Time-Resolved EPR spectra of Spin-correlated radical Pairs: Spectral and kinetic modulation resulting from electron - Nuclear hyperfine interactions

This paper expands the established four-state model of spin-correlated radical pairs (SCRPs) to include local nuclear spins which are ubiquitous in real-world systems and essential for the radical pair intersystem crossing (RP-ISC) mechanism. These nuclei are coupled to the unpaired electron spins by hyperfine interaction and split their electron paramagnetic resonance (EPR) lines. Rather than enumerating all possible nuclear states, an algorithm is devised to sort out the net hyperfine offset 2Q, which, along with the electron spin - spin coupling 2J, characterizes the behavior of SCRPs. Using this algorithm, the EPR spectra of SCRPs coupled to arbitrary nuclear spins can be efficiently simulated with only 2J and the EPR spectra of individual radicals as the inputs. Particularly illustrative is the case of a SCRP resulting from photoinduced electron transfer comprised of a spectrally narrow anion radical signal having small hyperfine splittings and a broad cation radical signal having many large hyperfine splittings and a Gaussian width o, where the EPR peak of the anion radical exhibits an effective splitting of 21/2J2/δ. For SCRPs having singlet and triplet pathways for charge recombination, their kinetic behavior is obtained concisely by considering the decay rate constants k_S and k_T as imaginary energies, while adhering to the existing derivation of the four-state model. These models are employed to interpret the diverse array of spectral and kinetic modulation patterns observed in the experimental EPR spectra of photogenerated SCRPs and to extract the 2J value, which reflects the donor - acceptor electronic coupling. During the first several hundred nanoseconds following photoexcitation, the spectral and time domain characteristics of the measured time-resolved EPR spectra manifest the consequences of the Uncertainty Principle, and the modulation patterns in either domain result from hyperfine splittings between the unpaired electron and the nuclear spins.