The ground state electronic structure and magnetic behaviors of curium dioxide (CmO$_{2}$) are controversial. In general, the formal valence of Cm ions in CmO$_{2}$ should be tetravalent. It implies a $5f^{6.0}$ electronic configuration and a non-magnetic ground state. However, it is in sharp contrast with the large magnetic moment measured by painstaking experiments. In order to clarify this contradiction, we tried to study the ground state electronic structure of CmO$_{2}$ by means of a combination of density functional theory and dynamical mean-field theory. We find that CmO$_{2}$ is a wide-gap charge transfer insulator with strong 5$f$ valence state fluctuation. It belongs to a mixed-valence compound indeed. The predominant electronic configurations for Cm ions are $5f^{6.0}$ and $5f^{7.0}$. The resulting magnetic moment agrees quite well with the experimental value. Therefore, the magnetic puzzle in CmO$_{2}$ can be appropriately explained by the mixed-valence scenario.
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