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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 Zr12Cu 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 Zr12Cu 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.

The stable geometries, electronic structures, and magnetic behaviors of the ScLi n (n = 2–13) clusters are investigated by using particle swarm optimization (PSO) and density functional theory (DFT). The results show that these clusters have three-dimensional (3D) structures except ScLi2, and ScLi12, and ScLi13 that possess the cage-like structures. In analyses of the average binding energy, second-order difference of energy, and fragmentation energy, ScLi12 cluster is identified as magnetic superatom. The magnetic moment for each of these clusters owns an oscillating curve of different cluster sizes, and their magnetic moments are further investigated using molecular orbitals and jellium model. Of ScLi n (n = 2–13) clusters, ScLi12 has the largest spin magnetic moment (3 μ B), and molecular orbitals of ScLi12 can be described as 1 S 2 1 P 6 1 D α 5 D β 2 . Additionally, Mulliken population and AdNDP bonding analysis are discussed and the results reveal that the Sc atom and Li n atoms make equal contribution to the total magnetic moment, and atomic charges transfer between Sc atoms and Li atoms.