Vibronic contributions to hyperfine-mediated spin kinetics

The hyperfine interaction is a cornerstone of spin-dependent processes, yet the kinetic modelling of this mechanism remains limited by the Born-Oppenheimer approximation, obscuring the observation of coherent pathways that underpin many photophysical systems. Here, we introduce a unified theoretical framework that rigorously incorporates vibronic contributions through a phase-consistent Herzberg-Teller expansion of the hyperfine Hamiltonian. Application to the FMNH•-Cys• radical pair shows that second-order vibronic coupling enhances h y perfine-mediated electronic transitions between spin states by up to 10 8 to 10 9 -fold. The S◦→T◦ rate increases from ~ 5 − 40 s −1 (Franck-Condon) to ~ 2 × 10 8 s −1 − 1 × 10 9 s −1 (Herzberg-Teller), while the T◦ →S◦ rate increases from ~ 4 × 10 2 − 1 × 10 3 s −1 to ~ 1 × 10 10 − 5 × 10 10 s −1 . This observed nanosecond timescale correlates well with the microsecond lifetime photoadduct formation central to its function. This work underscores the importance of incorporating a vibronic description in hyperfine-driven dynamics and provides a generalised and transferable methodology that captures essential non-Condon effects even at the single-structure level; thus serving as a complementary tool for systems where full ensemble sampling is impractical or not yet integrated into standard workflows.