An ab initio calculation of the optical absorption spectrum of Mn2+-doped CaF2 is performed in which electrostatic and quantum embedding effects originated by a relaxed and polarized CaF2 lattice on the ligand field ground, and excited states of a MnF86- cluster have been considered. The theoretical spectrum is calculated by means of the complete active space self-consistent-held (CASSCF) and average coupled pair functional (ACPF) methods, correlating up to 23 electrons. An excellent overall agreement with the experiments is found and a detailed analysis of the results is presented. The initial assignment of the 4(1g)(A)(4G) and (4)E(g)((4)G) states, lately reversed, is supported. The wrong assignment of the T-4(1g)(P-4) State is shown to be responsible for a recently proposed change of the value of the crystal field splitting paramenter initially accepted, 10Dq=4250 cm(-1) which is in turn supported here. Also, new assignments for the absorptions to th T-4(1g)(F-4) and T-4(2g)(F-4) excited states are suggested.