Hydrogen evolution reaction between small-sized Zr_n (n = 2–5) clusters and water based on density functional theory

Density functional theory (DFT) is used to calculate the most stable structures of Zr_n (n = 2–5) clusters as well as the adsorption energy values of Zr_n (n = 2–5) clusters after adsorbing single water molecule. The results reveal that there is a significant linear relationship between the adsorption energy values and the energy gaps of the Zr_n (n = 2–5) clusters. Furthermore, the calculations of the reaction paths between Zr_n (n = 2–5) and single water molecule show that water molecule can react with Zr_n (n = 2–5) clusters to dissociate, producing hydrogen, and O atoms mix with the clusters to generate Zr_nO (n = 2–5), all of which are exothermic reactions. According to the released energy, the Zr₄ cluster is the most efficient in Zr_n (n = 2–5) clusters reacting with single water molecule. The natural population analysis (NPA) and density of states (DOS) demonstrate the production of hydrogen and orbital properties in different energy ranges, respectively, jointly forecasting that Zr_nO (n = 2–5) will probably continue to react with more water molecules. Our findings contribute to better understanding of Zr’s chemical reactivity, which can conduce to the development of effective Zr-based catalysts and hydrogen-production methods.