First-Principles Investigation of the Atomic and Electronic Structure and Magnetic Moments in Gold Nanoclusters

Abstract

We determine the structure, energetics, and emerging magnetic propertiesof Aun clusters using first-principles plane-wave density functional theory. We compare and contrast the findings obtained with and without spin−orbit interaction in the gold clusters of sizes down to 0.5−1 nm. The shapes are chosen to be representative of spherical gold nanoparticles: (a) Au13 and Au12, with cuboctahedral, icosahedral, and decahedral structures, and (b) Au25 and Au24, with truncated octahedral structures. We find that the trends in the binding energies are unaltered with the choice of the exchange correlation (LDA or GGA) or the inclusion of relativistic effects. The cuboctahedral Au13 is found to have the lowest binding energy compared with others at a given level of theory. Within the scalar relativistic description, these gold clusters exhibit a wide variety of magnetic moments: the stability and magnetic properties can be readily understood in terms of degeneracies of the HOMO and LUMO levels. Further, there is evidence of Jahn−Teller activity in the cases of cuboctahedral Au12 and Au13 that leads to structural distortion, inducing magnetism in the 12-atom cluster. Analysis of electronic states with projection on atomic orbitals for the scalar relativistic case shows that the magnetism in these gold clusters has an sp rather than the otherwise believed s character. By employing a fully relativistic description with inclusion of spin−orbit interaction and noncollinear magnetization, the magnetic moment in the icosahedral-shaped clusters is found to reduce substantially and that in the 12- and 13-atom clusters with a cuboctahedral structure becomes vanishingly small. The loss of magnetism in Au12 and Au13 appears to originate from the splitting of degenerate HOMO states in these clusters and an overlap of the d and sp states, whereas the magnetic moment of around 1 μB in Au25 is mainly caused by the s states of the central atom.