The reactions CH n D 4−n + OH → P and CH 4 + OD → CH 3 + HOD as a test of current direct dynamics computational methods to determine variational transition-state rate constants. I. Potential energy surface for a seven-atom reaction. Thermal rate constants and kinetic isotope effects for CH 4 +OH Ab initio direct dynamics methods have been used to study the title reaction. The electronic structure information including geometries, gradients and force constants ͑Hessians͒ is calculated at the QCISD/6-31ϩG(d) level. With the aid of intrinsic reaction coordinate theory, the minimum energy path ͑MEP͒ is obtained at the same level, and the energies along the MEP are further refined by performing the single-point calculations at the PMP4/6-311ϩϩG(3d f ,3pd) level. For this reaction, the theoretical rate constants by using improved canonical variational transition state theory incorporating small-curvature tunneling correction are in excellent agreement with the more recent experimental values. Our calculated results show that for the CH 3 ϩHBr reaction, the rate constants have a strong nonlinear Arrhenius behavior, i.e., the CH 3 ϩHBr reaction has negative temperature dependence at TϽ536 K, but clearly shows positive temperature dependence at T Ͼ536 K. The current work predicts that the kinetic isotope effect for the title reaction is normal in the temperature range 200-482 K, i.e., k HBr /k DBr Ͼ1. This result is in good agreement with the experimental one.