The electronic structure of Pd/Pt dimer and the detailed reaction mechanism of H-2 and CH4 activation on these clusters have been studied with density functional (B3LYP) and complete active space second-order perturbation (CASPT2) theories. It was found that B3LYP calculations gave reliable results on the electronic structures of the Pd/Pt dimers, in comparison with our CASPT2 calculations and data from previous theoretical investigations. Full geometry optimization has been carried out in the current study in contrast to previous work where only limited potential energy scans have been carried out, which led to dramatically different reaction mechanisms. In the case of Pt-2+H-2/CH4, H-WC-H activation preferentially takes place at first on one metal atom via structures far from planar, then one of the H atoms migrates to the ether Pt atom with negligible barrier. On both the singlet and the triplet state, H-H activation is barrierless, while C-H activation has a distinct barrier on the singlet state for reaction starting from the ground triplet state Pt-2. In contrast, Pd-2 is found to activate the H-H bond without barrier on the singlet state, while the triplet states are very high in energy. In the CH4 activation, two paths, referred as symmetric and asymmetric paths, respectively, have been found. The characters of the metal dimers and the differences between Pd-2 and Pt-2 systems have been analyzed based on MO diagrams. Results from the current study are consistent with the recent experimental observations of Cox et al. on the reactivities of unsupported Pd-n and Pt-n.