## 1 Introduction  
The interaction between hydrogen and metal surfaces is an interesting topic in science and engineering, and has been investigated by both experimental [1; 2; 3] and theoretical [4; 5] approaches. Over 80 percent of synthetic chemicals are produced with the application of catalysts, meaning that the interactions of hydrogen with catalytic metal surfaces during heterogeneous catalysis are of great interest for several important processes [6; 7; 8] including petrochemical processing, pharmaceutical production [9], highly efficient electrocatalysis [10], fine chemical production [11], and conversion of biomass to fuels and chemicals [12]. Meanwhile, hydrogen-metal interactions have attracted further attention due to the central role of hydrogen as a clean and efficient energy source [13; 14]. With the increasing demand for high purity hydrogen in the fields of fuel cell, new materials for hydrogen separation/purification are being explored. Consequently, the study of the behavior of both absorbed and adsorbed hydrogen on/into the metal surface/subsurface is important for achieving a deep understanding of the hydrogen-permeation properties of such metallic membranes [15; 16]. Considerable experimental and theoretical studies of the hydrogen sorption on many single-crystal metal surfaces have been carried out. For example, [PERSON] et al. [4; 15] performed a comprehensive theoretical study addressing adsorption and absorption energies and subsurface penetration barriersof hydrogen on different low-index surface terminations of 17 transition metals (TM) by first-principles calculations. [PERSON] et al. further studied the diffusion of atomic hydrogen on Cu (001) via scanning tunneling microscope (STM) measurements. The diffusion of H atoms was measured as a function of temperature, and a transition from thermally activated diffusion to quantum tunneling was observed at 60 K [16]. Recently, [PERSON] et al. reported an extensive study of adsorption and diffusion of hydrogen atoms on the (100) surfaces of fcc Au, Cu, Ag, and Pt, performed by means of density functional theory (DFT) calculations [17; 18]. Based on elucidating the preferential adsorption sites of hydrogen on each metal, they calculated the adsorption distances and energies of atomic hydrogen at the top, hollow, and bridge sites of the (100) surfaces. The numerous studies focused on this topic have proved the importance of understanding the mechanism of hydrogen-metal-surface-related phenomena. Pd and its alloys are excellent materials for hydrogen separation and purification, but their high cost and scarcity should be noted. Currently, niobium (Nb), a Group VB (e.g., V, Nb, Ta, etc.) TM, has attracted much attention as one of the most promising hydrogen separation materials due to its relatively low price [3], excellent high-temperature mechanical properties, and corrosion resistance [19; 20; 21]. However, Nb often exhibit poor resistance to hydrogen embrittlement and therefore is limited in the practical application [22; 23; 24; 25]. Experimental and theoretical studies have verified that alloying Nb with other metals is an effective approach to solve this problem [26; 27; 28; 29; 30]. [PERSON] et al. [31] reported that the W doping is supposed to be the key role in enhancing the mechanical properties of Nb\({}_{16}\)H, and is not conducive to the structural stability of the Nb\({}_{15}\)WH (TIS) phase. Moreover, doping Nb with W can reduce the diffusion barrier of H, and enhance diffusion paths for H [32]. Both W and Mo are high-\(Z\) refractory metals (i.e., refractory metals containing impurities with high atomic numbers (\(Z\)) with similar physical properties. Comparing with W, Mo has a lower melting point (2883 K) and a lower erosion rate. Moreover, H has higher diffusivity and lower solubility in Mo, leading to lower H retention [33; 34; 35]. These characteristics make Mo an important alloying candidate of Nb-based membranes for hydrogen permeation.