A basin-hopping search strategy has been used to determine likely candidates for low-energy RhnS0,+/- (n = 1-9) cluster structures. Cluster structures were optimized at the density functional level of theory using the PBE and PBEO 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 RhnS0,+/- and Rhn+1S0,+/- (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.