We consider three reactions: H+H2→H2+H; Mu+H2→MuH+H; Mu+D2→MuD+D. We calculate accurate quantum mechanical reaction probabilities and thermal rate coefficients for all three reactions in collinear geometry using the Liu-Siegbahn-Truhlar-Horowitz (LSTH) accurate potential energy surface. These rate coefficients are used to test conventional transition state theory and the improved canonical variational theory with Marcus-Coltrin-path semiclassical adiabatic ground-state transmission coefficients (ICVT/MCPSAG). The ICVT/MCPSAG theory is found to be greatly superior and reasonably reliable. These conclusions are tested for sensitivity to variations in the potential energy surface by repeating the calculations for the less accurate Porter-Karplus surface. The conclusions are unaltered by this. The ICVT/MCPSAG theory and LSTH surface are then employed to predict the rate coefficients for all three reactions in three dimensions.