A highest stable cluster Au58 (C1) re-optimized via a density-functional tight-binding (DFTB) approachDedicated to Dr Valeri G. Grigoryan (A Retired Staff Scientist), University of Saarland, on the occasion of his 68th birthday, esteemed Professor Prasanta Kumar Panigrahi (FNASc), Department of Physical Sciences, IISER Kolkata, Mohanpur-741246, India, on the occasion of his 60th birthday, and Professor Asima Pradhan, Department of Physics and Center for Laser Technology, Indian Institute of Tech

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. The vibrational spectrum ω i of a re-optimized neutral gold cluster Au 58 has been calculated using a numerical finite-difference approach via a density-functional tight-binding (DFTB) method.