Main

Methane (CH4) comprises approximately 90% of natural gas, which is a naturally abundant carbon resource9,10. Use of methane as a C1 raw material for the synthesis of value-added chemicals has therefore become increasingly important in the chemical industry1,2. The selective conversion of CH4 to more-complex carbon-based compounds under mild conditions is one of the most important transformations both in nature11,12,13 and for the chemical industry3,4,14,15. At present, the large-scale conversion of CH4 to methanol (CH3OH) is typically performed through steam reforming in conjunction with catalysis by CuO/ZnO/Al2O3 (refs. 3,4) and applying high pressures and temperatures. Therefore, the development of efficient and selective catalytic systems for CH4 conversion that can be performed in aqueous media under mild conditions is considered a worthwhile goal related to sustainable development1,2.

The selective conversion of CH4 to CH3OH is one of the most challenging oxidation reactions1,2. This is because the C–H bonds in CH4 are highly inert, with a bond dissociation energy (BDE) of 105 kcal mol–1 (ref. 8), whereas the C–H bonds in CH3OH are weak, with a BDE of 96 kcal mol–1 (ref. 16). Therefore, the latter is more reactive. Heterogeneous catalysts have also been reported to promote direct CH4 oxidation to CH3OH2,17,18,19,20,21, but the conversion and selectivity obtained with these materials are not yet satisfactory3,4. In biological systems, metalloenzymes catalyse the conversion of CH4 to CH3OH under ambient conditions11,12,13. It has been proposed that during the hydroxylation of CH4 by soluble methane mono-oxygenase (sMMO)11, CH4 reacts with the reactive bis(μ-oxo)diiron(IV) core in the hydrophobic cavity formed by the amino acid residues of the protein and is converted to hydrophilic CH3OH, which is subsequently released to the surrounding aqueous medium12,13.

Numerous metal complexes have been prepared to artificially catalyse the oxidation of CH4 to CH3OH and the reactivity of these materials has been examined5,6,22,23,24,25,26. For example, the CH4 conversion to methyl bisulfate (CH3OS(O)2OH) with a selectivity of 81% using CH4 at high pressure (9.0 MPa), H2SO4 as the oxidant and Pt complex as the catalyst was previously reported6,7,14. This process was expensive and also involved further steps to produce CH3OH5,6,14,15. One of the most promising approaches to suppressing the overoxidation of CH3OH during the catalytic oxidation of CH4 is the use of catalysts with a substrate-trapping site or a hydrophobic cavity close to the catalytically active metal centre8,11,12,13. It would be beneficial to develop molecular oxidation catalysts enabling the efficient use of CH4 as a naturally occurring feedstock. Here we report the highly efficient and selective catalysis of gaseous alkane oxidation using FeII complexes (acting as molecular catalysts) with hydrophobic second coordination spheres (SCSs) made of mesityl or anthracenyl substituents. On the basis of the proposed mechanism of selective oxidation by sMMO13, we provide a concept for the design of catalysts with hydrophobic SCSs near the metal centre. These materials enable the selective and environmentally benign transformation of gaseous alkanes, including CH4, as hydrophobic substrates in aqueous media through a so-called catch-and-release mechanism.

We synthesized FeII complexes of pentadentate ligands with one N-heterocyclic carbene (NHC) moiety bearing hydrophobic SCSs. These complexes had the general formula [Fe(RPY4Cl2BIm)(CH3CN)](PF6)2 (2-AN, R = mesityl (Mes); 3-AN, R = anthracenyl (Ant); AN = CH3CN) (Fig. 1a). The detailed synthetic protocols used to obtain 2-AN and 3-AN are provided in the Methods. Complex 1-AN (R = H), without a hydrophobic SCS, was also synthesized for comparison purposes27. The low-spin FeII–NHC complexes 1-AN, 2-AN and 3-AN were characterized by 1H NMR spectroscopy (Supplementary Figs. 1–3) and electrospray ionization time-of-flight mass spectrometry (ESI-TOF-MS) (Supplementary Figs. 4–6). FeII complexes with benzonitrile (BN), 2-BN (Fig. 1b–d) and 3-BN (Fig. 1e–g), both of which contain a BN molecule as an axial ligand in place of AN, were also prepared to determine the crystal structures by X-ray crystallography (Supplementary Fig. 7 and Supplementary Table 1). The lengths of the Fe–C and Fe–N bonds determined were comparable, indicating that the electronic interactions in the first coordination sphere of each complex were almost identical.

Fig. 1: Structures of the Fe–NHC complexes used in this study.
figure 1

a, Schematic of 1-X, 2-X and 3-X (X: OH2, OD2, NCCH3 (= AN) or NCC6H5 (= BN)). b–g, ORTEP drawings of the cationic moieties of 2-BN (b–d) and 3-BN (e–g) were produced using 50% (2-BN) or 40% (3-BN) probability thermal ellipsoids: overall (b,e), top (c,f) and side (d,g) views. Hydrogen atoms and two PF6− ions have been omitted for clarity. Grey, carbon; blue, nitrogen; green, chlorine.

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We used n-butane, propane, ethane and methane as gaseous alkane substrates for catalytic oxidation. The oxidation was performed at 323 K under an atmosphere comprising one of the gaseous alkanes (butane, 0.1 MPa; propane, 0.7 MPa; ethane, 0.8 MPa; methane, 0.98 MPa) in a high-pressure glass tube containing a solution of 1-AN, 2-AN or 3-AN (1.0 μM) as the precatalyst and sodium persulfate (Na2S2O8, 5.0 mM) as the oxidant in D2O:CD3CN (95:5, v/v, 1.0 ml, pD (= −log[D+]) was not adjusted). Under these conditions, the FeII–AN complexes used as precatalysts were converted to the corresponding FeII–OD2 complexes 1-OD2, 2-OD2 and 3-OD2 through an exchange of the ligands (Supplementary Figs. 8–13).

Under the present conditions, the catalytic oxidation reactions afforded 2-butanol and 2-butanone from n-butane, 2-propanol and acetone from propane, ethanol and acetic acid from ethane, and methanol and formic acid from methane (Table 1 and Fig. 2). The catalytic turnover numbers (TONs) of the reactions when performed for 3 h were determined by 1H NMR spectroscopy. We found that the TONs for the catalytic oxygenations of the four gaseous substrates using 3-OD2 as the catalyst were the largest among the three catalysts used (Table 1) and were much larger than those obtained from catalysis using iron salts (Extended Data Table 1). In the case of n-butane, propane and ethane oxidation by 3-OD2, highly selective two-electron oxidation (that is, hydroxylation) was found to afford the corresponding alcohols with TONs of 1.8 × 103, 1.3 × 103 and 9.5 × 102, respectively (Table 1 and Fig. 2). The associated selectivity values were 78% for 2-butanol, 88% for 2-propanol and 89% for ethanol. The total TON of 5.0 × 102 and the 83% CH3OH selectivity obtained with the 3-OD2 during a 3-h CH4 oxidation trial are some of the highest values reported for catalytic CH4 oxidation using a molecular metal complex as the catalyst22,23,24,25,26. The 4.1% conversion of CH4 and 83% CH3OH selectivity by 3-OD2 at 323 K (see Methods) are higher than those of heterogeneous catalysts, such as metal-containing zeolite, which is active at 448–689 K (approximately 2% CH4 conversion and around 58–82% CH3OH selectivity)2. By contrast, we found that the oxidation of 2-propanol, ethanol and methanol using 3-OD2 as the catalyst had much smaller TONs for the corresponding oxidation products compared with those for the corresponding gaseous alkanes (Extended Data Table 2). These values were smaller than or comparable with the values observed without a catalyst. Thus, the oxidation of alcohols was predominantly attributed to the presence of Na2S2O8. The TON obtained for the oxidation reactions of 2-propanol, ethanol and methanol was found to decrease in the order of 1-OD2 > 2-OD2 > 3-OD2 (Extended Data Table 2). These results indicate that the hydrophobic SCSs efficiently promoted oxidation of the hydrophobic substrates while hydrophilic oxidation products were rapidly released, thus suppressing overoxidation of these two-electron-oxidized products.

Table 1 Summary for the catalytic oxidations of gaseous alkanes
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Fig. 2: Comparison of TONs and alcohol selectivity among the three catalysts.
figure 2

a–d, Data for the oxidation of butane (a), propane (b), ethane (c) and methane (d). Red, TONs for the alcohol products (that is, two-electron-oxidized products); blue, TONs for the four-electron- or six-electron-oxidized products; black dots, alcohol selectivity (TONs for alcohol product/total TONs × 100, %). For reaction conditions, see Table 1. Data are mean ± s.d. from three experiments.

Source Data

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The gas chromatography–mass spectrometry analysis for the reaction mixture of the catalytic CH4 oxidation using Na2S216O8 in H218O:CH3CN (95:5, v/v) indicated that only CH318OH was obtained and thus water acted as the sole oxygen source27 (for the detection of CH316OH, see Extended Data Fig. 1a,b and Supplementary Fig. 14). After a catalytic CH4 oxidation reaction for 3 h using 3-AN, the catalyst was found to be durable and 75% of the catalysts retained their original structure, as confirmed by ESI-TOF-MS, ultraviolet–visible (UV–vis) and 1H NMR spectroscopy analyses (Supplementary Figs. 15–19).

The capture of CH4 molecules in the hydrophobic SCSs of 3-OD2 was confirmed by titration experiments using 1H NMR spectroscopy experiments in which 3-OD2 was added to solutions of CH4 (0.05 mM) in D2O:CD3CN (1:1, v/v) at 298 K. The 1H NMR signal of CH4 was observed at δ = 0.221 ppm in the absence of 3-OD2. However, this signal was shifted upfield with increasing concentrations of 3-OD2 (Extended Data Fig. 2a). This phenomenon suggests that the CH4 molecules were trapped in the hydrophobic SCSs of 3-OD2, probably because of CH–π interactions. Furthermore, the 1H NMR signal of CH4 was observed as one singlet peak, indicating a rapid exchange between free CH4 molecules and those captured in the SCSs at 298 K (ref. 28). A nuclear Overhauser effect was observed between the hydrogen nuclei of CH4 and those of anthracenyl moieties and at the 6-position of the pyridine moieties. This shows that the CH4 molecules were located inside the hydrophobic cavities (Methods and Supplementary Figs. 20–31). Furthermore, the 1H NMR signals derived from the Ant groups and NHC moieties of 3-OD2 also displayed moderate shifts after bubbling CH4 through a solution of 3-OD2 in D2O:CD3CN (1:1, v/v) at 298 K (Extended Data Fig. 2b).

We assessed the thermodynamics of capturing CH4 molecules in the hydrophobic SCSs of 3-OD2 by performing titration experiments at various temperatures using 3-OD2 in D2O:CD3CN (1:1, v/v; 600 μl) containing CH4. We analysed the variations in the chemical shift of the CH4 1H NMR signal after increasing the concentration of 3-OD2 to determine the association constant, Ka (Extended Data Fig. 3 and Supplementary Fig. 32), for each temperature29 (equation (1) in Methods). On the basis of these data, we determined the thermodynamic parameters determined using van ’t Hoff plots and these were found to be ΔH° = –24 ± 1 kJ mol–1 and ΔS° = –19 ± 4 J K–1 mol–1 (Extended Data Fig. 3e). These values are comparable with those reported for the encapsulation of CH4 in a self-assembling superstructure (ΔH° = –38 kJ mol–1 and ΔS° = –84 J K–1 mol–1) (ref. 30). The results described above provide evidence for the formation of adducts between 3-OD2 and gaseous alkanes in the aqueous medium. Furthermore, the corresponding association constants, KaH and KaMes, for the entrapment of CH4 by 1-OD2 and 2-OD2, were also determined to be less than 10 M–1 and (1.7 ± 0.4) × 102 M–1 at 298 K, respectively (Extended Data Fig. 3f,g).

We investigated the kinetics of the catalytic oxidation of CH4 by 3-OH2 in H2O:CH3CN (95:5, v/v) at 323 K to gain further insights into the oxidation process. We found the rate constant (kHAnt) of CH4 oxidation by 3-OD2 to be (2.8 ± 0.1) × 10–6 s–1 (see Methods and Extended Data Fig. 1a–c). We also performed a kinetic isotope effect (KIE) analysis using CD4 in the same aqueous medium (H2O:CH3CN (95:5, v/v)) at 323 K. The kDAnt value was determined to be (7.6 ± 0.8) × 10–8 s–1 (see Methods and Extended Data Fig. 1d–f). The oxidation of CD4 was slower than that of CH4. The KIE value (kHAnt/kDAnt) for CH4 oxidation by 3-OH2 was determined to be 37. This large KIE value indicates that the abstraction of a hydrogen atom from a C–H bond of CH4 was a component of the rate-determining step for the overall process. It should also be noted that this extremely large KIE value indicates that non-classical hydrogen atom tunnelling is involved in the CH4 oxidation reaction, as has previously been reported for intermediate Q, which is the reactive intermediate to oxidize CH4 in the sMMO system31.

The reactive species formed by the two-electron oxidation of 3-OH2 was characterized by cold-spray ionization time-of-flight mass spectrometry, microscopic Raman, UV–vis, electron spin resonance (ESR) and 1H NMR spectroscopies; these analyses indicated the formation of a triplet FeIV–oxo complex, 3-O (Methods, Extended Data Fig. 4 and Supplementary Figs. 33–35). Furthermore, the kinetic studies showed that 3-O generated in situ immediately reacted with CH4 (Supplementary Figs. 36 and 37). We also explained the properties of 3-O by carrying out density functional theory (DFT) calculations for the FeIV–oxo complex derived from 3-OH2. We optimized the structure of triplet 3-O derived from the proton-coupled electron-transfer (PCET) oxidation of 3-OH2 and performed DFT calculations to ascertain an energy minimum (Supplementary Fig. 38). In the optimized structure, the spin density of 3-O was determined to be localized primarily at the Fe centre (1.14) and terminal oxo ligand (0.92) (Supplementary Table 2). The high spin density on the terminal oxo ligand and the small bond order (1.5) between the Fe centre and terminal O ligand suggest that 3-O involves a larger contribution of an FeIII(O·) electronic structure compared with typical FeIV(O) complexes, as reflected by the lower energy of Raman scattering (799 cm–1) derived from the Fe–O bond32,33. This leads to improved CH4 oxidation activity.

The energy profile for CH4 oxidation by 3-O as obtained from DFT calculations is shown in Extended Data Fig. 5. In this process, a CH4 molecule trapped in the SCS undergoes hydrogen atom transfer to the FeIV(O) moiety to generate an FeIII(OH) complex and a methyl radical (CH3·) as an intermediate (‘Int’ in Extended Data Fig. 5). The hydrogen atom transfer reaction proceeds through a transition state (‘TS’ in Extended Data Fig. 5) in conjunction with a barrier calculated to be 19.2 kcal mol–1. Finally, the hydroxo ligand bound to the FeIII centre forms a C–O bond with a CH3· radical to afford an FeII–CH3OH complex as the product (Extended Data Fig. 5). Furthermore, barriers of transition states and intermediates for the CH4 oxidation catalysed by 1-OH2 and 2-OH2 were calculated to be comparable with those by 3-OH2 (Supplementary Table 3). Thus, the reactivity of the FeIV=O moieties formed for the three catalysts should be comparable based on the same first coordination sphere, although 3-O has the highest CH4 oxidation reactivity. Furthermore, the FeII–CH3OH complex derived from 3-O was calculated to be more stable by approximately 7 kcal mol–1 than those derived from 1-O and 2-O (Supplementary Table 3). Therefore, the role of the hydrophobic SCS of 3-O is very important for enhancing the reactivity by trapping a CH4 molecule near the Fe centre.

On the basis of the results described above, we propose a mechanism for CH4 oxidation using 3-AN as a precatalyst in H2O:CH3CN (95:5, v/v), as shown in Fig. 3. In the first step, an AN ligand of 3-AN is substituted by an aqua ligand in the aqueous medium. The FeII–aqua complex, 3-OH2, is also assumed to undergo PCET oxidation to afford the corresponding FeIV(O) species with an FeIII(O·) character. A CH4 molecule captured in the hydrophobic SCS is oxidized through C–H bond cleavage—this being the rate-determining step—to afford CH3OH. In the final step, the weakly bound hydrophilic CH3OH molecule is substituted by a H2O molecule from the solvent and released to the aqueous medium to regenerate 3-OH2.

Fig. 3: Proposed mechanism for the catch-and-release oxidation of CH4 by 3-AN and S2O82–.
figure 3

In this mechanism, a hydrophobic CH4 molecule is captured in the hydrophobic SCS of 3-OH2 formed by ligand substitution of CH3CN in 3-AN with H2O. 3-OH2 undergoes PCET oxidation to generate the FeIV–oxo complex (3-O), which hydroxylates the CH4 molecule trapped in the vicinity. The resultant methanol complex undergoes ligand substitution with H2O to release the hydrophilic methanol molecule to the aqueous media to accomplish the catalytic cycle.

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Our approach to efficient and selective catalytic two-electron oxidation of gaseous alkanes, on the basis of catalyst SCSs differentiating between hydrophobic substrates and hydrophilic products, demonstrates the viability of a catch-and-release mechanism when targeting natural gas. We anticipate that further development of this strategy might result in efficient and selective catalytic processes that can use naturally abundant carbon feedstocks.

Methods

Synthesis of [FeII(MesPY4Cl2BIm)(CH3CN)](PF6)2 (2-AN)

To a suspension of FeII acetate (161 mg, 1.0 mmol) in dimethyl sulfoxide (DMSO; 5 ml), MesPY4Cl2BIm-H·Br (100 mg, 0.10 mmol; see Supplementary Information) was added. The mixture was stirred at room temperature for 24 h in the dark. After the addition of KPF6 (854 mg, 4.6 mmol) and distilled water (20 ml), the reaction mixture was filtered through a membrane filter to obtain a red solid. The crude product was re-crystallized from CH3CN/1,2-dimethoxyethane (DME) to obtain pale-red crystals of 2-AN (70 mg, 0.050 mmol) with a 50% yield. 1H NMR (CD3CN): δ = 1.62 (s, 12H, CH3), 1.80 (s, 12H, CH3), 2.24 (s, 12H, CH3), 6.84 (s, 4H, m-H of Mes), 6.90 (s, 4H, m-H of Mes), 7.53 (dd, J = 8, 2 Hz, 4H, 3-H of Pyr), 7.71 (s, 2H, CH-Pyr), 7.93 (d, J = 8 Hz, 4H, 4-H of Pyr), 8.45 (s, 2H, 5,8-H of BnImd), 9.09 (d, J = 2 Hz, 4H, 6-H of Pyr). UV–vis (CH3CN): λmax (nm) = 342, 400, 454. ESI-TOF-MS (CH3CN): m/z = 545.67 (sim for [M − 2PF6]2+: 545.69). Elemental analysis. Calculated for C67H63Cl2N7Fe·2PF6·H2O: H 4.68, C 57.44, N 7.00; found: H 4.45, C 57.49, N 7.23.

Synthesis of [FeII(MesPY4Cl2BIm)(PhCN)](PF6)2 (2-BN)

1,4-Dioxane was added slowly to a solution of 2-AN (5.0 mg, 3.6 μmol) in PhCN (1 ml) to obtain a red powder of 2-BN. The crude product was re-crystallized from CH2Cl2/hexane to obtain pale-red crystals of 2-BN (2.0 mg, 2.0 μmol) with a 55% yield. 1H NMR (CD2Cl2): δ  = 1.56 (s, 12H, CH3), 1.78 (s, 12H, CH3), 2.23 (s, 12H, CH3), 6.78 (s, 4H, m-H of Mes), 6.83 (s, 4H, m-H of Mes), 7.47 (t, J = 7 Hz, 2H, m-H of PhCN), 7.61 (dd, J = 8, 2 Hz, 4H, 3-H of Pyr), 7.65 (m, 3H, o, p-H of PhCN), 8.06 (s, 2H, CH-Pyr), 8.30 (d, J = 8 Hz, 4H, 4-H of Pyr), 8.63 (s, 2H, 5,8-H of BnImd), 8.76 (d, J = 2 Hz, 4H, 6-H of Pyr). ESI-TOF-MS (acetone): m/z = 576.60 (sim for [M − 2PF6]2+: 576.69). Elemental analysis. Calculated for C70H57Cl2N7Fe·2PF6·0.5CH2Cl2·0.5H2O: H 4.22, C 60.12, N 6.96; found: H 4.04, C 60.10, N 6.66.

Synthesis of [FeII(AntPY4Cl2BIm)(CH3CN)](PF6)2 (3-AN)

To a suspension of FeII acetate (132.9 mg, 0.76 mmol) in DMSO (5 ml), AntPY4Cl2BIm-H·Br (100 mg, 0.076 mmol; see Supplementary Information) was added and the mixture was stirred at 40 °C for 24 h in the dark. After the addition of KPF6 (703 mg, 3.8 mmol) and distilled water (20 ml), the reaction mixture was passed through a membrane filter to obtain a red solid. The crude product was re-crystallized from CH3CN/DME and pale-red crystals of 3-AN (70 mg, 0.036 mmol) were obtained with a 48% yield. 1H NMR (dmso-d6): δ = 6.85 (td, J = 8, 4 Hz, 4H, 7-H of Ant), 7.05 (d, J = 9 Hz, 4H, 8-H of Ant), 7.25–7.30 (m, 12H, 1,2,6-H of Ant), 7.41 (td, J = 8, 4 Hz, 4H, 3-H of Ant), 7.81 (dd, J = 8, 2 Hz, 4H, 4-H of Pyr), 7.91 (d, J = 8 Hz, 4H, 5-H of Ant), 7.96 (d, J = 8 Hz, 4H, 4-H of Ant), 8.06 (s, 2H, CH-Pyr), 8.22 (d, J = 8 Hz, 4H, 3-H of Pyr), 8.42 (s, 4H, 10-H of Ant), 8.69 (s, 2H, 5,8-H of BnImd), 9.27 (d, J = 2 Hz, 4H, 6-H of Pyr). UV–vis (CH3CN): λmax (nm) = 331, 386, 412. ESI-TOF-MS (CH3CN): m/z = 662.64 (sim for [M − 2PF6]2+: m/z = 662.64). Elemental analysis. Calculated for C87H55Cl2N7Fe·2PF6·2H2O: H 3.66, C 63.25, N 6.07; found: H 3.49, C 63.46, N 6.03.

Synthesis of [FeII(AntPY4Cl2BIm)(PhCN)](PF6)2 (3-BN)

1,4-Dioxane was added slowly by vapour diffusion to a solution of 3-AN (5.0 mg, 2.6 μmol) in PhCN (1 ml) to obtain red crystals of 3-BN (1.5 mg, 1.3 μmol) with a 55% yield. 1H NMR (CD2Cl2): δ = 6.70 (td, J = 8, 4 Hz, 4H, 7-H of Ant), 6.88–6.94 (m, 12H, 1,2,6-H of Ant), 7.03 (d, J = 9 Hz, 4H, 8-H of Ant), 7.23 (td, J = 8, 4 Hz, 4H, 3-H of Ant), 7.47 (t, J = 7 Hz, 2H, m-H of PhCN), 7.59 (dd, J = 8, 2 Hz, 4H, 4-H of Pyr), 7.65 (m, 3H, o,p-H of PhCN), 7.84 (s, 2H, CH-Pyr), 7.87 (d, J = 8 Hz, 4H, 5-H of Ant), 7.93 (d, J = 8 Hz, 4H, 4-H of Ant), 8.32 (s, 4H, 10-H of Ant), 8.54 (d, J = 8 Hz, 4H, 3-H of Pyr), 8.81 (s, 2H, 5,8-H of BnImd), 8.90 (d, J = 2 Hz, 4H, 6-H of Pyr). ESI-TOF-MS (acetone): m/z = 692.57 (sim for [M − 2PF6]2+: m/z = 692.64). Anal. Calcd. for C92H57Cl2N7Fe·PhCN·2PF6·6H2O: H 3.97, C 61.82, N 6.14; found: H 4.22, C 61.87, N 6.35.

Incubation of the catalysts in an aqueous medium

When 1-AN, 2-AN and 3-AN were incubated for 5 min in H2O:CH3CN (95:5, v/v) at 323 K, absorption spectra of the complexes changed as shown in Supplementary Fig. 8. The ESI-TOF-MS spectra also changed: the peak clusters assigned to the corresponding AN complexes disappeared (Supplementary Figs. 9–11). Furthermore, the 1H-NMR spectra of 1-AN after incubation for 5 min in D2O:acetone-d6 (95:5, v/v) at 323 K showed a singlet due to the dissociated CH3CN, indicating the formation of the corresponding D2O-bound FeII–aqua (FeII–OD2) complex, 1-OD2 (Supplementary Fig. 12). In the square-wave voltammograms of the FeII complexes in H2O:CH3CN (95:5, v/v) at 323 K, the oxidation waves assigned to the corresponding FeIII or FeII couple were observed at +0.75 V (compared with SCE) for 1-OH2, +0.86 V for 2-OH2 and +0.82 V for 3-OH2, reflecting the similarity of the electronic environments of the iron centres in the complexes as mentioned above (Supplementary Fig. 13).

General procedure for catalytic oxidation of gaseous alkanes

A schematic of the reaction set-up is shown in Supplementary Fig. 39. A 10-ml high-pressure-tolerable glass-tube reactor was charged with a solution of one of the catalysts (1.0 μM) and Na2S2O8 (5.0 mM) as an oxidant in D2O:CD3CN (95:5, v/v, 1.0 ml, pD was not adjusted). After passing one of the gaseous alkanes through the solution to force out air and saturate the solution with the gaseous alkane, the headspace of the reactor was filled with a gaseous alkane at the appropriate pressure. The reactions were performed at 323 K in a water bath. Qualitative and quantitative analyses of the reaction products were made by 1H NMR spectroscopy using sodium 3-(trimethylsilyl)propanesulfonate (DSS) as an internal standard. The conversion of CH4 was calculated based on the amount of CH4 by the ideal gas law in the solution of D2O:CD3CN (95:5, v/v, 2.9 ml) to be 4.1% as follows:

$$\begin{array}{c}{\rm{Conversion}}\,{\rm{of}}\,{{\rm{CH}}}_{4}\,( \% )=({\rm{[Products]}}\times 2.9\,{\rm{ml}})/{n}\times 100\\ \,\,\,\,\,=\,1.5\times 1{0}^{-3}/0.037\times 100=4.1 \% \end{array}$$

where n = 0.037 mmol: the mole of CH4 based on the ideal gas law (P = 0.98 MPa, V = 0.1 ml (gas phase), R = 8.31 × 103 Pa l  (K mol)−1, T = 323 K), [Products] (0.51 mM) × 2.9 ml (liquid phase) = 1.5 × 10–3 mmol. Conditions: A 3-ml high-pressure-tolerable J. Young valve NMR tube was charged with a solution of one of the catalysts (0.05 mM) and Na2S2O8 (250 mM) as an oxidant in D2O:CD3CN for 6 h (95:5, v/v, 2.9 ml, pD was not adjusted). The selectivity of CH3OH production under the same conditions was determined to be 83%.

Nuclear Overhauser effect experiments for investigation of interaction between 3-OD 2 and CH4

To explain the capture of CH4 molecules in the hydrophobic SCS of 3-OD2, we observed nuclear Overhauser effects (NOEs) in the 1H NMR measurements using 3-OD2 (0.10 mM) and CH4 (0.05 mM) in D2O:CD3CN (1:1, v/v) at room temperature. Differential NOE spectra were obtained by saturating resonances giving the 1H NMR signals of 5-H of the benzimidazole moiety at 8.69 ppm, methylene-H at 8.06 ppm, and 3-H and 4-H of the pyridine moieties at 8.22 and 7.81 ppm, respectively. The differential spectra between those with and without the irradiation show no correlation signals (Supplementary Figs. 20–23) and thus showed that these protons are not close to the CH4 molecule. Another set of the differential NOE spectra was obtained by saturating resonances giving the 1H NMR signals of aromatic protons of the anthracenyl groups at 8.42, 7.94, 7.41, 7.27, 7.05 and 6.85 ppm and that of 6-H of the pyridine moiety at 9.27 ppm. The differential spectra between those with and without the irradiation clearly indicate correlation signals (Supplementary Figs. 24–30). Thus, these protons should be close to the CH4 molecule. These results indicate that a CH4 molecule is captured inside the hydrophobic SCS constructed by the anthracenyl groups of 3-OD2 (Supplementary Fig. 31).

The K a value for CH4 capture

The Ka value for CH4 capture by 3-OD2 at 298 K was determined to be (2.1 ± 0.4) × 103 M–1 (Extended Data Fig. 3a), which is relatively high compared with the values reported so far for CH4 encapsulation30,35. The Ka values at 278 K, 308:K and 323 K were calculated to be (4.0 ± 0.5) × 103  M–1, (1.4 ± 0.2) × 103  M–1 and (0.9 ± 0.1) × 103 M–1, respectively (Extended Data Fig. 3b–d). The fitting curves in Extended Data Fig. 3a–d,f,g were calculated using equation (1).

$$\begin{array}{l}\Delta \delta \,=\,\frac{\Delta {\delta }_{\infty }}{2{K}_{{\rm{a}}}^{{\rm{R}}}{[{{\rm{CH}}}_{4}]}_{0}}\{1+{K}_{{\rm{a}}}^{{\rm{R}}}[{\rm{F}}{{\rm{e}}}^{{\rm{II}}}]+{K}_{{\rm{a}}}^{{\rm{R}}}{[{{\rm{CH}}}_{4}]}_{0}\{(1+{K}_{{\rm{a}}}^{{\rm{R}}}[{\rm{F}}{{\rm{e}}}^{{\rm{II}}}]\\ \,\,+{K}_{{\rm{a}}}^{{\rm{R}}}{[{{\rm{CH}}}_{4}]}_{0}{)}^{2}-4{K}_{{\rm{a}}}^{{{\rm{R}}}^{2}}[{\rm{F}}{{\rm{e}}}^{{\rm{II}}}]{[{{\rm{CH}}}_{4}]}_{0}{\}}^{1/2}\}\end{array}$$
(1)

Kinetic analysis of the catalytic oxidation of CH4 and CD4

Concentrations of the oxidation products were determined by gas chromatography–mass spectrometry (GC–MS) on the basis of a calibration curve using benzonitrile as an internal standard. Concentrations of CH4 and CD4 were calculated on the basis of the values reported36 for the aqueous solution (0.25 MPa, 2.5 mM; 0.50 MPa, 5.0 mM; 0.75 MPa, 7.5 mM; 0.98 MPa, 9.8 mM). The product concentrations were plotted against the reaction time to obtain time profiles of the product formation. Least-squares linear fitting was conducted for the plots in the range of about 0 h to 3 h. The slopes of the fitting lines obtained were used to determine the initial reaction rates, v0, of the CH4 and CD4 oxidation (Extended Data Fig. 1c,f). The initial rates, v0, of the CH4 and CD4 oxidation by 3-OD2 at various CH4 and CD4 concentrations were determined by the time courses of the product concentration obtained by GC–MS and were plotted against the initial CH4 or CD4 concentrations to estimate the rate constants, kHAnt and kDAnt (Extended Data Fig. 1c,f). GC–MS: column, DB-Wax UI capillary column (30 m); career gas, helium; interface and detector temperature, 200 °C; temperature programme, 30 °C for 4 min, increasing to 200 °C at a rate of 50  °C min–1, followed by 200 °C for 3.4 min.

One-electron-oxidized species of 3-OH2

We measured an electron spin resonance (ESR) spectrum of a sample obtained by quick freezing a portion of a solution of catalytic CH4 oxidation using 3-OH2 at 323 K in the presence of Na2S2O8 in a H2O:MeCN (95:5) mixed solvent. We detected an ESR signal at g = 2.492, 2.343 and 1.860 (Extended Data Fig. 4e). To assign the ESR signal, we separately prepared [FeIII(AntPY4Cl2BIm)(OH2)]2+ from 3-OH2 by adding 1.2 equivalent (equiv.) of cerium(IV) ammonium nitrate (CAN) as the oxidant in MeCN:H2O (3:1) at 298 K. The complex showed absorption bands at 700 nm (Extended Data Fig. 4d, blue line). On the basis of the increase in absorbance at 700 nm, the second-order rate constant for the formation of [FeIII(AntPY4Cl2BIm)(OH2)]2+, k2ET1, was determined to be (1.1 ± 0.1) × 107 M–1 s–1 in a MeCN:H2O (3:1) solution at 278 K (Supplementary Fig. 35a,b). The ESR signal of the FeIII–OH2 species (S = 1/2) was observed at g = 2.492, 2.343 and 1.860 (Extended Data Fig. 4e, blue line), consistent with those observed for the reaction mixture of the catalysis. All electron spin resonance (ESR spectra) were measured at 100 K. Microwave frequency, 9.572 GHz; microwave power, 1.0 mW; modulation frequency, 100.00 kHz; modulation amplitude, 3.00 G.

Characterization of 3-O

3-OH2 was oxidized by CAN as an oxidant, which was used instead of Na2S2O8 for the catalytic reactions, in a mixed solvent of CH3CN:H2O (3:1) at 278 K. In the cold-spray ionization time-of-flight mass spectrometry (CSI-TOF-MS) spectrum of 3-O formed with CAN measured at 278 K, a peak cluster was observed at m/z = 648.96, assigned to [3-O – 2PF6]2+ (sim: m/z = 649.14) (Extended Data Fig. 4a, top), as in the case of Na2S2O8. When the formation of 3-O was conducted with 5 equiv. of CAN in a mixed solvent of CH3CN:H218O (3:1), the peak cluster in the CSI-TOF-MS spectrum shifted to m/z = 650.01, assignable to [3-18O − 2PF6]2+ (sim: m/z = 650.14) (Extended Data Fig. 4b).

When 3-OH2 was reacted with 1.2 equiv. of CAN in a MeCN:H2O (3:1) solution at 278 K, a new absorption band appeared at 700 nm in the UV–vis spectrum, derived from the formation of the corresponding FeIII complex, [FeIII(AntPY4Cl2BIm)(OH2)]2+ (Extended Data Fig. 4d, blue line). Simultaneously, the absorption band of 3-OH2 at 420 nm disappeared. Furthermore, when 3-OH2 was treated with 5 equiv. of CAN in a MeCN:H2O (3:1) mixed solvent at 278 K, a new absorption band was observed at 800 nm, derived from the formation37 of 3-O (Extended Data Fig. 4d, green line). On the basis of the increase in the absorbance at 800 nm, the first-order rate constant for the formation of 3-O, k1ET2, was determined to be (2.25 ± 0.05) × 10–1 s–1 in a MeCN:H2O (3:1) solution at 278 K (Supplementary Fig. 35c,d).

The Raman spectrum of 3-O in a CH3CN:H2O (3:1) solution at 298 K upon excitation at 532 nm exhibited a Raman scattering at 799 cm–1, derived from the Fe–O bond stretching; the use of H218O caused a low-energy shift of the signal to 759 cm–1 (Extended Data Fig. 4c). The isotope shift (Δν) was calculated to be 40 cm–1, which was consistent with the theoretical value (Δν = 36 cm–1). The Raman shift of the stretching band for the Fe–O bond of 3-O was moderately smaller than those for other FeIV=O complexes reported so far (ν = 820–853 cm–1)38,39, suggesting that 3-O should have a weaker Fe–O bond than typical FeIV=O bonds. The excitation wavelength for the Raman measurements was 532 nm.

Because 3-O was ESR silent under the conditions examined, we used the Evans method40 based on 1H NMR spectroscopy to estimate the magnetic susceptibility of 3-O (Supplementary Fig. 34), which was formed by the treatment of 3-OH2 with 3 equiv. of CAN in D2O:CD3CN (1:3) at 278 K. The effective magnetic moment (μeff) of 3-O was calculated to be 2.75μB, allowing us to confirm the spin state of 3-O to be S = 1 (μeff calculated for the spin-only: 2.83μB).

Decomposition of 3-O

We also investigated the decomposition of 3-O under catalytic conditions—in H2O:CH3CN (95:5, v/v) before and after addition of Na2S2O8 at 323 K, in the absence of substrates. The ESI-TOF-MS spectrum of the reaction mixture was found to have a peak cluster at m/z = 649.02 (Supplementary Fig. 33b, filled red circle), which was assigned to 3-O (sim for [3-O – 2PF6]2+: m/z = 649.14). 3-O underwent oxidative decomposition accompanied by the loss of the dipyridylmethyl arm of the NHC ligand as confirmed by the ESI-TOF-MS and 1H NMR measurements of the reaction mixture after incubation for 3 h (Supplementary Fig. 33). The decomposition of 3-O was also observed by a decrease in the absorbance at 800 nm accompanied by an increase in the absorbance at 700 nm, derived from the corresponding FeIII–OH2 species (Supplementary Fig. 36). On the basis of the decrease in absorbance at 800 nm, the first-order rate constant for the decomposition of 3-O, kdecomp, was determined to be (2.52 ± 0.03) × 10–4 s–1 in a MeCN:H2O (3:1) solution at 278 K in the absence of substrates such as CH4 (Supplementary Fig. 36). The decomposition was also monitored by ESI-TOF-MS and 1H NMR measurements, which suggest the formation of a FeII species that has lost one dipyridylmethyl moiety (Supplementary Fig. 33).

Kinetic studies on the reaction of 3-O with CH4

When injecting CH4 after the formation of 3-O by reaction with CAN, the broad absorption band at 800 nm decayed and a new band at 682 nm appeared that showed an isosbestic point at 753 nm as the reaction progressed between 3-O and CH4 (Supplementary Fig. 37a). The pseudo-first-order rate constant, k1, for the reaction of 3-O with an excess amount of CH4 was determined to be (1.24 ± 0.02) × 10–3 s–1, on the basis of decrease of absorbance at 800 nm (Supplementary Fig. 37b). Therefore, 3-O can react with CH4 predominantly, because k1 was five times larger than kdecomp of 3-O.

Computational details

We performed the DFT calculations with the Gaussian 16 program package (revision C01)41. All geometry optimizations were carried out with the B3LYP functional42,43. We used the Wachters–Hay basis set44,45 for Fe and the D95** basis set46 for the other atoms. After geometry optimizations, we performed vibrational analyses for all reaction species to confirm stable and transition structures. Energy profiles of calculated pathways are presented as the Gibbs free energy (T = 323 K) considering the solvent effect of water on the basis of the polarizable continuum model47 and the Grimme-D3 dispersion energy corrections48. We calculated the kinetic isotope effect (KIE) (kH/kD) for the H-atom abstraction from CH4 or CD4 using transition-state theory49 as shown in equation (2).

$$\frac{{k}_{{\rm{H}}}}{{k}_{{\rm{D}}}}=\frac{{({I}_{x{\rm{D}}}^{R}{I}_{y{\rm{D}}}^{R}{I}_{z{\rm{D}}}^{R})}^{1/2}}{{({I}_{x{\rm{H}}}^{R}{I}_{y{\rm{H}}}^{R}{I}_{z{\rm{H}}}^{R})}^{1/2}}\frac{{({I}_{x{\rm{H}}}^{{\rm{\#}}}{I}_{y{\rm{H}}}^{{\rm{\#}}}{I}_{z{\rm{H}}}^{{\rm{\#}}})}^{1/2}}{{({I}_{x{\rm{D}}}^{{\rm{\#}}}{I}_{y{\rm{D}}}^{{\rm{\#}}}{I}_{z{\rm{D}}}^{{\rm{\#}}})}^{1/2}}\frac{{q}_{{\rm{D}}}^{{\rm{R}}}{q}_{{\rm{H}}}^{{\rm{\#}}}}{{q}_{{\rm{H}}}^{{\rm{R}}}{q}_{{\rm{D}}}^{{\rm{\#}}}}\exp \left(\frac{{E}_{{\rm{H}}}^{{\rm{\#}}}\,-\,{E}_{{\rm{D}}}^{{\rm{\#}}}}{RT}\right)$$
(2)

Here I, q and E indicate the moment of inertia, the vibrational partition function and the activation energy with thermal correction, respectively; R specifies the reactant complex; # indicates the transition state; the letters x, y and z correspond to the components of the three-dimensional space of each variable; H means the species including CH4; D means the species including CD4. The last exponential term is dominant in this equation because the other terms can be almost all cancelled between denominators and numerators.

The DFT-calculated KIE value at 323 K was 15 for CH4 oxidation accompanied by hydrogen atom tunnelling, which is consistent with the experimental KIE value of 37 and so provides support for a tunnelling effect in the hydrogen atom transfer process.