Exact formula of the bridge-mediated donor-acceptor effective coupling

An exact expression of the bridge-mediated donor-acceptor effective coupling, Hda, is derived. For systems represented by a tight-binding Hamiltonian with nearest-neighbor interactions, we show that $|H_{da}|^2$ is equal to the product over all squares of nearest-neighbor couplings divided by an appropriate product of level spacing of eigen energies of the Hamiltonian. These results are subsequently compared with those obtained using perturbation approaches.