Density functional method(B3LPY) has been used to optimize the possible structures of PdC，PdO and PdCO molecules with contracted valence basis set (LANL2DZ) for Pd atom and the AUG-cc-pVTZ basis set for C and O atoms respectively.It was found that the ground state of PdC molecule is 1Σ，whose equilibrium nuclear distance and dissociation energy are RPdC=0.17285nm and 4.919eV, respectively.The ground state of PdO molecule is 3Π with equilibrium geometry RPdO=0.18546nm and dissociation energy De=2.455eV. The ground state of the linear Pd—C≡O (C∞v) is 1Σ+ and the configuration and dissociation energy are RPdC=0.18721nm，RCO=0.11427nm and 12.563eV, respectively. At the same time， another metastable structure Pd—O≡C(C∞v) was found. Its equilibrium geometry and dissociation energy are RCO=0.11336nm， RPdO=0.23001nm and 10.937eV, respectively.The possible dissociation limit of PdCO molecule is determined.The analytical potential energy function for PdCO molecule has been obtained from the many-body expansion theory.The contour of the potential energy surface sheds light on the accurate structure and dissociative energy for PdCO molecule.Furthermore, the molecular static reaction pathway based on this potential energy function is investigated.