The electronic structures of BaMgF 4 crystals containing an F colour centre are studied within the framework of the fully relativistic self-consistent Direc-Slater theory,using a numerically discrete variational (DV-Xα) method. It is concluded from the calculated results that the energy levels of the F colour centre are located in the forbidden band. The optical transition energy from the ground state to the excited state for the F colour centre is about 5.12 eV,which corresponds to the 242-nm absorption band. These calculated results can explain the origin of the absorption bands. The electronic structures of BaMgF 4 crystals containing an F color center are studied within the framework of the fully relativistic self-consistent Direc-Slater theory, using a numerically discrete variational (DV-Xα) method. It is concluded from the calculated results that the energy levels of the F color center are located in the forbidden band. The optical transition energy from the ground state to the excited state for the F color center is about 5.12 eV, which corresponds to the 242-nm absorption band. explain the origin of the absorption bands.