In the first approach, the PES is constructed prior to the dynamics computation. This PES is then used to propagate the dynamics and no further electronic structure calculations need to be carried out. In this strategy the PES is often fitted to a set of electronic structure single points (SPs) for different molecular geometries of the system under investigation. The problem then becomes to determine which domains of the PES are relevant for the dynamics, in order to ensure sufficient accuracy of the PES representation for computing the dynamics at all necessary times. The computational cost of an electronic structure SP for a molecular system is non-trivial and in a fitted PES approach, the goal is thus to obtain a PES that is sufficiently accurate while requesting a minimal number of SPs. The strength of the fitted PES approach is that one obtains an analytical expression for the potential energy operator that can be expediently used in quantum simulations. Further, by fitting (or refitting) the PES it can be cast as a sum-over-products form which is optimal for the integral evaluations of the potential that is often required in quantum dynamics. The drawback of this method is that one might end up spending a lot of time computing expensive electronic structure SPs for domains of the PES that are not relevant for the dynamics or that the dynamics turn out to run outside the domains properly covered by the SPs and the fitted PES. In the latter case the results of the dynamics will be non-physical or at least inaccurate. Also, to obtain an actual high quality fit representation is by no means trivial.