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Medium-sized double magic metal clusters, Al@Ag54- and Al@54-, are predicted based on unbiased global search and density functional calculation. Both bimetallic core-shell clusters have icosahedral symmetry, and they are much lower in energies than all other low-lying isomers. In contrast, the icosahedral cluster Al@54- is a high-energy isomer. Both Al@54- and Al@Cu54- exhibit appreciable gaps between the highest occupied molecular orbital and the lowest unoccupied molecular orbital, and strong spherical aromaticity, which provide two additional evidences for the likelihood of their high stability. The simulated anion photoelectron spectra and optical absorption spectra are readily compared with future experiments.