Retracted Article: A highest stable cluster Au 58 ( C 1 ) re-optimized via a density-functional tight-binding (DFTB) approach.

The vibrational spectrum ω i of a re-optimized neutral gold cluster Au 58 has been calculated using a numerical finite-difference approach and the density-functional tight-binding (DFTB) method. We have exactly predicted the vibrational frequency ranging from 3.88 through to 304.49 cm -1 which depends on the size and the arrangement of the atoms in the nanoparticle morphology of the cluster at Δ E = 0. Our investigation has revealed that the vibrational spectrum is strongly influenced by size and structure. It is well known that gold atomic clusters can have planar or hollow cage-like structures due to their relativistic effect. However, in our study, by first principles calculations on a Au 58 cluster we have proposed that gold clusters of medium size can form a shell-like structure (skeleton/helmet), this is demonstrated by the remarkable robustness of a double shell structure with a hollow inner shell of about ten atoms. Finally, the structure symmetry ( C 1 ) is confirmed through the cluster size, vibrational spectroscopy, and by studying the effect of temperature on a neutral gold cluster for the first time.