Principal Magnetic Parameters

Within the SH formalism the MPs (gx, gy, gz, D, E, /tip) are thought of as physical constants associated with each particular system. The electronic-magnetic theory beyond the SH formalism reveals that there are only the electronic-structure parameters (like B, C, ) associated with the electron configuration and the CF parameters [like F2(L) and F4(I)] for each ligand. A more realistic approach brings the orbital reduction factors k (which must be anisotropic) and in a particular case of the degenerate electronic states also the force-field and vibronic coupling parameters (like Kee, Xe, Xee, and eventually Ktt, Xt, Xtt, or even more parameters). 

The electronic structure parameters (e.g., B, C, ) can be found among many sources [48,51], and they are retabulated in Appendix A. The interelectron repulsion (characterized by the Racah parameters) is solely reduced in a complex relative to the free ion for two reasons  

The lower effective charge on the metal center causes an orbital expansion manifesting itself in a reduced interelectron repulsion. 

The delocalization of the electrons into ligand orbitals lowers the interelectron repulsion. 

The nephelaxeutix (cloud-expanding) effect is usually accounted for by the empirical formula 

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To compare measured magnetic coupling constants with values obtained from theoretical calculations, the signs of the magnetic parameters should be known. In the following, different approaches for the determination of absolute and relative signs of the principal values of hf and quadrupole tensors will be discussed. 

The magnetic parameters have been interpreted using EHT-SCCC calculations189, 192. If C2h symmetry is assumed, the g tensor and the anisotropic part of the hfs tensors ACu and AN could satisfactorily be explained. According to these calculations the largest principal axis of the nitrogen hfs tensor lies in the complex plane and deviates 27° from the Cu-N direction (compared with 17° from ENDOR data)6. 

The ligand field was parameterised in terms of ea only, and values of this parameter, together with the spin-orbit coupling constant X, the orbital reduction factor k and the Racah parameter B were obtained by fitting the d-d spectra, zero-field splittings, principal magnetic susceptibilities and e.s.r. g-values. 

Identification of paramagnetic metal ions is straightforward because each metal ion has sufficiently distinct ESR parameters [5-7,18,195,196]. The principal magnetic axes, defined by dimensionless g values, the interaction of the electron spin with the nuclear spin, defined by the hyperfine coupling constants, and spin-lattice relaxation times characterize each paramagnetic ion. 

On the basis of the above relationships one can conclude that the three principal components of the /1-tensor can be used to express the complete set of magnetic parameters that describes zero-field splitting in mononuclear complexes, i.e. gxx, gyy, gzz, D and E. In addition, they define the temperature-independent paramagnetic term x - Therefore it is possible to reconstruct the components of the /1-tensor having the set of magnetic parameters determined from an appropriate fit of experimental data. However, an opposite procedure is possible to consider the components of the /1-tensor as the principal quantities which determine the ZFS parameters. Then one can consider Axx, Ayy, Azz and X as a set of free parameters subjected to optimisation. In performing such a procedure, the following optimisation scheme can be followed. 

HF ESR has been utilized to advantage for increasing the resolution in terms of the g tensor components Figure 4 presents a comparison of ESR spectra of a nitroxide radical at 9 GHz (top) and at 94.4 GHz (bottom) (11). Major advantages of HF ESR are improved accuracy in the determination of the principal values of the g tensor, the ability to measure splittings in the x and y directions that are not resolved at X band, and increased ability to resolve species with different magnetic parameters. 

Structural Studies Based on -Factor Measurements. - Accurate measurements of spin-label magnetic parameters provide important data about the structure of nitroxide radicals. These data are also required for the analysis of the molecular dynamics of spin probes. The high resolution of HF EPR makes possible accurate determination of the principal axis components of the -matrix and y4-tensor from powder pattern spectra eliminating the need to prepare and study single crystals. 

Fig. 88. Fe(pc), single crystal. Temperature dependence of principal magnetic moments. The experimental values of p ii and p j, are shown by full and open circles, respectively. The solid curves are the theoretical plots of principal moments using the parameters g, =gj =2.74, D=64 cm" (for details see reference), the broken curves represent theoretical plots using the parameters deduced by Dale et al. [70B9].

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