Zeeman resonances for radical-pair reactions in weak static magnetic fields

Recent reaction-yield-detected magnetic resonance experiments in weak static magnetic fields and the observation of resonance effects in animal orientation experiments provide the motivation for renewed studies of magnetic field effects on radical-pair reactions. Here, we investigate theoretically resonance patterns for weak static magnetic fields. We focus on the question: for which radical pairs can one expect Zeeman resonances to occur if the static field is weaker than typical hyperfine interactions? Using analytical approaches, we rationalize the occurrence of Zeeman resonances for simple radical pairs. Numerical solutions are presented for a wide range of radical pairs with up to seven hyperfine interactions employing the rotating-frame transformation. The results suggest that resonances occur close to either the Larmor frequency or half the Larmor frequency for a wide variety of radical pairs for spin Hamiltonians with a high degree of symmetry. For larger numbers of hyperfine interactions, Zeeman resonances decrease in size.