“…In this work, all density functional theory (DFT) calculations are conducted by the CASTEP (Cambridge Serial Total Energy Package) codes, employing the generalized gradient approximation (GGA) and Perdew–Wang (PW91) exchange-correlation energy. , The cutoff energy of 400 eV and the k-point meshes of 3 × 3 × 1 are used for the SrTiO 3 surface slab . The Coulombic interactions of transition metals are corrected by the GGA + U method, with self-consistent U values of 3.2 for Ti, 6.2 for Co, 4.0 for Mn, 4.2 eV for Fe, and 5.0 eV for Cu, respectively. ,, Especially, all methane calculations are performed by the DFT-D method to correct for van der Waals interactions. The convergence criteria for the maximum interatomic force, total energy, and displacement tolerances are 0.03 eV/Å, 1.0 × 10 –5 eV/atom, and 0.001 Å, respectively.…”