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 n O ( n = 2–5), all of which are exothermic reactions. According to the released energy, the Zr 4 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 n O ( 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.