thus obtaining an Mo–imide analogues complex. The Mo–nitride complex 1 was reacted with 1.1 equivalents of MeOTf in tetrahydrofuran (THF) at ‒78 °C for 1 h, affording the cationic Mo–methylimide complex [Mo(NMe)I(PCP)]OTf (2) in 64% yield (Fig. 2a). The ¹H NMR spectrum presented the signal assignable to methyl protons of the methylimide ligand at 3.26 ppm (Supplementary Figs. 1, 2). The detailed molecular structure of 2 was confirmed by X-ray crystallographic analysis (Supplementary Table 2 and Supplementary Fig. 6). As shown in the Oak Ridge Thermal Ellipsoid Plot (ORTEP) drawing Fig. 3a, complex 2 possesses a distorted square pyramidal geometry with a methylimide ligand at its apical position. Within this ligand, the Mo1–N1–C26 angle is 171.2(4)° and the Mo1–N1 bond length is 1.706(3) Å. DFT calculations on the first-step reaction shown in Fig. 2a indicate that formation of [Mo(NMe)I(PCP)]⁺ is significantly exergonic (Supplementary Fig. 9). The calculations further show that the activation free energy for the reverse reaction is higher for [Mo(NMe)I(PCP)]⁺ than for the corresponding [Mo(NH)I(PCP)]⁺, consistent with the experimental observation that only the methylated complex was isolated.

Fig. 2. Synthetic schemes of intermediate analogues.

a Conversion of Mo–nitride complex 1 to Mo–methylamide complex 4; b regeneration of Mo–nitride complex 1 from Mo–methylamide complex 4; c pseudo catalytic cycle for formation of MeNH₂ from N₂. [ColH]OTf, MeOTf, and MCp*₂ denote collidinium triflate, methyl triflate, and decamethylmetallocene, respectively.

Fig. 3. ORTEP drawings of the molybdenum complexes.

a The cationic part of [Mo(NMe)I(PCP)]OTf (2), b [Mo(NMe)I(PCP)] (3) and c [Mo(NHMe)I(PCP)] (4). Thermal ellipsoids are shown at the 50% probability level. Hydrogen atoms (excepting the amide proton in 4) are omitted for clarity.

Reduction of the cationic Mo–methylimide complex 2 with 1.0 equivalent of CoCp*₂ in toluene at ‒78 °C for 1 h gave the paramagnetic Mo–methylimide complex [Mo(NMe)I(PCP)] (3) in 64% yield (Fig. 2a). Although complex 3 was unstable in solution at room temperature, it was isolated as purple crystals via recrystallisation from toluene/hexane at ‒30 °C. Fig. 3b displays the ORTEP drawing of 3, whose detailed molecular structure was revealed by X-ray crystallographic analysis (Supplementary Table 2 and Supplementary Fig. 7). Upon reduction, complex 3 afforded a neutral complex in which the methylimide ligand adopts a slightly bent conformation (Mo1–N1–C26 angle = 158.5(3)°). The longer Mo1–N1 bond length in 3 than in 1 (1.752(3) Å vs. 1.662(8) Å)³¹ reflects the double-bond character (Mo=N) of 3.

Next, we attempted to protonate 3 with 1.0 equivalent of [ColH]OTf but failed to isolate the corresponding Mo–methylamide complex [Mo(NHMe)I(PCP)]OTf; instead, complex 2 was formed via one-electron oxidation. Alternatively, when 3 was reacted with 1.0 equivalent each of [ColH]OTf and CoCp*₂ in toluene at ‒78 °C for 1 h, an Mo–methylamide complex [Mo(NHMe)I(PCP)] (4) was obtained in 44% yield. The infrared (IR) spectrum of 4 presented an absorption peak attributable to ν(NH) at 3128 cm⁻¹ (Supplementary Fig. 5). The detailed molecular structure of 4 was determined by X-ray crystallographic analysis (Supplementary Table 2 and Supplementary Fig. 8), and the ORTEP drawing is shown in Fig. 3c. The hydrogen atom of the methylamide ligand was located in the Fourier difference map. The methylimide ligand was transformed into a methylamide ligand upon hydrogenation, in which the Mo1‒N1‒C26 angle bends to 138.9(2)° and the Mo1‒N1 bond length is 1.900(3) Å.

Subsequently, we attempted the protonation of 4 by treating it with 1.0 equivalent of [ColH]OTf; however, the corresponding Mo–methylamine complex could not be obtained. Therefore, we investigated the formation of free methylamine via hydrogenation of 4. After reacting 4 with 1.1 equivalents each of [ColH]OTf and CoCp*₂ in THF at ‒78 °C for 1 h under an Ar atmosphere, we obtained free methylamine (MeNH₂) in 72% NMR yield (based on the Mo atom, Fig. 2b and Supplementary Fig. 3). A separate reaction of 4 with 1.1 equivalents each of CoCp*₂ and [ColH]OTf under an N₂ atmosphere yielded the parent Mo–nitride complex 1 in 19% NMR yield (Fig. 2b). Replacing of CoCp*₂ with CrCp*₂ increased the yield of 1 to 55%, indicating that the milder reductant CrCp*₂ worked more effectively than CoCp*₂ for the formation of 1 (Fig. 2b and Supplementary Fig. 4). The Mo–nitride complex 1 was produced via cleavage of the N≡N triple bond of the bridging dinitrogen ligand (Fig. 1b). From the viewpoint of organic synthesis to obtain organonitrogen compounds directly from N₂, a novel synthetic cycle for the formation of MeNH₂ is established from the reaction of N₂ with MeOTf, [ColH]OTf, and metallocenes as reductants mediated by Mo–PCP complex (Fig. 2c)^54–56.

As revealed by the above stoichiometric experiments, methylamine is produced through a three-step sequence of methylation and hydrogenation of the Mo–nitride complex. The successful synthesis of methylamine using Mo–nitride complex 1 robustly supports the proposed catalytic cycle (Fig. 1b). In this cycle, the Mo–nitride complex is sequentially hydrogenated to the Mo–imide, Mo–amide and Mo–ammine complexes by proton/electron sources. Ultimately, NH₃ is released upon ligand exchange with dinitrogen, thereby reforming the starting Mo–nitride complex 1. Actually, we confirmed that the complexes 1-4 worked as effective catalysts toward ammonia formation with the combination of SmI₂ and H₂O under the same reaction conditions (Supplementary Table 1). Although the synthesised Mo–methylimide and Mo–methylamide complexes are analogues rather than the genuine catalytic intermediates, DFT calculations revealed high similarities between the methylated and protonated species in their Mo–N bond structures and electronic properties (Supplementary Table 3), supporting their relevance as structural and electronic models of the proposed intermediates.

Structure of SmI₂–H₂O complex in solution

During the NH₃ formation process in Fig. 1, the electron source SmI₂ and proton source H₂O can form a SmI₂–H₂O complex in a solvation system⁴⁶. The SmI₂–H₂O complex assumedly reacts with Mo–nitride complex yielding the Mo–ammine complex through cooperative reduction/protonation. Thus, to theoretically discuss the kinetics of the NH₃ formation mechanism, we must know the geometry of the SmI₂–H₂O complex. However, the structure of the SmI₂–H₂O complex in THF has not been experimentally determined. Recently, we elucidated the structure of SmI₂ in THF, revealing the co-existence of SmI₂(thf)₅ and [SmI(thf)₆]I species (Fig. 4). SmI₂(thf)₅ consists of a central Sm atom with seven ligands occupying the vertices of a pentagonal bipyramid. Two iodide ions are coordinated at the axial positions, while five THF molecules occupy the equatorial positions. X-ray crystallography has revealed a similar structure of the solid-state SmI₂–THF complex^57,58. Conversely, the central Sm atom in [SmI(thf)₆]I is coordinated by six THF molecules and one iodide ion, forming a seven-coordinate structure, while the other iodide ion is loosely bound to the Sm center.

Fig. 4. Coordination of a water molecule to the SmI₂ complex.

a Proposed structure of the SmI₂–H₂O complex in THF; b experimentally characterised SmI₂–H₂O complex⁴⁷.

Our EXAFS data showed that the Sm–O coordination number of SmI₂ in THF was 6.4 ± 1.2 and remained essentially unchanged (6.4 ± 1.3) upon addition of one equivalent of H₂O⁴⁶, suggesting that H₂O coordinates through substitution of a THF ligand. Accordingly, based on the THF-solvated SmI₂ structures, we replaced one THF ligand with an H₂O molecule to generate candidate structures of the SmI₂–H₂O complex. Geometry optimisations of these candidate structures yielded the SmI₂(H₂O)(thf)₄ and [SmI(H₂O)(thf)₅]I structures shown in Fig. 4a. Notably, geometry optimisation did not yield a seven-coordinate structure containing one H₂O and six THF ligands in the first solvation sphere of Sm. The computational details are given in the Computational Methods section. As SmI₂(H₂O)(thf)₄ contains one less THF molecule than [SmI(H₂O)(thf)₅]I, we optimised the geometry after placing an additional THF molecule near SmI₂(H₂O)(thf)₄. The iodide ion spontaneously dissociated during the optimisation process, leading to [SmI(H₂O)(thf)₅]I. Since both approaches led to the same SmI₂–H₂O structure, [SmI(H₂O)(thf)₅]I emerges as the more reasonable structural model of the SmI₂–H₂O complex in THF. Furthermore, calculations of the free energy changes associated with the sequential substitution of THF ligands by additional H₂O molecules demonstrated that [SmI(H₂O)(thf)₅]I (Sm:H₂O = 1:1) is the most thermodynamically stable species (Supplementary Table 4). Although experimentally characterised structures of SmI₂–H₂O complexes remain scarce, Albrecht and co-workers have recently reported the structure shown in Fig. 4b upon addition of one equivalent of H₂O to the Sm(dicyclohexano-18-crown-6)I₂ complex⁴⁷. In this structure, coordination of H₂O to the Sm centre induces elongation of one Sm–I bond, consistent with the structural features of the proposed [SmI(H₂O)(thf)₅]I complex in the present study.

To assess the validity of the proposed structure, we further evaluated the bond dissociation free energy (BDFE) of the O–H bond in the SmI₂–H₂O complex. The BDFE_O–H was calculated in terms of the homolysis of the O–H bond at 298.15 K (Fig. 5). The easy transfer of an electron and a proton from the SmI₂–H₂O complex promotes sequential reduction and protonation of the Mo–nitride complex 1 and consequent formation of the Mo–imide, Mo–amide and Mo–ammine complexes^37,59,60. As references, the BDFEs of the N–H bond in the Mo–imide, Mo–amide and Mo–ammine complexes were calculated as 32.1, 46.2, and 41.8 kcal/mol, respectively. The calculated BDFE_O–H of free water (107.2 kcal/mol) far exceeds that of BDFE_N–H in the Mo complexes, indicating that NH₃ formation cannot proceed in water alone. Meanwhile, the BDFEs of SmI₂(H₂O)(thf)₄ and [SmI(H₂O)(thf)₅]I were calculated as 43.8 and 36.1 kcal/mol, respectively. Coordinating the H₂O molecule to SmI₂ substantially weakens the O–H bond by 63.4 and 71.1 kcal/mol in SmI₂(H₂O)(thf)₄ and [SmI(H₂O)(thf)₅]I, respectively. The calculated BDFE_O–H of [SmI(H₂O)(thf)₅]I agrees well with the experimental value reported by Flowers and co-workers (BDFE_O–H = 34 kcal/mol in coordinated water)⁴⁹. They inferred that coordination of H₂O to SmI₂ decreases the BDFE_O–H by a substantial 74 kcal/mol. We thus propose that [SmI(H₂O)(thf)₅]I is the most plausible structural model of the SmI₂–H₂O complex in THF. The [SmI(H₂O)(thf)₅]I complex adopts a seven-coordinate structure in which the central Sm atom is coordinated by five THF molecules, one H₂O molecule and one iodide ion; while the other iodide ion is loosely bound to the Sm centre (Supplementary Fig. 10). As discussed later, the loosely bound iodide ion can play a crucial role in proton transfer from the H₂O ligand to the Mo–nitride complex.

Fig. 5. O–H bond dissociation and calculated bond dissociation free energies (BDFEs).

The corresponding O–H bond dissociation reactions are shown for (1) H₂O, (2) SmI₂(H₂O)(thf)₄ and (3) [SmI(H₂O)(thf)₅]I complexes.

Theoretical elucidation of the catalytic reaction mechanism

Next, we analysed the full catalytic reaction pathway through density functional theory (DFT) calculations (see the Computational Methods section for details). Figure 6 illustrates the free-energy profiles of catalytic NH₃ formation in the reaction system. The catalytic mechanism can be summarised as four main processes: (1) three sequential reduction/protonation steps of the Mo–nitride complex i (1) to yield the Mo–ammine complex x (the NH₃ formation process); (2) N₂-bridging of two molecules of complex x to form the N₂-bridged dinuclear Mo–ammine complex xiv (the dimerisation process); (3) sequential release of two ammine ligands from the complex xiv to form ammonia and the N₂-bridged dinuclear Mo complex xviii (the NH₃ release process) and (4) cleavage of the N≡N bond in xviii to regenerate the Mo–nitride complex i (the catalyst regeneration process, which completes the catalytic cycle). Each process is described in detail below.

Fig. 6. Plausible reaction pathway of ammonia formation catalysed by the Mo complex.

Detailed geometries, energies of the ground and low-lying excited spin states, and spin expectation values are provided in Supplementary Tables 6–8 and Supplementary Figs. 11–17.

The NH₃ formation process involves an endergonic imide formation reaction from the starting Mo–nitride complex i. The free energy change of this reaction at 298.15 K (ΔG₂₉₈) is +3.9 kcal/mol (i → iv). The activation free energy (ΔG^‡₂₉₈) of converting the Sm^III₂(H₂O)/Mo–nitride complex ii to the Sm^IIII₂(OH)/Mo–imide complex iii is 5.1 kcal/mol. Of particular note, proton transfer from the Sm^III₂(H₂O) complex to the Mo–nitride complex is assisted by the loosely bound iodide ion in the Sm^III₂(H₂O) complex (Supplementary Movie 1). After investigating various reaction routes, we observed that without the iodide ion, the imide formation pathway does not proceed. Next, the Mo–amide complex vii is formed from the Mo–imide complex iv via an exergonic reaction with a ΔG₂₉₈ of −10.1 kcal/mol (iv → vii). The ΔG^‡₂₉₈ of converting Sm^III₂(H₂O)/Mo–imide complex v to the Sm^IIII₂(OH)/Mo–amide complex vi is 1.9 kcal/mol. Finally, the Mo–ammine complex x is formed from the Mo–amide complex vii via an exergonic reaction with a ΔG₂₉₈ of −5.8 kcal/mol (vii → x). The ΔG^‡₂₉₈ of converting Sm^III₂(H₂O)/Mo–amide complex viii to the Sm^IIII₂(OH)/Mo–ammine complex ix is 4.2 kcal/mol. The overall ΔG₂₉₈ of the NH₃ formation process (i → iv → vii → x) was calculated as −12.0 kcal/mol. The most energy-demanding step of this process is imide formation from ii to iii, with a ΔG^‡₂₉₈ of 5.1 kcal/mol. The energy of the corresponding transition state TS_ii/iii lies 10.5 kcal/mol above the starting complex i. In the latter part of this paper, we will investigate the electron and proton transfers from Sm^III₂(H₂O) to the Mo complexes in detail during the NH₃ formation process, aiming to clarify whether these reductions/protonations proceed through PCET. Throughout the sequential protonation and reduction processes, the Mo–N bond lengths in the Mo–nitride, Mo–imide, Mo–amide and Mo–ammine complexes increase as follows: Mo–nitride complex i (1.67 Å) < Mo–imide complex iv (1.79 Å) < Mo–amide complex vii (1.94 Å) < Mo–ammine complex x (2.24 Å). The calculated Mo–N bond length of the Mo–nitride complex agrees with our experimentally determined bond length of Mo–nitride complex 1 (1.662(8) Å)³¹. In addition, the calculated Mo–N bond lengths of the Mo–imide and Mo–amide complexes are nearly identical to those of Mo–methylimide complex 3 (1.752(3) Å) and Mo–methylamide complex 4 (1.900(3) Å), respectively. The bond lengths, bond angles and dihedral angles around the Mo centre in the calculated Mo–imide and Mo–amide complexes well agree with those of the isolated analogue structures (Supplementary Table 5). Thus, the successfully synthesised Mo–methylimide and –methylamide complexes experimentally identify the key intermediates, strongly supporting the proposed reaction mechanism outlined in Fig. 6.

During the dimerisation process, molecular N₂ coordination to the Mo–ammine complex x yields the N₂–Mo–ammine complex xii with a ΔG₂₉₈ of −11.6 kcal/mol. The reaction from N₂/Mo–ammine complex xi to complex xii proceeds with ΔG^‡₂₉₈ = 10.3 kcal/mol. N₂ coordination is largely governed by stepwise weakening of the Mo–N bonds during the NH₃ formation process (Mo≡N → Mo=NH → Mo–NH₂ → Mo–NH₃). This progressive weakening gradually reduces the trans-influence of the Mo–N bonds, allowing N₂ coordination. Indeed, as demonstrated through geometry optimisations of the N₂-coordinated Mo–nitride and Mo–imide complexes, the N₂ ligand spontaneously dissociates from the complexes. Although the N₂-coordinated Mo–amide complex can be optimised, the free energy change associated with N₂ coordination is +3.5 kcal/mol. Therefore, the coordination of molecular N₂ to Mo is thermodynamically favourable only after formation of the Mo–ammine complex x. Coordination of another x molecule to the N₂ ligand on xii then forms an N₂-bridged dinuclear Mo–ammine complex xiv with a ΔG₂₉₈ of −12.9 kcal/mol. The reaction from Mo–ammine/N₂–Mo–ammine complex xiii to complex xiv occurs with ΔG^‡₂₉₈ = 4.1 kcal/mol. The dimerisation process (x → xii → xiv) proceeds through a highly exergonic pathway with a ΔG₂₉₈ of −24.5 kcal/mol.

During the NH₃ release process, the NH₃ ligand on each Mo centre of the N₂-bridged dinuclear Mo–ammine complex xiv dissociates to form the N₂-bridged dinuclear Mo complex xviii (xiv → xvi → xviii). The stepwise release of NH₃ from xiv is promoted by the trans-influence of the bridged N₂ ligand on the NH₃ ligands. The first release of NH₃ (ΔG^‡₂₉₈ = 9.6 kcal/mol) is exergonic by 2.9 kcal/mol. The other NH₃ ligand on xvi then dissociates to form xviii. The release of the second NH₃ (ΔG^‡₂₉₈ = 8.1 kcal/mol) is exergonic by 9.1 kcal/mol. Finally, the catalyst is regenerated via cleavage of the N≡N bond in xviii, which regenerates two molecules of i. Previously, we discussed the same process in the catalytic hydroboration reaction³⁸ involving the same Mo–PCP complex. The N≡N bond cleavage (ΔG^‡₂₉₈ = 19.1 kcal/mol for xviii → i + i) is highly exergonic by 24.9 kcal/mol.

Along our proposed pathway, this catalytic reaction is sufficiently exergonic at room temperature. Specifically, the initial NH₃ formation process (i + 3 Sm^III₂(H₂O) → x + 3 Sm^IIII₂(OH)) is exergonic by 12.0 kcal/mol. The subsequent dimerisation process through N≡N bond cleavage (2 x + N₂ → 2 i + 2 NH₃) is also highly exergonic by 61.4 kcal/mol. As revealed in the computed energy diagram, the highest-energy state in the imide formation reaction is the transition state TS_ii/iii (10.5 kcal/mol). Examining each elementary step, we find that almost all reactions are exergonic; only the imide formation is slightly endergonic. Furthermore, the activation free energies are all below 20 kcal/mol. According to our computational results, the most energy-demanding step in the catalytic reaction from intermediate i to xix is imide formation during the NH₃ formation process. Consistent with this finding, Mo–nitride complex i was the only isolable intermediate in our experimental observations^32,33.

Proton-coupled electron transfer in NH₃ formation

Employing combined SmI₂/H₂O as an electron and proton source markedly enhanced the rate of ammonia formation in our Mo-catalysed system^33,41. This rate acceleration has been attributed to PCET-driven delivery of an electron and a proton from the SmI₂–H₂O complex⁴¹. This section elucidates the detailed protonation and reduction mechanism mediated by the SmI₂–H₂O complex. To this end, we visualise the extent of electron transfer (ET) accompanying proton transfer (PT) in each of the three consecutive reduction/protonation steps towards NH₃ formation.

The progression of ET with the gradual progress of PT was systematically traced through the three target reactions: imide formation (ii → iii), amide formation (v → vi) and ammine formation (viii → ix) (Fig. 6). The ET evaluations were based on changes in the Mulliken spin density on the Mo complex [MoI(NH_x)(PCP)] (x = 0-2), the Sm complex and the transferring hydrogen. Meanwhile, PT was quantified through the changes in the Mayer bond orders of O–H bond cleavage and N–H bond formation. Figure 7 shows the changes in energies (ΔEs), Wiberg bond orders (BOs) and changes in natural spin densities (ΔSDs) along the reaction coordinate of the NH₃ formation process. Corresponding analyses based on Mayer bond order, Mulliken and Hirshfeld charges, leading to the same conclusions, are provided in Supplementary Tables 9–13 and Supplementary Fig. 18. The ΔEs and ΔSDs are referenced to the initial state of each elementary reaction. The reaction coordinate r₁ – r₂ is defined as the difference between the bond lengths of the breaking O–H bond and the forming N–H bond. This coordinate corresponds to the intrinsic reaction coordinate (IRC) of each reaction. The PT point is defined as the point of equal O–H and N–H bond orders on the reaction coordinate, whereas the ET point is defined as the point at which the spin density changes by 50%. The reaction coordinate r₃ represents dissociation of the product complex (iii, vi, and ix) into individual Mo complex [MoI(NH_x)(PCP)] (x = 1-3) and Sm complex [SmI(OH)(thf)₅]I.

Fig. 7. Changes in electronic structure and energy during NH₃ formation.

Energy changes (ΔEs), Wiberg bond orders (BOs), natural spin densities (ΔSDs) and highest occupied molecular orbitals (HOMOs) along the reaction coordinate during the three stages of NH₃ formation. a Imide formation, b amide formation and c ammine formation. The ΔSD is shown for three segments: the Mo complex [Mo], the Sm complex [Sm], and the transferring H atom [H]. In the HOMO plots, the hydrogen atoms bonded to carbons, tert-butyl groups, THF molecules and iodides are omitted for clarity. PT and ET points correspond to equal O–H/N–H bond orders and 50% spin density change, respectively. Computational level is B3LYP*-D3/SDD (Mo, I, Sm), 6-311+G** (other atoms) in THF//B3LYP-D3/SDD (Mo, I, Sm), 6-31G* (other atoms) in THF.

First, we discuss the imide formation reaction (ii → iii). Focusing on the BO and ΔSD plots in Fig. 7a, the O–H bond in the Sm complex is gradually cleaved while the N–H bond is progressively formed. In parallel with these structural changes, the spin densities on the Sm and Mo complexes gradually decrease and increase, respectively. The transferring hydrogen is characterised as a proton because its spin density remains at 0.0 throughout the imide formation reaction. That is, the ET proceeds concertedly with PT during the imide formation reaction. By tracking the molecular orbital changes, we confirmed that ET involves the 4f orbital of Sm and the 5d orbital of Mo. The highest occupied molecular orbital (HOMO) of intermediate ii comprises an Sm 4f orbital, whereas the HOMO of the product (r₃ = 20) primarily derives from an Mo 5d orbital. Notably, the HOMO of the transition state (TS_ii/iii) exhibits a mixed character of Sm 4f and Mo 5d orbitals, explicitly confirming a progressive ET from the Sm 4f orbital to the Mo 5d orbital at TS_ii/iii. This result strongly suggests that the imide formation reaction proceeds via PCET. Furthermore, as the PT point precedes the ET point in the plots, reduction/protonation during imide formation proceeds through a PT-driven PCET process.

Similarly analysing the amide and ammine formation processes, we found that amide formation (v → vi) proceeds via a nearly synchronous PCET mechanism driven by PT. Although the PT point slightly precedes the ET point, the two points are more closely spaced than those observed in imide formation (Fig. 7b). The molecular orbital changes indicate that an electron is transferred from an Sm 4f orbital to an Mo 5d orbital. Amine formation (viii → ix) also proceeds via a PT-driven PCET mechanism. The PT and ET points are further apart than those observed in imide and amide formation (Fig. 7c). Consequently, approximately 0.4 electrons are transferred along the reaction coordinate from viii to ix and ET completes as the Mo complex [MoI(NH₃)(PCP)] separates from the Sm complex [SmI(OH)(thf)₅]I. The molecular orbital changes reflect that ET proceeds from an Sm 4f orbital to an Mo 5d orbital.

The preceding analysis demonstrates that all three reduction/protonation reactions of NH₃ formation proceed via PT-driven PCET. The differences in the degree of PT–ET synergy among the individual steps are likely related to the reducibility of the Mo complexes. The LUMO energies of the Mo–nitride (i), Mo–imide (iv), and Mo–amide (vii) complexes were calculated to be −1.29, −1.74, and −1.06 eV, respectively. These values are consistent with the increasing delay of the ET point relative to the PT point in the PT/ET processes toward the Mo–imide, Mo–nitride, and Mo–amide complexes. We also investigated the feasibility of [MoI(NH_x)(PCP)]⁺ (x = 1-3) generation via PT from [SmI(H₂O)(thf)₅]I to [MoI(NH_x)(PCP)] (x = 0-2). No PT pathway was identified without concomitant ET, indicating that PT from the H₂O ligand is always accompanied by ET from the Sm centre to the Mo centre. These results indicate that PCET requires the optimal balance between the reductant and proton source. Recently, we showed that combined SmI₂ and H₂O dramatically accelerates the catalytic reaction^33,41, likely because the protonation and reduction reactions are promoted by the PCET mechanism elucidated in this study. The overall catalytic mechanism inferred from our calculations, including the key PCET steps, is summarised schematically in Fig. 8.

Fig. 8. Schematic representation of the proposed catalytic mechanism.

The catalytic reaction proceeds via successive hydrogenations of the Mo–nitride complex, formation of an N₂-bridged dinuclear Mo–NH₃ complex, release of NH₃ and regeneration of the Mo–nitride complex via N≡N bond cleavage.

In summary, we elucidated the full catalytic cycle of ammonia synthesis from dinitrogen using a mononuclear Mo–nitride complex bearing a PCP-type pincer ligand, employing SmI₂ and H₂O as the electron and proton sources, respectively. Combining experiments and quantum chemical calculations, we clarified that catalysis proceeds via (1) successive hydrogenations of the Mo–nitride complex, (2) formation of an N₂-bridged dinuclear Mo–NH₃ complex, (3) release of NH₃ and (4) regeneration of the Mo–nitride complex via N≡N bond cleavage.

Through experimental investigations of the catalytic mechanism, the Mo–methylimide complex was isolated as an intermediate analogue by methylation of the Mo–nitride complex. Subsequent protonation and reduction of the methylimide complex yielded the methylamide complex, which was further protonated and reduced to obtain methylamine while the Mo–nitride complex was regenerated. The collective outcomes of these stoichiometric reactions strongly evidence the formation of ammonia through the proposed catalytic pathway. Importantly, we successfully isolated and characterised the Mo–imide and Mo–amide complex analogues as pivotal reactive intermediates.

Theoretical investigations revealed the structure of the SmI₂–H₂O complex in solution and the catalytic reaction pathway. First, we proposed a [SmI(H₂O)(thf)₅]I structure for the SmI₂–H₂O complex in THF, in which the seven-coordinate Sm centre binds to five THF molecules, one H₂O molecule and one iodide ligand; the other iodide ion is loosely bound. The calculated BDFE of the O–H bond of the Sm-coordinated H₂O was 36.1 kcal/mol at 298 K, indicating substantially weaker O–H bonds after Sm coordination than in free H₂O (BDFE_O–H = 107.2 kcal/mol). Next, the full catalytic cycle was elucidated through DFT calculations. The transition state of imide formation exhibited the highest relative free energy among all intermediates and transition states, identifying this reduction/protonation process as the most energy-demanding step in the catalytic reaction from successive hydrogenations of the Mo–nitride complex to the regeneration of the Mo–nitride complex. Although the imide formation reaction is endergonic by 3.9 kcal/mol, the overall NH₃ formation process is exergonic by 12.0 kcal/mol. Subsequent formation of an N₂-bridged dinuclear Mo complex, release of NH₃ and N≡N bond cleavage were calculated as highly exergonic, confirming that the catalytic cycle is thermodynamically favourable at room temperature. According to these findings, enhancing the NH₃ formation process, particularly the imide formation reaction, is crucial for improving the catalytic efficiency. During the NH₃ formation process, ET and PT from the SmI₂–H₂O complex to the Mo complexes proceed through PT-driven PCET, where the PCET mechanism requires a delicate balance between the reducing power and proton-donating ability of the SmI₂–H₂O complex. These findings explain the pronounced acceleration of SmI₂/H₂O-driven ammonia formation. They also theoretically demonstrate the critical importance of selecting an appropriate pair of proton source and reductant.

This work comprehensively elucidates the catalytic cycle and highlights the crucial role of the PCET mechanism in catalytic ammonia synthesis. Furthermore, utilising the proposed THF-solvated structure of the SmI₂–H₂O complex, we discussed the kinetics of the NH₃ formation process. This study advances our understanding of reactions employing SmI₂/H₂O as an electron and proton source, clarifies the roles of the catalyst, reductant, and proton source in nitrogen fixation, and offers guiding principles for the rational design of highly efficient catalytic systems.

Methods

Detailed experimental procedures are provided in Supplementary Notes 1, 2. All density functional theory calculations were performed using the Gaussian 09 programme (Rev. E.01)⁶¹. Geometries were optimised using the B3LYP method^62–65 corrected by Grimme’s empirical dispersion (B3LYP-D3)⁶⁶ with the SDD basis set^67,68 for molybdenum, iodine and samarium; the 6-31G(d) basis set^69–72 for the other main group atoms. The structure of the SmI₂–H₂O complex in THF was estimated through structural optimisation using the SDD and 6-311+G(d,p)^73–75 basis sets. This level of theory has been employed in a previous study on the structural determination of the SmI₂ complex in THF⁴⁶. To accurately estimate the energy differences between different spin states, we performed single-point energy calculations on the optimised geometries using the B3LYP*-D3 functional^76–81. The energy expressions in Gaussian 09 program for DFT functionals are given in equation (1)⁶¹,

$$E_{\mathrm{XC}}=P_2{E_{\mathrm{X}}}^{\mathrm{HF}}+P_1\left(P_4{E_{\mathrm{X}}}^{\mathrm{Slater}}+P_3{{\mathrm{\Delta }E}_{\mathrm{X}}}^{\mathrm{non}-\mathrm{local}}\right)+P_6{E_{\mathrm{C}}}^{\mathrm{local}}+P_5{{\mathrm{\Delta }E}_{\mathrm{C}}}^{\mathrm{non}-\mathrm{local}}$$ 1

where P₁ = 1.00, P₂ = 0.20 for B3LYP and 0.15 for B3LYP*, P₃ = 0.72, P₄ = 0.80, P₅ = 0.81 and P₆ = 1.00. In this expression, E_X^HF denotes the Hartree–Fock exchange; E_X^Slater is the local exchange obtained from the local spin density approximation; E_X^non-local represents Becke’s gradient correction⁶² to the exchange functional; E_C^local is the local correlation functional of Vosko, Wilk and Nusair⁶⁵. Because the non-local correlation functional developed by Lee, Yang, and Parr (E_C^LYP)⁶⁴ includes both local and non-local terms, the total correlation functional is expressed as P₅E_C^LYP + (P₆ − P₅)E_C^non-local. For the single-point energy calculations, we employed the larger and more flexible 6-311+G(d,p) basis set rather than 6-31G(d). The exchange–correlation functional and basis set were selected based on comparisons of calculated structures and energetics for representative structures (Supplementary Tables 14–17). To account for solvent effects under the experimental conditions, the geometry optimisations and single-point energy calculations employed the polarisable continuum model (PCM)⁸² of THF (ε = 7.58). The stationary points on the reaction pathways were characterised as minima or transition states by normal mode analysis. The connectivity of the transition states and equilibrium structures were confirmed through intrinsic reaction coordinate (IRC) calculations^83,84. Thermal correction to the Gibbs free energy at 298.15 K was performed for evaluating free energy changes and activation barriers. Furthermore, natural bond orbital (NBO)⁸⁵ analysis was applied to investigate charge distributions, and the Wiberg bond index (WBI)⁸⁶ was used to estimate the bond strength.

Author contributions

K.Y. and Y.N. directed and conceived this project. T.N., A.K., and H.T. conducted the computational work. K.A. conducted the experimental work. All authors discussed the results and wrote the manuscript.

Peer review

Peer review information

Nature Communications thanks Junnian Wei, Chunming Yang and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

Funding

This work was supported by JSPS KAKENHI (Grant Numbers JP22H00335, JP20H05671, JP24H00049, JP24H01834, and JP24K21245). This study is based on results obtained from a project, JPNP21020, commissioned by the New Energy and Industrial Technology Development Organization (NEDO).

Data availability

Crystallographic data for the structures reported in this study have been deposited at the Cambridge Crystallographic Data Centre, under deposition numbers CCDC 2426954 (2), 2426955 (3) and 2426956 (4). Copies of the data can be obtained free of charge via https://www.ccdc.cam.ac.uk/structures/. The data supporting the findings of this study are provided in the Supplementary Information. Source data are provided with this manuscript. All data are available from the corresponding author upon request. Source data are provided with this paper.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at https://doi.org/10.1038/s41467-026-77505-0.