A classic example of a barrierless reaction, CH3+H-->CH4 is used as a model to test the extent of nonadiabatic coupling on the reaction rate constant. This coupling has two contributions. The first arises from the anisotropy of the CH3+H potential and the second is Coriolis coupling. A method is presented which calculates adiabats formally equivalent to those calculated by statistical adiabatic channel model (SACM) while still permitting the determination and inclusion of nonadiabatic coupling. Using the discrete variable representation (DVR) for the interfragment distance R, the re-vibrational Hamiltonian is solved at particular R values. The eigenvalues and eigenfunctions are calculated at each of these R values to create the surface and the coupling elements used in a wave packet propagation. The dynamics of the reaction are investigated through a study of the cumulative reaction probability N(E,J) using energy resolved flux methods. We find that for J=0, 1, and 2, neglecting the coupling due to the changing anisotropy as a function of R results in a 20% error in N(E,J). Neglecting the Coriolis coupling results in average errors of 2% lending support to the helicity-conserving approximation. Finally, within the adiabatic approximation, the calculated adiabats provide a more realistic view of the barriers than the analytic functions of SACM, require no fitting parameter, and are obtained at reasonable computational cost.