In this paper the electronic structures of the complex ion (CrO4)4- in the crystal Cr:Mg2SiO4 are calculated with the spin-polarizated MS(Xa method the one-electron eignevalues and eigenfunctions and the spin polarization splitting under the symmetry Tand C3v are given. Energies of some optical transitions and the charge transfer transition are calculated based on the transition state theory. The spin orbital coupling constants are calculated with the Case-Karplus charge partition method. The influence of the distance from the ligands on the one-lectron energy levels are discussed. The influence of symmetry changes is also discussed.