The energy band structure,density of state and Mulliken charge density of the F₃-center in α-Al₂O₃ are studied by an embedded-cluster model,when H-like wave function is used for F-center.The optical transition model of the color center is also discussed.It found one single energy level and one doubly-degenerate energy level in the fundamental gap of the crystal with F₃-center.There is a new transition from defect energy level to conduction band and the transition energy is 3.54 eV.Comparing with the absorption spectrum of α-Al₂O₃ by high-energy and great flux neutron radiation,shows that 0.356 μm(3.483 eV) experimental absorption peak should be due to the F₃-center.Also,it found the charge density is less in the site of F₃-center than that of Fcenter in α-Al₂O₃ crystal.

The electronic structure of rutile TiO₂ crystal with F-type color center is studied by using the H-like wave function and Discrite Variation method with the relaxation of ions around color center,and their energy band,density of states are obtained.The results show that F and F⁺ center have donor energy level in forbidden band,and F²⁺ center has acceptor energy level in forbidden band.The optical transition energy are 0.85 eV and 1.67 eV for F and F⁺ center,respectively.The optical absorption peaks 1.7μm(0.75 eV),760 nm(1.61 eV) in the reduced sample of TiO₂ are due to the F and F⁺ center,and a transferring of F⁺→F existed.