The correlated band theory implemented as a combination of the local density approximation with the exact diagonalization of the Anderson impurity model is applied to PuO$_2$. We obtain an insulating electronic structure consistent with the experimental photoemission spectra. The calculations yield the band gap of 1.8 eV and a non-magnetic singlet ground state that is characterized by a non-integer filling of the plutonium $f$ shell ($n_fapprox 4.5$). Due to sizeable hybridization of the $f$ shell with the $p$ states of oxygen, the ground state is more complex than the four-electron Russell--Saunders ${}^5{rm I}_4$ manifold split by the crystal field. The inclusion of hybridization improves the agreement between the theory and experiment for the magnetic susceptibility.
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