A detailed study of methods for generating the minimum energy path of a chemical reaction using ab initio electronic structure calculations is presented; the convergence with respect to step size of the geometry and energy along this path is studied with several algorithms. The investigations are extended to the calculation of chemical reaction rate coefficients by interfacing the POLYRATE code for variational transition-state theory and semiclassical tunneling calculations with a locally modified GAUSSIAN82 electronic structure package that now contains reaction path following capabilities at both the Hartree-Fock and perturbation theory levels. This combined package is used to study the kinetics of the abstraction reaction CH3 + H2 → CH4 + H, which is considered as a prototype organic reaction. We report calculations of reaction rates based on electronic structure theory and generalized transition-state theory, including a multidimensional tunneling correction, without performing an analytic fit to the potential surface. The calculation of dynamical processes directly from ab initio electronic structure input without the intermediary of a potential surface fit is called "direct dynamics", and this paper demonstrates the feasibility of this approach for bimolecular reactions.