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 experimen
tal 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.
Electronic structure calculations combining the local-density approximation with an exact diagonalization of the Anderson impurity model show an intermediate 5f^5-5f^6-valence ground state and delocalization of the 5f^5 multiplet of the Pu atom 5f-sh
ell in PuCoIn_5, PuCoGa_5, and delta-Pu. The 5f-local magnetic moment is compensated by a moment formed in the surrounding cloud of conduction electrons. For PuCoGa_5 and delta-Pu the compensation is complete and the Anderson impurity ground state is a singlet. For PuCoIn_5 the compensation is partial and the Pu ground state is magnetic. We suggest that the unconventional d-wave superconductivity is likely mediated by the 5f-states antiferromagnetic fluctuations in PuCoIn_5, and by valence fluctuations in PuCoGa_5.
