In the present work, all-electron ab initio multi-configuration self-consistent-field (CASSCF) and multi-reference configuration interaction (MRCI) calculations have been carried out to determine the low-lying electronic states of the molecule RhN. In addition, the relativistic corrections for the one-electron Darwin contact term and the relativistic mass-velocity correction have been determined in perturbation calculations. The spectroscopic constants for the seven low-lying electronic states have been derived by solving the Schrodinger equation for the nuclear motion numerically. The predicted ground state of RhN is (1) Sigma(+), and this state is separated from the states (II)-I-3, (II)-I-1, (5) Delta, (3) Sigma(-), (3) Delta and (1) Delta by transition energies of 1833, 4278, 6579, 8042, 9632, and 13886 cm(-1), respectively. For the (1) Sigma(+) ground state, the equilibrium distance has been determined as 1.640 (A) over circle, and the vibrational frequency as 846 cm(-1). The chemical bond in the (1) Sigma(+) electronic ground state has triple bond character due to the formation of delocalized bonding pi and sigma orbitals. The chemical bond in the RhN molecule is polar with charge transfer from Rh to N giving rise to a dipole moment of 2.08 Debye at 3.1 a.u. in the (1) Sigma(+) ground state. An approximate treatment of the spin-orbit coupling effect shows that the lowest-lying spin-orbit coupled state is 0(+). This state is essentially derived from the (1) Sigma(+) ground state. The second and third state, 0(+) and 0(-), mainly arise from the (II)-I-3 state. The dissociation energy of the RhN molecule in its (1) Sigma(+) ground state has been derived as 1.74 eV. (C) 1997 Elsevier Science B.V.