**2. Computational Methods and Model**

We employed the Vienna Ab-initio Simulation Package (VASP, version 5.4, developed by Vienna University) [22,23] to carry out our first-principles calculations. All calculations were implemented based on density-functional theory (DFT) [24,25], using a plane wave basis set [26]. The interactions between the core and valence electrons were described with the projector augmented wave (PAW) approach [27,28]. Generalized gradient approximation (GGA) of the Perdew–Burke–Ernzerhof (PBE) functional [29] was adopted in all the calculations. An energy cut-off for the plane-wave basis set was set to 380 eV for both the relaxed and static computations. The residual force for structure optimization was less than 0.02 eV/Å. The 7 × 7 × 1 k-point grids generated by the Monkhorst–Pack (MP) technique [30] was found to be sufficient for the present study.

The Mo (110) surface was used to explore the interaction between Na/O atoms and the Mo substrate because the Mo (110) surface has the lowest surface energy as reported in Materials Project Database [31]. Mo (110)-(2 × 2) surface cell was represented by a 5-layers slab model (8 atoms per layer) with the vacuum thickness of 10 Å. The upper two layers were fully relaxed and the bottom three layers were fixed as the bulk phase during structure optimization. In this study, we also investigated the effect of alloy element Re on the adsorption of Na and O atoms. For Mo-Re alloy, when the weight percentage of Re is less than 14%, Re atoms randomly replace Mo atoms at the lattice site [32]. We considered three adsorption sites for the Na and O atom on Mo/Mo-Re alloy: TOP site, Bridge site and Hollow site of Mo/Mo-Re (110) surface. Top site is located over the Mo atoms of the topmost layer, and bridge site is located between the two Mo atoms of the topmost layer, while Hollow site is above the Mo atoms of the second layer, as is shown in Figure 1. For one atom adsorbed on the (110)-(2 <sup>×</sup> 1) surface cell, the corresponding coverage (Θ) is <sup>1</sup> <sup>8</sup> ML.

The climbing image nudged-elastic-band (CI-NEB) method was employed to calculate the Na diffusion barriers between two most stable adsorption sites on Mo/Mo-Re (110) surface [33].

**Figure 1.** Structure of Mo/Mo-Re (110) surfaces and adsorption sites: (**a**) side view of Mo/Mo-Re (110) slab model; (**b**) Top view of Mo (110) surface and (**c**) top view of Mo-Re surface. Blue and green spheres represent Mo atoms, and yellow spheres represent Re atoms.
