Canonical variational transition-state theory (CVTST) is used to compare H + CH3 and H + diamond {111} association rate constants calculated from the Brenner empirical potential function and molecular anharmonic potentials written with switching (MAPS) functions. Previous work [J. Am. Chem. Soc. 1987, 109, 2916; J. Chem. Phys. 1994, 101, 2476] has shown that the MAPS functions, derived from ab initio calculations, give rate constants in agreement with experiment. For the 300−2000 K temperature range, the Brenner potential function gives CVTST H + CH3 and H + diamond {111} association rate constants which are 159−30 and 49−7 times smaller, respectively, than the values from the MAPS functions. An analysis of the Brenner potential function shows that it inaccurately represents the intermediate and long-range H- - -C association potential, which controls the structure of the variational transition state and the CVTST rate constant. The MAPS functions give H + CH3 and H + diamond {111} variational transition states with similar properties. Angular momentum and external rotation have no effect on the H + diamond {111} association rate constant, which makes it approximately an order-of-magnitude smaller than that for H + CH3 association.