An ab initio model potential embedded cluster study on the 4f8 and 4f7 5d manifolds of the long range compensated, cubic, substitutional Tb3+ defects of Tb-doped BaF2 is presented here. 4f–4f and 4f–5d transition energies and 4f–5d absorption electric dipole oscillator strengths for the dipole allowed transitions are reported and comparisons with emission and excitation experimental spectra are presented. We find good agreement with the energies of the experimental 4f–4f green and blue emissions. The characteristic features of the 4f–5d excitation spectrum (spin allowed vs. spin forbidden transitions) are well reproduced by the calculations. The transition energies from the ground state to the different spin nonet and spin septet levels of the 4f7 5d configuration of this ion in the center of the lanthanide series show an error of around 10%, which is in line with previous calculations on other lanthanide ions with lower spin multiplicities and simpler manifolds at the beginning and at the end of the series. The calculation supports a recent assignment of experimental excitation bands between 54,000 and 66,000 cm−1 as 4f→5d(t2g) transitions. On the other hand, a new assignment is made of the highest band in the excitation spectrum at around 76,000 cm−1: it corresponds to transitions to levels of the 4f7 5d configuration with the 4f7 subshell in the excited 6P term, rather than to a Tb-bound exciton. Preliminary studies on excitonic states of Tb-doped BaF2 indicate that energy levels that can be characterized as Tb-trapped excitons are found in the same spectral region as the spin forbidden 4f→5d(t2g) transitions at ground state Tb–F distances, and their energy lowers very much at shorter Tb–F distances.