The CHClF2 + Cl -> ClH + CClF2 gas-phase abstraction reaction was chosen as a model of asymmetrically substituted polyatomic reactions of type CWXYZ + A -> products. The analytical potential energy surface for this reaction was constructed with suitable functional forms to represent vibrational modes, and calibrated with respect to experimental thermal rate constants which are available over the temperature range 296-410 K. On this surface, the thermal rate constants were calculated using variational transition-state theory with semiclassical transmission coefficients over a wider temperature range, 200-2500 K, therefore obtaining kinetics information at lower and higher temperatures than are experimentally available. This surface was also used to analyze dynamical features, such as tunneling and reaction-path curvature. In the former, the influence of the tunneling factor was important since a light hydrogen atom passes through the barrier. In the latter, it was found that vibrational excitation of the C-F and C-Cl stretching modes can be expected in the exit channel.