Anion vacancies activate N2 to ammonia on Ba–Si orthosilicate oxynitride-hydride

Oxygen vacancies on oxide-based catalysts sometimes play a key role in various chemical reactions. For example, the oxidation of organic molecules effectively proceeds over a V₂O₅ catalyst, in which the lattice oxygen of V₂O₅ reacts with the substrate to form V₂O_5−x (x, oxygen vacancy) and is regenerated by gas-phase O₂ molecules¹. The redox between V⁵⁺ and V⁴⁺ is the driving force for this reaction, which is well known as the Mars–van Krevelen mechanism. In oxide-supported metal catalysts, oxygen vacancy sites directly activate the reactant molecule (Mars–van Krevelen mechanism) or indirectly promote the supported metal sites through electronic metal–support interaction^2,3. In any case, transition metal (TM) sites, including lattice metal cations and/or the supported metal, are essential to activate various molecules in catalysis. In other words, oxide materials do not work effectively as catalysts in the absence of TM sites.

Ammonia synthesis also occurs on the surface of TMs such as Fe and Ru (refs. ^4,5). The overall reaction rate is governed by the nitrogen binding energy (E_N) of the TM because the N₂ dissociation is the rate-determining step (RDS). This leads to the establishment of a volcano-shaped relationship between the ammonia synthesis activity and E_N (refs. ^6,7). Most studies in the past two decades have been focused on the development of efficient oxide-based supports or promoters that would enhance electron transfer to the TM sites and thus facilitate N≡N bond weakening through metal-to-N₂ π backdonation^8,9. Electride and hydride-based catalysts were recently demonstrated to exhibit enhanced activity for ammonia synthesis under mild reaction conditions^{10,11,12,13,14,15}. In addition, the N₂ reduction to NH₃ is facilitated by the redox properties of the lattice TM sites, such as Ce in BaCeO_1.80H_0.57N_0.23 (ref. ¹⁶) and Ti in ΒaTiΟ_2.5Η_0.5 (ref. ¹⁷). However, although these new strategies promote ammonia synthesis efficiency, TMs are still irreplaceable as active centres for N₂ dissociation in most cases. Only alkali or alkali earth metal hydrides such as KH and BaH₂ have been reported to function as catalysts for ammonia synthesis in the absence of TMs (refs. ^18,19). Reports on ammonia synthesis over TM-free oxide-based catalysts are lacking.

In this Article, we fabricate a Ba–Si orthosilicate oxynitride-hydride via low-temperature solid-state reaction and demonstrate its excellent ability for TM-free NH₃ synthesis under mild conditions. Although loading Ru on Ba₃SiO_5−xN_yH_z enhances the activity, Ru does not serve to dissociate N₂ molecules but facilitates the formation of electron-containing anion vacancy (V_a) sites at the Ru–support interface. This is a striking difference from the well-known role of Ru in NH₃ synthesis. As a result, an exceptionally high ammonia synthesis rate that outperforms existing heterogeneous ammonia synthesis catalysts is realized.

Synthesis and characterization of Ba₃SiO_5−xN_yH_z

The substitution of oxygen bonded to Si⁴⁺ with other anions is generally difficult due to the strong Si–O bonding, except under harsh conditions^20,21,22,23. In this Article, the following synthetic route was employed; the low-temperature (400–700 °C) solid-state reaction of Ba(NH₂)₂ and SiO₂ in a NH₃ flow was applied to the one-step synthesis of Ba₃SiO_5−xN_yH_z with heavily substituted H⁻ and N³⁻ (Methods and Supplementary Fig. 1). The X-ray diffraction (XRD) pattern for Ba₃SiO_5−xN_yH_z synthesized at 600 °C indicates a single Ba₃SiO₅ phase with a purity of >99% and a large shift to lower diffraction angles from that of Ba₃SiO₅ (Fig. 1 and Supplementary Fig. 2). The lattice parameters of Ba₃SiO_5−xN_yH_z are much larger than those of Ba₃SiO₅ as determined by Rietveld fitting analysis (∆V/V₀ = +9.0%; V and V₀ represent volume of sample and reference Ba₃SiO₅, respectively) (Supplementary Table 1). The H⁻ and N³⁻ contents of Ba₃SiO_5−xN_yH_z were determined to be 3.74 and 1.60 mmol g⁻¹, respectively, based on temperature-programmed desorption (TPD) and an acid dissolution method (Methods), which gave the composition of Ba₃SiO_2.87N_0.80H_1.86. Diffuse reflectance spectroscopy (DRS) and projected density of states analysis of Ba₃SiO_5−xN_yH_z suggest that the N2p bands are located above the H1s and O2p bands and thus contribute to bandgap narrowing compared to white Ba₃SiO₅ powder (Supplementary Fig. 3).

a, XRD patterns of Ba₃SiO_5−xN_yH_z and Ba₃SiO₅. b, Solid-state ¹H MAS NMR spectra of Ba₃SiO_5-xN_yH_z, BaH₂ and Ba(NH₂)₂. c, Solid-state ²⁹Si MAS NMR of Ba₃SiO₅ and Ba₃SiO_5−xN_yH_z. d, Calculated crystal structure of Ba₃SiO_2.5NH₂ (left) with SiO₂NH and Ba₆H₂ blocks (right). e, Lattice H⁻ and N³⁻ contents in Ba₃SiO_5−xN_yH_z before (fresh) and after heating in Ar at various temperatures. The used sample was obtained by heating the sample (Ar/650 °C) under ammonia synthesis conditions (400°C, 0.1 MPa) for 2 h. Insets: photographs of the corresponding Ba₃SiO_5−xN_yH_z powders. The error bars represent the standard deviation of the mean based on n = 3 independent measurements. f, X-band EPR spectra of Ba₃SiO_5−xN_yH_z before and after heating in Ar at various temperatures. a.u., arbitrary units.

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The location of N and H in Ba₃SiO_5−xN_yH_z has been confirmed by ¹H and ²⁹Si solid magic-angle spinning (MAS) NMR spectroscopy analysis. In the ¹H MAS NMR spectrum (Fig. 1b), the Ba₃SiO_5-xN_yH_z sample shows a main sharp signal at 8.3 ppm. This is assigned to Ba–H species as its chemical shift is very similar to that of BaH₂ (10.3 ppm). The peaks at 3.1 and 0.8 ppm are attributed to Si–H and N–H species, respectively. The former is well consistent with H-terminated Si nanocrystals and molecular silicon hydrides (3–6 ppm)²⁴ and the latter is close to those of Ba(NH₂)₂ (0.2 ppm) and Ca(NH₂)₂ (0.7 ppm)²⁵. The N–H peak is derived from surface NH_x species on the Ba₃SiO_5−xN_yH_z (Supplementary Fig. 4). In the ²⁹Si MAS NMR spectrum (Fig. 1c), both Ba₃SiO_5−xN_yH_z and Ba₃SiO₅ have signals at −66.8 ppm, which are attributed to the isolated SiO₄ tetrahedra (orthosilicate anion) unit (Q₀ site). As well as this signal, new signals at −53.6, −41.3 and −29.7 ppm appeared for Ba₃SiO_5−xN_yH_z. These peaks are assignable to the Q₀ site with different anion coordinations since the ²⁹Si chemical shift tends to be more shielded with increasing group electronegativity sums of ligands bonded to Si^26,27. Possible species are SiO₂NH, SiONH₂ and SiO_xNH_x with surface OH and/or NH species, respectively. The tetragonal Ba₃SiO₅ crystal has two types of oxygen site, that is four O_I sites in SiO₄ and one O_II site surrounded by six barium atoms (Ba₆O). Density functional theory (DFT) calculations suggest that the Ba₃SiO_2.5N_1.0H_2.0 unit cell is mainly comprised of N–H pairs that substitute two O_I sites (2O²⁻ ⇒ N³⁻+ H⁻) to form SiO₂NH blocks and extra H–H pairs that substitute one O_II site (O²⁻ ⇒ 2H⁻) to form Ba₆H₂ blocks (Fig. 1d and Supplementary Figs. 5 and 6). In the Ba₆H₂ block, one H⁻ ion is located at an O_II site and another H⁻ ion occupies an interstitial site adjacent to the Ba₆H₁ unit, resulting in lattice expansion (∆V/V₀ = +9.4%, Supplementary Tables 1–4). The Ba₃SiO₅, which is regarded as an antiperovskite, can accommodate a variety of combinations of elements because of its sufficient lattice space²⁸, enabling a unique mixed-anion structure.

The yellow-coloured Ba₃SiO_5−xN_yH_z powder was heated under Ar gas flow to monitor the thermal stability of lattice H⁻ and N³⁻. Upon increasing the temperature from 400 to 650 °C, the sample colour changed from light yellow to light green and finally to dark green (Fig. 1e). Most of the lattice H⁻ and a part of the N³⁻ (from the subsurface region) can be removed by heating at 650 °C in Ar flow (Fig. 1e, Supplementary Fig. 7 and Supplementary Table 5), leading to introduction of a high density of V_a sites into the crystal without destruction of the tetragonal Ba₃SiO₅ framework (Supplementary Figs. 8–11). The colour change due to the introduction of V_a sites is well understood by electron paramagnetic resonance (EPR) and DRS analysis (Fig. 1f and Supplementary Figs. 12–14). The as-prepared Ba₃SiO_5−xN_yH_z exhibits weak EPR signals at g of approximately 2.004, 2.003 and 2.002 (Fig. 1f and Supplementary Fig. 12). The intensity of these signals was enhanced with the heating temperature and a new EPR signal at g = 1.967 with strong intensity appeared above 600 °C. These two sets of peaks could be attributed to the unpaired electron trapped at the V_a of the SiO₂NH and Ba₆H₂ sites. The unpaired electron density of the sample heated at 650 °C was estimated to be 1.1 × 10²⁰cm⁻³ (Supplementary Fig. 13), which is smaller than the total electron density (approximately 7.4 × 10²⁰cm⁻³) that was evaluated by the iodometric titration method²⁹. This indicates that the sample has both unpaired electrons and paired electrons in the lattice. Moreover, when the dark green Ba₃SiO_5−xN_yH_z powder (Ar/650 °C) was heated under ammonia synthesis conditions, the lattice H⁻ and N³⁻ were regenerated and the dark green colour turned to the original yellow (used) (Fig. 1e).

Ammonia synthesis on Ba₃SiO_5−xN_yH_z

The fresh Ba₃SiO_5−xN_yH_z without any TM site shows continuous ammonia production at approximately 0.37 mmol g_cat⁻¹ h⁻¹ without degradation in activity for 150 h at 400 °C and 0.9 MPa (Fig. 2a and Supplementary Table 6). The total amount of ammonia was estimated to be approximately 5.25 mmol (per 0.1 g of catalyst), which is much higher than that of the amount of lattice N³⁻ (0.16 mmol) and H⁻ (0.37 mmol). This indicates that the ammonia produced originates from the activation of molecular N₂ and H₂ but not from the decomposition of Ba₃SiO_5−xN_yH_z (Supplementary Fig. 15). There was no colour change or alteration of the crystal structure after the 150 h reaction (Fig. 2b and Supplementary Figs. 8 and 9), which suggests that the Ba₃SiO_5−xN_yH_z is chemically stable under the ammonia synthesis conditions. When the Ba₃SiO_5−xN_yH_z was pretreated in Ar flow at 650 °C for 2 h, XRD peaks shifted towards higher angles because of removal of most lattice H⁻ and surface N³⁻ ions (Fig. 2b). The V_a-introduced Ba₃SiO_5−xN_yH_z exhibited more than three times the NH₃ synthesis rate (approximately 1.20 mmol g⁻¹ h⁻¹) than the original one, probably due to the increase of specific surface area from 8.0 to 19.5 m² g⁻¹. After the ammonia synthesis reaction, the V_a sites were re-occupied by H⁻ and N³⁻ (Supplementary Table 5), leading to a shift of XRD peaks towards the original positions and the recovery of the ¹H NMR signal (Fig. 2b,c and Supplementary Fig 11a). Neither white Ba₃SiO₅, Ba₃Si₆O₉N₄, BaSi₂O₂N₂ or Ba(NH₂)₂ nor SiO₂ powder exhibits activity for ammonia synthesis, even at temperatures up to 540 °C. By contrast, the Ba₃SiO_5−xN_yH_z powder (Ar/650 °C) can effectively activate N₂ to produce ammonia at temperatures down to 300 °C (0.20 mmol g⁻¹ h⁻¹, Fig. 2d) with a low apparent activation energy (E_a) of approximately 68.5 kJ mol⁻¹, which outperforms that of the conventional Ru-loaded MgO catalyst (300 °C, 0.01 mmol g⁻¹ h⁻¹, E_a = 114.5 kJ mol⁻¹). TPD and hydrogen temperature-programmed reduction (H₂-TPR) analysis results show that lattice N³⁻ ions in conventional Ba–Si oxynitrides with Si–N–Si bonding are very stable and could not be reduced to ammonia up to 900 °C (Supplementary Fig. 16). This is totally different from Ba₃SiO_5−xN_yH_z. We suggest that easy thermal desorption of N³⁻ and H⁻ mainly comes from the orthosilicate structure of Ba₃SiO_5−xN_yH_z, where SiX₄ tetrahedra (X = O, N, H) do not connect with each other and lattice N and H are coordinated by not only Si but also Ba. Therefore, when the V_a sites are formed, electrons at V_a sites are stabilized by the Coulombic interaction with Ba (Fig. 2c). The lattice H⁻ ions do not directly contribute to hydrogenation of N₂ but provide a number of V_a sites to capture N₂ molecules in the gas phase (Supplementary Fig. 17). It can be expected that lattice H⁻ and N³⁻ ions are continuously exchanged with molecular H₂ and N₂ via the V_a formation on Ba₃SiO_5−xN_yH_z during ammonia synthesis. Thus, the Ba–Si orthosilicate oxynitride-hydride was shown to function as a TM-free ammonia synthesis catalyst.

a, Time courses for ammonia synthesis over as-prepared Ba₃SiO_5−xN_yH_z, Ba₃SiO_5−xN_yH_z pretreated at 650 °C in Ar for 2 h and Ba₃SiO₅ at 400 °C and 0.9 MPa. b, XRD patterns of as-prepared Ba₃SiO_5−xN_yH_z (fresh) and Ba₃SiO_5−xN_yH_z pretreated at 650 °C in Ar for 2 h before and after the catalytic test in a. c, Schematic illustration of thermal induced V_a and electron formation and the N, H regeneration under NH₃ synthesis conditions in Ba₃SiO_5−xN_yH_z. d,e, Temperature dependence of the NH₃ synthesis rate over TM-free materials (d) and the Ru (1.5 wt%)-loaded samples under a pressure of 0.9 MPa (e). f, NH₃ synthesis rates for various Ru-based catalysts at 300 °C. g, HAADF-STEM image (top) and EDX-mapping (bottom) of used Ru/Ba₃SiO_5−xN_yH_z_HS.

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The Ru (1.5 wt%)/Ba₃SiO_5−xN_yH_z catalyst functioned as an efficient catalyst for ammonia synthesis at above 200 °C (0.32 mmol g_cat⁻¹ h⁻¹) and reached 27.1 mmol g_cat⁻¹ h⁻¹ at 400 °C (Fig. 2e and Supplementary Fig. 18), which is far beyond that of the Ru/Ba₃SiO₅, Ru/Ba₃Si₆O₉N₄ and Ru/BaSi₂O₂N₂ catalysts. The high ammonia synthesis activity was maintained for more than 170 h without crystal structure decomposition (Supplementary Fig. 19 and Supplementary Table 5), which demonstrates its excellent catalytic stability. This result is in contrast to that of the reported TM-free catalyst, potassium hydride-intercalated graphite composite catalyst (KH_0.19C₂₄). The activity of KH_0.19C₂₄ is not promoted by the supported TM catalysts¹⁹. The E_a of Ru/Ba₃SiO_5−xN_yH_z was as low as 64.4 kJ mol⁻¹, which is much lower than that of Ru/Ba₃SiO₅ (110.3 kJ mol⁻¹) and the reported conventional Ru-based catalysts (85–121 kJ mol⁻¹). When Ru/Ba₃SiO_5−xH_yN_z particles (Ru: 1.5 wt%) were dispersed on the SiO₂ surface, the resultant sample (Ba₃SiO_5−xN_yH_z_HS) with high surface area (105 m² g⁻¹) (Supplementary Fig. 20) exhibited much higher catalytic performance than that of Ru/Ba₃SiO_5−xH_yN_z. After the optimization of the reaction conditions (Supplementary Fig. 21), Ru (5.0 wt%)/Ba₃SiO_5−xN_yH_z_HS recorded the highest ammonia synthesis rate among the reported catalysts (Fig. 2f and Supplementary Table 7)^{12,15,16,30,31,32,33}. In addition, the activity of Ru/Ba₃SiO_5−xN_yH_z_HS was maintained even after exposure to air for 2 h (Supplementary Fig. 22). The excess SiO₂ may improve the stability of the catalyst in air.

High-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) analysis showed that small-sized Ru nanoparticles (approximately 3 nm) are highly dispersed on the surface of Ba₃SiO_5−xN_yH_z (Supplementary Fig. 23). The Ru particle size of Ru/Ba₃SiO_5−xN_yH_z is smaller than that of Ru/Ba₃SiO₅, while the large activity difference between them cannot be explained by the Ru particle size. For Ru/Ba₃SiO_5−xN_yH_z_HS, the Ba₃SiO_5−xN_yH_z particles with sizes of 100–200 nm are dispersed on the surface of SiO₂ (Fig. 2g and Supplementary Fig. 24). As a result, the active Ba₃SiO_5−xN_yH_z loaded with tiny Ru nanoparticles (approximately 2.5 nm) is effectively exposed on the catalyst surface for Ru/Ba₃SiO_5−xN_yH_z_HS. The valance state of Ru on Ba₃SiO_5−xN_yH_z is almost neutral (metallic) but slightly positive according to the Ru K-edge X-ray absorption near edge structure (XANES) (Supplementary Fig. 25) and X-ray photoelectron spectroscopy (XPS) results (Supplementary Fig. 26). This suggests that the electrons are donated from Ru to Ba₃SiO_5−xN_yH_z due to the strong Ru–N interaction. This result is rather different from those of conventional Ru-based ammonia synthesis catalysts that require negatively charged Ru to activate N₂. The reaction orders of N₂ (α), H₂ (β) and NH₃ (γ) for Ru/Ba₃SiO_5−xN_yH_z were determined to be 0.55, 0.48 and −0.63, respectively (Supplementary Fig. 27). In particular, the N₂ reaction order (α = +0.55) is only half that of conventional catalysts (α = ~1.0), where the overall reaction rate is limited by the N₂ cleavage step. This result indicates the change of RDS from N₂ dissociation to other elementary steps over the Ru/Ba₃SiO_5−xN_yH_z catalyst. The H₂ reaction order for Ru/Ba₃SiO_5−xN_yH_z is positive (β = +0.48), which suggests that the Ru/Ba₃SiO_5−xN_yH_z is not subject to H₂ poisoning.

Isotope-labelled ammonia synthesis on Ba₃SiO_5−xN_yH_z

Ammonia synthesis employing a mixed gas flow of ¹⁵N₂ and H₂ at 400 °C was conducted to elucidate the catalytic reaction mechanism over Ba₃SiO_5−xH_yN_z and Ru/Ba₃SiO_5−xH_yN_z. The m/z = 16, 17 and 18 signals gradually increased with decreasing m/z = 30 (¹⁵N₂) and m/z = 2 (H₂) (Supplementary Figs. 28 and 29), which indicates the effective formation of ammonia over Ba₃SiO_5−xH_yN_z in the absence of any TM sites (Fig. 3a). No ²⁹N₂ formation indicates that the N₂ isotope exchange reaction (N₂-IER) does not proceed since the Ba₃SiO_5−xH_yN_z does not have direct N₂ dissociation ability. In contrast to Ru/MgO (Supplementary Fig. 30), the mass signal intensity ratios of (m/z = 16)/(m/z = 18) and (m/z = 17)/(m/z = 18) over Ba₃SiO_5−xN_yH_z were much larger than the theoretical values of 0.8 and 0.075 (Fig. 3b), which indicates the formation of ¹⁵NH₃ as well as ¹⁴NH₃. N₂ gas with ¹⁵N was desorbed from the Ba₃SiO_5−xN_yH_z used after the isotope-labelled ammonia synthesis test (Fig. 3c), indicating that lattice ¹⁴N³⁻ of Ba₃SiO_5−xN_yH_z was partially replaced with ¹⁵N³⁻ from gaseous ¹⁵N₂ during the isotope test. Similar results were observed for Ru/Ba₃SiO_5−xH_yN_z (Fig. 3d–f and Supplementary Fig. 31), which suggests the Ru-loading does not change the V_a-mediated N₂ activation processes. The concentration of lattice ¹⁵N³⁻ in Ru/Ba₃SiO_5−xN_yH_z reaches approximately 37%, which is more than five times higher than that of bare Ba₃SiO_5−xN_yH_z (approximately 7%) and illustrates that loading of Ru nanoparticles would facilitate the formation of V_a sites at the Ru–support interface as N₂ activation centres. The catalytic cycle for V_a-mediated N₂ activation to ammonia was further confirmed by switching the reaction gas atmosphere between H₂ and N₂ (Supplementary Fig. 32). Accordingly, the lattice N³⁻ ions in Ba₃SiO_5−xN_yH_z were consumed by hydrogenation and were immediately regenerated by the reaction of V_a sites with molecular N₂. This shows that the transiently formed V_a sites function for N₂ activation. To confirm the validity of this model, we examined the effect of Ni (which is known to have weak interaction with N) loading, and found no significant enhancement of activity (2.1 mmol g⁻¹ h⁻¹ at 400 °C and 0.9 MPa) and V_a formation compared with the bare Ba₃SiO_5−xN_yH_z (Supplementary Figs. 33 and 34).

a,b, Reaction time profiles for NH₃ synthesis from ¹⁵N₂ and H₂ over Ba₃SiO_5−xN_yH_z (a) and the change in mass signal ratio over reaction time (b). c, TPD for Ba₃SiO_5−xN_yH_z collected after the isotope-labelled ammonia synthesis. d,e, Reaction time profiles for NH₃ synthesis from ¹⁵N₂ and H₂ over Ru/Ba₃SiO_5−xN_yH_z (d) and the change in mass signal ratio over reaction time (e). The dotted lines in b and e represent the theoretical fragment ratio (NH₂/NH₃ = 0.8 and NH/NH₃ = 0.075). f, TPD for Ru/Ba₃SiO_5−xN_yH_z collected after the isotope-labelled ammonia synthesis. The content of ¹⁵N in the desorbed nitrogen gas was calculated from the shaded area in panels c and f.

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Anion-vacancy-mediated N₂ activation on Ba₃SiO_5−xN_yH_z

N₂ activation on the Ba₃SiO_5−xN_yH_z catalyst was further examined using diffuse-reflectance infrared Fourier transform spectroscopy (DRIFTS). It should be noted that Ba₃SiO_5−xN_yH_z without Ru exhibits a peak centred at around 2,016 cm⁻¹, which is much lower than that of conventional Ru catalysts (Ru/MgO, 2,231 cm⁻¹)^34,35 and electride-based catalysts (Ru/C12A7:e⁻, 2,176 cm⁻¹)¹² (Fig. 4a and Supplementary Fig. 35). This is in contrast to N₂ adsorption on conventional non-TM sites through electrostatic interaction, where N₂ serves as a weak base molecule interacting with acid sites (electropositive sites) resulting in a blue-shift of the N≡N bond frequency^36,37,38. In the case of Ba₃SiO_5−xN_yH_z, electrons trapped at the V_a sites directly interact with N₂ and facilitate π backdonation into the antibonding orbital of the N₂ molecule, which leads to a red-shift of the N₂ adsorption band. The N₂ peak position slightly blue-shifts after Ru loading on the Ba₃SiO_5−xN_yH_z surface, which indicates that N₂ molecules are mainly captured at the V_a sites of Ba₃SiO_5−xN_yH_z accompanied by the influence of the positively charged Ru site. The N₂-IER rate of Ru/Ba₃SiO_5−xN_yH_z is negligibly smaller than that of Ru/MgO although Ru/Ba₃SiO_5−xN_yH_z showed an over ten times higher ammonia synthesis rate than Ru/MgO (Fig. 4b and Supplementary Fig. 36). This result indicates that the Ru nanoparticles on Ba₃SiO_5−xN_yH_z do not function to dissociate N₂, which is a striking difference from the well-known role of Ru in NH₃ synthesis^39,40,41.

a, DRIFTS N₂ adsorption on Ru/MgO, Ru/Ba₃SiO_5−xN_yH_z and Ba₃SiO_5−xN_yH_z at −170 °C. b, Comparison of N₂-IER rate and ammonia synthesis rate (0.9 MPa) at 400 °C for Ru/MgO and Ru/Ba₃SiO_5−xN_yH_z. The error bars represent the standard deviation of the mean based on n = 3 independent measurements. N.D., not detected. c, In situ DRIFTS observation of formation of intermediates on Ba₃SiO_5−xN_yH_z (Ru free) and Ru/Ba₃SiO_5−xN_yH_z (Ru loaded). The measurement temperature was increased from 30°C (blue) to 300°C (brown).

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In situ DRIFTS measurements (Fig. 4c and Supplementary Fig. 37) showed N₂ adsorption peaks at 2,161 and 1,976 cm⁻¹, which may be attributed to N≡N stretching of N₂ molecules adsorbed at different V_a sites close to Si and Ba sites on Ba₃SiO_5−xN_yH_z. In particular, the latter peak was red-shifted relative to that observed at −170 °C (2,016 cm⁻¹). This means that the N≡N bond is effectively weakened at reaction temperatures⁴². In addition, the peak intensity steeply increased with increasing reaction temperature especially above 200 °C. This is due to the accumulation of N₂ molecules at the V_a sites not only on the top surface but also in the subsurface region of Ba₃SiO_5−xN_yH_z. It should be noted that another intense band was observed at approximately 1,417 cm⁻¹, which can be assigned to the N=N bond⁴³. Moreover, the N–H stretching vibration was observed at 3,187–3,244 cm⁻¹ (Supplementary Fig. 37b), which is attributed to the formation of imide species. Similar intermediates were observed for Ru/Ba₃SiO_5−xN_yH_z, where N₂ peaks above 2,000 cm⁻¹ are immediately consumed to form other nitrogen species, giving negative peaks. Accordingly, NNH species could be generated as intermediates on this catalyst during ammonia synthesis. The N≡N (1,985 cm⁻¹) and N=N (1,439 cm⁻¹) stretching vibration of Ru/Ba₃SiO_5−xN_yH_z red-shifted to 1,903 cm⁻¹ and 1,386 cm⁻¹, respectively when ¹⁵N₂ and H₂ flow was conducted (Fig. 4c). The peak shift is reasonably explained by the isotope effect (1,985 cm⁻¹ × (14/15)^1/2 = 1,917 cm⁻¹, 1,439 cm⁻¹ × (14/15)^1/2 = 1,390 cm⁻¹). The 1,439 cm⁻¹ peak is not due to the H–N–H bending vibration since the peak position is not largely shifted under ¹⁴N₂ and D₂ flow conditions. On the other hand, the NNH bending vibration would appear at around 1,400–1,480 cm⁻¹, overlapping with the broad ν(N=N) band centred at around 1,420 cm⁻¹. The small shift from 1,439 to 1,422 cm⁻¹ is consistent with the isotope effect from the N=N bond in NNH (1,439 cm⁻¹) to NND (1,417 cm⁻¹). From these results, it can be concluded that the N₂ molecule is activated at V_a sites on Ba₃SiO_5−xN_yH_z and sequentially hydrogenated to form NNH_x (x = 1–3) species through the associative reaction mechanism.

DFT calculations

A DFT calculation study of reaction pathways was performed using Ba₄₈Si₁₆O₄₀N₁₅H₃₂ loaded with Ru₁₂ clusters and the reference Ru/MgO catalyst (Fig. 5 and Supplementary Figs. 38 and 39). First, H₂ was dissociated on Ru with a negligible energy barrier (I → II). The dissociated H* was then migrated from the Ru surface to a nearby lattice N of the support (II → III). Further hydrogenation reactions occurred sequentially to form NH₃ and a nitrogen vacancy site (V_N) site was formed after NH₃ desorption (III → VII). The formation energy of an N vacancy (E_NV of Ru/Ba₃SiO_5−xN_yH_z (−1.21 eV) is much lower than that of bare Ba₃SiO_5−xN_yH_z (−0.87 eV), which indicates that the supported Ru nanoparticles facilitate the formation of V_N sites (Supplementary Fig. 40). The adsorption energies of N₂ on both Ru and V_N sites of Ru/Ba₃SiO_5−xN_yH_z are calculated to be −0.4 eV (Supplementary Fig. 41), suggesting that N₂ is likely to be adsorbed on both sites. The energy barrier for N₂ dissociation on the Ru surface was 0.47 eV, which was lower than that of NNH formation (0.79 eV, TS IV). However, CO adsorption experiments confirmed that the Ru surface was barely exposed on Ru/Ba₃SiO_5−xN_yH_z (Supplementary Fig. 42). Therefore, the N₂ activation at the V_N site is more plausible than that on the Ru surface. The N₂ molecule adsorbed at the V_N site was coordinated to the adjacent Ba, Si and Ru sites, resulting in elongation of the N–N bond (1.31 Å) (Step IX). The hydrogenation of N₂ at the V_N site to form *NNH (IX → X) occurs in preference to direct dissociation of N₂ (Supplementary Fig. 43). *NNH₂ and *NNH₃ are generated by sequential hydrogenation (VIII → XII) via the distal pathway⁴⁴. The energy barriers for the hydrogenation of both lattice N and molecular N₂ are similar, in the range 0.44–1.18 eV, indicating that these hydrogenation steps are kinetically significant. Among them, the step for *NNH to *NNH₂ (1.18 eV) is the highest and is considered as the RDS. These calculation results agree well with the in situ DRIFTS observation result as shown in Fig. 4c, in which the NNH species is the main intermediate on the Ru/Ba₃SiO_5−xN_yH_z catalyst. After NH₃ desorption from NNH₃, the remaining nitrogen compensates the V_N site to restore the initial Ba₃SiO_5−xN_yH_z surface. The lattice hydrogen on Ba₃SiO_5−xN_yH_z easily migrates and covers the Ru surface (I in Fig. 5) and hydrogen is rapidly transferred to the Ru surface even when the H₂ molecule is adsorbed on the V_N site (Supplementary Fig. 44). These results support our proposed reaction mechanism, in which N₂ and H₂ molecules are activated at the V_N site and Ru surface, respectively.

The proposed reaction pathway for V_a-mediated ammonia synthesis on the Ru/Ba₃SiO_5−xN_yH_z surface. The central plot shows the energy profiles determined from DFT calculations. TS, transition state. The structures of reaction intermediates on Ru₁₂/Ba₄₈Si₁₆O₄₀N₁₅H₃₂ for each elementary step (I–XII) are shown around the outside of the central plot. The structure of *N₂ adsorbed on the V_N site is highlighted in the central plot.

Source data

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In summary, we employed a low-temperature solid-state reaction strategy for the synthesis of a Ba–Si orthosilicate oxynitride-hydride with a high concentration of lattice H⁻ and N³⁻ heteroanions. The anion vacancy of this TM-free oxide-based compound serves as an active site for efficient N₂ activation and hydrogenation to ammonia. The ammonia synthesis rate is dramatically increased upon Ru loading (1.5–5.0 wt%), where Ru does not work to dissociate N₂ but facilitates the formation of V_a sites at the Ru–support interface. Isotope-labelling ammonia synthesis, N₂ exchange and DRIFTS N₂ adsorption experiments showed that N₂ molecules are directly activated by the electron-containing V_a sites of Ba–Si orthosilicate oxynitride-hydride and thus facilitate ammonia synthesis via hydrogenation processes with low activation barriers. We suggest that easy formation of V_a sites and the flexibility of the crystal structure that allows it to accommodate large amounts of anion vacancies are essential to enable the higher catalytic activity. Our studies of V_a-mediated dinitrogen reduction to ammonia over this oxynitride-hydride catalyst illustrate the significant potential for the development of more efficient catalysts for low-temperature ammonia synthesis and other heterogeneous catalysis processes.

Synthesis of Ba₃SiO_5−xH_yN_z

The substitution of oxygen bonded to Si⁴⁺ with other anions is generally difficult due to the strong Si–O bonding. We have focused on tribarium silicate (Ba₃SiO₅) because its crystal structure is composed of isolated (ortho) SiO₄ tetrahedra and BaO units (isolated O²⁻ coordinated with Ba²⁺ ions) and the substitution of the latter oxygen ions is expected to be much easier than the former. This material is generally synthesized by solid-state reaction at elevated temperatures (over 1,200 °C)^20,21. Oxygen substitution with other anions such as H⁻ and N³⁻ does not readily proceed at low temperatures^22,23. Ba₃SiO_5−xH_yN_z powder was prepared by a low-temperature solid-state reaction. Dehydrated SiO₂ (Q-3, Fuji Silysia Chemical) and Ba (99.99%, Aldrich) with a molar ratio of 1:3 were set in a stainless-steel reactor operated in an Ar-filled glovebox. Ammonia gas was introduced to the reactor with a flow rate of 50 ml min⁻¹ at a temperature of approximately −50 °C for 30 min to obtain sufficient liquefied ammonia. Ba was dissolved in the liquefied ammonia under magnetic stirring for another 1 h at the same temperature. The well-sealed reactor was then heated under a temperature programme of 50 °C for 30 min, 75 °C for 30 min and 100°C for 1 h to obtain a barium amide–SiO₂ (3Ba(NH₂)₂–SiO₂) mixture. The mixture was collected in an Ar-filled glovebox after removal of the unreacted ammonia inside the reactor through discharging to the atmosphere by Ar gas introduction at 50 °C. The obtained powder mixture was then wrapped in molybdenum foil and heated in a quartz-tube reactor under a NH₃ flow (100 ml min⁻¹). The heating temperature was increased from room temperature to 400–700 °C with a heating rate of 5 °C min⁻¹ and maintained at the target temperature for 12 h. After cooling to room temperature, the obtained yellow Ba₃SiO_5−xH_yN_z powder was collected and stored in an Ar-filled glovebox for further use. High surface area Ba₃SiO_5−xH_yN_z_HS powder was prepared by the same method with only the molar ratio of SiO₂ to Ba changed from 1:3 to 1:1.05. The effect of TM impurities such as Fe, Co, Ru and Mo in Ba₃SiO_5−xH_yN_z after the ammonia synthesis test was determined by inductively coupled plasma atomic emission spectroscopy analysis (ICPS-8100, Shimadzu).

Synthesis of Ba₃SiO₅, Ba₃Si₆O₉N₄ and BaSi₂O₂N₂

Ba₃SiO₅ powder was prepared by high-temperature solid-state reaction of well-mixed SiO₂ and BaCO₃ at 1,240 °C in an Ar (95%)/H₂ (5%) flow. Typically, BaCO₃ (99.95%, High Purity Chemicals) and SiO₂ (Q-3, Fuji Silysia Chemical) in a stoichiometric ratio were thoroughly mixed in a small amount of ethanol and ground in an agate mortar for 1 h. After drying, the mixture was calcined at 1,240 °C in a tube furnace under an Ar (95%)/H₂ (5%) flow for 12 h. The conventional Ba₃Si₆O₉N₄ and BaSi₂O₂N₂ were synthesized by the reported two-step procedures using BaSiO₃ and Ba₂SiO₄ as precursors, respectively^45,46. First, a well-mixed BaCO₃ and SiO₂ mixture with a molar ratio of 1:1 (2:1) was calcined in a tube furnace at 1,150 °C for 5 h under a flow of N₂ (95%)/H₂ (5%) to obtain BaSiO₃ (Ba₂SiO₄). Subsequently, BaSiO₃ (Ba₂SiO₄) and Si₃N₄ with a molar ratio of 3:1 (1:1) were well mixed by grinding and the mixture was further calcined in a tube furnace at 1,350 °C for 5 h under the flow of N₂ (95%)/H₂ (5%) to obtain Ba₃Si₆O₉N₄ (BaSi₂O₂N₂).

Loading of TM nanoparticles

The loading of Ru nanoparticles (NPs) on various supports (Ba₃SiO_5−xN_yH_z, Ba₃SiO₅, Ba₃Si₆O₉N₄, BaSi₂O₂N₂, Ba(NH₂)₂, SiO₂ and MgO) was performed by the chemical vapour deposition method using triruthenium dodecacarbonyl (Ru₃(CO)₁₂, 99%, Aldrich) as a precursor. Typically, a mixture of support powder and Ru₃(CO)₁₂ with the desired weight ratio was set in a well-evacuated silica tube and heated in an oven under the following programme: heating from room temperature to 40 °C (2 °C min⁻¹) for 1 h, heating up to 70 °C (0.25 °C min⁻¹) and holding for 1 h, heating up to 120 °C (0.4 °C min⁻¹) and holding for another 1 h and finally heating up to 250 °C (0.9 °C min⁻¹) and holding for 2 h. The samples were collected and stored in an Ar-filled glovebox after naturally cooling to the ambient temperature. The actual amount of loaded Ru NPs on the support was determined using an X-ray fluorescence spectrometer (XRF, S8 TIGER, Bruker) (Supplementary Fig. 18). The Ni/Ba₃SiO_5−xN_yH_z was prepared by heating a mixture of nickelocene and Ba₃SiO_5−xN_yH_z powder at 250 °C for 2 h in a gas flow of N₂ (purity >99.99995%, 2 ml min⁻¹) and H₂ (purity >99.99999%, 6 ml min⁻¹) under a pressure of 0.1 MPa. Ba₃SiO_5−xN_yH_z powder synthesized at 600 °C showed the highest activity when Ru was loaded and thus its structural and catalytic properties were investigated further. The catalytic activities of Ru/Ba(NH₂)₂ and Ru/SiO₂ were negligibly low at 300 °C and so are not described in the main text.

Characterization

Powder X-ray diffraction (XRD) patterns of the samples were recorded on a diffractometer (D8 Advance, Bruker) with monochromatic Cu Kα radiation (λ = 1.5418 Å) at a voltage of 40 kV and a current of 40 mA. An X-ray transmitting capsule cell was used to avoid oxidation of the sample during the XRD measurements. The sample purity was determined by Rietveld analysis of the XRD pattern using the TOPAS code (Bruker AXS, version 4.2). Temperature-programmed desorption (TPD) experiments were performed on a catalyst analyser (BELCAT-A, MicrotracBEL). The sample (approximately 50 mg) was heated from room temperature to 950 °C with a heating rate of 10 °C min⁻¹ in a stream of pure He gas (>99.99995%) with a flow rate of 30 ml min⁻¹. The desorbed products during the heating process were monitored using a mass spectrometer (BELMass, MicrotracBEL). Calibration of the N₂ (m/z = 28) and H₂ (m/z = 2) mass peak areas was conducted by monitoring pulses of m/z = 28 and 2 more than five times to obtain average calibration data. The CO-pulse chemisorption experiment was conducted at 50 °C using a He flow (50 ml min⁻¹) and pulses of 0.031 ml (10% CO in He) to evaluate the number of exposed Ru sites by using a catalyst analyser (BELCAT-A, MicrotracBEL). Prior to the experiment, the samples were pretreated with a H₂ (5%)/Ar flow (50 ml min⁻¹) at 400 °C for 60 min, followed by a He flow (50 ml min⁻¹) at 400 °C for 15 min to remove hydrogen atoms adsorbed on the Ru surface. The lattice N³⁻ ions cannot be totally desorbed by the heating treatment. Therefore, the actual amount of lattice N³⁻ ions was further confirmed by an acid dissolution method accompanied by ion chromatography (Supplementary Fig. 45). Solid-state ¹H MAS NMR and ²⁹Si MAS NMR of Ba₃SiO₅ and Ba₃SiO_5−xN_yH_z were performed on a Bruker Biospin DSX-400 spectrometer (Bruker). The Q₀ signal appears at lower magnetic field when O²⁻ ions in the SiO₄ tetrahedral unit are replaced with more electropositive H⁻ and N³⁻ ions²⁷. Optical diffuse reflectance spectra were measured at room temperature with a spectrophotometer (U-4000, Hitachi) using MgO powder as a background. The Kubelka–Munk transformation was used to convert the measured spectra into absorption spectra. Electron paramagnetic resonance (EPR) measurements of the Ba₃SiO_5−xH_yN_z powder samples were conducted on a spectrometer (E580 X-band, Bruker) (approximately 9.7 GHz) at room temperature. Ru K-edge X-ray absorption fine structure (XAFS) measurements were performed on a synchrotron radiation ring at the NW-10A beamline (Photon Factory, KEK, Japan) using a Si(311) double-crystal monochromator and ionization chambers. A mixture of Ru/Ba₃SiO_5−xH_yN_z and dehydrated boron nitride powders was pressed into a pellet with a diameter of 10 mm and well-sealed in a polyethylene pack in an Ar-filled glovebox. The collected data were processed using the ATHENA software package. The filtered k³-weighted χ spectra were Fourier transformed into r space with a k range 3.0–16.0. High-angle annular dark-field-scanning transmission electron microscopy (HAADF-STEM) observations were conducted using a microscope (ARM-200F, JEOL) operated at 200 kV. The mean particle diameter and distribution of Ru NPs on the support were determined by measuring the size of 200 metal NPs in a STEM image. The specific surface area of the catalysts was determined by the analysis of N₂ adsorption–desorption isotherms collected on a BELSORP-mini II (MicrotracBEL) at 77 K using the Brunauer–Emmett–Teller (BET) method. X-ray photoelectron spectroscopy (XPS) measurements were performed on a spectrometer (ESCA 3200, Shimadzu) using Mg Kα radiation at <10⁻⁶ Pa. The XPS spectra were calibrated with respect to the C 1s signal at 284.8 eV.

Iodometric titration method

First, 10–20 mg of Ba₃SiO_5−xN_yH_z heated at 650 °C in Ar was set in a glass vial with 1 ml of pure ethanol in an Ar-filled glove box. Then, 2 ml of I₂ solution (5 mmol l⁻¹) and 0.5 ml concentrated hydrochloric acid were added. After magnetic stirring to dissolve the powder, electrons in the sample were consumed by the reduction of I₂ into I⁻ ions. Then, the residual I₂ was titrated using a standard sodium thiosulfate (Na₂S₂O₃) solution (4 mmol l⁻¹). To confirm the endpoint of the titration, a few drops of starch solution were added, which induced a violet colouration. The measurements were repeated three times to obtain an average value.

Ammonia synthesis reactions

Ammonia synthesis over various catalysts (0.1 g) was conducted in a stainless-steel reactor in a gas flow of N₂ (purity >99.99995%, 15 ml min⁻¹) and H₂ (purity >99.99999%, 45 ml min⁻¹) with a pressure of 0.9 MPa and under a steady-state temperature in the range 200–500 °C. The ammonia gas produced was trapped in a 5 mmol l⁻¹ sulfuric acid solution to obtain NH⁴⁺ solution and the concentration of NH⁴⁺ was then monitored using ion chromatography (Prominence, Shimadzu) with a conductivity detector. All the catalysts were treated under the ammonia synthesis conditions at 400 °C for 20 h to remove surface carbon species that remained after the chemical vapour deposition processes for TM loading, as well as to reach a stable catalytic state. The apparent E_a of the measured catalysts was calculated from Arrhenius plots of the ammonia synthesis rates at different temperatures. To avoid the thermal equilibrium effect, the ammonia yield for E_a calculation was less than 20% of that at equilibrium. For comparison with the most active catalyst (Ba₂RuH₆/MgO) reported, we also measured the activity under similar experimental conditions (0.03 g catalyst, 1.0 MPa).

Kinetic analysis

The reaction orders of N₂ (α), H₂ (β) and NH₃ (γ) were measured at a steady-state temperature of 340 °C and pressure of 0.9 MPa with a weight hourly space velocity (WHSV) of 36,000 ml g⁻¹ h⁻¹. The activity of the catalysts measured under these conditions was far from the thermal equilibrium to avoid the effects of thermodynamic limits. Calculation of the ammonia synthesis rate (r) was based on equation (1), while equations (2)–(5) were used for the kinetic analysis.

where r, W, y₀, q and (1−m) represent the NH₃ synthesis rate, the catalyst weight, the outlet NH₃ mole fraction, the total volume flow rate and the reaction order with respect to NH₃ (γ), respectively. k and k₂ are the rate constants. Finally, the α and β parameters can be determined by plotting the logarithm of a constant within the limited range q (C) versus the partial pressure of N₂ (P_N2) or H₂ (P_H2).

Isotope-labelled experiment and isotopic N₂ exchange measurement

Ammonia syntheses over Ru/Ba₃SiO_5−xN_yH_z and conventional Ru/MgO from heavy ¹⁵N₂ (purity 98%) and H₂ were performed in a closed U-shaped glass circulation reactor connected to a gas chromatograph (GC, GC-8A, Shimadzu) with a Chromosorb 103 column and a quadrupole mass spectrometer (M-101QA-TDM, Canon Anelva) using He as the carrier gas. Before the reaction, the catalyst set in the closed glass circulation reactor was evacuated using a vacuum pump with a liquid nitrogen trap to remove the adsorbed water on the catalyst. The mixture of ¹⁵N₂ (15.0 kPa) and H₂ (45.0 kPa) gases was introduced into the glass reactor and kept circulating using an electromagnetic drive gas circulator. The catalyst (0.1 g) set in the system was heated at 400 °C. The gases produced were abstracted with a gas-sampling loop and flushed out with He gas (0.1 MPa) and then injected into the GC. The outlet gases from the GC were then analysed using the quadrupole mass spectrometer and the corresponding masses of m/z = 2, 16, 17, 18, 28, 29 and 30 were monitored as a function of time. The isotope N₂ exchange experiments were conducted using the same system. A mixed gas flow of ¹⁵N₂ (4 kPa) and ¹⁴N₂ (16 kPa) was introduced and circulated in the system over the catalyst (0.1 g) heated at 400 °C and the mass signals of m/z = 28, 29 and 30 were monitored with respect to the reaction time. The influence of H₂O for this measurement can be ignored because the mass signal of m/z = 18 was not increased with reaction time when ¹⁵N₂ was replaced with ¹⁴N₂ (Supplementary Fig. 29).

DRIFTS of N₂ absorption experiments

All the samples for DRIFTS of N₂ absorption analysis were pretreated under the ammonia synthesis conditions for 20 h. To confirm the role of V_a sites in N₂ activation, both Ba₃SiO_5−xN_yH_z and Ru/Ba₃SiO_5−xN_yH_z catalysts were heated at 650 °C under an Ar atmosphere before the DRIFTS measurements. The powder samples were placed in an alumina sample cup and introduced into a stainless-steel heat chamber equipped with a KBr window (STJ-0123-HP-LTV, S.T. Japan). The samples were heated to above 400 °C in an Ar flow (10 ml min⁻¹) for 5 h to remove surface adsorbed species and were then well evacuated. After the pretreatment, the samples were cooled to −170 °C under vacuum to obtain a background spectrum. The catalysts were then exposed to pure ¹⁴N₂ (99.99995%) or heavy ¹⁵N₂ (98%) to collect infrared spectra for adsorbed N₂. The infrared spectra were measured using a spectrometer (IRTracer-100, Shimadzu) equipped with a mercury–cadmium–tellurium (MCT) detector at a resolution of 4 cm⁻¹.

In situ DRIFTS observations

The powder samples were placed in an alumina sample cup and introduced into a stainless-steel heat chamber equipped with a BaF₂ window (160-1147, S.T. Japan). The samples were placed under a flow of ¹⁴N₂ (or ¹⁵N₂) (3 ml min⁻¹) and H₂ (or D₂) (9 ml min⁻¹) at 30 °C for 1 h and the spectra were measured as the background spectra (Supplementary Fig. 37a). Then the sample was gradually heated from 30 to 300 °C and the spectra at different reaction temperatures were recorded on a spectrometer (FT/IR-6XV, JASCO) equipped with a mercury–cadmium–tellurium (MCT) detector at a resolution of 0.25 cm⁻¹. Figure 4c shows the difference spectra using the spectra measured at 30 °C under the same reaction gas atmosphere as the background spectra (Supplementary Fig. 37a). The band at 1,424 cm⁻¹ due to the v(¹⁵N=¹⁴N) is also observed, which may be caused by the recombination of lattice ¹⁴N and ¹⁵N in Ba₃SiO_5−xN_yH_z at the elevated temperature.

DFT calculations

All structure relaxation and electronic structure calculations were performed using the DFT method as implemented in the Vienna ab initio simulation package (VASP)⁴⁷. The calculation settings of 600 eV cutoff energy and Γ-centred k-points with a mesh resolution of 2 × 0.04 Å were adopted for all structures. To obtain the total energy, the possible structures were fully relaxed using the Perdew–Burke–Ernzerhof (PBE) functional with the projector augmented wave (PAW) method until the convergence criteria of energy and force were met (less than 1.0 × 10⁻⁶ eV and 1.0 × 10⁻² eV Å⁻¹, respectively)⁴⁸. On the basis of the chemical stoichiometry determined by the experiments, the computational models Ba₃SiO_5−2xN_xH_x (N–H pair replaces O–O pair), Ba₃SiO_5−yH_2y (H–H pair replaces oxygen) and Ba₃SiO_5−2x−yN_xH_x+2y (N–H pair replaces O–O pair with an extra H–H pair) were derived from the optimized Ba₃SiO₅ primitive cell. As for the H–H pair, two hydrogen atoms were placed at one oxygen site with the H–H distance set to approximately 0.8 Å for charge compensation. Among all the computation models listed in Supplementary Tables 2-4, the computation model of Ba₃SiO_5−2x−yN_xH_x+2y with x = 1 and y = 0.5 (that is Ba₃SiO_2.5NH₂) well reproduces the experimental result (Supplementary Table 1) and therefore, it was selected as a benchmarking computational model for further reaction pathway calculations. The density of states of the Ba₃SiO_2.5NH₂ system was calculated using the tetrahedron method with a Γ-centred k-point mesh of 7 × 7 × 4. The atom-projected densities of states were evaluated with Wigner–Seitz radii (R_WS) of 1.62 Å satisfying R_WS = (3V_cell/4πN)^1/3, where V_cell is the unit cell volume (682.89 ų) and N is the number of total atoms in the unit cell (N = 38). The calculation settings of 400 eV cutoff energy and a Monkhorst–Pack mesh k-point grid of 2 × 2 × 1 were adopted for surface structures. The bottom two layers were fixed for the slab model. The Ba₃SiO₂NH₂(001) surface is the most stable among the low-index surfaces calculated using the DFT method. At the (001) surface, SiO₂NH units are preferentially exposed over Ba₆H₂ units. Therefore, the anion vacancy site is formed at SiO₂NH units on the Ba₃SiO₂NH₂(001) surface in our simulation. The convergence criteria were set as 1.0 × 10^–5 eV in energy and <1.0 × 10^–2 eV Å⁻¹ in force for the structure relation (1.0 × 10^–5 eV in energy and <5.0 × 10^–2 eV Å⁻¹ in force for intermediates and transition state structures in the climbing image nudged elastic band method^49,50, reaction path analysis). These calculation conditions are almost the same as those in the previously reported work for the simulation of catalytic ammonia synthesis⁵¹.