Magnetic parameters

Transition-metal (dn) complexes with open shells belong to the class of paramagnetic materials their magnetic susceptibility is positive (the sample is attracted to the magnetic field) and is temperature dependent. At high enough temperatures and in small fields, the molar magnetic susceptibility normally obeys the Curie law 

The Curie constant C can be considered a magnetic parameter (MP) associated with the sample. Theory, however, tells us that such a phenomenological parameter could be made of fundamental physical constants and the magnetogyric-ratio parameter g in the following way  

The Curie paramagnets [e.g., octahedral Fe(III) complexes] are rather rare, and the temperature dependence of the magnetic susceptibility requires more parameters, depending on the actual spacing of the low-lying energy levels. Let us enumerate the MPs associated with the SH formalism  

Under the SH formalism it is understood that the energy levels are reconstructed by considering only the formal spin kets S,Ms) that are under the action of the SH involving the spin-spin interaction and the spin-Zeeman term 

Zeeman term appropriate to the Curie paramagnet.) The MPs gx, gy, gz, D, and E are understood as constants that characterize the sample under study. 

Normally only some of them are considered in the energy expression up to the second order of the Taylor expansion [1-4]. 

Let us consider a simple case where the energy depends upon two parameters, E = f(B, fig). The wave function P(5, jle) of the system is expanded around the zero-field values of B and jle 

The last expression contains 6x3 terms but these can be collected according 

Each magnetic parameter can be expressed as an appropriate second derivative of the energy, i.e. 

The derivatives are evaluated at the point B = p,M = p,N = fle = 0. These reduced magnetic parameters may require a transformation when compared with experimental data (unit homogeneity). Note that 1c is a symmetric tensor whereas aN is not. 

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The compounds formed were studied by esr spectroscopy, with the magnetic parameters being used to determine the geometries. Mn02 is linear, whereas MnOa is trigonal planar (Dsh), and Mn04 is distorted tetrahedral with Csv symmetry. 

Fig. 6. The logarithm of the selectivity coefficient of the exchange in the wall is plotted as a function of a magnetic parameter of copper adsorbed on high affinity sites.

These high affinity sites determine most of the selectivity of the ion exchange. This is deduced from Fig. 6 in which the selectivity of the whole ion exchange (In Kn) is plotted as a function of g n, a magnetic parameter of cupric ions adsorbed on high affinity sites. This parameter is particularly sensitive to the degree of covalence of the bound between copper and its... 

Blinc R (2007) Order and Disorder in Perovskites and Relaxor Ferroelectrics. 124 51-67 Boca R (2005) Magnetic Parameters and Magnetic Functions in Mononuclear Complexes Beyond the Spin-Hamiltonian Formalism 117 1-268 Bohrer D, see Schetinger MRC (2003) 104 99-138 Bonnet S, see Baranoff E (2007) 123 41-78... 

In the case of paramagnetic complexes their experimental magnetic parameters are determined by computer simulation of the powder spectra [59], Together with the corresponding calculated values, obtained using a relativistic spin-unrestricted ZORA approach, they all are collected in Table 2.8. 

Table 2.8. Calculated and experimental magnetic parameters for selected nitrosyl surface complexes hosted in the ZSM-5 framework or silica surface...

Table 13 Structural and magnetic parameters for dimers with the [Ni(/r-l,3-N3)Ni] unit Ni—N bond distances (A), Ni—N—N and r angles (°), J incm 1.a...

Table 16 Structural and magnetic parameters for ID traw5-[Ni(/i-l,3-N3)Ni] systems angles Ni—N—N and...

Table 20 Structural and magnetic parameters for F-AF ID systems with both /i-l,3-N3 and /i-l,l-N3 bridges.a... 

ESR studies of methylzinc radicals in a solid neon matrix found the expected 1 3 3 1 quartet for the lzCH3Zn radicals.19 The spectra of the isotopomers 13CH3Zn, 13CD3Zn, 12CH367Zn, and 12CH367Zn were also recorded, and 12CH367Zn (7=5/2) exhibited the expected widely spaced sextet of quartets. The magnetic parameters of these species and of ZnH were determined and compared to those obtained from theoretical studies. 

Table 4.2 Most relevant magnetic parameters of selected examples of lanthanide-based chains giving rise either to slow relaxation or 3D ordering. 

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 interpretation of magnetic parameters of transition metal complexes has been extensively discussed in the literature. Since a comprehensive summary of the subject is out of the scope of this paper, the reader is referred to a number of textbooks and review articles2,120"124>. In this section we shall restrict ourselves to a brief outline of some of the approaches commonly used to interpret hf and quadrupole data obtained from ENDOR spectra. 

Table 5.1. Magnetic parameters of Cu(sal)2 in Ni(sal)2 (data from Schweiger and Giinthard62 A( and Qj in MHz)...

An extensive EPR and ENDOR study of Cu(TPP) and Ag(TPP) (Fig. 32) doped into (H20)Zn(TPP) single crystals has been published by Brown and Hoffman66,171. The complete set of hfs and quadrupole tensors for the 14N nuclei and the hfs tensors of the Ag(II) and Cu(II) ions and of the pyrrole protons are reported. A detailed analysis of the magnetic parameters (Table 6.1), which are measured with high accuracy, has been presented using the standard MO treatment66. ... 

Table 6.1. Magnetic parameters of Ag(TPP) and Cu(TPP) in (H20)Zn(TPP) (data from Brown and Hoffman in MHz)...

A single crystal nitrogen and proton ENDOR study of Cu(salen) (Fig. 33) doped into Ni(salen) has been published by Kita et al.173,174). The magnetic parameters obtained for this Schiff base complex are summarized in Table 7. 

Table 10. Magnetic parameters of Cu(gly)2 in a-glycine (data from Fujimoto et al.58) Aj and Q in MHz)...

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. 

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