Finally, we investigate the computational time required for propagating CT-TSH trajectories versus TSH trajectories. Table provides information on the total time required for propagating 10 up to 30 trajectories in parallel using CT-TSH and TSH algorithms. In TSH, the total time was calculated as the sum of the time used in each trajectory. For CT-TSH and TSH-S, the trajectories run synchronized in parallel using the same MPI strategy. Consequently, the total time is just the time of one trajectory multiplied by the number of trajectories. The computations were carried out on a machine equipped with an Intel Xeon CPU E5-2450 0 with 32 CPUs, 2 sockets, 8 cores per package, and 2 threads per core. In general, the computational time required in the CT-TSH algorithm is approximately two to three times higher than that of the traditional TSH algorithm. There are several factors that contribute to this increased computational time. One crucial factor to consider is the synchronization of trajectories. In the case of CT-TSH, the propagation of electronic coefficients requires the reconstruction of the nuclear density at each time step. Consequently, the trajectories need to be propagated in a synchronized manner. It is important to stress that the timing of a single time step in the different trajectories can be variable, because of iterative processes (such as SCF) that can require an almost arbitrary number of cycles, which may depend on the nuclear geometry. As a result, all other trajectories must also accommodate these additional computational costs, resulting in a cumulative increase in computational time throughout the dynamics. To evaluate the impact of trajectory synchronization on the overall computational time, we conducted simulations using a synchronized TSH approach, referred to as TSH-S in Table . The results clearly demonstrate the crucial role of synchronization in the additional time required in CT-TSH when compared with TSH. However, the most significant time-consuming factor in CT-TSH is the communication among processes necessary for the computation of quantum momentum. It is important to note that the electronic structure method used in this study is extremely efficient, meaning that the time spent on communication and synchronizing trajectories becomes significant in comparison. If a more expensive electronic structure method, such as any ab initio approach, were employed, the higher computational time required to perform CT-TSH simulations would be significantly less pronounced.