TSH has a systematic problem due to the disconnect between how electrons and nuclei evolve, an issue commonly referred to as "overcoherence": throughout time, the nuclei evolve on a single Born-Oppenheimer (BO) potential energy surface (PES) but can, at any time, hop to another PES according to a stochastic algorithm, while the electronic evolution remains in a coherent superposition of BO states. To demonstrate the problem of overcoherence, let's examine the scheme shown in Fig. . In this scheme, a trajectory moves from left to right in one dimension and passes through two consecutive avoided crossings of BO PESs. The trajectory starts on the excited state S 1 , with 100% of the electronic populations corresponding to that state (t = 0). As the trajectory passes through the first avoided crossing (t = t ′ ), 70% of its population is transferred to the lower state S 0 and a surface hop occurs. From that point on, the trajectory follows the S 0 PES, and hence the trajectory is able to move further to the right. Without the hop, the trajectory would have been reflected by a classically forbidden barrier in the upper state. The central problem is that the 30% of the population remaining in S 1 also follows the gradient of the lower state and moves to the right, although this should be classically forbidden. When the trajectory reaches the second crossing point (t = t ′′ ), unphysical interference occurs between the 30% of population on the upper state and the 70% on the lower state. Such interference might strongly affect the transferred population depending on the relative complex phase between the two states. As the upper amplitudes should not have reached this crossing at all, no interference should occur. To overcome this inconsistency, several decoherence corrections have been proposed, which, like the TSH procedure itself, are somewhat ad hoc, even if physically motivated . Usually, those corrections have the effect of reducing the difference between the quantum electronic populations, the |C| 2 of Fig. , and the classical populations, obtained by running many trajectories and determining the fraction associated to each state. In the following, these two populations will be indicated as P (t) and F (t), respectively. Instead, in the CT-TSH algorithm, the electronic evolution is directly affected by the coupling of trajectories, which naturally arises in the classical limit of the nuclear dynamics in the exact factorization. As a result, decoherence naturally is included, thereby improving internal consistency without requiring additional ad hoc corrections. The coupling among the trajectories