Wave function-based embedded cluster ab initio calculations have been carried out in order to study the 4f(2) and 4f5d energy levels of the cubic substitutional defect of Pr-doped CaF2. The 4f(2) -> 4f5d absorption spectrum and 4f5d -> 4f(2) emission spectrum have been calculated. The 4f2 S-1(0) level is found to be immersed in the 4f5d(e(g)) manifold, so that no quantum cutting from S-1(0) can occur and only strong 4f5d(e(g)) -> 4f(2) emission is predicted, which supports previous assumptions made in order to explain results in CaF2:Pr3+. The details of the 4f(2) -> 4f5d(e(g)) and 4f(2) -> 4f5d(t(2g)) bands of the absorption spectrum are interpreted and assignments are made. The lowest level of the 4f5d(e(g)) 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 4f5d(e(g)) -> 4f(2) high resolution emission spectrum of the cubic site of CaF2:Pr3+ and the calculated emission spectra from the two lowest 4f5d(e(g)) states 1T(2u)(T-1(2u)) and 1E(u)(1(3)T(2u)) suggests the possibility that the experimental emission of the cubic Pr defect of CaF2:Pr3+ is in fact a multiple emission.