A practical approach to calculate the time evolutions of magnetic field effects on photochemical reactions in nano-structured materials

Abstract

A practical method to calculate time evolutions of magnetic field effects (MFEs) on photochemical reactions involving radical pairs is developed on the basis of the theory of the chemically induced dynamic spin polarization proposed by Pedersen and Freed. In theory, the stochastic Liouville equation (SLE), including the spin Hamiltonian, diffusion motions of the radical pair, chemical reactions, and spin relaxations, is solved by using the Laplace and the inverse Laplace transformation technique. In our practical approach, time evolutions of the MFEs are successfully calculated by applying the Miller-Guy method instead of the final value theorem to the inverse Laplace transformation process. Especially, the SLE calculations are completed in a short time when the radical pair dynamics can be described by the chemical kinetics consisting of diffusions, reactions and spin relaxations. The SLE analysis with a short calculation time enables one to examine the various parameter sets for fitting the experimental date. Our study demonstrates that simultaneous fitting of the time evolution of the MFE and of the magnetic field dependence of the MFE provides valuable information on the diffusion motions of the radical pairs in nano-structured materials such as micelles where the lifetimes of radical pairs are longer than hundreds of nano-seconds and the magnetic field dependence of the spin relaxations play a major role for the generation of the MFE.

Magnetic Field Effects on Triplet Pair Generated by Singlet Fission in an Organic Crystal: Application of Radical Pair Model to Triplet Pair

“…For the analysis of the MFE observed by the time-resolved measurements, we first simulated time dependence of a population of the ground singlet state. The inverse Laplace transformation achieved by the Miller− Guy method 82. Then the time dependences of the fluorescence intensity were estimated by differentiations of the timedependence of the population of the ground singlet state.…”

Time-Resolved Detection of Magnetic Field Effects on Radical Pairs in Micelles: Two-Step Two-Laser Fluorescence Spectroscopy of Transient Radicals

“…It has been suggested and demonstrated that RP dynamics in the absence and presence of magnetic fields are rich in information not only regarding the mechanisms of MFEs − but also regarding spatial RP motions in various media such as uniform solutions, , micelles, − proteins, and ionic liquids. , Transient absorption spectroscopy, in which the absorption of transient radicals can be observed with high time resolution, is surely the first choice for the direct observation of RP dynamics under magnetic fields. In transient absorption measurements, however, the absorption of the photoexcited states, which are precursors of the radicals, is often overlapped with the absorption of the radicals.…”