Density functional theory study of the structure, stability, magnetic properties, and (hyper)polarizability of (sub-nm) rare-earth (RE) doped gold clusters: Au5RE with RE = Sc, Y, La-Lu.

Rare-earth doped materials are of immense interest for their potential applications in linear and nonlinear photonics. There is also intense interest in sub-nanometer gold clusters due to their enhanced stability and unique optical, magnetic, and catalytic properties. To leverage their emergent properties, here we report a systematic study of the geometries, stability, electronic, magnetic, and linear and nonlinear optical properties of Au5RE (RE = Sc, Y, La-Lu) clusters using density-functional theory. Several low-energy isomers consisting of planar or non-planar configurations are identified. For most doped clusters, the non-planar configuration is energetically favored. In the case of La-, Pm-, Gd-, and Ho-doped clusters, a competition between planar and non-planar isomers is predicted. A distinct preference for the planar configuration is predicted for Au5Eu, Au5Sm, Au5Tb, Au5Tm, and Au5Yb. The distinction between the planar and non-planar configurations is highlighted by the calculated highest frequencies, with the stretching mode of the non-planar configuration predicted to be stiffer than the planar configuration. The bonding analysis reveals the dominance of the RE-d orbitals in the formation of frontier molecular orbitals, which, in turn, facilitates retaining the magnetic characteristics governed by RE-f orbitals, preventing spin-quenching of rare earths in the doped clusters. In addition, the doped clusters exhibit small energy gaps between frontier orbitals, large dipole moments, and enhanced hyperpolarizability compared to the host cluster.