A general formulation for magnetic exchange coupling within long-distance radical ion pairs

A Hubbard model-based expression for the magnetic exchange interaction, 2J, between the spins of a radical ion pair is derived for a generic donor-bridge-acceptor (D- Bn -A) system in terms of the superexchange coupling, t, between molecular orbitals of the donor, bridge, and acceptor and the energies, ε, and same-site Coulomb repulsions, U, of these orbitals. The formulation is used to predict 2J for the photophysically well-characterized series phenothiazine- p- (phenylene)n -perylene diimide, n=2,3,4,5, where the superexchange coupling is calculated with multipathway, second- and third-order perturbation theory coupled with the extended Huckel formalism. U and ε are estimated through experimentally determined electrochemical potentials. Due to multiple interactions arising from the large distance between magnetic centers in these donor-bridge-acceptor systems, agreement with experiment was substantially improved when third-order corrections were included in the calculation of t and 2J.