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 hyperfine-mediated electronic transitions between spin states by up to 10 8 − 10 9 -fold. The S◦ →T◦ rate increases from ~5− 40 s −1 (Franck-Condon) to ~2 × 10 8 − 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. Comparison to spin-orbit coupling (SOC) places these rates within the broader landscape of spin-mixing mechanisms, indicating that the hyperfine interaction operates on chemically relevant timescales. Despite the larger magnitude, SOC-mediated transitions are incoherent; the hyperfine interaction in contrast preserves coherence and is therefore crucial to spin evolution models. This work underscores the importance of incorporating a vibronic description in hyperfine-driven dynamics and provides a generalised 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.