High-level ab initio calculations were performed to determine accurate analytic potential energy functions for interactions a gas-phase H-atom has with H-atoms attached to the diamond (111) surface and with C-atom radical sites on this surface. The nonbonded potential between the gas-phase H-atom and H-atoms attached to the surface was determined from coupled-cluster at; initio calculations, including single, double, and perturbatively applied triple excitations [CCSD(T)], with the 6-311++G(2df,p) basis set. The resulting nonbonded potential is nearly identical to that found previously from both theory and experiment for interactions between II-atoms on different hydrocarbon molecules. In the ab initio calculations, a C-atom radical, site on the diamond surface is represented by a constrained tert-butyl radical. Radial and small-displacement angular potentials for a H-atom interacting with this radical were determined from unrestricted quadratic configuration interaction calculations, with single, double and perturbatively applied triple excitations [UQCISD(T)], with the 6-31G** basis set. UQCISD(T) calculations were performed on the H+CH3-->CH4 reaction system with both the 6-31G** and 6-311++G(3df,3pd) basis sets to calibrate the accuracy of the 6-31G** basis set results for the H-atom plus constrained tert-butyl radical. The above information was used to construct an analytic potential energy function for H-atom association with a radical site on the (111) surface of diamond, which was then employed in a canonical variational transition state theory (CVTST) calculation of the association rate constant. The resulting rate constant is 1.8-2.1x10(13) cm(3) mol(-1) s(-1) for the 1000-2000 K cm temperature range. It is insensitive to the gas-phase H-atom/surface H-atom nonbonded potential and the potential for the diamond lattice. The H+diamond (111) CVTST rate constant is used to estimate a rate constant of 4X10(13) cm(3) mol(-1) s(-1) for H+tert-butyl association at 298 K. The UQCISD(T)/6-31G* calculations give a H-C(CH3)(3) bond dissociation energy which is only 1 kcal/mol lower than the experimental value.