Electron spin relaxation time

Schell S A J, Mehran F, Eaton G R, Eaton S S, Viehbeck A, O Toole T R and Brown C A 1992 Electron spin relaxation times of< , in solution Chem. Phys. Lett. 195 225-32... 

Electronic relaxation is a crucial and difficult issue in the analysis of proton relaxivity data. The difficulty resides, on the one hand, in the lack of a theory valid in all real conditions, and on the other hand in the technical problems of independent and direct determination of electronic relaxation parameters. Proton relaxivity is essentially influenced by the longitudinal electron spin relaxation time, Tle, of Gd111. This decay is too fast to be assessed by commonly available techniques, though very recently Tlc values have been directly measured.74 Nevertheless,... 

The symbol xso denotes the electron spin relaxation time at zero magnetic field, where Ti = and is another correlation time, associated with distortions of the paramagnetic complex caused by molecular collisions. 

As stated in Section II.B of Chapter 2, the actual correlation time for electron-nuclear dipole-dipole relaxation, is dominated by the fastest process among proton exchange, rotation, and electron spin relaxation. It follows that if electron relaxation is the fastest process, the proton correlation time Xc is given by electron-spin relaxation times Tie, and the field dependence of proton relaxation rates allows us to obtain the electron relaxation times and their field dependence, thus providing information on electron relaxation mechanisms. If motions faster than electron relaxation dominate Xc, it is only possible to set lower limits for the electron relaxation time, but we learn about some aspects on the dynamics of the system. In the remainder of this section we will deal with systems where electron relaxation determines the correlation time. 

In Eqs. (4)-(7) S is the electron spin quantum number, jh the proton nuclear magnetogyric ratio, g and p the electronic g factor and Bohr magneton, respectively. r//is the distance between the metal ion and the protons of the coordinated water molecules, (Oh and cos the proton and electron Larmor frequencies, respectively, and Xr is the reorientational correlation time. The longitudinal and transverse electron spin relaxation times, Tig and T2g, are frequency dependent according to Eqs. (6) and (7), and characterized by the correlation time of the modulation of the zero-field splitting (x ) and the mean-square zero-field-splitting energy (A. The limits and the approximations inherent to the equations above are discussed in detail in the previous two chapters. 

Another important parameter that influences the inner sphere relaxivity of the Gd(III)-based contrast agents is the electronic relaxation time. Both the longitudinal and transverse electron spin relaxation times contribute to the overall correlation times xa for the dipolar interaction and are usually interpreted in terms of a transient zero-field splitting (ZFS) interaction (22). The pertinent equations [Eqs. (6) and (7)] that describe the magnetic field dependence of 1/Tie and 1/T2e have been proposed by Bloembergen and Morgan and... 

In this case the planar complex is diamagnetic and possesses the usual narrow line, high-resolution diamagnetic spectrum. The tetrahedral complex in Td symmetry would possess a 3T ground state. In approximately tetrahedral nickel(II) complexes the orbital angular momentum is incompletely quenched the result is a very short electron spin relaxation time and an NMR spectrum with relatively narrow, paramagnetic shifted resonances. 

These spectra, taken at variable temperatures and a small polarizing applied magnetic field, show a temperature-dependent transition for spinach ferredoxin. As the temperature is lowered, the effects of an internal magnetic field on the Mossbauer spectra become more distinct until they result at around 30 °K, in a spectrum which is characteristic of the low temperature data of the plant-type ferredoxins (Fig. 11). We attribute this transition in the spectra to spin-lattice relaxation effects. This conclusion is preferred over a spin-spin mechanism as the transition was identical for both the lyophilized and 10 mM aqueous solution samples. Thus, the variable temperature data for reduced spinach ferredoxin indicate that the electron-spin relaxation time is around 10-7 seconds at 50 °K. The temperature at which this transition in the Mossbauer spectra is half-complete is estimated to be the following spinach ferredoxin, 50 K parsley ferredoxin, 60 °K adrenodoxin, putidaredoxin, Clostridium. and Axotobacter iron-sulfur proteins, 100 °K. 

The present paper will outline some of our recent EPR and NMR studies using Mn2+ as a paramagnetic probe of sheep kidney (Na+ + K+)-ATPase and Gd2+ as a paramagnetic probe of sarcoplasmic reticulum Ca2+-ATPase. Estimates of the relevant electron spin relaxation times and some features of the interaction between substrates and activators with the enzyme-metal complexes will be inferred from the EPR spectra and the accompanying nuclear relaxation data. 

A. Mn(II) EPR. The five unpaired 3d electrons and the relatively long electron spin relaxation time of the divalent manganese ion result in readily observable EPR spectra for Mn2+ solutions at room temperature. The Mn2+ (S = 5/2) ion exhibits six possible spin-energy levels when placed in an external magnetic field. These six levels correspond to the six values of the electron spin quantum number, Ms, which has the values 5/2, 3/2, 1/2, -1/2, -3/2 and -5/2. The manganese nucleus has a nuclear spin quantum number of 5/2, which splits each electronic fine structure transition into six components. Under these conditions the selection rules for allowed EPR transitions are AMS = + 1, Amj = 0 (where Ms and mj are the electron and nuclear spin quantum numbers) resulting in 30 allowed transitions. The spin Hamiltonian describing such a system is... 

The impact of solvent molecules and the resulting transient distortions of the Mn2+ complex determine the electron spin relaxation time of the system (26). Thus efficient solvent collisions at the bound Mn2+ will yield broad EPR lines, while narrow lines should result when Mn + is inaccessible to this rapid, fluctuating motion. 

These values are too short to be influenced significantly by Tr, the rotational correlation time of the enzyme-Gd3+ complex, or Tm, the mean residence time of water molecules in the first coordination sphere of the metal. Moreover, the minima in the plots of Tj p vs. Wj2 indicate that Tc must be dominated by Ts, the electron spin relaxation time. The Ts values for Gd + in this system are longer than most of those determined previously for Gd3+. The electron spin relaxation time for aqueous Gd3+ is (4-7) x 10 10s at 30 MHz (42), while values for Ts of (2-7) x 10 10s have been reported for complexes of Gd3+ with pyruvate kinase (37) and a value of 2.2 x 10- s has been found for a Gd 1"-lysozyme complex (36). Moreover, we have estimated a Tc of 6,8 x 10 10s for Gd + bound to parvalbumin.3 The long Gd3+ correlation times found in the present study are consistent with a poor accessibility of these Gd3+ sites to solvent water molecules. 

The electron spin relaxation time, Tg, is given by eq. 5 (42) where T is a correlation time which is related to the rate at... 

Such a decrease in the linewidth may result from a decrease in the Gd3+ coordination number upon formation of the macromolecular complex, which could result in greater symmetry and a lower zero-field splitting for the Gd3+ ion. This spectrum is independent of temperature between 4 and 25°C and is independent of the Gd3+/ ATPase ratio up to 2 Gd + ions/ATPase molecule. The peak-to-peak linewidth of 285 G sets a lower limit of 2,3 x 10"10s Qn the electron spin relaxation time of enzyme-bound Gd +t This symmetric, narrow EPR spectrum for the Gd3+-ATPase complex is compared in Figure 13B to that of Gd3+ bound to parvalbumin, a Ca2+-binding protein from carp. In this case, the spectrum is extremely broad and suggests a greatly distorted Gd3+ coordination geometry compared to the Ca2+-ATPase. 

Fig. 9. Electron spin relaxation times (x 1013) for Ln(III) hydrates in water. Note the big difference between the first and second half of the series...

In the case of rapid reactions of lanthanide complexes if Tie the electron spin relaxation time is short compared to the rotational reorientation time, rr, the electron—nuclear dipolar interaction will give rise to nuclear relaxation rates given by [27]... 

Mean life-times and electron spin relaxation times of R(fod)3 pinacolone adducts obtained from line-broadening data at 90 MHz. 

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