The geometries and electronic structures of Zr _n Cu(n=2~12) clusters: A joint machine learning potential-density functional theory investigation

Abstract Zr-based amorphous alloys have attracted extensive attention because of the large glassy formation ability, wide supercooled liquid region, high elasticity and unique mechanical strength induced by their icosahedral local structures. To dig out the microstructures of Zr-Cu clusters, the stable and metastable geometry of Zr n Cu ( n =2~12) clusters are screened out via CALYPSO method using machine learning potentials, and then the electronic structures are investigated using the density functional theory. The results show that the Zr n Cu ( n ≥3) clusters possess the three-dimensional geometries, Zr n Cu ( n ≥9) possess cage-like geometries and the Zr 12 Cu cluster has icosahedral geometry. The binding energy per atom gradually enlarged with increased size of clusters, and Zr n Cu ( n =5, 7, 9, 12) have relative stronger stability than their neighbors. The magnetic moment of most Zr n Cu clusters is just 1μ B , and the main components of HOMOs in Zr 12 Cu cluster comes from Zr-d state. There are hardly any localized two-center bonds, and there are about 20 σ-type delocalized three-center bonds.