Principal magnetic axes

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... 

By diagonalizing the y-matrix, the principal magnetic axes can be determined. Ignoring the uninteresting constant term and performing a little bit of algebra, the more common form of the anisotropy Hamiltonian in the rotated coordinate system is given by ... 

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. 

Both through-bond and pseudocontact contributions can be easily factorized into a series of products of two terms, each term depending either on the nucleus i (topologic and geometric location) or from the lanthanide j (electronic structure and crystal-field effects). For axial complexes, that is, possessing at least a three-fold axis as found in triple-stranded helicates, the molecular magnetic susceptibility tensor written in the principal magnetic axes system is symmetrical xx = mag-... 

In order to evaluate the Cartesian components of the SOC vector, the principal magnetic axes have to be determined by considering the spin-spin dipolar coupling [23]... 

If one wishes to extract stereochemical information about substrates in solution from the data obtained in the NMR experiments, two physical-mathematical models are available. For shifts induced by a dipolar (pseudocontact) mechanism, the McConnell-Robertson equation (Equation 1) (28, 29)—where r, i, and are the spherical polar coordinates of the ith resonating nucleus in the coordinate system of the principal magnetic axes—relates the direction and magnitude of the shift to the geometry of the substrate-chelate complex. If the substrate-chelate... 

In the orthorhombic system, it is o=l=f =t=c, a=j8=y=90°. The crystal possesses three mutually perpendicular twofold axes of rotation parallel to the crystal axes, a, b, c. Consequently, the principal magnetic axes and the crystal axes coincide ij/ = 9=0 the principal susceptibilities usually being denoted by x, X. and Xc ([Pg.3]

Here, r, 9, and (p are the spherical coordinates of the observed nucleus with respect to the principal magnetic axes... 

Bleaney has calculated PCSs with the assumption that the ligand field splittings for the lowest J state in the Ln + complexes are small compared to klP If the principal magnetic axes system is used, equation (3) can be written as equation (6) or (7),... 

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