Symplectic Integration of Classical Trajectories:  A Case Study

Classical trajectory calculations for a triatomic, complex forming system are used to assess the effectivity (correctness at given computational expense) of new, symplectic integrators of sixth and fourth orders (S6 and S4) compared to a traditional predictor−corrector scheme of sixth order (G). With respect to energy conservation and positional error, S6 is two to three orders better than G, while S4 is no improvement. However, comparison with quadruple precision calculations shows that even with S6 the correct computation in double precision arithmetic is limited to trajectory lifetimes of about 25 typical molecular vibrations. Moreover, in contrast to common assumptions, even energy conservation to 10-12 does not guarantee that the trajectory is correct, or even that it reaches the correct reaction channel.