Spin dynamics of radical pairs with restricted geometries and strong exchange coupling: the role of hyperfine coupling.

Subnanosecond radical pair (RP) formation by electron transfer from an excited singlet state or by bond breaking produces two correlated spins coupled by their spin-spin exchange (J) and magnetic dipole (D) interactions. In the high magnetic field limit, the two-spin system can be described by a singlet state (S) and three triplet states (T₀, T(+1), T(-1)). When J is small relative to the electron Zeeman interaction, |T₀⟩ is the only triplet state that is populated by coherent spin mixing with the |S⟩ state because the |T(+1)⟩ and |T(-1)⟩ states are well-separated from |S⟩ by a large energy gap. Herein, we describe the spin dynamics for RPs having restricted geometries in which J is similar in magnitude to the electron Zeeman interaction and does not fluctuate significantly. Under these circumstances, depending on the sign of J, the energies of |T(+1)⟩ or |T(-1)⟩ are close to that of |S⟩ so that weak isotropic electron-nuclear hyperfine coupling leads to population of |T(+1)⟩ or |T(-1)⟩. An approximate relationship for the triplet quantum yield is developed for a RP in the large J regime, where one or both electrons interact with nearby spin-1/2 nuclei. This relationship also yields the net spin polarization transfer to the nuclear spins.