Interestingly, the quantum (orange) and classical (green) estimates of the electronic population in CT-TSH are very close all along the dynamics, even though this has not been imposed in the derivation of the algorithm. The quantum estimate is, however, closer to CT-MQC, as the population reaches a plateau at around 180-190 fs, which is not observed in the classical estimate. The classical estimate of the S 1 population resembles closely the reference curve as well as TSH-ED results. In addition, the prediction of the trans probability by CT-TSH is very close to the exact curve, and shows a slight (quantitative) improvement with respect to both CT-MQC and TSH-ED.