Two-dimensional Ga2XY monolayer containing vacancies for highly efficient electrocatalytic hydrogen reaction: based on first-principles calculations

Hydrogen energy as an excellent substitute for traditional fossil fuels, has received widespread attention. There is an urgent need to find an efficient and environmentally friendly electrocatalyst to increase hydrogen production. In this study, the Ga2XY (X, Y=O, S, Se, Te, X≠Y) system of group III-VI compounds was constructed, and the HER catalytic properties of its vacancy structure were investigated based on first principles. The research results show that all the structures are stable, and the introduction of O vacancy and Ga vacancy can significantly improve the structure’s Gibbs free energy (ΔGH). When the H atom is adsorbed on the bottom Ga atom, the HER with Ga2OSe structure containing outer Ga vacancy is very excellent, and its ΔGH can reach 0.07 eV, which is significantly superior to the currently recognized best HER catalyst Pt. Our research provides a new strategy for the design of HER electrocatalysts and a new method for the regulation of Ga2XY monolayers.


Introduction
The widespread use of traditional fossil fuels causes a serious threat and irreversible demage to the global climate and environment.Finding energy materials that are beneficial to the environment is an urgent issue.Hydrogen energy due to its excellent environmental performance, good combustion performance, and high energy density becoming the focus of current attention [1][2][3] , so most people believe that it is one of the best alternatives to fossil fuels.Electrocatalytic hydrogen and photocatalytic hydrogen are two main methods for producing hydrogen gas.Among them, electrocatalytic hydrogen production is given priority due to its good feasibility and easy control [4] .Traditional electrocatalytic hydrogen production catalytss mainly include metal Pt and alloy catalysts [5] , carbon-based composite materials [6] , transition metal oxides [7] , transition metal sulfides [8] , etc. Precious metal Pt has high catalytic activity, strong corrosion resistance, and good structural stability, and is considered to be the best HER catalyst.However, it is expensive and rare, so there is still a need for us to find a feasible alternative.
Through continuous research, researchers have found that two-dimensional materials can be used as excellent HER electrocatalysts due to their unique structure and adjustability.Among them, Janus material and transition metal catalysts have become hotspot in this year.Janus materials break the traditional symmetrical structure, have more active sites on the surface, and have adjustable band gaps, which can better improve the HER performance of materials [9][10][11] .Among them, research on the catalytic performance of III-VI group compounds is rare.In the experiment, two-dimensional GaX (X=S, Se, Te) monolayers have been successfully synthesized through mechanical and liquid stripping.Among them GaSe has been proven to have good photocatalytic hydrogen production ability [12][13][14] .
At present, research on two-dimensional GaX (X=S, Se, Te) monolayers mostly focuses on photocatalytic hydrogen generation, but their electrocatalytic performance has not been successfully explored.In this work, studied the structures of GaX (X=O, S, Se, Te) monolayers, Ga2XY (X, Y=O, S, Se, Te, X ≠ Y) monolayers, and Ga2XY structures containing vacancies.Through the analysis of Gibbs free energy (∆GH), formation energy, and band gap, the catalyst with better HER performance was selected.The results show that all the structures are stable, and the adsorption of H on the GaX monolayer is weaker than that on the Ga2XY monolayer.After the introduction of vacancy, the HER performance of Ga2XY is improved.The HER performance of Ga2OSe monolayer with Ga vacancy has the best performance with a ∆GH of 0.07eV.Our research provides a research direction for the design of efficient electrocatalytic hydrogen generation.

Computational methods
In this work, the first principle of density functional theory (DFT) is used to calculate the energy and interaction between atoms and complete the theoretical calculation using the Vienna Ab initio Simulation Package (VASP) [15] .Explained by Perdew-Burke-Ernzerhof (PBE) functions and the Projection Augmented Wave (PAW) method [16][17] .The DFT-D3 method was selected for relevant calculations, with a plane cutoff energy set at 450 eV, an energy convergence standard of 1.0 e -6 , and a force convergence standard of 0.01 eV•A -1 .Considering the inevitable interaction forces between periodic elements, added a 15Å vacuum layer in the c-axis direction to avoid it.Select a grid of 4×4×1 generated around the G point for calculation.

Results and Discussion
The geometric structures of the GaX monolayer and Ga2XY monolayer are shown in Fig 1 .The atomic arrangement follows the four-layer structure of X-Ga-Ga-X/Y, the upper and lower layers can form a hexagonal structure [18] .In the calculation, selected 4×4×1 crystal cells to maximize the accuracy of the calculation and avoid the influence of periodic unit interactions.For the Ga2XY monolayer, have considered its vacancy structure by the inner and outer layers of atoms (as shown in the dashed rhombic in  In order to analyze the structural stability of GaX and Ga2XY, the structural formation energy is calculated as following: In the equation, + and represent formation energy after and before H adsorption. , it can be intuitively seen that the formation energy of H atoms adsorbed on the upper layer is significantly lower than that adsorbed on the lower layer.Among the 9 structures, the Ga2OSe monolayer has the smallest formation energy, so its structure is most conducive to the adsorption of H atoms. Therefore, in subsequent calculations mainly consider the H atom that is adsorbed on the upper layer of the Ga2OSe structure.The free energy of the Ga2OSe structure is calculated as 0.46 eV, which has not yet reached the standard of an efficient HER electrocatalyst.Therefore, a Ga2OSe structure containing vacancies.According to the representation in Fig 1(b), based on the distribution of atoms in the inner and outer layers, six vacancy sites were considered, namely O, Se, and Ga in the inner and outer layers.Four H adsorption positions were considered for each vacancy structure.First of all, calculated the formation energies of these 24 adsorption models, and the results are shown in Fig 2(b).Through the calculation results, it can be intuitively seen that the adsorption energy of the Ga vacancy is superior to the other two vacancies.Next, calculated their Gibbs free energy (∆GH), ∆GH is a recognized descriptor of material HER performance, the closer ∆GH is to 0, the better the catalytic performance of the material, the ∆GH using the following equation: In the equation, and represent the formation energy and zero-point energy correction of the structure, respectively, and T represents the temperature, ∆S represents an entropy correction value.Through further processing of ∆GH, a volcanic curve is shown in Fig 3(a).In the volcanic curve, the material at the top of the volcano is the material with the best performance of HER.If it is distributed on the left side of the volcanic curve, it means that the adsorption of H is too strong, and the distribution on the right side indicates unstable adsorption of H. Fig. 3(b) comparison of ∆GH through step diagram shows the catalytic performance of the structure represented by the blue dotted line segment is closer to 0 eV.From the two figures in Fig. 3, the catalytic performance of Ga@Ga2OSe is significantly better than O@Ga2OSe, and Oin@Ga2OSe is slightly better than Oout@Ga2OSe at the same time.Gaout-Gadown@Ga2OSe has the best HER performance, with ∆GH is only 0.07 eV.To explore their underlying principles, further analyzed their band structures.All the energy band structures of O@Ga2Ose and Ga-Gadown@Ga2Ose are calculated and analyzed for their bandgap variation, as shown in Table 1.According to the calculation results, the construction of vacancy structures will significantly reduce the bandgap value of the Ga2OSe monolayer.The smaller bandgap means that it is easier to transfer electrons between VBM and CBM, and the material is more inclined towards metallicity.The conductivity is improved, thereby improving the HER performance of the Ga2OSe monolayer.Ga@Ga2OSe has always been metallic, although its bandgap changes are not significant, the catalytic performance is known to be very good through Figure 3.

Conclusion
In this work, constructed a vacancy structure of Ga2XY (X, Y=O, S, Se, Te, X ≠ Y) monolayer and studied its stability, catalytic activity, and electronic properties based on first principles.The research results showed that all the structures are stable.The introduction of vacancies can significantly improve the HER performance of the structure.Among them, the O vacancy and the Ga vacancy have the best effect.When H atoms are adsorbed on the bottom Ga atoms, the HER with Ga2OSe structure containing outer Ga vacancies is optimal, its free energy can reach 0.07 eV.Through analysis of the structural bandgap, it is found that the introduction of vacancies reduced the bandgap of the structure, improved the conductivity of the material, and improved HER catalytic performance.Our work is providing new ideas for Ga2XY (X, Y=O, S, Se, Te, X ≠ Y) monolayer adjustment, while also providing new strategies for designing excellent HER catalysts.
Fig 1(b)), and six atomic positions were selected to introduce vacancy.In Fig 1(b), the atom positions of the inner and outer layers are displayed through solid and dot lines, the positions of Ga and X/Y atoms are displayed in red and green, and represented by Xin and Xout in the following text.Four different H adsorption positions are selected based on vacancy sites (For Ga atoms, the adsorption of H onto Ga atoms below vacancies is also considered, represented by -Gadown), and represented by -Xin, -Xout, -Ga, -vacancy in the following text.Taking the vacancy of O inside as an example, hydrogen adsorption sites in it represented by numbers in Fig 1(b).As a result, the HER performance of the vacancy structure of the Ga2XY monolayer is analyzed by comparing these 24 different structures.

Figure 1 .
Figure 1.(a) Geometric structure of GaX (X=O, S, Se, Te) monolayer and (b) Ga2XY (X, Y=O, S, Se, Te, X ≠ Y) monolayer aerial view (above) and side view (below), respectively.The gray, yellow, and orange balls represent Ga, X, and Y atoms, respectively.The red and green circle represents the selected vacancy site, the number represents the H adsorption site, and the black dashed rhombic represents the inner and outer atoms level.

2
represents the energy of hydrogen.The calculation of formation energy is shown in Fig 2. Due to the different atoms in the upper and lower layers of Janus material, separately considered the formation energy of H atom adsorption on the upper and lower layers.The calculation results of Fig 2(a) indicate that the formation energy of these 9 structures is less than 2 eV, most of them are stable and have the promising for the next calculation.According to Fig 2(a)

Figure 2 .
Figure 2. The formation energy of (a) GaX and Ga2XY monolayer, (b) Ga2OSe vacancy structures.The yellow column in Figure (a) indicates that H atoms are adsorbed on the upper layer, while the purple column indicates that H atoms are adsorbed on the lower layer.The abscissa of Figure (b) represents vacancy sites, and columns of different colors represent different adsorption sites.The red dashed line represents the formation energy of 2 eV.

Figure 3 .
Figure 3. (a) Volcano curve diagram and (b) free energy step diagram of Ga2OSe vacancy structure.In Figure (a), different colors represent different vacancy types, and different shapes represent different adsorption sites.In Figure (b), different colors represent different vacancy types, and different lines represent different adsorption sites.

Table 1
Bandgap changes in Ga2OSe structures containing O and Ga atomic vacancies and their original structures.