ESDs are then shown as schematic kets containing the site states. (b) Schematic representation of the full-system Hamiltonian matrix in the ECI basis of a bi-chromophoric system (hexagon and pentagon) with three site states (ground and two excited states) supplied on each fragment. The notation for chromophores, site states, and ESDs is the same as in (a). The Roman numbers denote the excitation rank between the two involved ESDs, and thus which ECI equation is used to calculate the matrix element. Numbers 0, I, and II correspond to equations ( ), (9), and (10) (each with modifications ( )), respectively. The blocks H 00 , H SS and H DD are denoted by yellow, red, and blue frames, respectively. etc.). Similarly, the modified expression (10) covers the couplings between local excitations on the different sites (the ones also accounted for in the FEM), but, additionally covers the couplings between any other pair of ESDs differing in exactly two site states.