J. Boiden Pedersen

Theory of magnetic field effects on radical pair recombination in micelles

Abstract Magnetic field effects (MPE) of radical pair (RP) recombination in micelles are investigated both analytically and numerically. The confinement effect of a micelle is modeled by a spherically symmetric potential well. The results show that the contribution from ST_ transitions to all kind of MFEs is significantly increased due to the confinement effect. The spin exchange relaxation is also increased causing the ST o -contribution to CIDEP to be essentially reduced. Surprisingly a pronounced effect of ST + transitions on CIDEP is found when the confinement is strong. Simple analytical expressions for the recombination probability and for CIDNP and CIDEP are rigorously derived and a high accuracy is found by comparison with the numerical results. The results are interpreted in terms of a simple supercage model which is based on the assumption that the process can be separated into two stages: (1) a fast initial geminate stage in which the radicals are thermalised within the micelle and (2) a slower decay of a quasi-equilibrium state by escape from the micelle.

Magnetic field dependent yield of geminate radical pair recombination in micelles: Test of the Johnson-Merrifield approximation

Abstract The magnetic field dependence of the radical pair recombination yield in micelles is investigated by an accurate numerical solution of the stochastic Liouville equation and by the Johnson-Merrifield approximation. Despite the simplicity of the approximation which is based on simple balance equations for the populations of the states it is found that useful results (~ 10% accuracy) are obtained in the expected region of applicability which includes typical experimental situations.

An analytical and numerical investigation of multiplet CIDEP

Abstract A detailed analysis of the accuracy of the analytical expressions for the chemically induced dynamical electron polarization (CIDEP) generated in radical pair (RP) recombination is performed by comparison with very accurate numerical calculations. The numerical results are obtained by a direct numerical solution of the stochastic Liouville equation. A large variety of limiting cases corresponding to different relations between the parameters of the problems are analyzed. For example, strong and weak exchange interactions, low and high reactivity of RPs, etc. The dependences of CIDEP on spin-lattice relaxation in the radicals and other dephasing processes are also considered. The analyses of the accuracy is accompanied by a short discussion of the basic concepts of the theory and, in particular, the important concept of effective radii of the spin exchange relaxation and the reactivity. New expressions were derived to correctly describe the slow diffusion region in the weak exchange interaction limit. It is shown that the analytical formulae reproduce the numerical results with a very high accuracy for all realistic values of the parameters.

The reactivity dependence of the recombination probability

An exact relation for the reactivity dependence of the recombination probability in the presence of a scavenger is derived. For a spherical symmetric system with a uniformly distributed scavenger this relation expresses the partially diffusion controlled recombination probability in terms of the totally diffusion controlled recombination probability. The relation is valid for a space‐dependent diffusion coefficient and for an arbitrary potential energy between the particles. The relation is proved only for a three‐dimensional system, but it appears to be valid also for one‐ and two‐dimensional systems.

Diffusion in inhomogeneous and anisotropic media

Despite common practice, inhomogeneous and/or anisotropic diffusion cannot be considered without regarding the microscopic details breaking the translational and/or angular symmetry. The macroscopic diffusion equation and the stationary solution are determined by the microscopic model and depend in general on all the microscopic parameters and not simply on the combination in the diffusion tensor. The traditional diffusion equation is only valid under special conditions and it cannot, in general, be used for anisotropic diffusion. An alternative form of the diffusion equation has a wider range of applicability. It is shown that for isotropic diffusion all variants of the diffusion equation are mathematically (but not physically) equivalent and can be transformed into each other by introduction of effective potentials. This is not the case for anisotropic diffusion where the traditional diffusion equation in most cases will give incorrect results. Two examples illustrate the differences between the two dyn...

ON THE MECHANISM OF ANTIPHASE ELECTRON SPIN RESONANCE SPECTRA OF RADICAL PAIRS

We have investigated the origin of the antiphase structure of the mw-induced ESR spectrum of a radical pair in a micelle. By applying an accurate numerical method we have examined various specially designed cases that clearly distinguish between the proposed mechanisms for the production of antiphase structure. It is demonstrated that neither of the previously proposed mechanisms can explain the observations. We argue that the only possible mechanism is a coherent, reencounter type mechanism involving two consecutive steps similar to the well established S–T0 mechanism.

An optimal numerical solution of diffusional recombination problems

Abstract The Smoluchowski equation used to describe recombination of particles that undergo diffusive motion is traditionally solved numerical by truncating the region of interparticle distances and employing a varying discretization which is manually adjusted according to the form of the interparticle interaction and the problem to be solved. By using a transformed quantity as independent variable rather than the interparticle distance it is possible to cover the complete region of space and to use an equidistant discretization that is automatically optimal for the given interaction. Furthermore by transforming the equation into a self-adjoint form and using the backward equation the recombination probability can be calculated directly for all initial distributions at once. This implies that the bulk recombination or the rate constant is obtained simultaneously. The method has a controllable accuracy and it is applied to a calculation of the time independent limiting quantities and the Laplace transformed solutions.

The spectral forms of transient ESR spectra of radical pairs and the origin of the antiphase structure

We show that transient electron spin resonance (ESR) spectra of short lived radical pairs can be written formally as a superposition of Lorentzian-like lines and the corresponding dispersive lines. The coefficients to these spectral components depend strongly on the frequency and amplitude of the microwave (mw) field and consequently a variety of spectral forms may result. The coefficients, and thus the spectral form, are determined by the interradical interaction induced rate of change of the longitudinal and transversal electron spin polarization. The longitudinal polarization is responsible for the well known chemically induced dynamic electron polarization (CIDEP) which changes the intensity of the lines without affecting the line shape. The transversal polarization is shown to be responsible for the antiphase structure (APS) in accordance with our previous proposition [J. Chem. Phys. 109, 8743 (1998)]. A simple one re-encounter model calculation illustrates and explains qualitatively most of the obse...

Magnetic field dependent yield of geminate radical pair recombination in micelles. Effect of intraradical spin lattice relaxation

Abstract The combined effect of coherent spin evolution and spin lattice relaxation on the magnetic field dependent yield of radical pair (RP) recombination in micelles is analyzed quantitatively using the exponential model (EM) and its supercage extension. Furthermore we show that the much simplier Johnson-Merrifield approximation agrees with the EM when the coherent transition frequencies are larger than the rate of escape from the micelle; but for nearly degenerate states only the EM is applicable. Relaxation induced by anisotropic hyperfine- and g -tensors is investigated. For large values of the anisotropic interactions and for long residence times of the RP in the micelle (i.e. small escape rates) the effect is substantial. The most pronounced effect is the decrease of the escape yield Y(B) caused by the τg -relaxation at high fields ( B > 1 T). Some hitherto unobserved spikes in the Y ( B ) curve are found at high fields. These are due to accidental degeneracies of the high field states.

Multiscale description of avian migration: from chemical compass to behaviour modeling

Despite decades of research the puzzle of the magnetic sense of migratory songbirds has still not been unveiled. Although the problem really needs a multiscale description, most of the individual research efforts were focused on single scale investigations. Here we seek to establish a multiscale link between some of the scales involved, and in particular construct a bridge between electron spin dynamics and migratory bird behaviour. In order to do that, we first consider a model cyclic reaction scheme that could form the basis of the avian magnetic compass. This reaction features a fast spin-dependent process which leads to an unusually precise compass. We then propose how the reaction could be realized in a realistic molecular environment, and argue that it is consistent with the known facts about avian magnetoreception. Finally we show how the microscopic dynamics of spins could possibly be interpreted by a migrating bird and used for the navigational purpose.