Paramagnetic proton nuclear spin relaxation theory of low-symmetry complexes for electron spin quantum number S = 52

A generalization of the modified Solomon-Bloembergen-Morgan (MSBM) equations has been derived in order to describe paramagnetic relaxation enhancement (PRE) of paramagnetic complexes characterized by both a transient (DeltaZFSt) and a static (DeltaZFSs) zero-field splitting (ZFS) interaction. The new theory includes the effects of static ZFS, hyperfine coupling, and angular dependence and is presented for the case of electron spin quantum number S = 52, for example, Mn(II) and Fe(III) complexes. The model gives the difference from MSBM theory in terms of a correction term delta which is given in closed analytical form. The theory may be important in analyzing the PRE of proton spin-lattice relaxation dispersion measurements (NMRD profiles) of low-symmetry aqua-metal complexes which are likely to be formed upon transition metal ions associated with charged molecular surfaces of biomacromolecules. The theory has been implemented with a computer program which calculates solvent water proton T1 NMRD profiles using both MSBM and the new theory.     

Determination of the electron relaxation rates in paramagnetic metal complexes: applicability of available NMR methods

Four different approaches for determining the electron relaxation rates in paramagnetic metallo-proteins are investigated, using a paramagnetic Ni2+ complex of a protein as an example. All four approaches rely on the determination of the longitudinal paramagnetic relaxation enhancements, R1p, of the 1H nuclei and the backbone 15N nuclei. Three of the methods utilize the field dependence of the R1p rates. It is found that the applicability of each of these methods depends on whether the fast-motion condition, omegaS2tau2<1, applies to the electron relaxation, omegaS being the Larmor frequency of the electron spin S and tau the correlation time of the electron relaxation. If the fast-motion condition is fulfilled, the electron relaxation rate can be obtained from the ratio of the R1p rates of one or more protons at two magnetic field strengths (method A). On the other hand, if the fast-motion condition does not apply, more elaborate methods must be used that, in general, require a determination of the R1p rates over a larger range of magnetic field strengths (method C). However, in the case of paramagnetic metal ions with relatively slow electron relaxation rates only two magnetic field strengths suffice, if the R1p rates of a hetero nucleus are included in the analysis (method B). In the fourth method (method D), the electron relaxation is estimated as a parameter in a structure calculation, using distance constraints derived from proton R1p rates at only one magnetic field strength. In general, only methods B and C give unambiguous electron relaxation rates.     

NMR paramagnetic relaxation enhancement: test of the controlling influence of zfs rhombicity for S = 1

Prior theoretical work has predicted that the NMR paramagnetic relaxation enhancement (NMR-PRE) produced by electron spin S = 1 ions is highly sensitive to orthorhombic terms in the static zero field splitting (zfs) tensor. Zfs orthorhombicity (which implies chemical inequivalence of the three principal directions of the zfs-principal axis system and is described by the zfs E-parameter) is predicted to suppress the NMR-PRE profoundly relative to the reference cylindrical zfs-limit situation. This expectation was tested experimentally by a comparison of the zfs-limit NMR-PRE produced by [Ni(II)(en)(3)](2+) (en = ethylenediamine), a trigonal complex which lacks zfs-rhombicity, with the zfs-limit NMR-PRE produced by two orthorhombic complexes, [Ni(II)(en)(2)(H(2)O)(2)](2+) and [Ni(II)(en)(H(2)O)(4)](2+). As predicted, the zfs-limit NMR-PRE produced by the orthorhombic complexes in the proton resonance of a dioxane probe species in the solvent was strongly suppressed (by factors of approximately 5 and 7, respectively) relative to the comparable measurement on the trigonal complex. The suppression of the NMR-PRE due to the orthorhombic zfs terms is counteracted by an applied Zeeman field, leading to a predicted rise in the NMR-PRE with increasing Zeeman field strength; this rise occurs when the Zeeman energy is comparable to the orthorhombic zfs splitting, 2E. This second prediction of theory was likewise confirmed: the expected rhombicity-induced magnetic field dependence in the NMR-PRE was observed for the orthorhombic complexes but not for the trigonal complex.     

Outer-sphere nuclear spin relaxation in paramagnetic systems: a low-field theory

A low-field theory for paramagnetic relaxation enhancement (PRE), appropriate for the outer-sphere relaxation, is presented for the electron spin quantum number S = 1, 3/2, 2, 5/2, 3 and 7/2. The theory is used to calculate the PRE at low magnetic field, as a function of the translational diffusion coefficient, for various values of the electron spin quantum number, for small and fairly large values of the static zero-field splitting (ZFS), and for a given set of parameters determining the electron spin relaxation. We have found earlier that the static ZFS has a profound influence on the electron spin relaxation; such effects are also evident in the present study. Comparisons are made with other existing models for the outer-sphere PRE, and significant differences are found for slowly diffusing systems with large ZFS. The theory is also used to obtain a novel interpretation of experimental data for an acetone solution of a Mn(III) complex.     

Low-field theory of nuclear spin relaxation in paramagnetic low-symmetry complexes for electron spin systems of S = 1, 3/2, 2, 5/2, 3 and 7/2

(Molecular Physics, 2000, 98, 1617)     

Application of commercially available fluorophores as triplet spin probes in EPR spectroscopy

ABSTRACT

In recent years, photoexcited molecular triplet states became increasingly popular in magnetic resonance, e.g. as spin probes to measure distances relative to other electron-paramagnetic species or as moieties that transfer light-generated electron–spin polarisation of the triplet state to surrounding magnetic nuclei. In this study, the triplet states of three commercially available dyes, Erythrosin B, Rose Bengal and Atto Thio 12, all typically utilised as fluorophores in optical spectroscopies and microscopies, are investigated in aqueous solutions by using transient absorption spectroscopy and transient electron paramagnetic resonance (EPR). From these methods, the triplet-state lifetimes as well as their zero-field splitting parameters, D and E, which reflect the electronic structures of the triplet state wavefunctions, were obtained. Atto Thio 12 exhibits much smaller D and E values as compared to Rose Bengal and Erythrosin B. On the basis of density functional theory calculations of the triplets’ energy splittings at zero magnetic field, these findings were rationalised. As a proof of concept for applications, the triplet-state properties of Atto Thio 12 bound to an aptamer were also determined and the results are discussed.     

Extension of Yafet's theory of spin relaxation to ferromagnets

By making use of Kramer's degeneracy of the electronic states in a nonmagnetic material, Yafet has derived an expression for the spin relaxation time T₁ due to scattering of electrons at phonons which involves the properties of electronic and phononic states and the matrix elements for the scattering. It is shown that an analogous expression for T₁ can be derived for ferromagnets (where Kramer's degeneracy does not hold) when taking into account the conservation of the total number of electrons. This expression can be used as a starting point for the ab initio calculation of T₁, and this quantity is required for an interpretation of the ultrafast demagnetization of ferromagnets after excitation with a femtosecond laser pulse.     

Molecular dynamics and interactions of human ceruloplasmin: A spin labelling study

Summary Ceruloplasmin, a paramagnetic copper-containing protein, has been spin labelled with different nitroxide spin labels in order to study its molecular dynamics and to gain further information about its interaction with other biosystems. Spin labelling with a maleimide derivative resulted in an electron spin resonance spectrum which was a superposition of two different absorptions due to paramagnetic species in different microenvironments. The first one, a three-line isotropic spectrum, is due to a fast-moving spin label (with a rotational correlation time τ_c≃10^-9s); the second one is an anisotropic, asymmetrical signal arising from an immobilized spin in a slow-motion domain (τ_c=10^-7). The assumption of a spherical shape for the molecule provided, through the Stokes-Einstein relation, an estimate of the molecular-radius value consistent with smallangle neutron scattering measurements. The interaction with other biosystems, as deduced from the protein molecule dynamics, is discussed.

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Riassunto La ceruloplasmina, una proteina umana contenente ioni Cu⁺⁺ paramagnetici, è stata marcata con differenti spin labels per studiarne la dinamica molecolare e la sua interazione con altri biosistemi. Il marcaggio mediante spin labels di tipo maleimidico ha portato ad uno spettro di risonanza elettronica di spin composto da due differenti gruppi di righe dovuti a specie paramagnetiche in differenti microambienti. Il primo segnale è costituito da un tripletto isotropico dovuto ad uno spin label in rapida rotazione (τ_c≃10^-9s), mentre il secondo è alquanto asimmetrico (anisotropico) e deriva da uno spin label ruotante in un dominio temporale piuttosto lento (τ_c=10^-7). L'assunzione di una forma sferica per la proteina in soluzione ha portato, attraverso la relazione di Stokes-Einstein, ad una determinazione del raggio molecolare in buon accordo con il risultato di misure di diffrazione a basso angolo di neutroni. Si discute inoltre l'interazione con altri biosistemi come desunta dalla dinamica molecolare della proteina.

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Резюме Церулоплазмин, человеческий белок, содержащий парамагнитные ионы меди Cu⁺⁺, помечается с помощью различных спиновых меток для исследования молекулярной динамики и взаимодействий с другими биосистемами. Спиновая метка в случае производной меламида приводит к спектру электронного спинового резонанса, который представляет суперпозицию двух различных групп линий, обусловленных парамагнитными разновидностями при различных микро-окружениях. Первый спектр, изотропный триплет линий, обусловлен быстро движущейся спиновой меткой (с временем ротационной корреляции (τ_c≃10^-9 c); второй спектр представляет анизотропный асимметричный сигнал, возникающий от медленно движущейся спиновой метки (τ_c=10^-7 c). Предположение сферической формы бекла в растворе, которое следует из соотношения Стокса-Эйнштейна, позволяет оценить радиус молекулы, величина которого хорошо согласуется с измерениями малоуг лового рассеяния нейтронов. Обсуждается взаимодействие с другими биосистемами на основе анализа динамики молекул белка.

     

Effect of oxygen diffusion on the relaxation parameters of paramagnetic centers on the surface of alumina

The present article is concerned with theoretical consideration of the effect of oxygen diffusion on the relaxation parameters of paramagnetic centers (PC) located on a surface. Proceeding from a model of dipole-dipole interaction between paramagnetic molecules of O₂ and PC that is modulated by translational diffusion motion of O₂ molecules in the volume and on surface of an adsorbent and in its pores, we give an explanation for the observed dependence of the intensity of the EPR signal on the pressure of O₂. In the present case, diffusion in the volume is the decisive factor. We also managed to explain the presence of an SHF field power threshold for the indicated phenomenon to be observed. In the calculations we used correlation functions obtained earlier for diffusion in a volume. Institute of Physicoorganic Chemistry, National Academy of Sciences of Belarus, 13, Surganov St., Minsk, 220072, Belarus. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 65, No. 2, pp. 230–235, March–April, 1998.     

Nuclear spin relaxation in solution of paramagnetic complexes with large transient zero-field splitting

A theory for paramagnetic relaxation enhancement (PRE) in systems with S> 1 at low magnetic field is developed for the case when the fluctuations of zero-field splitting (ZFS) in the molecular frame are larger than the averaged ZFS. The validity limits of the new theory are discussed, and its performance is evaluated by comparisons with the general slow-motion approach. The relevance of the new approach for the proton PRE in aqueous solution of Ni(II) is discussed.     

The theory of nuclear spin diffusion due to paramagnetic impurities in a diamagnetic crystal

The diffusion of nuclear magnetization inside a diffusion barrier, due to modulation of the fluctuation spin operator of a magnetic ion by the interaction between nuclei, is treated to third order of perturbation theory. Cross-relaxation transitions of two types are being modulated. These are the transitions in which a pair of nuclei is mutually reoriented either due to a dipole-dipole interaction between them or by the coupling of each nucleus to the electron spin. The relative effectiveness of these processes depends on the experimental conditions.Translated from Izvestiya Vysskikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 76–80, November, 1975.The author is grateful to B. I. Kochelaev for discussing the results of this work.     

Determination of T1-spin-lattice relaxation time in a two-level system by continuous wave multiquantum electron paramagnetic resonance spectroscopy in a presence of tetrachromatic microwave irradiation

Applicability of continuous wave multiquantum EPR methods to study relaxation times at X-band is examined. Multiquantum transitions excited in a two-level system by tetrachromatic irradiation are used for these studies. The Bloch equation model is applied to simulate lineshapes of the three quantum transitions as a function of frequency difference between exciting fields. The dependence of multiquantum transition signals on relaxation times and microwave amplitude is shown. On this basis a method of deducing relaxation times from these signals is formulated. The case of a homogeneously and inhomogeneously broadened resonance line is considered. Two experimental methods are used to verify the proposed hypothesis: the X-band continuous wave multiquantum EPR with four frequencies microwave field and saturation recovery EPR. The values of T₁ obtained from CW MQ EPR and SR EPR are compared.     

Generalized Elliott-Yafet theory of electron spin relaxation in metals: origin of the anomalous electron spin lifetime in MgB2

The temperature dependence of the electron-spin relaxation time in MgB2 is anomalous as it does not follow the resistivity above 150 K; it has a maximum around 400 K and decreases for higher temperatures. This violates the well established Elliot-Yafet theory of spin relaxation in metals. The anomaly occurs when the quasiparticle scattering rate (in energy units) is comparable to the energy difference between the conduction and a neighboring bands. The anomalous behavior is related to the unique band structure of MgB2 and the large electron-phonon coupling. The saturating spin relaxation is the spin transport analogue of the Ioffe-Regel criterion of electron transport.     

InAs量子点中自旋-轨道相互作用下电子自旋弛豫的参量特征

本文在处理InAs单电子量子点哈密顿模型时,将自旋-轨道(SO)相互作用作为微扰项,计算在Fock-Darwin本征函数下SO相互作用的矩阵元,利用其对能级和波函数的二阶修正,并且考虑新的能级对g因子和有效质量m^*的影响,计算得到在声子协助下电子的自旋弛豫率Γ的表达式.给出了InAs量子点中声子协助的电子自旋弛豫率Γ对于限制势频率ω₀、温度T、纵向高度z_{0关键词： 自旋弛豫率 自旋-轨道(SO)相互作用 InAs量子点 Fock-Darwin本征函数}     

Mechanical detection of nuclear spin relaxation in a micron-size crystal

A room temperature nuclear magnetic resonance force microscope (MRFM), fitted in a 1 tesla electromagnet, has been used to measure the nuclear spin relaxation of ¹H in a micron-size (70 ng) crystal of ammonium sulfate. NMR sequences, combining both pulsed and continuous wave radio-frequency fields, have allowed us to measure mechanically T₂ and T₁, the transverse and longitudinal spin relaxation times. Because two spin species with different T₁ values are measured in our 7 μm thick crystal, magnetic resonance imaging of their spatial distribution inside the sample section have been performed. To understand quantitatively the measured signal, we carefully study the influence of spin-lattice relaxation and non-adiabaticity of the continuous-wave sequence on the intensity and time dependence of the detected signal. Received 23 February 2000     

Probing interaction of paramagnetic electron with conduction electrons in high Tc superconductor LaSrCuO by (μ-O) spin relaxation

The paramagnetic (μ^-O) state formed at the oxygen site in high T_c LaSrCuO was used to probe an interaction between the localized moment of the paramagnetic electron and the conduction electrons via zero field μ^- spin relaxation. The enhanced relaxation rates consistently observed in the superconducting state of various Sr concentrations are explained as an effect of spin‐pairing in the high T_c supercurrent. This revised version was published online in August 2006 with corrections to the Cover Date.     

An electron paramagnetic resonance study of conformational substate distribution in high spin heme-proteins

The electron paramagnetic resonance spectra of high spin ferric horse myoglobin and human hemoglobin have been analyzed by computer simulation in terms of a distribution of the metal ion crystal field energies Δ₁ and Δ₂. The widths of these distributions have been put into relation 0 to the distribution of the conformational substates which may be sampled by the biomolecules during their physiological activity and become eventually arrested at low temperature. These distributions are found to be dependent upon both the solvent used and the cooling history to which the samples were submitted. The results are discussed in connection with the physical analogies displayed by these biomolecules and the glassy systems in general.