A method for calculating anharmonic vibrational energy levels in asymmetric top and linear systems that is based on second-order perturbation theory in curvilinear coordinates is extended to the bound generalized normal modes at nonstationary points along a reaction path. Explicit formulas for the anharmonicity coefficients, x(ij), and the constant term, E-0, are presented, and the necessary modifications for resonance cases are considered. The method is combined with variational transition state theory with semiclassical multidimensional tunneling approximations to calculate thermal rate constants for the HCN/HNC isomerization reaction. Although the results for this system are not very sensitive to the choice of coordinates, we find that the inclusion of anharmonicity leads to a substantial improvement in the vibrational energy levels. We also present detailed comparisons of rate constants computed with and without anharmonicity, with various approximations for incorporating tunneling along the reaction path, and with a more practical approach to calculating the vibrational partition functions needed for larger systems.