The electronic structure of Rh, RhH, and Rh2 in their ground and low-lying electronic states has been studied using nonempirical relativistic pseudopotentials and moderately large basis sets including f-type functions. The energy splitting 4F-2D, ionization potential and electron affinity of Rh have been obtained and compared with experimental results. A rather good agreement being found in all cases. For RhH the 3Δ, 3Π, 3Φ, 3Σ- and 1Σ+ electronic states were studied. The ground state being 3Δ in agreement with previous theoretical studies. The calculated De for RhH was found to be in a nice agreement with the experimental value. For Rh2 eight electronic states symmetrically dissociating into the ground state of the isolated atoms have been selected. Moreover a search for lowest electronic states has also been performed among those electronic states dominated by electronic configurations which (at r e) do not correlate with the ground state of the isolated atoms. The lowest electronic state was a 5Δu, the De corresponding to this state is 1.500 eV which is only 62% of the experimental value. The possibility of a metal-metal multiple bond in Rh2 has also been considered by studying the lowest 1Σ+ electronic state. This state was found to lie higher than all the quintuplets considered in this work. © 1990 American Institute of Physics.