Vibronic contributions to hyperfine-mediated spin kinetics

Abstract

The hyperfine interaction is a cornerstone of spin-dependent processes, yet the kinetic modeling of this mechanism remains limited by the Born–Oppenheimer approximation, obscuring the observation of spin evolution that underpins 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 108–109-fold. The S° → T° rate increases from ∼5−40 s−1 (Franck–Condon) to ∼2×108−1×109 s−1 (Herzberg–Teller), while the T° → S° rate increases from ∼4×102−1×103 s−1 to ∼7×108−2×109 s−1. This observed nanosecond timescale correlates well with the microsecond lifetime photoadduct formation central to its function. Comparison to spin–orbit coupling places these rates within the broader landscape of spin-mixing mechanisms, indicating that the hyperfine interaction operates on chemically relevant timescales. This work underscores the importance of incorporating a vibronic description in hyperfine-driven dynamics and provides a generalized 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.