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

Zr-based amorphous alloys have attracted extensive attention because of their large glassy formation ability, wide supercooled liquid region, high elasticity, and unique mechanical strength induced by their icosahedral local structures. To determine the microstructures of Zr–Cu clusters, the stable and metastable geometry of Zr n Cu ( n = 2–12) clusters are screened out via the CALYPSO method using machine-learning potentials, and then the electronic structures are investigated using density functional theory. The results show that the Zr n Cu ( n ≥ 3) clusters possess 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 gets enlarged with the increase in the size of the clusters, and Zr n Cu ( n = 5, 7, 9, 12) have relatively better stability than their neighbors. The magnetic moment of most Zr n Cu clusters is just 1 μ B , and the main components of the highest occupied molecular orbitals (HOMOs) in the Zr 12 Cu cluster come from the Zr-d state. There are hardly any localized two-center bonds, and there are about 20 σ -type delocalized three-center bonds.