Potential energy curves of 22 electronic states of RhN have been calculated by the complete active space second-order perturbation theory method. The X1Σ0+ is assigned as the ground state, and the first excited state a3Π0+ is 978 cm−1 higher. The 1Δ(I) and B1Σ+ states are located at 9521 and 13,046 cm−1 above the ground state, respectively. The B1Σ+ state should be the excited state located 12,300 cm−1 above the ground state in the experimental study. Moreover, two excited states, C1Π and b3Σ+, are found 14,963 and 15,082 cm−1 above the X1Σ+ state, respectively. The transition C1Π1–X1Σ0+ may contribute to the experimentally observed bands headed at 15,071 cm−1. There are two excited states, D1Δ and E1Σ+, situate at 20,715 and 23,145 cm−1 above the X1Σ+ state. The visible bands near 20,000 cm−1 could be generated by the electronic transitions D1Δ2–a3Π1 and E1Σ+0–X1Σ+0 because of the spin–orbit coupling effect. © 2013 Wiley Periodicals, Inc.