Bridge-mediated Donor-Acceptor Effective Coupling: Exact theoretical description

An exact expression of the bridge-mediated donor-acceptor effective coupling, is derived. For systems represented by a tight-binding Hamiltonian with nearest-neighbor interactions, we show that the effective coupling, is equal to the product over all square of nearest-neighbor couplings divided by an appropriate product of level spacing of eigen energies of the Hamiltonian. Results of this calculation are compared to those obtained by perturbative approaches and some drawbacks of the latter are pointed out.