C-H bond activations of benzene and methane by M(eta(2)-O2CH)(2) (M = Pd or Pt) are theoretically investigated with density functional theory (DFT), MP2-MP4(SDQ), and CCSD(T) methods. The C-H bond activation of benzene takes place with activation energies (E-a) of 16.1 and 21.2 kcal/mol and reaction energies (Delta E) of -16.5 and -25.8 kcal/mol for M = Pd and Pt, respectively, to afford M(eta(2)-O2CH)(CsH5)(eta(1)-HCOOH), where MP4(SDQ) values are given hereafter and a negative Delta E value represents that the reaction is exothermic. The C-H bond activation of methane proceeds with E-a values of 21.5 and 17.3 kcal/mol and Delta E values of -8.3 and -13.3 kcal/mol for M = Pd and Pt, respectively, to afford M(eta(2)-O2CH)(CH3)(eta(1)-HCOOH). However, C-H bond activations of benzene and methane by Pd(PH3)2 need a large E-a value, and these reactions are significantly endothermic: E-a = 26.5 kcal/mol and Delta E = 22.1 kcal/mol for benzene and E-a = 34.7 kcal/mol and Delta E = 31.5 kcal/mol for methane. Also, the C-H bond activation of methane by Pt(PH3)2 needs a large E-a value (28.1 kcal/mol) with moderate endothermicity (Delta E = 7.0 kcal/mol), while the C-H bond activation of benzene by Pt(PH3)(2) occurs with a moderate E-a value (17.3 kcal/mol) and a negative Delta E value(-3.9 kcal/mol). From these results, the following conclusions are presented: (1) Pd(eta(2)-O2CH)(2) can perform easily the C-H bond activations of benzene and methane but Pd(PH3)(2) cannot. This is because the formate ligand assists the C-H bond activation through formation of a strong O-H bond. (2) Pt(eta(2)-O2CH)(2) more easily performs the C-H bond activation of methane but much less easily the C-H bond activation of benzene than Pd(eta(2)-O2CH)(2), because the intermediate, Pt(II)-benzene complex, is too stable. (3) Benzene more easily undergoes C-H bond activation than does methane. The higher reactivity of benzene is interpreted in terms of M-C6H5 and M-CH3 bond energies and the bonding interaction of benzene pi and pi* orbitals with M d orbitals. Analysis Df electron distribution implicitly indicates that the C-H bond activation by M(eta(2)-O2CH)(2) is characterized to be heterolytic C-H bond fission, while the C-H bond activation by M(PH3)(2) is characterized to be homolytic C- H bond fission.