The reaction-path Hamiltonian formulation reported in the preceding paper, where the Hamiltonian is described with quasirectilinear vibrational coordinates related nonlinearly to curvilinear internal coordinates, was applied to the examination of the reaction CH4 + F --> CH3 + HF. For this reaction we made ab initio calculations and determined the harmonic vibrational frequencies along the reaction path by each of (1) a method using the new formulation, (2) the method of Miller [J. Chem. Phys. 72, 99 (1980)], and (3) that of Truhlar [J. Chem. Phys. 102, 3188 (1995)]. We found that the harmonic vibrational frequencies determined by the new method differ significantly from those determined by the other two methods in the region away from the stationary states. This difference is attributed to the limitations of the latter two methods. We concluded that the reaction-path Hamiltonian determined by the new method should be used to obtain an accurate picture of the reaction-path dynamics under the zero-angular-momentum assumption.