This paper is organized as follows. Section II provides an overview on the fundamental aspects of the theory of NAMD, by comparing the traditional Born-Huang representation to the exact factorization. In Section II A, we present, rather qualitatively, the NAMD schemes that are used in the simulations, namely TSH, MTE, CTMQC and (C)CTTSH. There, we discuss only the basic ideas of the algorithms and we refer the interested reader to more technical works cited throughout for details on the working equations. Section III illustrates the LVC models and reports on the computational details, whereas Section IV presents the results of our simulations. We conclude in Section V.