In many cases, variational transition states for a chemical reaction are significantly displaced from a saddle point because of zero-point and entropic effects that depend on the reaction coordinate. Such displacements are often controlled by the competition between the potential energy along the minimum-energy reaction path and the energy requirements of one or more vibrational modes whose frequencies show a large variation along the reaction path. In calculating reaction rates from potential-energy functions we need to take account of these factors and - especially at lower temperatures - to include tunneling contributions, which also depend on the variation of vibrational frequencies along a reaction path. To include these effects requires more information about the activated complex region of the potential-energy surface than is required for conventional transition-state theory. In the present article we show how the vibrational and entropic effects of variational transition-state theory and the effective potentials and effective masses needed to calculate tunneling probabilities can be estimated with a minimum of electronic structure information, thereby allowing their computation at a higher level of theory than would otherwise be possible. As examples, we consider the reactions OH + H2, CH3 + H2, and Cl + CH 4 and some of their isotopic analogs. We find for Cl + CH4 → HCl + CH3 that the reaction rate is greatly enhanced by tunneling under conditions of interest for atmospheric chemistry.