First, in Section IV A, we will report on a dynamics in the vicinity of a conical intersection in a Jahn-Teller model, recently engineered in a quantum simulator. In this study, it was discussed the fundamental difference between the concept of topological phases due to the presence of conical intersections that arise in the Born-Huang representation of the dynamics and the concept of dynamics-induced geometric phase that is independent of the underlying theoretical representation used to analyze the dynamics. Then, in Section IV B, we report on various applications of exact-factorization-based algorithms to study the dynamics of molecules induced by the creation of a vibrational wavepacket produced by photoexcitation. In Section IV B 1, we describe in some detail the work of our group that employs a coupled-trajectory scheme, in particular, the photo-isomerization process of trans-azobenzene upon nπ * and ππ * excitation with CTTSH in full dimensionality using the semi-empirical Floating Occupation Molecular Orbitals-Configuration Interaction (FOMO-CI) electronic structure method with the reparametrized semi-empirical electronic-structure model AM1. The results of CTTSH dynamics are compared to surface hopping w/o accounting for decoherence corrections. In Section IV B 2, an overview of the auxiliary-trajectory scheme SHXF is provided, highlighting the works of Min and of Maitra on a large variety of molecular systems and properties. Finally, in Section IV C, we discuss a recent analysis reported on the different strategies to initialize the dynamics simulated by various trajectorybased procedures for excited-state dynamics in a model potential upon creation of a coherent superposition of electronic states, usually referred to as electronic wavepacket. Such an electronic wavepacket can be created by an attosecond laser pulse, and the ensuing dynamics is usually simulated using the (multi-trajectory) Ehrenfest method, whose performance in comparison to CTMQC have been discussed.