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 (1)Sigma, whose equilibrium nuclear distance and dissociation energy are R-PdC = 0.17285 nm and 4.919 eV, respectively. The ground state of PdO molecule is (3)Pi with equilibrium geometry R-PdO = 0. 18546 nor and dissociation energy D-e = 2.455 eV. The ground state of the linear Pd-C = O (C-infinity nu) is (1)Sigma(+) and the configuration and dissociation energy are R-PdC = 0.18721 nm, R-CO = 0.11427 nm and 12.563 eV, respectively. At the same. time, another metastable structure Pd-O-C(C-infinity nu) was found. Its equilibrium geometry and dissociation energy are R-CO = 0.11336 nm, R pdo = 0.23001 nm and 10.937 eV, 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.