Canonical variational transition-state theory (CVTST) rate constants, for H atom association to terrace and ledge sites on the diamond {111} surface, are calculated using anharmonic energy levels for the transitional modes orthogonal to the reaction path. The reaction path and transitional modes, required for the calculation, are defined by the reaction path Hamiltonian. A separable Einstein-Brillouin-Keller (EBK) semiclassical quantization model is used to determine anharmonic energy levels for the transitional modes. The free energy, calculated from these anharmonic levels, has multiple maxima along the reaction path, which become more pronounced as the temperature is increased. CVTST association rate constants, calculated from the highest maxima, are somewhat larger than the harmonic CVTST rate constants. A canonical unified statistical theory (UST), which incorporates the effect of the multiple free energy maxima and minima, gives association rate constants in remarkably good agreement with those determined from quasiclassical trajectory calculations. The rate constant for the terrace site is significantly larger than those for the ledge sites. The multiple maxima and minima in the free energy curve result from strong couplings between the transitional bending and surface modes, which changes the eigenvectors for the transitional modes as the reactive system moves along the reaction path, This work illustrates the possible importance of coupling between transitional and conserved modes in VTST calculations for barrierless association reactions.