Electron Self-Exchange Kinetics Determined by MARY Spectroscopy: Theory and Experiment

Magnetic field effects on radical pair reactions: estimation of B1/2 for flavin-tryptophan radical pairs in cryptochromes

Magnetic field effects on the yields of radical pair reactions are often characterised by the "half-field" parameter, B_1/2, which encodes useful information on spin relaxation, radical recombination kinetics and electron-electron couplings as well as electron-nuclear hyperfine interactions. Here we use a variety of spin dynamics simulation methods to estimate the hyperfine-only values of B_1/2 for the flavin-tryptophan radical pair, [FAD˙^- TrpH˙⁺], thought to be the detector in the magnetic compass sense of migratory songbirds. The main findings are: (a) in the absence of fast recombination and spin relaxation, [FAD˙^- TrpH˙⁺] radical pairs in solution and in the putative magnetoreceptor protein, cryptochrome, have B_1/2 ≈ 1.89 mT and 2.46 mT, respectively. (b) The widely used expression for B_1/2 due to Weller et al. (Chem. Phys. Lett, 1983, 96, 24-27) is only applicable to small, short-lived (∼5 ns), rapidly tumbling radical pairs in solution, and is quantitatively unreliable in the context of magnetoreception. (c) In the absence of molecular tumbling, the low-field effect for [FAD˙^- TrpH˙⁺] is predicted to be abolished by the anisotropic components of the hyperfine interactions. Armed with the 2.46 mT "base value" for cryptochrome, measurements of B_1/2 can be used to understand the impact of spin relaxation on its performance as a magnetic compass sensor.

Geometrization for Energy Levels of Isotropic Hyperfine Hamiltonian Block and Related Central Spin Problems for an Arbitrarily Complex Set of Spin-1/2 Nuclei

Description of interacting spin systems relies on understanding the spectral properties of the corresponding spin Hamiltonians. However, the eigenvalue problems arising here lead to algebraic problems too complex to be analytically tractable. This is already the case for the simplest nontrivial (Kmax−1) block for an isotropic hyperfine Hamiltonian for a radical with spin-12 nuclei, where n nuclei produce an n-th order algebraic equation with n independent parameters. Systems described by such blocks are now physically realizable, e.g., as radicals or radical pairs with polarized nuclear spins, appear as closed subensembles in more general radical settings, and have numerous counterparts in related central spin problems. We provide a simple geometrization of energy levels in this case: given n spin-12 nuclei with arbitrary positive couplings ai, take an n-dimensional hyper-ellipsoid with semiaxes ai, stretch it by a factor of n+1 along the spatial diagonal (1, 1, …, 1), read off the semiaxes of thus produced new hyper-ellipsoid qi, augment the set {qi} with q0=0, and obtain the sought n+1 energies as Ek=−12qk2+14∑iai. This procedure provides a way of seeing things that can only be solved numerically, giving a useful tool to gain insights that complement the numeric simulations usually inevitable here, and shows an intriguing connection to discrete Fourier transform and spectral properties of standard graphs.

Development of lock-in based overtone modulated MARY spectroscopy for detection of weak magnetic field effects

Modulated magnetically altered reaction yield (ModMARY) spectroscopy is a derivative variant of fluorescence detected magnetic field effect measurement, where the applied magnetic field has both a constant and a modulated component. As in many derivative spectroscopy techniques, the signal to noise ratio scales with the magnitude of the modulation. High modulation amplitudes, however, distort the signal and can obscure small features of the measured spectrum. In order to detect weak magnetic field effects (including the low field effect) a balance of the two has to be found. In this work we look in depth at the origin of the distortion of the MARY signal by field modulation. We then present an overtone detection scheme, as well as a data analysis method which allows for correct fitting of both harmonic and overtone signals of the modulation broadened MARY data. This allows us to robustly reconstruct the underlying MARY curve at different modulation depths. To illustrate the usefulness of the technique, we show measurements and analysis of a well known magnetosensitive system of pyrene/1,3-dicyanobenzene (Py/DCB). The measurements of first (h1) and second (h2) harmonic spectra are performed at different modulation depths for both natural isotopic abundance (PyH10), and perdeuterated (PyD10) pyrene samples.

Peptoid-Conjugated Magnetic Field-Sensitive Exciplex System at High and Low Solvent Polarities

The magnetic field effect (MFE) in exciplex emission (ExE) has been studied for decades, but it has been observed to occur only in solvents with a limited range of polarity. This limitation is mainly due to the reversible interconversion collapse between two quenching products of the photoinduced electron transfer, the exciplex and magnetic field-sensitive radical ion pair (RIP) beyond that polarity range. In a nonpolar solvent, the formation of RIPs is suppressed, whereas in a polar solvent, the probability of their re-encounter forming the exciplexes decreases. In this study, we developed new exciplex-forming (phenyl-phenanthrene)-(phenyl-N,N-dimethylaniline)-peptoid conjugates (PhD-PCs) to overcome this limitation. The well-defined peptoid structure allows precise control of the distance and the relative orientation between two conjugated moieties. Steady-state and time-resolved spectroscopic data indicate that the PhD-PCs can maintain the reversibility, which allows MFEs in ExE regardless of the solvent polarity. Subtle differences between the ExEs of the PhD-PCs were observed and explained by their exciplex geometries obtained through time-dependent density functional theory (TD-DFT) calculations.

Determination of Hyperfine Coupling Constants of Fluorinated Diphenylacetylene Radical Anions by Magnetic Field-Affected Reaction Yield Spectroscopy

Magnetic field-affected reaction yield (MARY) spectroscopy is a spin chemistry technique for detecting short-lived radical ions. Having sensitivity to transient species with lifetimes as short as nanoseconds, MARY spectroscopy usually does not provide detailed information on their magnetic resonance parameters, except for simple systems with equivalent magnetic nuclei. In this work, the radical anions of two fluorinated diphenylacetylene derivatives with nonequivalent magnetic nuclei and unknown hyperfine coupling constants ( A_HF) were investigated by MARY spectroscopy. The MARY spectra were found to be resolved and have resonance lines in nonzero magnetic fields, which are determined by the A_HF values. Simple relationships between the positions of resonance MARY lines and the A_HF values were established from the analysis of the different Hamiltonian block contributions to the MARY spectrum. The obtained experimental A_HF values are in agreement with the results of quantum chemical calculations at the density functional theory level.

Magnetic Field-Sensitive Radical Pair Dynamics in Polymethylene Ether-Bridged Donor-Acceptor Systems

Donor-acceptor systems forming exciplexes are versatile models for the study of magnetic field effects (MFEs) on charge recombination reactions. The MFEs originate from singlet-triplet interconversion within transient radical ion pairs (RIPs), which exist in a dynamic equilibrium with the exciplexes. Here, we describe the synthesis and MFEs of the chain-linked N,N-dimethylaniline (DMA)/9-methylanthracene (MAnt) donor-acceptor system MAnt-(CH2) n -O-CH2-CH2-DMA for n = 6, 8, 10, and 16. The MFEs are found to increase with increasing chain length. Effects as large as 37.5% have been observed for the long-chain compound with n = 16. The solvent dependence of the MFEs at magnetic field intensity 75 mT is reported. For the range of solvent static dielectric constants εs = 6.0-36.0, the MFEs go through a maximum for intermediate polarities, for which the direct formation of RIPs prevails and their dissociation and reencounter are balanced. Field-resolved measurements (MARY spectra) are reported for solutions in butyronitrile. The MARY spectra reveal that for n = 8, 10, 16, the average exchange interaction is negligible during the coherent lifetime of the radical pair. However, singlet-triplet dephasing broadens the lineshape; the shorter the linker, the more pronounced this effect is. For n = 6, a dip in the fluorescence intensity reveals a nonzero average exchange coupling of the order of ±5 mT. We discuss the field-dependence in the framework of the semiclassical theory taking spin-selective recombination, singlet-triplet dephasing, and exchange coupling into account. Singlet recombination rates of the order of 0.1 ns-1 and various degrees of singlet-triplet dephasing govern the spin dynamics. In addition, because of a small free energy gap between the exciplex and the locally excited fluorophore quencher pair, a fully reversible interconversion between the RIP, exciplex, and locally excited fluorophore is revealed by spectrally resolved MFE measurements for the long-chain systems (n = 10, 16).

Spin-chemistry concepts for spintronics scientists

Spin chemistry and spintronics developed independently and with different terminology. Until now, the interaction between the two fields has been very limited. In this review, we compile the two "languages" in an effort to enhance communication. We expect that knowledge of spin chemistry will accelerate progress in spintronics.

Effects of Preferential Solvation Revealed by Time-Resolved Magnetic Field Effects

External magnetic fields can impact recombination yields of photoinduced electron transfer reactions by affecting the spin dynamics in transient, spin-correlated radical pair intermediates. For exciplex-forming donor–acceptor systems, this magnetic field effect (MFE) can be investigated sensitively by studying the delayed recombination fluorescence. Here, we investigate the effect of preferential solvation in microheterogeneous solvent mixtures on the radical pair dynamics of the system 9,10-dimethylanthracene (fluorophore)/N,N-dimethylaniline (quencher) by means of time-resolved magnetic field effect (TR-MFE) measurements, wherein the exciplex emission is recorded in the absence and the presence of an external magnetic field using time-correlated single photon counting (TCSPC). In microheterogeneous environments, the MFE of the exciplex emission occurs on a faster time scale than in iso-dielectric homogeneous solvents. In addition, the local polarity reported by the exciplex is enhanced compared to homogeneous solvent mixtures of the same macroscopic permittivity. Detailed analyses of the TR-MFE reveal that the quenching reaction directly yielding the radical ion pair is favored in microheterogeneous environments. This is in stark contrast to homogeneous media, for which the MFE predominantly involves direct formation of the exciplex, its subsequent dissociation to the magneto-sensitive radical pair, and re-encounters. These observations provide evidence for polar microdomains and enhanced caging, which are shown to have a significant impact on the reaction dynamics in microheterogeneous binary solvents.

Estimation of the Fraction of Spin-Correlated Radical Ion Pairs in Irradiated Alkanes using Magnetosensitive Recombination Luminescence from Exciplexes Generated upon Recombination of a Probe Pair

We suggest a convenient probe exciplex system for studies in radiation spin chemistry based on a novel acceptor-substituted diphenylacetylene, 1-(phenylethynyl)-4-(trifluoromethyl)benzene that has a very short fluorescence lifetime (<200 ps) and low quantum yield (0.01) of intrinsic emission, provides efficient electron capture in alkanes and efficient exciplex formation upon recombination in pair with DMA radical cation, while exhibiting a shifted to red exciplex emission band as compared to the parent system DMA – diphenylacetylene. After chemical, luminescent, radiation and spin-chemical characterization of the new system we used the magnitude of magnetic field effect in its exciplex emission band for experimental estimation of the fraction of spin-correlated radical ion pairs under X-irradiation with upper energy cutoff 40 keV in a set of 11 alkanes. For linear and branched alkanes magnetic field effects and the corresponding fractions are approximately 19–20% and 0.28, while for cyclic alkanes they are lower at 16–17% and 0.22, respectively.

Exciplexes versus Loose Ion Pairs: How Does the Driving Force Impact the Initial Product Ratio of Photoinduced Charge Separation Reactions?

Many donor-acceptor systems can undergo a photoinduced charge separation reaction, yielding loose ion pairs (LIPs). LIPs can be formed either directly via (distant) electron transfer (ET) or indirectly via the dissociation of an initially formed exciplex or tight ion pair. Establishing the prevalence of one of the reaction pathways is challenging because differentiating initially formed exciplexes from LIPs is difficult due to similar spectroscopic footprints. Hence, no comprehensive reaction model has been established for moderately polar solvents. Here, we employ an approach based on the time-resolved magnetic field effect (MFE) of the delayed exciplex luminescence to distinguish the two reaction channels. We focus on the effects of the driving force of ET and the solvent permittivity. We show that, surprisingly, the exciplex channel is significant even for an exergonic ET system with a free energy of ET of -0.58 eV and for the most polar solutions studied (butyronitrile). Our findings demonstrate that exciplexes play a crucial role even in polar solvents and at moderate driving forces, contrary to what is usually assumed.

Time-resolved magnetic field effects distinguish loose ion pairs from exciplexes

We describe the experimental investigation of time-resolved magnetic field effects in exciplex-forming organic donor–acceptor systems. In these systems, the photoexcited acceptor state is predominantly deactivated by bimolecular electron transfer reactions (yielding radical ion pairs) or by direct exciplex formation. The delayed fluorescence emitted by the exciplex is magnetosensitive if the reaction pathway involves loose radical ion pair states. This magnetic field effect results from the coherent interconversion between the electronic singlet and triplet radical ion pair states as described by the radical pair mechanism. By monitoring the changes in the exciplex luminescence intensity when applying external magnetic fields, details of the reaction mechanism can be elucidated. In this work we present results obtained with the fluorophore-quencher pair 9,10-dimethylanthracene/N,N-dimethylaniline (DMA) in solvents of systematically varied permittivity. A simple theoretical model is introduced that allows discriminating the initial state of quenching, viz., the loose ion pair and the exciplex, based on the time-resolved magnetic field effect. The approach is validated by applying it to the isotopologous fluorophore-quencher pairs pyrene/DMA and pyrene-d₁₀/DMA. We detect that both the exciplex and the radical ion pair are formed during the initial quenching stage. Upon increasing the solvent polarity, the relative importance of the distant electron transfer quenching increases. However, even in comparably polar media, the exciplex pathway remains remarkably significant. We discuss our results in relation to recent findings on the involvement of exciplexes in photoinduced electron transfer reactions.

Spin-locking in low-frequency reaction yield detected magnetic resonance

The purported effects of weak magnetic fields on various biological systems from animal magnetoreception to human health have generated widespread interest and sparked much controversy in the past decade. To date the only well established mechanism by which the rates and yields of chemical reactions are known to be influenced by magnetic fields is the radical pair mechanism, based on the spin-dependent reactivity of radical pairs. A diagnostic test for the operation of the radical pair mechanism was proposed by Henbest et al. [J. Am. Chem. Soc., 2004, 126, 8102] based on the combined effects of weak static magnetic fields and radiofrequency oscillating fields in a reaction yield detected magnetic resonance experiment. Here we investigate the effects on radical pair reactions of applying relatively strong oscillating fields, both parallel and perpendicular to the static field. We demonstrate the importance of understanding the effect of the strength of the radiofrequency oscillating field; our experiments demonstrate that there is an optimal oscillating field strength above which the observed signal decreases in intensity and eventually inverts. We establish the correlation between the onset of this effect and the hyperfine structure of the radicals involved, and identify the existence of 'overtone' type features appearing at multiples of the expected resonance field position.

Solvation dynamics of a radical ion pair in micro-heterogeneous binary solvents: a semi-quantitative study utilizing MARY line-broadening experiments

This work aims at elucidating the mechanism of solvation of a radical ion pair (RIP) in a micro-heterogeneous binary solvent mixture using magnetically affected reaction yield (MARY) spectroscopy. For the exciplex-forming 9,10-dimethylanthracene/N,N-dimethylaniline system a comparative, composition-dependent MARY line-broadening study is undertaken in a heterogeneous (toluene/dimethylsulfoxide) and a quasi-homogenous (propyl acetate/butyronitrile) solvent mixture. The half-saturation field extrapolated to zero-quencher concentration, B(1/2), and the self-exchange rate constants are analyzed in the light of solvent dynamical properties of the mixtures and a dielectric continuum solvation model. The dependence of B(1/2) on the solvent composition is explained by cluster formation giving rise to shortened RIP lifetimes. The results are in qualitative agreement with the continuum solvation model suggesting that it could serve as a theoretical basis for quantitative modeling.

Experimental observation of preferential solvation on a radical ion pair using MARY spectroscopy

The effect of preferential solvation on the exciplex luminescence detected magnetic field effect has been studied using magnetic-field-effect-on-reaction-yield (MARY) spectroscopy. By designing solvent mixtures which can provide a micro-environment around the magneto-sensitive radical ion pair (RIP) from highly heterogeneous to quasi-homogenous, the effect of the polarity scan on an absolute magnetic field effect (χ(E)) and B(1/2) (the field value marking half saturation) has been studied on the system 9,10-dimethylanthracene (fluorophore)/N,N'-dimethylaniline (quencher). While the trend in χ(E) (although with subtle differences) follows the usual norm of passing through maxima with increasing polarity, the B(1/2) values show either a large monotonic decrease (for heterogeneous solvents) or remain constant (for quasi-homogenous systems) with increasing polarity. The observations have been interpreted invoking the concept of amplification of the "cage-effect" as a result of preferential solvation in binary solvents and its influence on the decaying exciplex. The use of ternary solvents further confirms the proposed mechanism. Additionally electron hopping from the radical ion pair to the surrounding neutral donor molecules could also possibly contribute to the observed trend.

Magnetic field effects on exciplex-forming systems: the effect on the locally excited fluorophore and its dependence on free energy

This study addresses magnetic field effects in exciplex forming donor-acceptor systems. For moderately exergonic systems, the exciplex and the locally excited fluorophore emission are found to be magneto-sensitive. A previously introduced model attributing this finding to excited state reversibility is confirmed. Systems characterised by a free energy of charge separation up to approximately -0.35 eV are found to exhibit a magnetic field effect on the fluorophore. A simple three-state model of the exciplex is introduced, which uses the reaction distance and the asymmetric electron transfer reaction coordinate as pertinent variables. Comparing the experimental emission band shapes with those predicted by the model, a semi-quantitative picture of the formation of the magnetic field effect is developed based on energy hypersurfaces. The model can also be applied to estimate the indirect contribution of the exchange interaction, even if the perturbative approach fails. The energetic parameters that are essential for the formation of large magnetic field effects on the exciplex are discussed.

ESR-Investigations on the Dynamic Solvent Effects of Degenerate Electron Exchange Reactions. Part I: Cyanobenzenes

The rates of degenerate electron exchange (electron self-exchange) of various cyanobenzenes have been measured by EPR line broadening technique in nine different solvents at room temperature. The molecules studied comprise besides benzene-1,2-dicarbonitrile, benzene-1,4-dicarbonitrile and benzene-1,2,4,5-tetracarbonitrile, the two isomeric tricyanobenzenes, benzene-1,2,3-tricarbonitrile and benzene-1,2,4-tricarbonitrile, the anion radicals of which have not been characterized before.

The experimentally observed rates vary from 4.5 × 108 to 44.0 × 108 M−1 s−1 and show the pronounced dependence on the longitudinal relaxation times, τL, of the solvents. The solvent dynamical effect so manifested is confirmed with remarkable clarity using solvents spanning a wide range of τL-values, which comprise acetonitrile (0.2 ps) and o-dichlorobenzene (6.0 ps) at its extremes. The rate constants are compared with Marcus theory using the continuum model (CM) and the mean spherical approximation (MSA) for the outer sphere reorganization energies and Nelson’s method for the inner sphere reorganization energies. Furthermore, an estimation of the resonance splitting energies, V RP, is given based on the experimental rates.

Difficulties in building radiation-generated three-spin systems using spin-labeled luminophores

Aromatic compounds are well-known acceptors of primary radical ions that are formed under high-energy irradiation of nonpolar systems. Thus formed radical ion pairs recombine and produce magnetosensitive fluorescence, which helps study the short-lived radical ions. It was initially suggested that a simple introduction of a spin label into the original arene would allow an easy transition from two-spin to three-spin systems, retaining the experimental techniques available for radical pairs. However, it turned out that spin-labeled arenes often do not produce magnetosensitive fluorescence in the conditions of a conventional radiochemical experiment. To understand the effect of the introduced spin label, we synthesized a series of compounds with the general structure "stable 3-imidazoline radical-two-carbon bridge-naphthalene" as well as their diamagnetic analogues. By use of this set of acceptors, we determined the processes that ruin the observed signal and established their connection with the chemical structure of the compound. We found that the compounds with flexible (saturated) two-carbon bridges between the luminophore and the stable radical moieties exist in solution in folded conformation, which leads to suppression of luminescence from naphthalene due to efficient through-space exchange quenching of the excited state by the radical. Increasing the rigidity of the bridge by introducing the double bond drastically increases the reactivity of the extended pi-system. In these compounds, the energy released upon recombination is spent in radiationless processes of chemical transformations both at the stage of the radical ion and at the stage of the electronically excited molecule.

The spin mixing process of a radical pair in low magnetic field observed by transient absorption detected nanosecond pulsed magnetic field effect

The spin mixing process of the radical pair in the sodium dodecyl sulfate (SDS) micelle is studied by using a novel technique nanosecond pulsed magnetic field effect on transient absorption. We have developed the equipment for a nanosecond pulsed magnetic field and observed its effect on the radical pair reaction. A decrease of the free radical yield by a reversely directed pulsed magnetic field that cancels static field is observed, and the dependence on its magnitude, which is called pulsed MARY (magnetic field effect on reaction yield) spectra, is studied. The observed spectra reflect the spin mixing in 50-200 ns and show clear time evolution. Theoretical simulation of pulsed MARY spectra based on a single site modified Liouville equation indicates that the fast spin dephasing processes induced by the modulation of electron-electron spin interaction by molecular reencounter affect to the coherent spin mixing by a hyperfine interaction in a low magnetic field.

Determination of radical re-encounter probability distributions from magnetic field effects on reaction yields

Measurements are reported of the effects of 0-23 mT applied magnetic fields on the spin-selective recombination of Py*- and DMA*+ radicals formed in the photochemical reaction of pyrene and N,N-dimethylaniline. Singlet <--> triplet interconversion in [Py*- DMA*+] radical pairs is probed by investigating combinations of fully protonated and fully deuterated reaction partners. Qualitatively, the experimental B1/2 values for the four isotopomeric radical pairs agree with predictions based on the Weller equation using known hyperfine coupling constants. The amplitude of the "low field effect" (LFE) correlates well with the ratio of effective hyperfine couplings, aDMA/aPy. An efficient method is introduced for calculating the spin evolution of [Py*- DMA*+] radical pairs containing a total of 18 spin-1/2 and spin-1 magnetic nuclei. Quantitative analysis of the magnetic field effects to obtain the radical re-encounter probability distribution f (t )-a highly ill-posed and underdetermined problem-is achieved by means of Tikhonov and maximum entropy regularization methods. The resulting f (t ) functions are very similar for the four isotopomeric radical pairs and have significant amplitude between 2 and 10 ns after the creation of the geminate radical pair. This interval reflects the time scale of re-encounters that are crucial for generating the magnetic field effect. Computer simulations of generalized radical pairs containing six spin-1/2 nuclei show that Weller's equation holds approximately only when the radical pair recombination rate is comparable to the two effective hyperfine couplings and that a substantial LFE requires, but is not guaranteed by, the condition that the two effective hyperfine couplings differ by more than a factor of 5. In contrast, for very slow recombination, essentially any radical pair should show a significant LFE.

The integral encounter theory of multistage reactions containing association-dissociation reaction stages. III. Taking account of quantum states of reactants

The formalism developed in Part I [K. L. Ivanov, N. N. Lukzen, A. A. Kipriyanov, and A. B. Doktorov, Phys. Chem. Chem. Phys. 6, 1706 (2004)] of the present contribution is extended to treat the reacting particles with internal quantum states. Initial spatial correlations of reactants are considered in the framework of this formalism as well.