As mentioned above, some of the approximations of the FEM were lifted in different FEMlike models developed in the last decade. For example, Menger et al. and Gil et al. developed FEM-based exciton models in which the FDA was mitigated by means of QM/MM schemes based on electrostatic embedding. In these models, the site states on a single fragment are obtained by an electronic structure calculation of that fragment in the presence of all other fragments represented as point charges, where the latter are obtained via some molecular mechanics force field (MM-FF). The inclusion of the MM-FF charges perturbs the site states of the considered fragment, approximately like the other sites in their ground states would do in the full system. The excitonic basis obtained from these perturbed site states is expected to be variationally more favorable than a basis generated from FDA-based site states in the original FEM. Furthermore, the QM/MM approach enables those models to approximately account for the cross-fragment interaction energy on the diagonal (see the J and K terms in Equation ( )), although under the assumptions that MM fragments are always in the ground state and that parts of the interaction energy are evaluated using additional MM calculations. In the mentioned two models, all other approximations of FEM were inherited. Nonetheless, both models have been already used in surface hopping simulations of the nonadiabatic dynamics of multichromophoric systems, showing promising performance. Re-garding the embedding-improved FEM-like models, we emphasize the model of in which a self-consistent point-charge embedding scheme has been used in the site-state calculations, based on the so-called XPol approach. This is supposed to be more sophisticated pointcharge embedding than the QM/MM electrostatic embedding, as it takes into account the self-consistency between chromophores. Further, some other works extend the FEM by including CT products in the excitonic basis, although we note Li et al. neglected the GS-LE and GS-CT couplings, stressing that these would break the size extensivity of the model. Finally, there are improvements of the FEM in which the non-orthogonality between the antisymmetrized products is also taken into account, going beyond the GFT framework.