Despite numerous approximations, the original FEM appears to perform quite well for systems with weakly interacting chromophores, such as molecular aggregates. However, motivated by the desires to describe multichromophoric systems with more strongly interacting fragments and to include states not having LE character, many improvements of the FEM were developed in the last decade, each of them lifting some approximations of the FEM in a certain way. GFT, FEM, and some of the recent extensions of the FEM will be presented in more detail in Section 2, which reviews the mathematical background used in this work.