Our findings showed that the CT-TSH method improved the internal consistency compared to the TSH method and accelerated the excited-state population decay. Notably, using frozen Gaussians (fixed widths) during the dynamics leads to a significant improvement in the agreement between classical and quantum populations. Internal consistency is lost at long times when thawed Gaussians (variable widths) are used to calculate quantum momentum. In fact, as the trajectories delocalize in space, the widths of the individual Gaussians used to reconstruct the nuclear density increases. Therefore, the quantum momentum, i.e., the spatial derivative of the density, becomes smaller, leading to a decrease of the internal consistency. However, we believe that by significantly increasing the number of coupled trajectories, we can achieve an accurate representation of the nuclear distribution in configuration space without requiring a substantial increase in the Gaussians width. In an ideal scenario, the total number of trajectories would be chosen such that they do not become lonely when using frozen Gaussians, and the Gaussian width can be kept constant or almost so. This would ensure that both frozen and thawed Gaussians yield identical results. In our current work, we have utilized approximately 2 trajectories per number of internal coordinates (TAB has 72 internal coordinates, and we employed 100-150 trajectories). Unfortunately, it was not possible to increase the number of trajectories due to technical limitations.