MaterialsPhosphotungstic acid hydrate (H3[P(W3O10)4]·xH2O, PTA), absolute ethanol (99.5%), n-hexane (99.5%) and cyclohexane (99.5%) were purchased from Sinopharm Chemical Reagent Beijing Co., Ltd. Lanthanum nitrate hydrate (La(NO3)3·xH2O, > 95%), chromic nitrate hydrate (Cr(NO3)3·6H2O, > 95%), manganese nitrate hydrate (MnCl2, > 95%), ferric nitrate hydrate (Fe(NO3)3·9H2O, > 95%) cobalt nitrate hydrate (Co(NO3)2·6H2O) ( > 95%), and nickel nitrate hydrate (Ni(NO3)2·6H2O) ( > 95%) were purchased from Shanghai Macklin Biochemical Technology Co., Ltd., Sodium carbonate (Na2CO3, 98%) and oleylamine were purchased from Alfa Aesar Co., Ltd. 13CH4/Ar (10%/90% in v/v) was provided by Beijing Huanyu Jinghui capital gas Technology Co., LTD. All the chemicals were used as received.CharacterizationThe X-ray diffraction patterns (XRD) were acquired via powder XRD using a Bruker D8-Focus X-ray diffractometer operating at 40 kV and 30 mA with Cu-Kα (λ = 1.5418 Å) radiation, employing a scanning rate of 1° min−1. The morphology of subnano-HELMO-PTA and nano-HELMO was examined using transmission electron microscopy (TEM, HITACHI H-7700) operating at 100 kV and high-resolution transmission electron microscopy (HRTEM, JEOL JEM 2100 F) operating at 200 kV. Inductively coupled plasma atomic emission spectra (ICP-AES, Thermo IRIS Intrepid II) was employed to investigate composition of subnano-HELMO-PTA and nano-HELMO. The surface potential images of the samples were acquired via Kelvin probe force microscopy using a Pt/Ir coated Si tip on Cypher VRS (Oxford Instruments). The in situ AFM test process employed 405 nm light-emitting component. UV-Vis diffuse reflectance spectra were collected in the 200–1200 nm spectral range on a Shimadzu SolidSpec-3700 spectrophotometer with BaSO4 as reference.Synthesis of subnano-HELMO-PTAThe subnano-HELMO-PTA was synthesized via a facile solvothermal approach. Initially, 0.05 mmol La(NO3)3·xH2O, 0.01 mmol Cr(NO3)3·6H2O, 0.01 mmol MnCl2, 0.01 mmol Fe(NO3)3·9H2O, 0.01 mmol Co(NO3)2·6H2O, 0.01 mmol Ni(NO3)2·6H2O and 0.0196 g PTA were co-added into a 50 mL flask. Afterwards, 2 mL of absolute ethanol, 6 mL of n-hexane, and 1 mL of oleylamine were added to the mixture. The flask was then equipped with an allihn condenser and heated at a temperature of 100 °C for a duration of four hours while being stirred continuously for thirty minutes prior to the reaction. Following the reaction, the products were collected and washed with cyclohexane and ethanol before being centrifuged at a speed of 10000 rpm for ten minutes. This washing process was repeated three times in order to obtain the final product which could be dispersed in cyclohexane.Synthesis of nano-HELMOThe preparation process of nano-HELMO was analogous to that of subnano-HELMO-PTA, except for the absence of PTA in the system. Specifically, 0.05 mmol La(NO3)3·xH2O, 0.01 mmol Cr(NO3)3·6H2O, 0.01 mmol MnCl2, 0.01 mmol Fe(NO3)3·9H2O, 0.01 mmol Co(NO3)2·6H2O and 0.01 mmol Ni(NO3)2·6H2O were introduced into a 50 mL flask. Afterwards, 2 mL of absolute ethanol, 6 mL of n-hexane, and 1.9 mL of oleylamine were introduced into the mixture. Following a stirring period of 10 minutes, the flask was equipped with an allihn condenser and heated at a temperature of 100 °C for a duration of 4 h. Upon completion of the reaction process, the product was collected and subjected to washing with 10 mL cyclohexane and 10 mL ethanol before being centrifuged at a speed of 2000 × g for 10 min. This washing procedure was repeated three times in order to obtain the final ~0.46 g products which could be dispersed in cyclohexane.Synthesis of subnano-LMO-PTAThe subnano-LMO-PTA was synthesized via a facile solvothermal approach. Initially, 0.05 mmol La(NO3)3·xH2O, 0.05 mmol MnCl2 and 0.0196 g PTA were co-added into a 50 mL flask. Afterwards, 2 mL of absolute ethanol, 6 mL of n-hexane, and 1 mL of oleylamine were added to the mixture. The flask was then equipped with an allihn condenser and heated at a temperature of 100 °C for a duration of 4 h while being stirred continuously for 30 min prior to the reaction. Following the reaction, the products were collected and washed with 10 mL cyclohexane and 10 mL ethanol before being centrifuged at a speed of 2000 × g for 10 min. This washing process was repeated three times in order to obtain the final ~0.1 g product which could be dispersed in cyclohexane.Synthesis of subnano-MELMO-PTAThe subnano-MELMO-PTA was synthesized via a facile solvothermal approach. Initially, 0.05 mmol La(NO3)3·xH2O, 0.017 mmol Cr(NO3)3·6H2O, 0.017 mmol MnCl2, 0.017 mmol Co(NO3)2·6H2O and 0.0196 g PTA were co-added into a 50 mL flask. Afterwards, 2 mL of absolute ethanol, 6 mL of n-hexane, and 1 mL of oleylamine were added to the mixture. The flask was then equipped with an allihn condenser and heated at a temperature of 100 °C for a duration of four hours while being stirred continuously for 30 min prior to the reaction. Following the reaction, the products were collected and washed with 10 mL cyclohexane and 10 mL ethanol before being centrifuged at a speed of 2000 × g for 10 min. This washing process was repeated three times in order to obtain the final ~0.078 g product which could be dispersed in cyclohexane.Synthesis of HELMO/PTAAccording to the ICP-AES results, La and W elements exhibited almost identical contents with a mole ratio of 1:1.01. Subsequently, 1 mmol nano-HELMO and 1 mmol PTA were dispersed in a mixture of ethanol and water (v/v = 1/1) at a volume of 40 mL. The resulting mixture was subjected to ultrasonic dispersion and stirred for 30 minutes before being dried under conditions of 60 °C. Finally, the powder obtained was calcinated at temperatures reaching up to100 °C for 6 h.Synthesis of HELMO with sol-gel methodThe following metal precursors were added to a 250 mL beaker: 3.5 mmol La(NO3)3·xH2O, 0.7 mmol Cr(NO3)3·6H2O, 0.7 mmol MnCl2, 0.7 mmol Fe(NO3)3·9H2O, 0.7 mmol Co(NO3)2·6H2O and 0.7 mmol Ni(NO3)2·6H2O. Subsequently, the mixture was dissolved by adding and stirring in 133.5 mL of water for 10 minutes. After that, a solution containing 3.5 mmol citric acid and 14 mmol glycol was added and stirred for another 10 min before being aged to form a gel at a temperature of 100 °C. Finally, the gel was calcinated at either 650 °C or 700 °C for a duration of 5 h.Photoelectrochemical testsPEC conversion of CH4 was investigated using an electrochemical workstation (CHI 660E) in a customized (500 mL), sealed H-type cell with Nafion 117 proton exchange membrane. A 300 W Xenon lamp provided by Beijing Perfect Light was utilized to simulate solar light, emitting wavelengths ranging from 320–780 nm and providing a power density of 100 mW cm−2. A mixture with a catalyst concentration of 1 mg/mL was prepared by dispersing 10 mg of catalysts, 10 mg of Vulcan XC-72 carbon, and 200 μL of Nafion (5 wt%) in 10 mL cyclohexane. Subsequently, the gas diffusion electrode (area: 1.4 cm × 1.4 cm) was uniformly coated with 1 mL ink (containing 1 mg catalyst) at room temperature. Thirdly, the gas diffusion electrode, Pt foil, and Ag/AgCl electrode were used as the working electrode, the counter electrode, and reference electrode, respectively. The photocurrent was recorded from 0.3 to 1.8 V vs. Ag/AgCl recorded at a scan rate of 5 mV/s in 0.5 M Na2CO3 without and with the CH4 gas purging for 60 min.Synchrotron X-ray absorption spectroscopyX-ray absorption spectroscopy (XAS) was performed at the Ni-K edge (8339 eV) and Fe K-edge (7112 eV) using beamline BL11B of the Shanghai Synchrotron Radiation Facility (SSRF), with a Si(111) double-crystal monochromator for beam tuning. Prior to analysis, samples were compressed into thin sheets measuring 1 cm in diameter and sealed with Kapton tape film. The X-ray absorption fine structure (XAFS) spectra were recorded at room temperature using a lytle fluorescence ionization chamber, calibrated according to the absorption edge of pure Ni or Fe foil. The storage ring had a typical energy of 2.5 GeV with a maximum current of 250 mA. Fluorescence mode was used to record Ni-K edge and Fe K-edge extended X-ray absorption fine structure (EXAFS) spectra, which showed negligible changes in line-shape and peak position between two scans taken for each sample. Data processing and analysis were conducted using Athena and Artemis software codes.In situ diffuse reflectance infrared Fourier transform spectra experimentsThe Bruker Tensor 27 spectrometer equipped with a mercury cadmium telluride (MCT) detector was utilized to conduct in situ diffuse reflectance infrared Fourier transform spectra (DRIFTs). The in situ DRIFT spectra were acquired at a spectral resolution of 4 cm−1. After being pre-treated in N2 flow (20 mL/min) at 90 °C for 1 h, the sample underwent background spectrum collection prior to in situ DRIFTs experiments. The N2 flow was subsequently switched to a CH4 flow and maintained for 0.5 hours to achieve saturated adsorption of CH4. Following this, light with a wavelength of 405 nm was introduced, and the signal was recorded every minute.In situ XPS experimentsThe in situ XPS was conducted using the XPS Thermo Fisher 250i instrument. The radiation source employed was a laser from Williden Technology Co., Ltd. with a wavelength of 405 nm. The XPS photoelectron spectrum analysis was performed under complete darkness, followed by in situ irradiation for 15 min using the laser and subsequent re-analysis of the XPS photoelectron spectrum. Data processing and analysis were carried out using software associated with the XPS Thermo Fisher 250i.In situ Raman experimentsFor the photocatalysis, in situ Raman experiments were conducted using a Raman spectrometer (HORIBA Jobin Yvon Inc., Model: HR Evolution) equipped with an optical microscope. Prior to the reaction, a monocrystalline Si wafer was used for spectrometer calibration. The catalysts were then heated at 90 oC for 1 h to remove physically adsorbed H2O and CO2 from the surface. Subsequently, N2 and CH4 were introduced stepwise into the system. A near-infrared laser (λ = 785 nm) was employed as the excitation source while a laser with a wavelength of 405 nm was utilized.For the electrocatalysis, a specially designed three-electrode cell was employed, featuring a platinum mesh counter electrode, an Ag/AgCl reference electrode, and subnano-HELMO-PTA working electrode. The reactions took place at ambient temperature in 0.5 M aqueous Na2CO3 solutions saturated with CH4 gas. A near-infrared laser (λ = 785 nm) served as the excitation source, while utilizing a laser operating at a wavelength of 532 nm.EPR tests for the detection of ·OH and ·CH3
In the PEC reaction system, 5, 5-dimethyl-1-pyrroline N-oxide (DMPO) was utilized as a capture agent to trap the generated ·OH and ·CH3. The dried catalyst was first dispersed in cyclohexane with a concentration of 10 mg/mL. The catalyst was subsequently rinsed with ethanol and subjected to a drying process at 70 °C for 12 h, aiming to effectively eliminate the physically adsorbed oleylamine molecules on its surface. Subsequently, the resulting dry powder was ground in a mortar for 10 min. The resulting 4 mg catalyst and 2 mg Vulcan XC-72 carbon was deposited on gas diffusion electrode with area of 1.41 × 1.41 cm2. Then, 200 μL of Nafion (5 wt%) in 10 mL cyclohexane was deposited on the surface of gas diffusion electrode to fix the catalysts. The sealed H-type cell (50 mL) contained 40 mL 0.5 M Na2CO3 aqueous solution with DMSO at a concentration of 50 mg/mL. The air in reaction chamber was evacuated by introducing methane or Ar at a flow rate of 20 mL/min for a duration of 30 min. Then, the applied potential was set to be 1.2 V (vs. Ag/AgCl). At last, the light (405 nm) was introduced and the solution inside the reaction tank was circulated to the chamber by a peristaltic pump (50 mL/min) for testing.Mott–Schottky experimentsThe nano-HELMO and PTA were dispersed ultrasonically in 10 mL of cyclohexane at a concentration of 1 mg/mL before being dropwise added onto three indium tin oxide substrates measuring 1 × 1 cm each. Mott–Schottky plots were obtained using a CHI 760E electrochemical workstation, with Ag/AgCl serving as the reference electrode and platinum wire mesh as the counter electrode. The samples, examined in a 1 M Na2SO4 solution, were tested at frequencies of 500, 800, and 1000 Hz.EIS testsThe electrochemical impedance spectroscopy (EIS) tests were conducted at open circuit voltage (OCV) conditions, employing a potential amplitude of 5 mV and frequencies ranging from 105 to 1 Hz.Product analysisGas products were analyzed using an online gas chromatograph (Shimadzu, GC-2014C) equipped with molecular sieve 5 A and propark Q packed column with argon as the carrier gas. Flame ionization detector (FID) and discharge ionization detector (DFID) were utilized for the examination of C1 compounds (CO, CO2 and CH4), C2 compounds (C2H2, C2H4, and C2H6), and C3 (C2H6, C3H4, and C3H6) respectively. The concentration of gas products was determined by calculating the peak areas from the gas chromatogram based on standard curves of pure samples.The liquid products underwent qualitative and quantitative analysis using 1H NMR and 13C NMR (JEOL ECS-400 400 MHz NMR). Following electrocatalysis, the electrolyte was mixed with an internal standard consisting of 0.1 mL D2O and 0.05 μL DMSO in a volume of 0.5 mL. The resulting solution was subjected to water suppression during measurement of the 1H NMR.The colorimetric method was utilized to determine the concentration of HCHO in liquid product. A reagent aqueous solution consisting of 15 g ammonium acetate, 0.3 mL acetic acid, and 0.2 mL pentane-2,4-dione dissolved in water was prepared first with a volume of 100 mL. Subsequently, a mixture containing 0.5 mL liquid product, 2.0 mL water and 0.5 mL reagent solution was subjected to UV−vis absorption spectroscopy51.The selectivity of acetic acid was calculated as the following equation:Selectivity = Yield of acetic acid/Conversion of methaneThe conversion of CH4 (η) was presented as follow:$${{{\rm{\eta }}}}=1-({{{{\rm{C}}}}}_{2}/{{{{\rm{C}}}}}_{1})$$where C1 and C2 are molar concentration of CH4 in feeding gas and effluent stream, respectively.Computational detailsThe Vienna ab initio simulation package (VASP) software package was utilized to perform spin-polarized DFT calculations using plane-wave pseudopotentials54,55,56. A kinetic energy cutoff of 450 eV was applied. The Perdew-Burke-Ernzerh of (PBE) functional, based on the generalized gradient approximation (GGA) approach57, was employed to incorporate exchange and correlation energies. Core-valence interactions were represented using the PAW method58. The Monkhorst-Pack method was utilized to sample the Brillouin zone using a k-points grid of 1 × 1 × 1. To accurately consider the localized 3d orbitals of transition metals, spin-polarized DFT + U calculations were performed with Ueff values of 6.4, 6.5, 4.0, 4.0, and 3.3 for Ni, Cr, Fe, Mn, and Co respectively59,60. The atomic positions were relaxed until the force on each atom reached a convergence threshold below 0.01 eV/Å and electronic energies were converged within an accuracy of 10−4 eV. To adequately account for van der Waals (vdW) interactions, a technique incorporating Becke-Johnson damping function was employed61.The LaMnO3 perovskite structure with a lattice parameter of 3.799 Å (optimized in the Pm3m space group) closely matched the experimental value of a0 = 3.808 Å62. The Special Quasirandom Structures (SQSs) for La(Cr0.2Mn0.2Fe0.2Co0.2Ni0.2)O3 were generated using the GENSQS module within the Alloy Theoretic Automated Toolkit (ATAT)63. To simulate the (110) surface of high-entropy LaMnO3-type perovskite terminated with LaMnO2, a primitive supercell of La(Cr0.2Mn0.2Fe0.2Co0.2Ni0.2)O3 was employed, and a six-layer slab was created by fixing the bottom three layers and relaxing the topmost ones accordingly while ensuring no interaction between replicated slabs in all dimensions through a 15 Å vacuum region.”The subnano-HELMO-PTA structure was initially constructed based on the ICP-AES findings and our previous research. To prevent any interaction between the replicated slabs in three-dimensional space, a 15 Å vacuum was incorporated along the Z-axis. Throughout the optimization process of the initial slab, there were no restrictions imposed on atom positions, axis lengths, or box shape, except for the Z-axis.Gibbs free energies for each gaseous and adsorbed species were calculated at 298.15 K, according to the following expressions:$$\Delta {{{\rm{G}}}}=\Delta {{{\rm{E}}}}+\Delta {{{{\rm{E}}}}}_{{{{\rm{ZPE}}}}}-{{{\rm{T}}}}\Delta {{{\rm{S}}}}$$where \(\Delta {{{\rm{E}}}}\) is the electronic energy difference between the free standing and adsorption states of reaction intermediates; \(\Delta {{{{\rm{E}}}}}_{{{{\rm{ZPE}}}}}\) and \(\Delta {{{\rm{S}}}}\) represent the changes in zero point energies and entropy, respectively, which are obtained from the vibrational frequency calculations51. In this work, the temperature (T) was set to be 298.15 K.The values of \(\Delta {{{{\rm{E}}}}}_{{{{\rm{ZPE}}}}}\) and TS for each reaction intermediate can be calculated using the following equations.$$\Delta {{{{\rm{E}}}}}_{{{{\rm{ZPE}}}}}\,=\,\frac{1}{2} {\sum}_{i}{{hv}}_{i}$$$${{{\rm{S}}}}\,={\sum}_{i}{{{\rm{R}}}}\left[{{\mathrm{ln}}}{\left(1-{{{{\rm{e}}}}}^{-\frac{{\varTheta }_{i}}{{{{\rm{T}}}}}}\right)}^{-1}\,+\,\frac{{\varTheta }_{i}}{{{{\rm{T}}}}}{\left({{{{\rm{e}}}}}^{\frac{{\varTheta }_{i}}{{{{\rm{T}}}}}}-1\right)}^{-1}\right]$$where h is the Planck constant, \({{\sum }_{i}v}_{i}\) is cumulative value of the computed vibrational frequencies, R is the molar gas constant, \({\varTheta }_{i}\) is the characteristic temperature of vibration and could be calculated as \({\varTheta }_{i}\,=\,\frac{{{hv}}_{i}}{{k}_{B}}\), where \({k}_{B}\) is the Boltzmann constant51. For adsorbates, all 3 N degrees of freedom were treated as frustrated harmonic vibrations with negligible contributions from the catalysts’ surfaces.The charge of system was treated in accordance with the widely-recognized computational hydrogen electrode model51, wherein each reaction step was considered as a simultaneous transfer of the proton-electron pair based on the applied potential. Consequently, alterations in free energy can be represented as follows.For HELMO catalyst:$${{{{\rm{II}}}}}^{*}+{{{{\rm{CH}}}}}_{4}\to {*}{{{\rm{CH}}}}_{4}$$$$\Delta {{{{\rm{G}}}}_{II}}={{{\rm{G}}}}\left[{*}{{{{\rm{CH}}}}_{4}}\right]-\,({{{\rm{G}}}}[*]+{{{\rm{G}}}}[{{{{{\rm{CH}}}}}}_{4}])$$$${{{\rm{III}}}}{*}{{{\rm{CH}}}}_{4}\to {*}{{{\rm{CH}}}}_{3}+{{{{\rm{H}}}}}^{+}+{{{{\rm{e}}}}}^{-}$$$$\Delta {{{{\rm{G}}}}}_{{{{\rm{III}}}}}={{{\rm{G}}}}[{*}{{{\rm{CH}}}}_{3}]+{{{\rm{G}}}}[{{{{\rm{H}}}}}^{+}+{{{{\rm{e}}}}}^{-}]-{{{\rm{G}}}}[{*}{{{\rm{CH}}}}_{4}]$$$${{{\rm{IV}}}}{*}{{{\rm{CH}}}}_{3}\to {*}{{{\rm{CH}}}}_{2}+{{{{\rm{H}}}}}^{+}+{{{{\rm{e}}}}}^{-}$$$$\Delta {{{{\rm{G}}}}}_{{{{\rm{IV}}}}}={{{\rm{G}}}}[{*}{{{\rm{CH}}}}_{2}]+{{{\rm{G}}}}[{{{{\rm{H}}}}}^{+}+{{{{\rm{e}}}}}^{-}]-{{{\rm{G}}}}[{*}{{{\rm{CH}}}}_{3}]$$$${{{\rm{V}}}}{*}{{{\rm{CH}}}}_{2}+{{{{\rm{H}}}}}_{2}{{{\rm{O}}}}\to {*}{{{\rm{CH}}}}_{2}{{{\rm{OH}}}}+{{{{\rm{H}}}}}^{+}+{{{{\rm{e}}}}}^{-}$$$$\Delta {{{{\rm{G}}}}}_{{{{\rm{V}}}}}={{{\rm{G}}}}[{*}{{{\rm{CH}}}}_{2}{{{\rm{OH}}}}]+{{{\rm{G}}}}[{{{{\rm{H}}}}}^{+}+{{{{\rm{e}}}}}^{-}]-{{{\rm{G}}}}[{*}{{{\rm{CH}}}}_{2}]-{{{\rm{G}}}}[{{{{\rm{H}}}}}_{2}{{{\rm{O}}}}]$$$${{{\rm{VI}}}}{*}{{{\rm{CH}}}}_{2}{{{\rm{OH}}}}\to {*}{{{\rm{CH}}}}{{{\rm{OH}}}}+{{{{\rm{H}}}}}^{+}+{{{{\rm{e}}}}}^{-}$$$$\Delta {{{{\rm{G}}}}}_{{{{\rm{VI}}}}}={{{\rm{G}}}}[{*}{{{\rm{CH}}}}{{{\rm{OH}}}}]+{{{\rm{G}}}}[{{{{\rm{H}}}}}^{+}+{{{{\rm{e}}}}}^{-}]-{{{\rm{G}}}}[{*}{{{\rm{CH}}}}_{2}{{{\rm{OH}}}}]$$$${{{\rm{VII}}}}{*}{{{\rm{CH}}}}{{{\rm{OH}}}}\to {*}{{{\rm{C}}}}{{{\rm{OH}}}}+{{{{\rm{H}}}}}^{+}+{{{{\rm{e}}}}}^{-}$$$$\Delta {{{{\rm{G}}}}}_{{{{\rm{VII}}}}}={{{\rm{G}}}}[{*}{{{\rm{C}}}}{{{\rm{OH}}}}]+{{{\rm{G}}}}[{{{{\rm{H}}}}}^{+}+{{{{\rm{e}}}}}^{-}]-{{{\rm{G}}}}[{*}{{{\rm{CH}}}}{{{\rm{OH}}}}]$$$${{{\rm{VIII}}}}{*}{{{\rm{C}}}}{{{\rm{OH}}}}\to {*}{{{\rm{C}}}}{{{\rm{O}}}}+{{{{\rm{H}}}}}^{+}+{{{{\rm{e}}}}}^{-}$$$$\Delta {{{{\rm{G}}}}}_{{{{\rm{VIII}}}}}={{{\rm{G}}}}[{*}{{{\rm{C}}}}{{{\rm{O}}}}]+{{{\rm{G}}}}[{{{{\rm{H}}}}}^{+}+{{{{\rm{e}}}}}^{-}]-{{{\rm{G}}}}[{*}{{{\rm{C}}}}{{{\rm{OH}}}}]$$$${{{\rm{IX}}}}{*}{{{\rm{C}}}}{{{\rm{O}}}}+{{{{\rm{H}}}}}_{2}{{{\rm{O}}}}\to {*}{{{\rm{C}}}}{{{\rm{OOH}}}}+{{{{\rm{H}}}}}^{+}+{{{{\rm{e}}}}}^{-}$$$$\Delta {{{{\rm{Gl}}}}}_{{{{\rm{X}}}}}={{{\rm{G}}}}\left[{*}{{{\rm{CO}}}}{{{\rm{OH}}}}\right]+{{{\rm{G}}}}\left[{{{{\rm{H}}}}}^{+}+{{{{\rm{e}}}}}^{-}\right]-{{{\rm{G}}}}\left[{*}{{{\rm{C}}}}{{{\rm{O}}}}\right]-{{{\rm{G}}}}[{{{{\rm{H}}}}}_{2}{{{\rm{O}}}}]$$$${{{\rm{X}}}}{*}{{{\rm{CO}}}}{{{\rm{OH}}}}\to {*}{{{\rm{C}}}}{{{\rm{OO}}}}+{{{{\rm{H}}}}}^{+}+{{{{\rm{e}}}}}^{-}$$$$\Delta {{{{\rm{G}}}}}_{{{{\rm{X}}}}}={{{\rm{G}}}}[{*}{{{\rm{C}}}}{{{\rm{OO}}}}]+{{{\rm{G}}}}[{{{{\rm{H}}}}}^{+}+{{{{\rm{e}}}}}^{-}]-{{{\rm{G}}}}[{*}{{{\rm{CO}}}}{{{\rm{OH}}}}]$$$${{{\rm{XI}}}}{*}{{{\rm{C}}}}{{{\rm{OO}}}}\to {{{{\rm{CO}}}}}_{2}$$$$\Delta {{{{\rm{G}}}}}_{{{{\rm{XI}}}}}={{{\rm{G}}}}[{*}{{{\rm{C}}}}{{{\rm{OO}}}}]+{{{\rm{G}}}}[{{{{\rm{CO}}}}}_{2}]$$For subnano-HELMO-PTA catalyst:$${{{{\rm{II}}}}}^{*}+{{{{\rm{CH}}}}}_{4}\to {{*}{{{\rm{C}}}}{{{\rm{H}}}}}_{4}$$$$\Delta {{{{\rm{G}}}}}_{{{{\rm{II}}}}}={{{\rm{G}}}}[{{*}{{{\rm{C}}}}{{{\rm{H}}}}}_{4}]-({{{\rm{G}}}}[*]+{{{\rm{G}}}}[{{{{\rm{CH}}}}}_{4}])$$$${{{{\rm{III}}}}}^{*}+{{{{\rm{CH}}}}}_{4}\to {{*}{{{\rm{C}}}}{{{\rm{H}}}}}_{3}+{{{{\rm{H}}}}}^{+}+{{{{\rm{e}}}}}^{-}$$$$\Delta {{{{\rm{G}}}}}_{{{{\rm{III}}}}}={{{\rm{G}}}}[{{*}{{{\rm{C}}}}{{{\rm{H}}}}}_{3}]-({{{\rm{G}}}}[{{{{\rm{H}}}}}^{+}+{{{{\rm{e}}}}}^{-}]-{{{\rm{G}}}}[{{*}{{{\rm{C}}}}{{{\rm{H}}}}}_{4}])$$$${{{\rm{IV}}}}{{*}{{{\rm{C}}}}{{{\rm{H}}}}}_{3}+{O}_{t}\to {{*}O_{t}{{{\rm{C}}}}{{{\rm{H}}}}}_{2}+{{{{\rm{H}}}}}^{+}+{{{{\rm{e}}}}}^{-}$$$$\Delta {{{{\rm{G}}}}}_{{{{\rm{IV}}}}}={{{\rm{G}}}}[{{*}O_{t}{{{\rm{C}}}}{{{\rm{H}}}}}_{2}]+{{{\rm{G}}}}[{{{{\rm{H}}}}}^{+}+{{{{\rm{e}}}}}^{-}]-{{{\rm{G}}}}[{{*}{{{\rm{C}}}}{{{\rm{H}}}}}_{3}]$$$${{{\rm{V}}}} {*}O_{t}{{{\rm{C}}}}{{{\rm{H}}}}_{2}\to {*}O_{t}{{{\rm{C}}}}{{{\rm{H}}}}_{2}+{{{\rm{H}}}}^{+}+{{{{\rm{e}}}}}^{-}$$$$\Delta {{{{\rm{G}}}}}_{{{{\rm{V}}}}}={{{\rm{G}}}}[{*}O_{t}{{{\rm{C}}}}{{{\rm{H}}}}_{2}]+{{{\rm{G}}}}[{{{{\rm{H}}}}}^{+}+{{{{\rm{e}}}}}^{-}]-{{{\rm{G}}}}[{*}O_{t}{{{\rm{C}}}}{{{\rm{H}}}}_{2}]$$$${{{\rm{VI}}}} {{*}O_{t}{{{\rm{C}}}}{{{\rm{H}}}}}_{2}+{{{{\rm{H}}}}}_{2}{{{\rm{O}}}}\to {{*}O_{t}{{{\rm{C}}}}{{{\rm{HOH}}}}}+{{{{\rm{H}}}}}^{+}+{{{{\rm{e}}}}}^{-}$$$$\Delta {{{{\rm{G}}}}}_{{{{\rm{VI}}}}}={{{\rm{G}}}}\left[{*}O_{t}{{{\rm{C}}}}{{{\rm{HOH}}}}\right]+{{{\rm{G}}}}\left[{{{{\rm{H}}}}}^{+}+{{{{\rm{e}}}}}^{-}\right]-{{{\rm{G}}}}\left[{{*}O_{t}{{{\rm{C}}}}{{{\rm{H}}}}}_{2}\right]-{{{\rm{G}}}}[{{{{\rm{H}}}}}_{2}{{{\rm{O}}}}]$$$${{{\rm{VII}}}} {*}O_{t}{{{\rm{C}}}}{{{\rm{HOH}}}}\to {*}O_{t}{{{\rm{C}}}}{{{\rm{OH}}}}+{{{{\rm{H}}}}}^{+}+{{{{\rm{e}}}}}^{-}$$$$\Delta {{{{\rm{G}}}}}_{{{{\rm{VII}}}}}={{{\rm{G}}}}\left[{*}O_{t}{{{\rm{C}}}}{{{\rm{OH}}}}\right]+{{{\rm{G}}}}\left[{{{{\rm{H}}}}}^{+}+{{{{\rm{e}}}}}^{-}\right]-{{{\rm{G}}}}\left[{*}O_{t}{{{\rm{C}}}}{{{\rm{HOH}}}}\right]$$$${{{\rm{VIII}}}} {*}O_{t}{{{\rm{C}}}}{{{\rm{OH}}}}\to {*}O_{t}{{{\rm{C}}}}{{{\rm{O}}}}+{{{{\rm{H}}}}}^{+}+{{{{\rm{e}}}}}^{-}$$$$\Delta {{{{\rm{G}}}}}_{{{{\rm{VIII}}}}}={{{\rm{G}}}}\left[{*}O_{t}{{{\rm{C}}}}{{{\rm{O}}}}\right]+{{{\rm{G}}}}[{{{{\rm{H}}}}}^{+}+{{{{\rm{e}}}}}^{-}]-{{{\rm{G}}}}[{*}{{{\rm{O}}}}_{{{{\rm{t}}}}}{{{\rm{C}}}}{{{\rm{OH}}}}]$$$${{{\rm{IX}}}}{*}O_{t}{{{\rm{C}}}}{{{\rm{O}}}}\to {{{{\rm{CO}}}}}_{2}$$$$\Delta {{{{\rm{G}}}}}_{{{{\rm{IX}}}}}={{{\rm{G}}}}[{{{\rm{CO}}}}_{2}]+{{{\rm{G}}}}\left[{*}O_{t}{{{\rm{C}}}}{{{\rm{O}}}}\right]$$The energy barrier of the reaction pathway was determined by evaluating the disparity in overall energy prior to and following the reaction. This assessment involved utilizing specific chemical equations, wherein * represented catalysts and Ot symbolized the terminal oxygen atom of PTA within subnano-HELMO-PTA. To calculate the energy of (H+ + e−), G[H+ + e‒] = 1/2 G [H2] – eU, where U denoted the applied overpotential and e represented the elementary charge64. For this particular study, U was set at 0 V compared to a reversible hydrogen electrode.Potential energy surfaces play a crucial role in determining both the diffusion barrier and adsorption configuration. In this study, we focused on the most stable surface of the subnano-HELMO-PTA material. To construct the potential energy surface, discrete points were used with H atoms serving as detectors. Specifically, we gridded the surface and calculated the adsorption energy of H atoms on the lattice. Subsequently, contour maps were generated based on these adsorption energies. It is important to note that many of the initial adsorption sites proved to be unstable; therefore, we employed a strategy where we fixed the adsorbed molecules in their x and y directions while allowing relaxation in the z direction until achieving adsorption equilibrium.
High-entropy-perovskite subnanowires for photoelectrocatalytic coupling of methane to acetic acid
