Some of the factors affecting the accuracy of following reaction paths and calculating projected frequencies perpendicular to the reaction path have been examined. The S(N)2 reaction of Cl- with CH3Cl computed at the HF/6-31G* level of theory has been used as a test case. The symmetric C-H stretching mode couples strongly to the reaction path, and the projected frequency of this mode is very sensitive to the numerical accuracy of the path following and frequency projection methods. The transition state geometry must be converged very tightly so that the path steps in the correct direction. For second order implicit algorithms, improved accuracy can be obtained by computing the tangent used for path following and frequency projection from the displacement along the path rather than from the gradient. An even greater increase in accuracy can be achieved by employing the Hessian, used to compute the frequencies, to take a Newton-Raphson step to improve the convergence of the reaction path following. Taken together, these techniques yield a one to three order of magnitude decrease in the errors in the projected frequencies along the reaction path. (C) 1997 American Institute of Physics.