Canonical variational transition state theory is applied to a set of 37 atom-diatom reactions involving transfer of halogens, first-row atoms, and Al to survey the effect of varying the location of the generalized transition state on thermal rate constants. Potential energy surfaces are generated by a reduced-variable bond energy-bond order method. Rate constants are calculated by maximizing the generalized free energy of activation using a formalism presented in a previous paper. The average ratio of the conventionally calculated rate to the canonical variational one increases from 1.2 at 200 K to 2.1 at 4000 K. The error is generally larger for systems with relatively loose saddle points, although all the systems we consider here have bound bending modes at the saddle point. Ten representative systems are discussed in detail to illustrate the roles of various degrees of freedom in determining the effects.