An analytical potential-energy function for ⋅CH3 association with carbon-atom radical sites on diamond surfaces is derived from experimental energies, structures, and vibrational frequencies, high-level ab initio calculations, and properties of potential-energy functions for H⋅+⋅CH3, ⋅CH3+⋅CH3, and H⋅+⋅C(CH3)3 association. This ⋅CH3+diamond potential-energy function is a molecular anharmonic potential written with switching (MAPS) functions and is identified by MAPS/MeDIAM. It is a sum of lattice (Vlattice), nonbonded (Vnonbonded), and radial site (VCH3,site) potential terms. There are many general properties of potential-energy functions for alkyl radical association reactions which are transferable and can be used to help construct VCH3,site. Additional properties of VCH3,site are determined by ab initio calculations using the restricted and unrestricted quadratic configuration-interaction method, with single, double, and perturbative triple excitations and the 6-31G** basis set. The MAPS/MeDIAM potential function is used to study ⋅CH3 association with a carbon-atom radical site on the diamond {111} terrace. The energy for ⋅CH3 adsorption with this site is calculated to be 17 kcal/mol lower than the ab initio CH3-C(CH3)3 bond dissociation energy. A canonical variational transition-state theory calculation, based on the MAPS/MeDIAM potential, gives a value of 0.06×1013 cm3 mol-1 s-1 for the ⋅CH3+diamond {111} terrace site association rate constant at 1500 K. A linear free-energy relationship is shown for the kinetics of ⋅H and ⋅CH3 association with a diamond {111} terrace site.