Lowest-energy structural and electronic properties of Cu Zr13− (n = 3–10) clusters in metallic glasses via CALYPSO search and density functional theory calculations

Bimetallic Cu–Zr clusters containing 13 atoms are intimately linked with the best glass former chemical compositions of Cu–Zr metallic glasses. Thus far, the ground-state geometric structures of CunZr13−n (n = 3–10) clusters have not been reported and are not well known because of the complexity of the energetic potential surface. In this study, a series of novel ground-state geometric structures of CunZr13−n (n = 3–10) clusters were found via an unbiased structure search using Crystal structure AnaLYsis by Particle Swarm Optimization (CALYPSO) code and density functional theory (DFT) calculations. Three new parameters for the second-order difference in energy gap, chemical hardness, and electronegativity were proposed to evaluate the relative chemical activity dependence of the chemical composition for the lowest-energy CunZr13−n (n = 3–10) clusters. Results show that although Cu5Zr8 and Cu7Zr6 are double-layered schistose and distorted face-centered cubic (FCC) structures, respectively, the lowest-energy structures of Cu–Zr clusters exhibit irregular nested structures based on a pentagonal bipyramid (existing nearly golden ratio order (NGRO)) with low symmetry, and the entire evolutionary configuration exhibits a stable transient from Cu3Zr10 to Cu10Zr3. Analysis of the electronic shell structure showed that the chemical compositions of Cu6Zr7 and Cu8Zr5 clusters have good correspondence with the best glass formers, Cu50Zr50 and Cu64Zr36, respectively, which is mainly due to the odd and even number of valence electrons rather than the geometric structure for a given Cu–Zr cluster. Moreover, the molecular orbital contours showed that the highest occupied molecular orbital and lowest unoccupied molecular orbital of the lowest-energy structure of CunZr13−n (n = 3–10) clusters are mainly contributed by the 4d electrons of Zr, which are consistent with the density of electronic states. The infrared spectra of the lowest-energy structure of CunZr13−n (n = 3–10) clusters provide a pathway for future experimental research.