The effect of hydrogen, carbon, and oxygen impurity atoms on the structure of gas-phase and zeolite-supported Rh-6 clusters was studied computationally with a gradient-corrected density functional method. Measured metal-metal distances of Rh-6 clusters on zeolite support were 10-20 pm longer than the optimized distances of a ligand-free Rh-6 cluster. Variations of the cluster charge and adsorption of a ligand-free cluster on a model zeolite fragment did not substantially increase the Rh-Rh distances. Structures with impurity atoms inside the metal cluster were calculated to be less stable than structures where light atoms were adsorbed at the cluster surface. A structure with three H impurity atoms bridging Rh-Rh bonds of a zeolite-supported Rh-6 cluster was found to agree best with EXAFS data on experimentally observed clusters. Model clusters with C or 0 impurity atoms were not considered pertinent due to the large variation of calculated Rh-Rh distances in these clusters, at variance with experimental findings. Analysis of the charge distribution in neutral and ionic clusters suggested that C and 0 impurity atoms affect the electron density distribution on the metal atoms of the Rh-6 cluster in opposite ways and that adsorption of a Rh-6 cluster on a zeolite fragment polarizes the cluster electron density resulting in two types of Rh centers of different reactivity, cationic and neutral as well as negatively charged Rh species. Impurity atoms substantially affected the electron distribution in supported Rh-6 clusters, and they changed the chemical reactivity of the clusters. In the model structure that corresponded best to the experimental distances, Rh atoms in direct contact with the support were oxidized after reaction with zeolite hydroxy groups.