Recently, a breakthrough has been achieved in laser-spectroscopic studies of short-lived radioactive compounds with the first measurements of the radium monofluoride molecule (RaF) UV/vis spectra. We report results from high-accuracy ab initio calculations of the RaF electronic structure for ground and low-lying excited electronic states. Two different methods agree excellently with experimental excitation energies from the electronic ground state to the (2)Pi(1/2) and (2)Pi(3/2) states, but lead consistently and unambiguously to deviations from experimental-based adiabatic transition energy estimates for the (2)Sigma(1/2) excited electronic state, and show that more measurements are needed to clarify spectroscopic assignment of the (2)Delta state.