Hyperfine coupling anisotropy

Paramagnetic species with g-factor and hyperfine coupling anisotropy were analysed by simulations at an early stage in frozen solutions of, for instance, copper enzymes [25]. In this section the powder spectra of two well-known species, the NO2 molecule and the isotope labelled COj anion radical are used to illustrate visual and simulation procedures for the analysis. The reader is referred to the classical textbook by Carrington and McLachlan [1] for an account of the electronic structures of these isoelectronic molecules (23 electron system) based on ESR data. 

Rao and Symons49 studied the formation of radicals in y-radiolysis of dilute solutions of dimethyl sulfoxide in fluorotrichloromethane. By ESR studies they found the radical cation (CH3)2SOt whose ESR spectrum show considerable g anisotropy and small methyl proton hyperfine coupling. 

The Florence NMRD program (8) (available at www.postgenomicnmr.net) has been developed to calculate the paramagnetic enhancement to the NMRD profiles due to contact and dipolar nuclear relaxation rate in the slow rotation limit (see Section V.B of Chapter 2). It includes the hyperfine coupling of any rhombicity between electron-spin and metal nuclear-spin, for any metal-nucleus spin quantum number, any electron-spin quantum number and any g tensor anisotropy. In case measurements are available at several temperatures, it includes the possibility to consider an Arrhenius relationship for the electron relaxation time, if the latter is field independent. 

In general, fluctuations in any electron Hamiltonian terms, due to Brownian motions, can induce relaxation. Fluctuations of anisotropic g, ZFS, or anisotropic A tensors may provide relaxation mechanisms. The g tensor is in fact introduced to describe the interaction energy between the magnetic field and the electron spin, in the presence of spin orbit coupling, which also causes static ZFS in S > 1/2 systems. The A tensor describes the hyperfine coupling of the unpaired electron(s) with the metal nuclear-spin. Stochastic fluctuations can arise from molecular reorientation (with correlation time Tji) and/or from molecular distortions, e.g., due to collisions (with correlation time t ) (18), the latter mechanism being usually dominant. The electron relaxation time is obtained (15) as a function of the squared anisotropies of the tensors and of the correlation time, with a field dependence due to the term x /(l + x ). 

The Orbach-type process as well as the collisional process (inducing either ZFS, g anisotropy or hyperfine coupling modulation) are mechanisms that can provide electron relaxation independently on reorientation. Electron relaxation is certainly not modulated by reorientational motions... 

Complexes in which the spin rbit coupling gives rise to anisotropy in the hyperfine coupling to the metal nucleus and in the g tensors. 

The electron relaxes through modulation of the A and g anisotropy. Typical examples are copper(II), oxovanadium(IV) and silver(II) aqua ions. The electronic relaxation times are relatively long (10 -10 ° s at room temperature) and the hyperfine coupling with the metal nuclear spin is usually present. No field dependence of the electron relaxation time is usually evident up to 100 MHz. 

In addition to g tensor anisotropy, EPR spectra are often strongly affected by hyperfine interactions between the nuclear spin I and the electron spin S. These interactions take the form T A S, where A is the hyperfine coupling tensor. Like the g tensor, the A tensor is a second-order third-rank tensor that expresses orientation dependence, in this case, of the hyperfine coupling. The A and g tensors need not be colinear in other words, A is not necessarily diagonal in the coordinate systems which diagonalize g. 

The angle dependence of the spin soliton in randomly oriented ladder poly-diactylene has also been investigated79 by pulsed HFEPR at 94 GHz. The shape of the 0-anisotropy-resolved nutation spectrum was discussed on the basis of the EPR transition moments and the differences between spin relaxation times. Reliable assignments of hyperfine couplings to the p-protons (P-H) of the alkyl side chains were achieved with the support of W-band ENDOR measurements. No significant orientational dependence of the 7i and Ti processes was found in terms of the isotropy of the p-H-hyperfine interaction. 

These workers (Adrian et al., 1962) also studied the spin resonance spectrum of DCO radicals and obtained remarkably narrow lines and shoulders which gave sufficient detail that the anisotropic hyperfine tensor could be deduced. This result then enabled them to extract the data tabulated from the spectrum of HCO. In particular, it is pointed out that as the g- and hyperfine-anisotropies have different principal axes, there has to be an extra term (Ayz) where the hyperfine tensor is expressed in terms of the axes of the gr-tensor. A careful analysis of all the data led these authors to the conclusion, based entirely upon experiment, that the large isotropic hyperfine coupling must be positive. 

We report an electron spin resonance (ESR) study on a C60 anion and a metal (M) encapsulated in fullerene (C ) (a metallofullerene M C ). The anisotropy components of the g-factor of Cg0 were determined accurately from the analysis of angular-dependent ESR spectra of single crystal Cg0 salt. The evaluation of the g-factor was performed according to the classification of symmetry of the C60 geometry. It was found out from the evaluation that the molecular structure of Cg0 should he distorted to lower symmetry, C2h or C,. The variety of ESR spectra of metallofullerenes of La C s was obtained in terms of a g-factor, a hyperfine coupling constant, and a line width. In the case of the isomer I of La C80 and the isomer II of La C84, an abnormally large line width was measured. The molecular structure with high symmetry would reflect on the specific spin dynamics. 

The spectra of polycrystalline samples are broad and represent the envelope of all the anisotropic couplings together with the g-anisotropy. Although in favourable cases it is possible to extract the principal values of the g- and hyperfine coupling tensors from such... 

Figure 11. The best fit has been found for 5 = 0.7 0.01 nuns, Aitg =—3.25 0.01 nuns, " =(2.11, 2.19, 2.00), "T/ nMn = (-45, 10, 19) T, tj = 0.74 0.1, D = 7.2 0.5 cm, and EID = 0.16 0.02. The zero-field splitting parameter D = 7.2 0.5 cm is comparable to that found for rabredoxin from Clostridium pasteurianum (D = 7.6cm Surprisingly, the rhombicity parameter E/D = 0.16 0.02 differs somewhat from that of rubre-doxin from C. pasteurianum (E/D = 0.28). The hyperfine coupling tensor has been determined to be A = (-14.5, -9.2, -27.5) T. The anisotropy of the hyperfine conpling tensor is cansed by spin-orbit confribntions to the internal magnetic hyperfine field.

Figure 8 Solution spectrum of V0(H20)5 showing eight lines (/ = 7/2). Line intensity variation arises from slow tumbling of the ion resulting in coupled g-factor and hyperfine splitting anisotropy effects...

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