4.7 Density functional theory (DFT)
Quantum ESPRESSO (QE) code version 7.2 was used to theoretically determine the effect of the heterostructure and Pt decoration.[27] The projected augmented wave (PAW) pseudopotentials were employed to show core–valence interactions. The Perdew–Burke–Ernzerhof (PBE) functional of the generalized gradient approximation (GGA) was used. The Van der Waals force was also corrected using the “Grimme-D3” code, built in QE. The cutoff values, including the plane-wave wavefunction of 55 Ry and charge density of 310 Ry, were considered for convergence. A smearing code (marzari-vanderbilt) was introduced to enhance the convergence.
The crystallographic information file (CIF) of MoSe2(mp-1634) on Materials Project website was used to design the supercell.[28] The supercell of MoSe2 was optimized using the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm with a force threshold of 3.8×10−4 Ry/Bohr (≈0.01 eV/Å) and a total energy convergence threshold of 1.0×10−5 Ry (≈0.0001 eV). The Monkhorst-pack k-point grid of 4 × 4 × 1 was selected to obtain the optimized structure without spin polarization calculation owing to non-magnetic property.[29] Additionally, to prevent interactions between the periodic boundaries along the z-axis, a vacuum of 20 Å was applied in the supercell. Subsequently, the Gibbs free energies (ΔG) of the reactions in the HER mechanism for MoSe2 and MoSe2 with Pt cluster were calculated and are presented below.[23]
\(\Delta G_{H}=\Delta E_{H}+\Delta E_{\text{ZPE}}-T\Delta S_{H}\)(4)
\(\Delta E_{H}=E_{\text{MoS}e_{2}+H}-E_{\text{MoS}e_{2}}-\frac{1}{2}E_{H_{2}}\)(5)
where ΔGH is the Gibbs free energy of hydrogen adsorption. ΔEH, EMoSe2+H, EMoSe2, and EH2 is the adsorption energy of hydrogen, the total energies of the MoSe2 slab with hydrogen and the same structure without hydrogen, respectively. EH2 indicates the total energy of a gas-phase hydrogen molecule. ΔEZPE and ΔSH represent the changes in zero-point energy, entropy between the adsorbed atomic hydrogen and hydrogen in gas phase, respectively.
The DOS of 2H MoSe2, 1T+2H MoSe2, and 1T+2H MoSe2 with Pt cluster were calculated for a k-point grid of 6 × 6 × 1 to obtain the exact electronic structure. To reveal heterostructure effect, p-band center of Se (Ep) was calculated using following equation:[23]
\(E_{p}=\frac{\int_{-\infty}^{+\infty}{E\times\rho dE}}{\int_{-\infty}^{+\infty}\text{ρdE}},\)(6)
where Ep, ρ, and E represent the p-band center, density of p states projected onto the Se atom, and energy level, respectively. When Pt cluster was decorated on the heterostructure slab, d-band center (Ed) was estimated as follows:[24]
\(E_{d}=\frac{\int_{-\infty}^{+\infty}{E\times\rho dE}}{\int_{-\infty}^{+\infty}\text{ρdE}},\)(7)