Fig. 1. The calculation structures and activity descriptor determination. (a) Schematic illustration of transition metal (TM) doping and the induced formation of double-Sv in the WS2 basal plane. (b) The periodic table of elements showing the TMs considered as dopants in WS2, shaded in red. (c) Linear relationship between the doping energy of TM heteroatoms and the formation energy of double-Sv. (d) C2H2 and H2 adsorption configuration at a Sv site of the M@WS2-Sv catalysts. M represents a TM heteroatom. ST and SB represent the top and bottom sulfur atoms in M@WS2-Sv, respectively. (e) The linear relationship between the adsorption free energies of C2H2 and H2 on the M@WS2-Sv catalysts.

Fig. 2. Analyses of reaction thermodynamics for AHE. (a) Schematic diagram illustrating the reaction mechanism of the AHE process. The dark grey, white, blue, and yellow spheres represent the C, H, W, and S atoms, respectively. The linear free energy scaling relations (LFESRs) of ΔGC2H2* with ΔG2 (b) and ΔG4 (c) for the elementary steps involved in the AHE process on the M@WS2-Sv catalysts. The lines are derived from the linear fit to the data points listed in Table S3. (d) The combined LFESRs for the five elementary steps (ΔG1, ΔG2, ΔG3, ΔG4, and ΔG5) involved in the AHE process on the M@WS2-Sv catalysts. The resulting volcano plot, which shows the activity trend, is formed by the ΔG4 and ΔG2 lines and is indicated by a solid line. The green area represents the region for ideal dopants. (e) The projected density of states (PDOS) of the 3d orbitals of Cu and Ti atoms, and the C 2p orbitals for C2H2* on Cu@WS2-Sv and Ti@WS2-Sv catalysts. The Fermi level is at 0 eV. εd denote the d-band center. The Cu@WS2-Sv and Ti@WS2-Sv active sites are shown for reference. The atom encircled by the dashed line are those considered for the PDOS plot.

Fig. 3. AIMD simulations for the screened catalysts. (a) The PDOS on the d and 3p orbitals of the M-S bond for the Cu@WS2-Sv, Pd@WS2-Sv, Ag@WS2-Sv, and Au@WS2-Sv catalysts, respectively. The Fermi level is at 0 eV. The atoms denoted by red and black dotted circles in the inserted images are considered for the PDOS plots. (b) The variations of temperature vs. time for AIMD simulations of Cu@WS2-Sv, Pd@WS2-Sv, Ag@WS2-Sv, and Au@WS2-Sv catalysts at 573 K, respectively. The snapshots for the highest temperature points are shown in the right panel. The longest M-S bond distances are indicated in the snapshots, where dashed lines represent broken or partially broken bonds.

Fig. 4. Reaction free energy pathways for the AHE over the Cu@WS2-Sv and Pd@WS2-Sv. The free energy diagram and the optimized structures of the intermediates and transition states for the C2H2 hydrogenation reaction pathway on the Cu@WS2-Sv (a) and Pd@WS2-Sv (b) at 298.15 K, respectively. The values enclosed in parentheses represent the free energy barriers in eV.

Fig. 5. Machine learning-based predictive descriptor of activity. (a) Linear relation between Φ = and ΔGC2H2*. (b) Comparison between the Φ-predicted and DFT-calculated ΔGC2H2*.