Estimation of electronic coupling in pi-stacked donor-bridge-acceptor systems: correction of the two-state model

Comparison of donor-acceptor electronic couplings calculated within two-state and three-state models suggests that the two-state treatment can provide unreliable estimates of V(da) because of neglecting the multistate effects. We show that in most cases accurate values of the electronic coupling in a pi stack, where donor and acceptor are separated by a bridging unit, can be obtained as V(da) = (E(2)-E(1))mu(12)R(da) + (2E(3)-E(1)-E(2))2mu(13)mu(23)R(da) (2), where E(1), E(2), and E(3) are adiabatic energies of the ground, charge-transfer, and bridge states, respectively, mu(ij) is the transition dipole moments between the states i and j, and R(da) is the distance between the planes of donor and acceptor. In this expression based on the generalized Mulliken-Hush approach, the first term corresponds to the coupling derived within a two-state model, whereas the second term is the superexchange correction accounting for the bridge effect. The formula is extended to bridges consisting of several subunits. The influence of the donor-acceptor energy mismatch on the excess charge distribution, adiabatic dipole and transition moments, and electronic couplings is examined. A diagnostic is developed to determine whether the two-state approach can be applied. Based on numerical results, we showed that the superexchange correction considerably improves estimates of the donor-acceptor coupling derived within a two-state approach. In most cases when the two-state scheme fails, the formula gives reliable results which are in good agreement (within 5%) with the data of the three-state generalized Mulliken-Hush model.