Atomistic insights into highly active reconstructed edges of monolayer 2H-WSe2 photocatalyst

Ascertaining the function of in-plane intrinsic defects and edge atoms is necessary for developing efficient low-dimensional photocatalysts. We report the wireless photocatalytic CO2 reduction to CH4 over reconstructed edge atoms of monolayer 2H-WSe2 artificial leaves. Our first-principles calculations demonstrate that reconstructed and imperfect edge configurations enable CO2 binding to form linear and bent molecules. Experimental results show that the solar-to-fuel quantum efficiency is a reciprocal function of the flake size. It also indicates that the consumed electron rate per edge atom is two orders of magnitude larger than the in-plane intrinsic defects. Further, nanoscale redox mapping at the monolayer WSe2–liquid interface confirms that the edge is the most preferred region for charge transfer. Our results pave the way for designing a new class of monolayer transition metal dichalcogenides with reconstructed edges as a non-precious co-catalyst for wired or wireless hydrogen evolution or CO2 reduction reactions.

Supplementary Table 2 Turnover   It is also observed that the peak of the degenerated 2 1 + 1 modes slightly blue-shifted and broadened with decreasing . The ( ), ( ), and 1 2 ( ) + 2 (Σ) peaks colored in violent, dark yellow, and dark purple, respectively, do not draw for the sake of presentation.   images, respectively. c room-temperature PL and d Raman spectra, respectively, were recorded by using a red laser (632 nm). the PL intensity of the VT-WSe2 (grown by low-pressure vapor deposition) is much lower than that of the ME-WSe2 (prepared by a micromechanical exfoliation) due to the presence of mid-gap states and a high non-radiative recombination rate. In addition, the high − -to-0 ratios are 0.46 and 1.25 for the ME-WSe2 and VT-WSe2, respectively. This implies that the presence of localized charge carriers is due to the higher defect density in the VT-WSe2 sample. In contrast to VT-WSe2, the Raman spectrum of the ME-WSe2 shows an intense ( ) peak with a small shoulder at ~250 cm -1 ( 2 1 + 1 ).
10 μm 1 μm     Density of states (arb. units)   Yellow arrows, dark orange, and blue circles display the antisite defects, VSe, and VW, respectively. eis the magnitude of the negative electric charge carried by a single electron.   transfer mechanism is not good that is the same as the main scan. , , and ↔ stand for applied electric field, charge transfer, and redox reactions, respectively. acetaldehyde is a minor product because its yield is in the order of the blank tests. Acetaldehyde can be formed from the reduction reaction of impurity as our blank tests show. This side product can consume holes and also form methane. We believe our blank test appropriately subtracts the contribution of the methane from the acetaldehyde side product.     Tables   Supplementary Table 1 Examples of different materials for PC production of CO2. and stand for apparent and internal quantum efficiencies. CH4 production rates were calculated based on the geometrical reported area that was exposed to the light irradiation of the samples inside the reactor. It should be noted that the efficiencies presented in two different ways: for overall or for a narrow band (a certain wavelength) of the irradiation spectrum, that we called them "overall" or "at λ nm", respectively. "N/A" and " ▲ " means not available and data provided by the authors' response.
Year Co-catalyst @ Catalyst (mass, exposed area) Finally, the furnace center was heated up to 950 °C (with a rate of 31 °C min -1 ) and kept for 5 min before it was cooled to 300 °C naturally, followed by a fan-assisted fast cooling to room temperature. Supplementary Note Fig. 1 illustrates the detailed growth recipe of the growth.    Fig. 4b and c). Notably, the density of the BL region is much lower in the smaller flakes due to the less feeding rate during the growth process.

Supplementary Note
Supplementary Note Fig. 4d and e reveal that the second layer is already twisted to a small angle due to an energetically favorable stacking structure, displaying moiré patterns. So, the ensemble averaging estimates a few percent of BL flakes in each sample. facing up at a distance of 7.5 cm downstream from the center of the WO3 source. Before the growth, the system was flushed with 100 sccm Ar for 20 min Finally, the center of the furnace was heated up to 925 °C (with the rate of 30 °C min -1 ) and kept for 5 min before a slow cooling to 800 °C in 1 h, followed by a naturally cooling to room temperature. Notably, both Ar and H2, with a flow rate of 50 and 2.5 sccm, respectively, were introduced as the carrier gases during the chemical vapor deposition process.

Supplementary Note 2. Monolayer WSe2 transfer
The where is the coverage, i.e. ⁄ there, and are the area of the transferred film and optical slit of the apparatus, respectively. The absorbance of the transferred film can be given by, where , = 8 Å (measure by atomic force microscope height profile), and ( ) are the absorption coefficient, the thickness of ML flakes, and coverage-independent absorbance, respectively.
Therefore, the corrected transmittance can be calculated by the following equation, method was applied to relax the geometry until the residual force on each atom was smaller than 0.01 eV Å -1 , and the criterion for converging total electronic energies was less than 10 -5 eV.
For the DOS calculations, since the GGA is well-known for underestimating band gaps of semiconductors, we used the HSE06 hybrid functional 43 to perform the static electronic calculation based on the optimized structure at the PBE level. Due to the high demand for the HSE06 calculation, the energy cutoff was set to 400 eV, and -centered -point meshes of 6 × 6 × 6 and 3 × 1 × 1 were adopted to calculate the DOS for the monolayer and nanoribbon models, respectively. were fixed in each model.

4-4. Models of defective edges.
There can be a large number of defective edges. However, we focused on specific defects occurring at the ZZse and Anse edges due to a Se-rich condition of our grown WSe2 nanoflakes (Fig. 1d in the manuscript). Notably, a W-terminated edge can already adsorb CO2. So, our focus in this calculation was on the defects at the Se-terminated edge. As shown in Fig. 3 in the manuscript, we proved that the stronger interaction between WSe2 nanoflakes and CO2 molecules is via the bonding of exposed W atoms and CO2. Due to this reason, V2Se, Wse, and Wadd (W adatom to the edges) defects that can provide exposed W atoms were ZZSe + WSe,III Se (4) replaced by W (asymmetric relaxed structure) Supplementary Fig. 18 ZZSe + WSe,IV Se (4) replaced by W (symmetric relaxed structure) Supplementary Fig. 18 AnSe

An + V2Se
Se (1) and Se (2) are removed An + WSe,II Se (4) replaced by W (relaxed configuration I) Supplementary Fig. 18 An + WSe,III Se (4) replaced by W (relaxed configuration I) Supplementary Fig. 18 An + Wadd,II W is added between Se (1) and Se (3) (relaxed configuration II) Supplementary Fig. 18 4-5. CO2 adsorption calculation. To find the most stable CO2 adsorption results, various initial configurations of a CO2 molecule were considered to cover the different sites of the basal plane and edge models. Before optimization, the introduced CO2 molecule was located more than 3.2 Å far from the atoms of optimized WSe2 models with the CO bonds of 1.177 Å and an angle of 180°. The binding energy ( 2 ) is defined as: where is the calculated total energy of the WSe2 monolayer or nanoribbon with a CO2 molecule adsorbed on it. 2 is the total energy of the isolated WSe2 monolayer or nanoribbon, and 2 is the total energy of an isolated CO2 molecule. The amount of charge transfer (charge difference ) between the CO2 molecule and adsorbent was evaluated by using the Bader charge analysis 46 .

4-6.
Calculation of formation energy. The defect formation energies were calculated by 47 , where and are the total energies of the supercell with specific defects and the related pristine system (the perfect monolayer or the corresponding nanoribbon without defects), respectively. is the number of atoms (for = W and Se) being added to (> 0) or removed from (< 0) the pristine system when creating specific defects, and is the chemical potential of atom .
In thermodynamics, the chemical potential is defined as the change of Gibbs free energy with respect to a change of the particle number of a species at a constant temperature, pressure, and particle number of the other components, For calculations in the solid phase, the temperature and pressure dependence are ignored with acceptable accuracy, and the chemical potential is set to be the calculated total energy per atom at 0 K 48,49 . Hence, for the ML WSe2 system, the chemical potential of W and Se are represented by, where ( 2 ) is the calculated total energy of the ML WSe2, and 2 is the number of WSe2 units. Equation (S10) also shows that or are variable with a constraint.
Conventionally, the calculated total energy per atom of the elementary phase of a species at 0 K, i.e., ( ), is the reference and upper bound of the chemical potential . When is equal to ( ) in a mixture, it means that the element is excess and its bulk starts to form 50 . Bounds on the chemical potentials of our WSe2 system are: where ( ) and ( ) are the total energy of bulk W with the body-centered cubic structure and bulk Se with the trigonal structure 44 , respectively. From a calculation point of view, chemical potentials vary as different atomic constituents or phases due to the different total energy.
With the elementary phases as references, the amount of chemical potential change is equal to the calculated enthalpy at T = 0 K. The enthalpy calculation of the ML WSe2 is given by, which can also be represented by, where we have defined the change of the chemical potential from its bulk reference as, When combined with the above-mentioned equations, the lower bounds can be determined and the ranges of and can be given by, and, Since our system is the ML WSe2, the relation of equation (S14) should be held in thermodynamic equilibrium. Different values of and can be regarded as different conditions of W and Se ratio in the experiment. The calculated range of ∆ spans from 0 to -0.63 eV for forming the ML WSe2. When ∆ is close to 0 eV, it represents a Se-rich (W-poor) condition; when ∆ is close to -0.63 eV, it represents a Se-poor (W-rich) condition.

4-7. Convergence of adsorption and formation energy.
For testing the convergence of the CO2 adsorption energies, larger 4 × 9 nanoribbon models were used (Supplementary Note Fig. 6).
A CO2 molecule was introduced to interact with one of the 4 × 9 nanoribbon models at one time; for a brief representation, the optimized results were represented together in Supplementary Note Fig. 6 a and b. Compared to the results by using 4 × 9 nanoribbon models, the CO2 adsorption configurations are similar, the 2 for the CO2 adsorption on ZZW,II, ZZSe, and AC edges are the same, and the 2 for the CO2 adsorption on AnSe and Anw edges are 0.01 eV and 0.03 eV, respectively, larger when the smaller nanoribbon models were used ( Supplementary Fig. 21).
Supplementary Note Table 1 shows the convergence test of defect formation energies on ZZSe and AnSe edges. For the ZZSe and AnSe edges, the differences of ∆ are less than 0.04 and 0.15 eV between the 4 × 4 and the 4 × 9 models, respectively. Supplementary Note Table 2  . Table 2 The convergence test for the defect formation energies.
where 1 ± , 2 ± , 3 ± , and 4 ± are dimensionless constants. And (where is the radius of the Pt tip) is the normalized tip-surface distance. Supplementary Note 6. Photocatalytic CO2 reduction 6-1. Photocatalytic setup. Photocatalytic (PC) CO2 reduction experiments were performed using a home-built stainless steel reactor at room temperature. Before starting the PC experiment, the reactor was degassed at 80 °C and 150 °C for 24 and 3 h, respectively, followed by blowing with an N2 gun for several minutes. Then, ultrapure CO2 gas was purged into the reactor at a flow rate of 90 and 30 sccm for 10 and 30 min, respectively, to provide a constant humidity level and equilibrium gas adsorption-desorption inside the reactor. After that, a commercial 150 W Xe lamp (> 320 nm, AM 1.5G, 100 mW cm -2 ) was placed as a light source directly above the quartz window of the reactor. The background signal of the CH4 molecules was measured by injecting Ar gas several times to reach a constant peak area, and finally, subtracted from the total yield. The PC reaction was terminated after each reaction cycle to avoid the adsorbed product on the catalyst surface. Then, the photocatalyst was degassed by N2 flush followed by keeping in a vacuum box for 24 h. We have further performed a 13 CO2 isotope test by using RT-Msieve 5A (15m I.D.: 0.25 mm) column at 35 °C under a He flows at a rate of 1 mL min -1 . Supplementary Note Fig. 8 shows the presence of both 13 CH4 and also 12 CH4. The presence of 12 CH4 can be due to the dissolved 12 CO2 in water or carbonate species which pre-adsorbed on the surface under the ambient atmosphere 55,56 . Fig. 8 Gas chromatography-mass spectrometry of the CH4 product.

Supplementary Note
The gas chromatograph (GC) shows the presence of methane as the product. Inset shows the GC-Mass, illustrating the presence of 13 CH4 with = 17. The fragment at = 16 can be assigned to 13 CH3 and 12 CH4.
Therefore, we have also performed the blank tests 57 : (i) With WSe2 photocatalyst/with CO2/without light (with the production of 1 ), (ii) With WSe2 photocatalyst/without CO2/with light (with the production of 2 ), and (iii) Without WSe2 photocatalyst/with CO2/with light (with the production of 3 ). Finally, the values of products measured in the blank experiments have subtracted from the product yield in the photocatalytic reaction as, Additionally, helium ionization detector (HDI) and GC-MS were used to check the presence of CO and qualitatively measure the oxidation products.
where , , and are the total CH4 yield, Avogadro's number, and irradiation time, respectively. is independent of the total area ( ). Further, the total product ( ) was modeled with ( + ̅ ) where and are fitting factors depicting the contributions of the basal plane and edge, respectively, and is the total area. Notably, these fitting factors are obtained by fitting the , which is independent of , where is a constant coefficient that is a function of the number of electrons used for CH4 production, the total adsorbed photon flux, and Avogadro's number. So, the edge contribution in the final product is proportional to the perimeter-dependent factor where is the total area of the flakes. Edge atoms have a size-depended density of ≲ 2×10 13 . By adding the edge contribution, i.e. + , to the equation (S11), 4 was calculated to be about 0.48 ± 0.04 s -1 from the following equation: where is the number of reacted electrons in a reduction reaction. For example, are 2 and 8 for H + to H2 and CO2 to CH4 reactions, respectively.