A basin-hopping search strategy has been used to determine likely candidates for low-energy Rh(n)S(0,±) (n = 1-9) cluster structures. Cluster structures were optimized at the density functional level of theory using the PBE and PBE0 functionals. Ionization energies, electron detachment energies, HOMO-LUMO gap energies, UV-visible spectra, low-lying fragmentation channels and energies, cluster structures, spin multiplicities, and vibrational spectra are predicted for Rh(n)S(0,±) and Rh(n+1)(0,±) (n = 1-9). Donation from valence sulfur atomic p orbitals to valence rhodium atomic d orbitals and back-donation to valence sulfur atomic d orbitals leads to electron density delocalization and metal-like behavior for rhodium sulfide clusters.