Quasiclassical direct dynamics trajectories, calculated at the MP2/6-31G* level of theory, are used to study the central barrier dynamics for the Cl- + CH3Cl SN2 reaction. Extensive recrossings of the central barrier are observed in the trajectories. The dynamics of the Cl- -CH3Cl complex is non-RRKM and transition state theory (TST) is predicted to be an inaccurate model for calculating the Cl- + CH3Cl SN2 rate constant. Direct dynamics trajectories also show that Cl- + CH3Cl trajectories, which collide backside along the SN2 reaction path, do not form the Cl- -CH3Cl complex. This arises from weak coupling between the Cl- -CH3Cl intermolecular and CH3Cl intramolecular modes. The trajectory results are very similar to those of a previous trajectory study, based on a HF/6-31G* analytic potential energy function, which gives a less accurate representation of the central barrier region of the Cl- + CH3Cl reaction than does the MP2/6-31G* level of theory used here. Experiments are suggested for investigating the non-RRKM and non-TST dynamics predicted by the trajectories.