In summary, we have studied the optical properties of CeO$_{2}$ using HSE, HSE+ U , and GW + U three methods. Using HSE+ U method, our calculated band gaps and the central position of 4 f orbitals are in good agreement with the experimental values, and the resulting optical dielectric function, adsorption spectrum and energy-loss function obtained by HSE+ U are also well reproduced. 

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This work was supported by the National Basic Re- search Program of China (973 Program) grant No. G2009CB929300 and the National Natural Science Foun- dation of China under Grant Nos. 60521001, 60776061 and 90921003, and by the Foundations for Development of Science and Technology of China Academy of Engi- neering Physics under Grant No. 2009B0301037. 

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