In this work we outline a Classical Trajectory Calculation Direct Simulation Monte Carlo (CTC-DSMC) implementation that uses the no-time-counter scheme with a cross-section that is determined by the interatomic potential energy surface. CTC-DSMC solutions for translational and rotational relaxation in one-dimensional shock waves are compared directly to pure Molecular Dynamics simulations employing an identical potential energy surface, where exact agreement is demonstrated for all cases. A preliminary algorithm for determining the three body collision rate in CTC-DSMC simulations is presented. This algorithm is validated for the simple case of molecules with no interatomic potential, and is found to be in excellent agreement with molecular dynamics simulations. A parallelization technique for CTC-DSMC simulations involving only two body collisions using a hetero- geneous multicore CPU/GPU system is demonstrated. This scheme shows good scaling as long as a sufficiently large number of collisions are calculated simultaneously per GPU (~100,000) at each DSMC iteration. We achieve a maximum speedup of 140× on a 4 GPU/CPU system vs. the performance on one CPU core in serial for a diatomic nitrogen shock. The parallelization approach presented here significantly reduces the cost of CTC- DSMC simulations and has the potential to scale to large CPU/GPU clusters, which could enable future application to 3D flows in strong thermochemical nonequilibrium.