Transient nutation electron spin resonance spectroscopy on spin-correlated radical pairs: A theoretical analysis on hyperfine-induced nuclear modulations

The influence of anisotropic hyperfine interaction on transient nutation electron paramagnetic resonance (EPR) of light-induced spin-correlated radical pairs is studied theoretically using the density operator formalism. Analytical expressions for the time evolution of the transient EPR signal during selective microwave excitation of single transitions are derived for a model system comprised of a weakly coupled radical pair and one hyperfine-coupled nucleus with I=1/2. Zero-quantum electron coherence and single-quantum nuclear coherence are created as a result of the sudden light-induced generation of the radical pair state from a singlet-state precursor. Depending on the relative sizes of the nuclear Zeeman frequency and the secular and pseudo-secular parts of the hyperfine coupling, transitions between levels with different nuclear spin orientations are predicted to modulate the time-dependent EPR signal. These modulations are in addition to the well-known transient nutations and electron zero-quantum precessions. Our calculations provide insight into the mechanism of recent experimental observations of coherent nuclear modulations in the time-resolved EPR signals of doublets and radical pairs. Two distinct mechanisms of the modulations are presented for various microwave magnetic field strengths. The first modulation scheme arises from electron and nuclear coherences initiated by the laser excitation pulse and is “read out” by the weak microwave magnetic field. While the relative modulation depth of these oscillations with respect to the signal intensity is independent of the Rabi frequency, ω1, the frequencies of this coherence phenomenon are modulated by the effective microwave amplitude and determined by the nuclear Zeeman interaction and hyperfine coupling constants as well as the electron-electron spin exchange and dipolar interactions between the two radical pair halves. In a second mechanism the modulations are both created and detected by the microwave radiation. Here, the laser pulse merely defines the beginning of the microwave-induced coherent time evolution. This second mechanism appears the most consistent with current experimental observations.