Time-Resolved EPR Spectra of Spin-Correlated Radical Pairs: Spectral and Kinetic Modulation Resulting from Electron−Nuclear Hyperfine Interactions

Abstract

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 sigma, where the EPR peak of the anion radical exhibits an effective splitting of 2(1/2)J(2)/sigma. 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.

Origin of Light-Induced Spin-Correlated Radical Pairs in Cryptochrome

“…However, the stronger the magnetic field B 0 is relative to the size of the dipolar interaction (parameterized by D and E ) in the triplet state, the smaller the population difference between the high-field levels |T + 〉 and |T − 〉 despite the non-Boltzmann population of the zero-field levels. 70 In this so-called “high-magnetic-field limit”, where the energies of |T + 〉 and |T − 〉 states increase and decrease, respectively, in a linear fashion with the external magnetic field B 0 , one expects increasingly symmetric TREPR spectra. In other words, the higher the magnetic field, the more efficiently the enhanced absorptive and emissive spectral contributions will cancel out, and the more the integral of the signal intensity over the magnetic field will approach zero.…”

Zero Quantum Coherence in a Series of Covalent Spin-Correlated Radical Pairs

“…Coherent spin states of electrons and nuclei are being actively investigated for quantum information processing (QIP) applications using pulse magnetic resonance techniques. − An important challenge in this field is the development of spin systems in which the initial spin states are well-defined. Photoexcitation of covalently linked donor (D)–chromophore (C)–acceptor (A) triads (D–C–A) has been shown to result in sub-nanosecond nonadiabatic electron transfer leading to D •+ –C–A •– spin-correlated radical pairs (SCRPs) with well-defined initial singlet spin states (| S ⟩). − The initially formed singlet SCRP, 1 (D •+ –C–A •– ), undergoes hyperfine coupling-induced intersystem crossing in a few nanoseconds to produce the triplet SCRP, 3 (D •+ –C–A •– ), provided that the electron spin–spin exchange ( J ) and dipolar ( D ) interactions between the two radicals are comparable to, or smaller than, the electron–nuclear hyperfine interactions in the radicals. Application of a magnetic field, B 0 , results in Zeeman splitting of the SCRP triplet sublevels, which at the high fields typical of EPR spectroscopy are the | T +1 ⟩, | T 0 ⟩, and | T –1 ⟩ eigenstates that are quantized along B 0 , while the | S ⟩ state energy remains field invariant (Figure A). − …”

Investigation of Liquid‐Phase Inhomogeneity on the Nanometer Scale Using Spin‐Polarized Paramagnetic Probes

“…Due to its physical clarity, the CFN model has enjoyed impressively wide applications [75][76][77][78][79][80]. However, as new experimental observations become available, it was gradually recognized that the CFN model fit experimental data only under certain conditions.…”