Wave-function-based embedded cluster ab initio calculations have been carried out in order to study the f2 and 4f 5d energy levels of the cubic substitutional defect of Pr-doped CaF2. The 4f -> 4f 5d absorption spectrum and 4f 5d -> 4f emission spectrum have been calculated. The 4f2 1S0 level is found to be immersed in the 4f 5d(eg ) manifold, so that no quantum cutting from 1S0 can occur and only strong 4f 5d(eg ) -> 4f emission is predicted, which supports previous assumptions made in order to explain results in CaF2 :Pr3+ . The details of the 4f 2 -> 4f 5d(eg ) and 4f 2 -> 4f 5d(t2g) bands of the absorption spectrum are interpreted and assignments are made. The lowest level of the 4f 5d(eg ) configuration is found to have 80% of singlet character, in opposition to Hund's Rules, and the issue is discussed in detail. The comparison between the experimental 4f 5d(eg ) -> 4f2 high resolution emission spectrum of the cubic site of CaF2 :Pr3+ and the calculated emission spectra from the two lowest 4f 5d(eg ) states 1T2u (1T2u) and 1Eu (13T2u), suggests the possibility that the experimental emission of the cubic Pr defect of CaF2 :Pr3+ is in fact a multiple emission.