Non-Markovian Dynamics of a Localized Electron Spin Due to the Hyperfine Interaction

We review our theoretical work on the dynamics of a localized electron spin interacting with an environment of nuclear spins. Our perturbative calculation is valid for arbitrary polarization p of the nuclear spin system and arbitrary nuclear spin I in a sufficiently large magnetic field. In general, the electron spin shows rich dynamics, described by a sum of contributions with exponential decay, nonexponential decay, and undamped oscillations. We have found an abrupt crossover in the long-time spin dynamics at a critical shape and dimensionality of the electron envelope wave function. We conclude with a discussion of our proposed scheme to measure the relevant dynamics using a standard spin–echo technique.     

Manipulating Einstein-Podolsky-Rosen Steering by Quantum-Jump-Based Feedback in Dissipative Environment

In this paper, we investigate the behaviors of Einstein-Podolsky-Rosen (EPR) steering manipulated via quantum-jump-based feedback (QJBF) in noisy environment. We firstly derived the master equation that governs the system evolution. It is shown that the QJBF with an appropriate feedback parameter can preserve and generate the EPR steering destroyed by the dissipative environment. EPR steering quickly decays as dissipative time increases. For feedback parameter \(\lambda =\frac {\pi }{2}\), EPR steering oscillatorily develops to zero with evolution time, while entanglement decreases monotonously with decoherent time, so QJBF with feedback parameter \(\lambda =\frac {\pi }{2}\) can effectively protect EPR steering in some certain time.     

Evaluation of spin labels for in-cell EPR by analysis of nitroxide reduction in cell extract of Xenopus laevis oocytes

Spin-label electron paramagnetic resonance (SL-EPR) spectroscopy has become a powerful and useful tool for studying structure and dynamics of biomacromolecules. However, utilizing these methods at physiological temperatures for in-cell studies is hampered by reduction of the nitroxide spin labels and thus short half-lives in the cellular environment. Consequently, reduction kinetics of two structurally different nitroxides was investigated in cell extracts of Xenopus laevis oocytes using rapid-scan cw-experiments at X-band. The five member heterocyclic ring nitroxide PCA (3-carboxy-2,2,5,5-tetramethylpyrrolidinyl-1-oxy) under investigation features much higher stability against intracellular reduction than the six member ring analog TOAC (2,2,6,6-tetramethylpiperidine-N-oxyl-4-amino-4-carboxilic acid) and is therefore a suitable spin label type for in-cell EPR. The kinetic data can be described according to the Michaelis–Menten model and thus suggest an enzymatic or enzyme-mediated reduction process.     

Dynamic susceptibility of a spin ice near the critical point

We consider spin ice magnets (primarily, Dy₂Ti₂O₇ in the vicinity of their critical point on the (H, T) plane. We find that the longitudinal susceptibility diverges at the critical point, leading to the behavior qualitatively similar to the one which would result from non-zero conductance of magnetic charges. We show that dynamics of critical fluctuations belongs to the universality class of easy-axis ferroelectric and calculate logarithmic corrections (within two-loop approximation) to the mean-field critical behavior.     

An SCMO calculation of the spin densities in the methyl substituted benzene negative ions

Most of the many attempts to explain ‘hyperconjugation’ invoke an explicit delocalization of the electrons of the methyl group. This work is part of an attempt to calculate these effects by a method which requires no such delocalization. A calculation of the spin densities in the methyl substituted benzene negative ions is reported here.

In this work the methyl substituent is considered to exert a purely inductive effect which manifests itself in a change in the scale of the orbital exponent of the 2pπ atomic orbital at the carbon to which it is attached. (This is in contrast to previous ‘inductive’ treatments in the HMO method which alter only the α of the substituted carbon.) This change is evaluated by considering the change in the ionization potential of the methyl radical on successive methyl substitution. (There is no reference to any EPR data for the calibration of the parameters.)

A comparison with the EPR results for the toluene, m-xylene and p-xylene negative ions reveals excellent agreement for these compounds.

An open-shell SCMO procedure based on that of Roothaan is used in the calculations.     

Cavity correlation and bridge functions at high density and near the critical point: a test of second-order Percus–Yevick theory

ABSTRACT

Cavity correlation functions, pair correlation functions, and bridge functions for the Lennard-Jones fluid are calculated from first Percus–Yevick (PY) theory and second-order Percus– Yevick (PY2) theory, molecular dynamics, and grand canonical Monte Carlo techniques. We find that the PY2 theory is significantly more accurate than the PY theory, especially at high density and near the critical point. The pair correlation function near the critical point has the expected slowly decaying long-range behaviour. However, we do not observe any long-range behaviour in the bridge function for the state points near the critical point we have simulated. However, we do note that the bridge function, which is usually negative near r = 0, becomes positive as r → 0. This behaviour is seen for the bridge functions computed from both PY2 and molecular dynamics, but not from PY.     

Theory of chemical bonds in metalloenzymes XX: magneto-structural correlations in the CaMn4O5 cluster in oxygen-evolving complex of photosystem II

ABSTRACT

Magneto-structural correlations in oxygen-evolving complex (OEC) of photosystem II (PSII) have been elucidated on the basis of theoretical and computational results in combination with available electron paramagnetic resonance (EPR) experimental results, and extended x-ray absorption fine structure (EXAFS) and x-ray diffraction (XRD) results. To this end, the computational methods based on broken-symmetry (BS) UB3LYP solutions have been developed to elucidate magnetic interactions in the active manganese catalyst for water oxidation by sunlight. The effective exchange interactions J for the CaMn(III)Mn(IV)₃O₅(H₂O)₃Y(Y = H₂O or OH^?) cluster (1) model of OEC of PSII have been calculated by the generalised approximate spin projection (GAP) method that eliminates the spin contamination errors of the BS UB3LYP solution. Full geometry optimisations followed by the zero-point energy (ZPE) correction have been performed for all the spin configurations of 1 to improve the J values that are compared with accumulated EPR in the S₂ state of Kok cycle and magnetic susceptibility results of Christou model complex Ca₂Mn(IV)₃O₄ (2). Using the calculated J values, exact diagonalisation of the spin Hamiltonian matrix has been carried out to obtain excitation energies and spin densities of the ground and lower excited states of 1. The calculated excitation energies are consistent with the available experimental results. The calculated spin densities (projection factors) are also compatible with those of the EPR results. The calculated spin densities have been used to calculate the isotropic hyperfine (A_iso) constants of ⁵⁵Mn ions revealed by the EPR experiments. Implications of the computational results are discussed in relation to the structural symmetry breaking (SSB) in the S₁, S₂ and S₃ states, spin crossover phenomenon induced by the near-infrared excitation and the right- and left-handed scenarios for the O–O bond formation for water oxidation.     

Spin-labeled photosynthetic reaction centers fromRhodobacter sphaeroides studied by electron paramagnetic resonance spectroscopy and molecular dynamics simulations

A new strategy has been applied that combines molecular dynamics (MD) simulations and electron paramagnetic resonance (EPR) spectroscopy to study the structure and conformational dynamics of the spin-labeled photosynthetic reaction center (RC) ofRhodobacter sphaeroides. This protein serves here as a model system to demonstrate the applicability of this new methodology. The RC contains five native cysteines and EPR experiments show that only one cysteine, located on the H subunit, is accessible for spin labeling. The EPR spectra calculated from MD simulation trajectories of spin labels bound to the native cysteines C156 and C234 in subunit H reveal that only the spin label side chain at position 156 provides a spectrum which agrees with the experimental EPR spectrum.     

Light induced radical pair intermediates in photosynthetic reaction centres in contact with an observer spin label: spin dynamics and effects on transient EPR spectra

A novel strategy is discussed using site directed spin labelling to study the electron transfer process in photosynthetic reaction centres. An algorithm is presented for numerical simulations of the time resolved EPR spectra of radical pair states in the presence of an observer spin label. This algorithm accounts for spin dynamics, charge recombination and relaxation processes. It is shown that satisfactory agreement between experimental and simulated EPR spectra of the first stabilized radical pair state in photosystem I is achieved for various microwave frequencies. Transient EPR spectra for the radical pair state P^?+Q^?- in photosystem I were simulated for various distances and positions of the observer spin label with respect to the acceptor quinone molecule. It is shown that distances up to more than 20 Å give rise to observable changes in the transient EPR spectra. Both the additional spin-spin coupling between the quinone radical and the label and the polarization transfer processes contribute to the changes. Furthermore, the shape and intensity of the EPR spectrum of the spin label is altered by the coupling with the radical pair spins for distances up to 25 Å. Experiments on site directed spin labelled photosystem I are thus expected to provide valuable information on the dynamics of electron transfer in photosystem I.     

A novel approach to the simulation of nitroxide spin label EPR spectra from a single truncated dynamical trajectory

A simple effective method for calculation of EPR spectra from a single truncated dynamical trajectory of spin probe orientations is reported. It is shown that an accurate simulation can be achieved from the small initial fraction of a dynamical trajectory until the point when the autocorrelation function of re-orientational motion of spin label has relaxed. This substantially reduces the amount of time for spectra simulation compared to previous approaches, which require multiple full length trajectories (normally of several microseconds) to achieve the desired resolution of EPR spectra. Our method is applicable to trajectories generated from both Brownian dynamics and molecular dynamics (MD) calculations. Simulations of EPR spectra from Brownian dynamical trajectories under a variety of motional conditions including bi-modal dynamics with different hopping rates between the modes are compared to those performed by conventional method. Since the relatively short timescales of spin label motions are realistically accessible by modern MD computational methods, our approach, for the first time, opens the prospect of the simulation of EPR spectra entirely from MD trajectories of real proteins structures.     

Manifestation of the Hanle effect in submillimeter EPR spectroscopy of thulium impurity ions in synthetic forsterite

A signal related to the spin level crossing in a zero magnetic field—the Hanle effect—has been registered for the first time in the EPR spectrum. It has been shown that, in the general case, the shape of the signal is determined by two qualitatively different mechanisms: (i) the interference of unsteady-state contributions to the dynamics of atomic coherences (electric or magnetic quantum transition moments with certain phases) with close frequencies (“beats at a zero frequency”) and (ii) the summation of resonant signals determined by the steady-state dynamics of the same atomic coherences. The relaxation time of spin coherences has been determined for the EPR transition of Tm³⁺ ions in synthetic forsterite.     

The Temperature Dependence of Nitroxide Spin–Label Interaction Parameters: a High-Field EPR Study of Intramolecular Motional Contributions

High-field W-band electron paramagnetic resonance (EPR) spectroscopy was utilized to study the temperature dependence of the magnetic interaction parameters (g-, hyperfine-, quadrupole tensors) of two types of doublet-state nitroxide spin probes in glass-forming ortho-terphenyl solution: a five-membered ring system of pyrroline type (model for the commonly used methane thiosulfonate spin label) and a six-membered ring system of piperidine type (model for the commonly used TOAC spin label). The analysis of the g- and hyperfine tensors in terms of their isotropic and anisotropic parts reveals at least two mechanisms of motion that are responsible for the temperature dependence of the interaction parameters. The first mechanism is attributed to the overall small-angle motion of the nitroxide molecule in the glassy matrix; it leads to an averaging of the anisotropies of the EPR parameters. The second mechanism originates in an intramolecular out-of-plane motion of oxygen in the nitroxide group. This type of motion is evidenced by comparing the experimental findings for the spin-interaction parameters with the results of density functional theory calculations. The harmonic oxygen out-of-plane vibrations result in a variation of both the isotropic and anisotropic parts of the g- and hyperfine tensors. In contrast, the quadrupole tensor is not influenced by this vibration mechanism in the temperature range under study (90–240 K). Consequences of the applicability of such typical nitroxide radicals for probing details of their protein environment and for studying librational dynamics in frozen solutions are discussed.     

Effective field and the Bloch-Siegert shift at bichromatic excitation of multiphoton EPR

The dynamics of multiphoton transitions in a two-level spin system excited by transverse microwave and longitudinal RF fields with the frequencies ω_mw and ω_rf, respectively, is analyzed. The effective time-independent Hamiltonian describing the “dressed” spin states of the “spin + bichromatic field” system is obtained by using the Krylov-Bogoliubov-Mitropolsky averaging method. The direct detection of the time behavior of the spin system by the method of nonstationary nutations makes it possible to identify the multiphoton transitions for resonances ω₀ = ω_mw + rω_rf (ω₀ is the central frequency of the EPR line, r = 1, 2), to measure the amplitudes of the effective fields of these transitions, and to determine the features generated by the inhomogeneous broadening of the EPR line. It is shown that the Bloch-Siegert shifts for multiphoton resonances at the inhomogeneous broadening of spectral lines reduce only the nutation amplitude but do not change their frequencies.     

Features of spin exchange in nitroxide biradicals in the ionic liquid bmimPF<Subscript>6</Subscript>

The intramolecular electron spin exchange has been studied by electron paramagnetic resonance (EPR) spectroscopy in the ionic liquid 1-butyl-3-methylimidazolium hexafluorophosphate (bmimPF₆) for various nitroxide biradicals as a function of temperature and the nature of the connecting bridge between two >NO^· centers. Temperature variations of the isotropic nitrogen hyperfine splitting constant a and exchange integral values |J/a| were measured from EPR spectra and analyzed. Thermodynamic parameters of the conformational rearrangements were obtained. The spin exchange in rigid and flexible biradicals dissolved in the ionic liquid bmimPF₆ was compared with that in toluene solutions. Interesting features of the spin exchange in biradicals in ionic liquid were observed and explained as a result of the specific intramolecular conformational transitions. The first example of a rather rigid biradical molecule becoming flexible under the influence of an ionic liquid is reported.     

EPR investigation of nanosized La0.67Ca0.33MnO3−δ manganites

We report an electron paramagnetic resonance (EPR) investigation of the spin dynamics in the paramagnetic regime of nanosized La_0.67Ca_0.33MnO_3?δ manganites. The temperature dependences of the EPR line width and integral intensity have been analyzed in terms of the bottlenecked spin relaxation and small polaron hopping scenarios. The exchange coupling integral between Mn³⁺ and Mn⁴⁺ ions and the polaron activation energy decrease with the reduction of grain size. A discussion is given concerning the factors which could explain the observed changes.     

EPR of photo-excited triplet states: A personal account

A sketch is presented of the path that has led from Zavoisky’s pioneering experiments to modern investigations by electron paramagnetic resonance (EPR) of the phosphorescent (S = 1) triplet state of polyatomic molecules or ions. The group-theoretical method first introduced by Wigner in his analysis of the multiplets of atomic spectroscopy, likewise provides a key for understanding the zero-field splitting and selection rules for radiative decay of the phosphorescent triplet state. Examples to illustrate the progress made through EPR experiments are selected from three fields. (i) Conformational instability on excitation. Both the zero-field splitting and the electron spin density distribution provide unique fingerprints of a triplet state’s geometry — structural information of a kind that is nonexistent for singlet states! Illustrations are provided by benzene C₆H₆ and fullerene C₆₀. (ii) The optical pumping cycle. The spin selectivity of singlet-to-triplet intersystem crossing and radiative decay of the individual spin components of the triplet state is discussed. In practice this selectivity is put to advantage by performing EPR on triplet states in zero-field by means of optical detection. In turn, such experiments have led to a detailed insight into the spin-orbit coupling mechanisms responsible for the spin selectivity of the above processes. The high sensitivity attainable with optical detection has recently culminated in EPR experiments on single molecules. (iii) Quantum interference. In a triplet state of low symmetry two of the spin sublevels may decay to the ground state by the emission of photons of a common polarization (i.e., out of plane for an aromatic hydrocarbon). In such a situation quantum interference between the two decay channels can be induced by an appropriate preparation of the excited state. An example is shown where flash-excitation in the singlet manifold followed by rapid intersystem crossing causes theS = 1 spin angular momentum to be created in a spin state which is not an eigenstate of the zero-field splitting tensor. This nonstationary character of the initial triplet state, which reflects the spin-orbit coupling pathway, is observed through the detection of a spontaneous microwave signal following the 25 ps laser flash.     

A hierarchically constrained kinetic Ising model

A concrete model for hierarchically constrained dynamics in the sense proposed by Palmer et al. (Phys. Rev. Lett.53, 958 (1984)) is presented. The model is a kinetic Ising chain with an asymmetric kinetic constraint, allowing a spin to flip only if its neighbour to the right is in the up spin state. The spin autocorrelation function is obtained by numerically exact calculation for finite chain length up toL=9 and by Monte Carlo simulation for effectively infinite chain length. The Kohlrausch-Williams-Watts formula is found to fit the results only with limited accuracy, and within limited time intervals. We also performed an analytical calculation using an effective-medium approximation. The approximation leads to a spurious blocking transition at a critical up spin concentrationc=0.5.     

A μSR Study of Er Spin Dynamics in (Y1−x Er x )Ni2B2C Superconductors

Zero field μSR has been used to probe rare earth spin dynamics in the magnetic superconductors, Y_1−x Er _x Ni₂B₂C. The muon spin relaxation function is stretched exponential, exp (−(λt)^β), in form, as usually found for spin glass systems above the glass temperature. However, the Y_1−x Er _x Ni₂B₂C compounds show no evidence of coexisting superconducting and static spin glass ground states even at concentrations below the critical value (x=0.6) for long range antiferromagnetic order. The temperature dependence of both the muon spin relaxation rate λ and the exponent β suggests that Er spin dynamics change significantly at the superconducting transition temperature. This revised version was published online in September 2006 with corrections to the Cover Date.