Magnetic susceptibility tensor

Rotating single-crystal measurements also permitted the extraction of the orientation of the magnetic tensor in the molecular reference frame and the experimental easy axis was found to coincide with the idealized tetragonal axis of the coordination dodecahedron of Dy. Crystal field calculations assuming idealized tetragonal symmetry permitted the reproduction of magnetic susceptibility data for gz = 19.9 and gxy 0 [121]. More elaborated calculations such as ab initio post Hartree-Fock CASSCF confirmed this simple analysis [119]. 

The isotropic shift. The isotropic shift is the sum of two contributions the contact and the dipolar contributions. The former is due to the presence of unpaired electron density on the resonating nucleus. The latter arises from the anisotropy of the magnetic susceptibility tensor, modulated by the distance between the unpaired electron and the resonating nucleus, and is also dependent on the orientation of the metal nucleus vector with respect to the principal axes of the magnetic susceptibility tensor. Some problems arise when the spin delocalization is taken into account in calculating the dipolar coupling, but we will not address this problem except when strictly necessary. 

Eq. (2.20), or its simplified version in the axial case, Eq. (2.18), are of general validity. However, the principal directions and components of the molecular X tensor are seldom available. Pseudocontact shifts can be still evaluated by expressing the principal molecular magnetic susceptibility values as a function of the principal g values, in analogy with Eq. (1.38) ... 

Pseudocontact shift is expected every time there are energy levels close to the ground state. This causes orbital contributions to the ground state, and such contributions are orientation dependent. Therefore, the magnetic susceptibility tensor is anisotropic. Anisotropy of the magnetic susceptibility tensors arises also from sizable ZFS of the S manifold (Section 1.4). 

In the case of cobalt substituted Zn-fingers [102], the differences between the chemical shifts for corresponding resonances in the Co(II) and Zn(II) complexes allow the determination of the orientation and anisotropy of the magnetic susceptibility tensor [103]. Similar studies are available for pseudotetrahedral Co(II) in the zinc site of superoxide dismutase [104] and five coordinated carbonic anhydrase derivatives [105]. 

Cj Bleaney s factor of lanthanide / (scaled to —100 Tr(z) trace of the magnetic susceptibility tensor... 

X is the magnetic susceptibility tensor, y is the angle between the metal-nucleus vector r and the external magnetic field. Integration of eq. (25) over all molecular orientations averages... 

Since this dipolar interaction remains in isotropic media as similarly found for the contact shift (see sect. 2.1), it is often termed as the pseudo-contact shift. For the general case of a complex possessing an anisotropic magnetic susceptibility tensor, Kemple et al. (1988) show that the pseudo-contact shift spherical coordinates of the resonating nucleus in an arbitrary axes system with the lanthanide metal ion i (III) located at the origin (fig. 1)... 

In the principal magnetic axes system, the magnetic susceptibility tensor is diagonal and the three last terms of eq. (27) vanish, thus leading to eq. (28) for the pseudo-contact shifts... 

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