A systematic study of the chemisorption of both atomic ͑H, O, N, S, C͒, molecular (N 2 , CO, NO), and radical (CH 3 , OH) species on Rh͑111͒ has been performed. Self-consistent, periodic, density functional theory ͑DFT-GGA͒ calculations, using both PW91 and RPBE functionals, have been employed to determine preferred binding sites, detailed chemisorption structures, binding energies, and the effects of surface relaxation for each one of the considered species at a surface coverage of 0.25 ML. The thermochemical results indicate the following order in the binding energies from the least to the most strongly bound: N 2 ϽCH 3 ϽCOϽNOϽHϽOHϽOϽNϽSϽC. A preference for threefold sites for the atomic adsorbates is observed. Molecular adsorbates, in contrast, favor top sites with the exceptions of NO ͑hcp͒ and OH ͑fcc or bridge tilted͒. Surface relaxation leads to insignificant changes in binding energies but to considerable changes in the spacing between surface rhodium atoms, particularly for on-top adsorption where the rhodium atom directly below the adsorbate is lifted above the plane of the surface. RPBE binding energies are found to be in remarkable agreement with the available experimental values. All atomic adsorbates, except for H, have a significant diffusion barrier ͓between 0.4 and 0.6 eV ͑RPBE͔͒ on Rh͑111͒. Atomic H and molecular/radical adsorbates appear to be much more mobile on Rh͑111͒, with an estimated diffusion barrier between 0.1 and 0.2 eV ͑RPBE͒. Finally, the thermochemistry for dissociation of CO, NO, and N 2 on Rh͑111͒ has been examined. In all three cases, decomposition is found to be thermodynamically preferable to desorption.