Abnormal electron spin echo and multiple-quantum coherence in a spin-correlated radical pair system

The phenomena of the abnormal “out-of-phase” electron spin echo in a photo-induced spin-correlated radical pair system are examined theoretically. It is shown that such abnormal phenomena are a consequence of initial non-Boltzmann distribution and zero-quantum coherence produced by laser excitation. The analysis of echo amplitude versus the pulse-angle of the microwave pulse reveals two sources for the formation of the echo. The method of excitation and detection of multiple-quantum coherence using a phase-cycled 2-pulse sequence is also discussed. Such a technique is complementary to the ESE method.     

Spin dynamics and EPR spectra of consecutive spin-correlated radical pairs. Model calculations

Time-resolved continuous wave EPR signals of two consecutive radical pairs are found in the linear response limit. Numerical simulations of the EPR observables visualize two characteristic features. First, there is a shift of a phase of quantum beats of the EPR line intensities of the secondary pairs. This phase shift originates from a certain time delay in a formation of the secondary pairs (due to time spent by electron spins in the primary radical pair state) and from the difference of the spin dynamics in the secondary and the primary pairs. This phase shift might be detected even in the cases when the primary radical pair has the very short lifetime and, as a result, the EPR spectrum of the primary pair cannot be detected directly. Second, for two consecutive radical pairs, there might be a pronounced non-equality of intensities of EPR lines at the EPR resonance frequencies of the secondary pairs. Indeed, in a case of two consecutive pairs there is the additional mechanism which induces the non-equality of the EPR line intensities: a polarization transfer from the primary to secondary pair and the change of a electron spin quantization axis when a primary radical pair transforms to a secondary radical pair. A possibility to detect experimentally these features of the EPR signals when studying consecutive charge separated states in photosynthetic reaction centers is discussed briefly.     

Amplitudes of gamma detected NMRON spin echo signals

The amplitudes of the spin echo and the baseline components of gamma detected NMRON signals have been calculated for the pure Zeeman case using a density matrix approach. Optimum turn angles and the separate and combined influences of line broadening and skin effect, appropriate to bulk ferromagnetic metals, are examined. For narrow line, zero skin effect samples, the triple pulse sequence (cos⁻¹(1/√3))−180°−(180°−cos⁻¹(1/√3)) affords the largest principal echo. However, its advantage is diminished with the introduction of either line broadening or skin effect and is subsequently lost when both these effects are included or either becomes severe. The skin effect distortion of the spin echo signal can dominate over intermediate-to-broad line distortions, for that range of experimental conditions generally applicable tometallic ferromagnetic hosts.     

On the three-pulse excitation of spin echo signals

Three variants of three-pulse excitation of the quadrupole spin echo are considered. The specific features are determined for each variant of the excitation.     

A Manifestation of two-quantum transitions in the ODEPR spectra of the spin-correlated radical pairs in micelles

Optically detected electron paramagnetic resonance spectra of the spin-correlated radical pairs diffusing inside a spherical region are numerically simulated taking into account an exchange interaction between partners of the pairs. It is shown that these spectra contain the lines induced by the two-quantum transitions. The shape and the width of this two-quantum transition line are analyzed as depending on magnetic resonance parameters, on molecular kinetic parameters and chemical reactivity of radicals.     

Exploring hyperfine interactions in spin-correlated radical pairs from photosynthetic proteins: High-frequency ENDOR and quantum beat oscillations

Electron paramagnetic resonance (EPR) and related spectroscopic tools remain among the most important probes of structure and function of natural photosynthetic systems. Indeed, the challenging questions in the study of photosynthesis have to a great extent dictated the directions taken in the development of EPR and associated spectroscopies. In this overview we demonstrate, with recent examples from our laboratories, the potential of high-frequency and time-resolved EPR spectroscopy to reveal unique information about electron transfer processes and the structure of photosynthetic systems. A common feature of these experiments is that they probe hyperfine interactions of the spincorrelated radical pair. Thus, the analysis of the results requires consideration of three interacting spins: two correlated electron spins with one nuclear spin. The results illustrate the importance of resolving nuclear hyperfine structure for obtaining details of structure-function relationships in photosynthetic electron transfer.     

Comment on a shape of EPR spectra of spin-correlated radical pairs and separate radicals escaped geminate recombination

For model spin-correlated radical pairs (RPs) the EPR spectra are simulated and their shape is analyzed in detail. It is demonstrated that the widths and intensities of the EPR spectra are determined essentially by the rate of the singlet-triplet dephasing and the scale of the spin-spin interactions. It is also shown that chemical exchange of the RPs between states with different values of the exchange and the dipole-dipole interactions can produce the apparent antiphase structure lines in the EPR spectra.     

Line shape of spin echo signals in imperfect bulk metals

The quadrupole part of the spin echo signal is measured in the case of doped (Cu⁶³+3.2 mol % Sn) and of highly deformed (i.e. distorted dislocation) bulk metals (Al²⁷), where the NMR-signal is distorted by the skin effect. Theoretical expressions for the quadrupolar part due to point defects and dislocations are found to be in agreement with the experimental curves.     

Three-pulse spin echo signals from quadrupolar nuclei in magnetic materials

The time evolutions of the three-pulse spin echo signals from quadrupolar nuclei ⁶³Cu and ⁵³Cr in ferromagnetic CuCr₂S₄:Sb have been investigated at the temperature T=77 K. The experimental results were well explained by the developed theory of the time evolutions of the three-pulse echoes. The main assumption of this theory is the assumption that the temporal fluctuations in the electron magnetization lead to the fluctuations in the hyperfine and quadrupole interaction Hamiltonians.     

Peculiarities of femtosecond photon echo signals in dye-doped polymer films at high temperatures

Some results of femtosecond echo experiments on polyvinylbutyral polymer films doped with phtalocyanine molecules at high (up to room) temperatures are reported. Special attention is paid to the stimulated femtosecond photon echo (SFPE), which was observed in a solid-state medium at room temperature for the first time. A decay curve of the SFPE signal has been obtained and theoretically analyzed. The results of the analysis indicate that the random interaction between impurity molecules and quasi-localized low-frequency vibration modes in an amorphous matrix plays the dominant role in the character of optical dephasing at high temperatures.     

Nuclear spin relaxation in free radicals as revealed in a stimulated electron spin echo experiment

Electron spin echo envelope modulation (ESEEM) in a three-pulse stimulated echo experiment, when the time interval between the first and second pulses τ is varied, is attributed to a spontaneous change of the electron spin Larmor frequency in the time intervalT between the second and third pulses, due to the longitudinal relaxation of nearby nuclei. It is observed for nitroxide radicals in glassy matrices in the temperature range of 130–240 K. Nuclear relaxation is assumed to arise from fluctuation of the proton hyperfine interaction, due to fast rotation of the methyl groups. This contribution to ESEEM and the conventional one that is induced by the simultaneous excitation of allowed and forbidden electron spin transitions were found to be multiplicative. As the latter does not depend on the timeT, both contributions can be easily separated. The rate of nuclear spin relaxation was determined, and correlation time of methyl group rotation was estimated by Redfield theory of spin relaxation. Arrhenius parameters of this motion were estimated on the basis of these data and those at 77 and 90 K, where the previously developed approach was used (L.V. Kulik, I.A. Grigor’ev, E.S. Salnikov, S.A. Dzuba, Yu.D. Tsvetkov, J. Phys. Chem. A 106, 12066–12071, 2003).     

Two dimensional FT-EPR spectroscopy for spin-correlated radical pairs — Application to photoinduced electron transfer reaction between ZnTPPS and DQ in a micellar solution

Two pulsed EPR methods for studying spin-correlated radical pairs (SCRPs) transiently generated in photochemical reactions are presented. One is two dimensional (2D) EPR nutation method which uses anomalous flip angle dependence of SCRPs for microwave (MW) pulses and the other is application of the so called 2D J spectroscopy in NMR to studies of paramagnetic SCRPs. The methods were applied to observation of the SCRP generated in the photoinduced electron transfer reaction between zinctetraphenylporphyrinsulphonate (ZnTPPS) and duroquinone (DQ) in cetyltrimethylammonium chloride (CTAC) micellar solution in which SCRP alives for a relatively long period at the early stage of the reaction processes.     

Application of electron spin echo ESR-tomography to study radical diffusion in porous media

ESR-tomography based on electron spin echo was used to study the translational diffusion of stable radical 2,2,6,6-tetramethyl-4-pipyridinoxyl in the solutions filling the pore space of silica gel. The values of the efficient diffusion coefficients were measured for the solution of radicals 2,2,6,6-tetramethyl-4-pipyridinoxyl in methanol and 2-methyl-tetrahydrofuran, depending on the mean size of the silica gel pore. It was shown that the value of the diffusion coefficient decreased as pore size decreased, and furthermore depended on the solvent type. A linear relation between the diffusion coefficient and the spin exchange constant was established within the scope of the quasihomogeneous diffusion model.     

Refocused primary echo: A zero dead time detection of the electron spin echo envelope modulation

We report on the two-dimensional (2D) implementation of the refocused primary electron spin echo envelope modulation (ESEEM) technique, its theory and experimental application to a model system and a system of biological interest. This technique is virtually free of dead time along one time coordinate. The ESEEM obtained by integration of the 2D time-domain data of the refocused primary ESEEM over one of the time coordinates shows the intensity of the sum combination harmonics proportional to k² for k 1 and proportional to k for k 1 (k is a usual notation for the modulation amplitude factor). This feature, in combination with the adjustment of k by means of variation of the operational frequency of the spectrometer, was found to be very useful for detection of protons with distributed hyperfine interaction parameters situated close to the electron spin.     

Spin-vibrational interactions in geminate radical pairs: Effective spin Hamiltonian including anharmonicity

An equation for the effective spin Hamiltonian including the interaction of radical pair spins with vibrations in both linear and higher approximations was obtained. Even in the linear approximation, the Hamiltonian was found to be non-Heisenberg. The influence of a sound field on the probability of geminate radical pair recombination is considered in the Appendix. The results obtained can be of use for solving certain nanochemistry problems.     

Magnetic field dependence of spin dynamics of radical pairs studied by time-resolved RYDMR

The photochemical reaction of 2-methyl-1,4-naphthoquinone in sodium dodecyl-sulphate micellar solution was investigated with an optical detection ESR apparatus working at 17.44 GHz (Ku-band). The Ku-band RYDMR spectra are obtained from the transient optical absorption and the stationary absorption of the reaction product, and the shift of the spectral peak compared with the spectra at 331 mT is reproduced well by the difference in g of the component radicals. The microwave pulse length dependence shows the quantum beat originated from the conversion between triplet ±1 states and the mixed state of singlet and triplet 0 states by the microwave field. The decay rate of the radical pair in triplet ±1 at 622 mT was determined to be 7.1 ± 1.1 × 10⁵ s^?1 by changing the irradiation time of a short (20 ns) microwave pulse with reference to the laser excitation. This value is smaller than that at 331 mT, as expected by the relaxation mechanism.     

Development of fluorinated,NMR-active spin traps for studies of free radical chemistry

Five fluorinated analogs of the spin trap phenyl-t-butyl nitrone (PBN) have been synthesized and evaluated for use as NMR-active traps. The introduction of the fluorine substituent allows selective observation of chemical reactions involving the spin traps. Although the paramagnetic adducts themselves are not directly observable by this approach as a consequence of extensive broadening, the reduced forms (hydroxylamines) can be readily observed. NMR studies of the trapping of the phenyl radical produced from the thermal decomposition of phenylazotriphenyl methane have been carried out. The observation of fluorinated benzaldehydes in these studies reflects the formation and subsequent degradation of oxygen-centered radicals under some conditions. Relative trapping efficiencies for the phenyl radical in the series 2-F, 4-F, 2,6-difluoro, 2-CF₃, and 4-CF₃ substituted PBN analogs have been determined based on an analysis of the ¹⁹F NMR resonance intensities of the reduced phenyl radical adducts. The relatively large proton hyperfine coupling constants observed for 2,6-difluoro and 2-CF₃ PBN analogs allow direct observation by ESR of adduct formation in solutions containing both PBN and either of these analogs. The introduction of fluorine substituents into the trap has only a small effect on trapping efficiency.     

Electron spin polarization in consecutive spin-correlated radical Pairs: Application to short-lived and long-lived precursors in type 1 photosynthetic reaction centres

An analytical treatment of the spin dynamics in sequential photoinduced correlated coupled radical pairs is presented and applied to the spectra of the states P⁺A ₁ ^? and P⁺F _x ^? in type 1 photo-synthetic reaction centres. Expressions for the spin polarized spectra are derived for the specific limiting cases of a very short-lived and very long-lived primary radical pair which correspond to the situation found in heliobacteria and photosystem I (PSI), respectively. The inhomogeneous line-broadening due to the unresolved hyperfine couplings is taken explicitly into account. It is shown that the density matrix of the secondary pair ρ₂ can be written as the sum of two terms corresponding to (i) the part which is independent of the spin dynamics in the precursor, (ii) the additional spin polarization which is generated during the lifetime of the precursor and transferred to the secondary pair. The latter term contains two contributions which arise from the difference of the Zeeman interactions of the radicals in the primary pair and from the inhomogeneous line broadening. The predicted polarization patterns are compared to those established for chemically induced dynamic electron polarization (CIDEP) when uncoupled radicals are generated from a radical pair precursor. The expressions are then used to simulate the experimental spectra of the consecutive pairs P⁺A ₁ ^? and P⁺F _x ^? in PSI using parameters derived entirely from independent experimental data. Excellent agreement with the experimental results is obtained. The spectra of P⁺F _x ^? in heliobacteria at X- and K-band are also simulated and it is shown that the observed polarization patterns can be reproduced assuming direct electron transfer from A₀ to F_x with a time constant ofτ = 600 ps.