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A new method of using quasiclassical trajectories to study the dynamics of elementary reactions is described. Trajectories are initiated in the phase space of a suitably chosen transition state and run forwards and backwards in time from the same starting point to simulate a complete collision. Calculations on a wide range of collinear A+BC reactions involving vibrationally excited reagents reveal that the optimum choice of transition state is a periodic orbiting dividing surface (pods) for which the action over one cycle of the pods is (v+0.5)h The method is extended to three dimensional reactions using the adiabatic periodic reduction scheme to find pods on fixed angle potential surfaces. The complete transition state is defined by joining these pods together. Methods for pseudorandomly sampling the transition state are described and the combined transition state theory-quasiclassical trajectory (TST-QCT) method is applied to the H+H2(v), N+N2(v) and F+H2(v = O) reactions at constant temperature. The TST-QCT method produces relative quantities directly, absolute values are readily obtained using transition state theory. The results of the new method are compared with conventional quasiclassical trajectory studies in the literature. Agreement is very good and the combined method brings about a very great saving in computer time by eliminating trajectories which fail to reach the strong interaction zone as well as revealing the extent of vibrational adiabaticity between reagents and the transition state. Finally, a modification to the TST-QCT method to allow the simulation of fixed collision energy reactions is described and tested on the F+H2 reaction.

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