We present a general formulation that allows physically intuitive curvilinear internal coordinates to be used for the calculation of potential energy expansions and generalized normal-mode vibrational frequencies in reaction-path calculations. The reaction path is defined, as usual, as the minimum-energy path in the mass-scaled Cartesian coordinate system, and curvilinear coordinates are used for vibrational frequency calculations at nonstationary points. The method is well adapted for use in variational transition state theory with semiclassical multidimensional tunneling (VTST/ MT) approximations to calculate thermal rate constants. We present VTST/MT calculations for five reactions, H+H2→H2+H, O+H 2→OH+H, CH3+H2→CH4+H, H+O2→HO2, and Cl+HBr→HCl+Br, to illustrate the use of the new curvilinear coordinates, and we compare the results to calculations employing rectilinear coordinates. We make detailed comparisons not only of the calculated rate constants but also of the vibrationally adiabatic ground-state potential energy curves and bound-state vibrational frequencies as functions of the reaction coordinate.