The ground electronic state X 5Σ + g and the reasonable dissociation limits of the PuO2 molecule are derived based on the Atomic and Molecular Reactive Statics. In the MP2 (The HF calculation followed by a second-order Moller-Plesset correlation) level, using the RECP(relativistic effective core potential) for Pu atom and 6 311G* basis for O atom , the present work has optimized the equilibrium geometry for the linear O-Pu-O( D ∞h ), ground state X 5Σg + of PuO2, whose equilibrium nuclear distance and dissociation energy are 0.180 04nm and 12.551 eV respectively. And the metastable structure Pu-O-O( C ∞v )is found for the first time, which is 6.79 eV higher than the stable structure. The analytical potential energy function for the ground state X 5Σg + of PuO 2 has also been derived using many body expansion method, the potential energy function is successfully used for describing the equilibrium geometry of PuO 2 and PuOO, which is adequately accurate in the whole region for the dynamical research.