Variational transition state theory with semiclassical tunneling calculations is used to calculate rate constants which are compared to the best available quantum mechanical results for three cases involving H atom transfer and three cases involving D atom transfer. The mass combination is heavy-light-heavy, as appropriate for testing semiclassical methods for proton and deuteron (or hydride) transfer in organic and biochemical systems. In five of the six cases at 312.5 K and five (but not the same five) of the six cases at 423.2 K, semiclassical results based on an uncoupled treatment of the vibrational-rotational modes agree with the the best available quantum results within the reliability of the latter. In the other two cases the discrepancies are larger, a factor of 3.1 at 312.5 K and a factor of 2.3 at 423.2 K, and possible reasons for this are discussed. In particular, the effect of a coupled treatment of the bending degrees of freedom in these two cases is presented and compared to the uncoupled treatment. Coupling the bending modes reduces the maximum discrepancy at 312.5 K to a factor of 2.4 but increases the largest discrepancy at 423.2 K to a factor of 4.5. The approximate semiclassical calculations are used to interpret the dynamics, especially in cases where agreement with the fully quantal results is very good.