A new algorithm [Nguyen, T. L.; Stanton, J. F.; Barker, J. R. Chem. Phys. Lett. 2010, 9, 499] for the semiclassical transition-state theory (SCTST) formulated by W. H. Miller and co-workers is used to compute rate constants for the isotopologues of the title reaction, with no empirical adjustments. The SCTST and relevant results from second-order vibrational perturbation theory (VPT2) are summarized. VPT2 is used at the CCSD(T) level of electronic structure theory to compute the anharmonicities of the fully coupled vibrational modes (including the reaction coordinate) of the transition structure. The anharmonicities are used in SCTST to compute the rate constants over the temperature range from 200 to 2500 K. The computed rate constants are compared to experimental data and theoretical calculations from the literature. The SCTST results for absolute rate constants and for both primary and secondary isotope effects are in excellent agreement with the experimental data for this reaction over the entire temperature range. The sensitivity of SCTST to various parameters is investigated by using a set of simplified models. The results show that multidimensional tunneling along the curved reaction path is important at low temperatures and the anharmonic coupling among the vibrational modes is important at high temperatures. The theoretical kinetics data are also presented as fitted empirical algebraic expressions.