Spin-Orbit versus Hyperfine Coupling-Mediated Intersystem Crossing in a Radical Pair

While spin-orbit coupling (SOC) is typically the dominant interaction that couples singlet and triplet states within individual chromophores, hyperfine coupling (HFC) becomes important in multichromophoric systems, particularly in relation to the radical pair mechanism. Here, we use TD-DFT to calculate the spin-orbit coupling and hyperfine coupling between the first singlet and triplet charge transfer states of the radical pair ²Pyrene^- and ²N,N-dimethylaniline⁺. We show that, as the intermolecular donor-acceptor distance grows, SOC decays to zero (as one would expect) because singlet and triplet states are characterized by identical orbitals in space, while the HFC remains comparatively constant. The switching region occurs around 4 Å, beyond which HFC dominates over SOC as far as defining the rate of intersystem crossing (ISC).