The application of FMS to study molecules in their full dimensionality is hindered by the cost of the evaluation of the Hamiltonian matrix elements as they require multidimensional integrals that contain the potential energy surfaces and nonadiabatic coupling terms over the full molecular configuration space. Therefore, the framework of AIMS makes the simulation of molecules accessible by introducing two main approximations. 1) The saddle-point approximation (SPA) alleviates the nuclear-coordinate dependence of the potential energy surfaces or nonadiabatic couplings in the integrand by expanding them in a truncated Taylor series centered at the centroid position of the two TBFs. Usually, a SPA of order zero, SPA0, is used where the truncation is applied after the first term. 2) The independent first generation approximation treats the initial (parent) TBFs describing the nuclear wavefunction (or wavepacket) at time t = 0 as uncoupled. Accurate propagation depends on careful treatment of the nonadiabatic couplings, which become singular at conical intersections (CoIns). The first derivative couplings are computed using the norm-preserving interpolation approximation, which ensures accurate propagation even at trivially avoided crossings. 57