To provide insight and understanding of the thermochemistry underlying hydrocarbon rearrangements on transition metal surfaces, we report systematic studies of hydrocarbon radicals chemisorbed on metal clusters representing the closest packed surfaces of the six second and third row group VIII transition metals. Using first principles quantum mechanics [nonlocal density functional theory with exact HF exchange (B3LYP)], we find that (i) CH3-m(CH3)(m) forms one bond to the surface, preferring the on-top site (eta(1)), (ii) CH2-m(CH3)(m) forms two bonds to the surface, preferring the bridge site (eta(2)), and (iii) CH1-m(CH3)(m) forms three bonds to the surface, preferring the 3-fold site (eta(3)). For all six metals, the adiabatic bond energy is nearly proportional to the number of bonds to the surface, but there are dramatic decreases in the bond energy with successive methyl substitution. Thus from CH3 to CH2CH3, CH(CH3)(2), and C(CH3)(3), the binding energy decreases by 6, 14, and 23 kcal/mol, respectively (out of similar to 50). From CH2 to CHCH3 and C(CH3)(2), the binding energy decreases by 8 and 22 kcal/mol, respectively (out of similar to 100). These decreases due to methyl substitution can be understood in terms of steric repulsion with the electrons of the metal surface. For CH to C(CH3), the bond energy decreases by 13 kcal/mol (out of similar to 160), which is due to electronic promotion energies. These results are cast in terms of a thermochemical group additivity framework for hydrocarbons on metal surfaces similar to the Benson scheme so useful for gas-phase hydrocarbons. This is used to predict the chemisorption energies of more complex adsorbates.