The matrix elements of the full-system Hamiltonian in the FEM are given by the GFT expressions ( )-( ), but with the J and K terms in expressions ( ) and ( ) neglected. In other words, the diagonal matrix elements in the FEM are just the sums of site energies, and the crossfragment interaction contribution is neglected. Further, the GS-LE couplings, 0 Ĥ 0 F a F F 0 , and the couplings between two local excitations on the same site,