Molecular magnetic 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]. 

These conclusions can be obtained on the nonrelativistic level, and it is possible in theory to practice proton and electron spin resonance without permanent magnets, at much higher resolution, without the need for very high homogeneity, and with a novel chemical shift pattern, or spectral fingerprint, determined by a site-specific molecular property tensor, to be described later in this section. 

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) ... 

From the lJ residual dipolar coupling the molecular magnetic anisotropy tensor is obtained, which differs from the metal contribution by an extent which depends on the magnetic anisotropy of the diamagnetic part. For example, in cytochrome b the diamagnetic, the paramagnetic and the total susceptibility anisotropy values are A Xax = —0.8, 2.8, 2.20 x 10 32 m3, respectively, and Axrh = 0.1, —1.1, — 1.34 x 10-32 m3, respectively [60]. The corresponding tensors sum up as expected. 

Then, as case study, we consider the glycine and glycyl radicals (Fig. 6.2) in solution. As mentioned above, the calculation of magnetic tensors needs to take into account the several factors such as the geometries, environmental effects, and dynamical effects (vibrational averaging from intramolecular vibrations and/or solvent librations). We use an integrated computational approach where the molecular... 

As mentioned in Section 2, we basically focus on experiments with nuclei with 1= 1/2 (as, e.g., or under high power decoupling. In this case, the dominating interaction of the nucleus with its molecular surroundings consists of the anisotropic chemical shift. It is fully determined by three principal values an, 0 2, and cr33 which correspond to the diagonal values (7, (7, and of the chemical shift tensor in a magnetic tensor system M (Fig. 2) ... 

Finally, in the third section of this paper, we describe a semiempirical atom dipole model that allows a reliable prediction of molecular electric dipole and quadrupole moments, diamagnetic susceptibilities, and diamagnetic nuclear shieldings. A set of localized bond and atom values are developed for the individual diagonal elements in the total molecular magnetic susceptibility tensor. 

It is evident from the results in Table 7 that the molecular susceptibilities obtained from the local values in Table 8 are in good agreement with experimental results. These local values can now be used to predict the molecular susceptibility of nonstrained, nonaromatic compounds on which measurements are not available. In conclusion we have extended the well-known Pascal s rules for bulk susceptibility to the individual diagonal elements in the molecular magnetic susceptibility tensor. Of course, the diagonal sums of the values given in Table 8 also allow a prediction of the bulk susceptibilities. 

Fig. 1.2. The field induced magnetic moment is depicted schematically in this drawing. This effect is most pronounced in aromatic molecules such as fluorobenzene, where comparatively strong electron ring currents may be induced, leading to a field induced, molecular magnetic dipole moment which opposes the exterior field. Trying to align the induced moment, the exterior field will exert a torque ind X H on the molecule and will thus perturb the overall rotation. This perturbation is seen as a splitting in the rotational spectra. Since there will be a torque only in the case that md and H are not aligned, i.e., if Jg is anisotropic, only the anisotropies of the molecular susceptibility tensor can be obtained from the splittings of the rotational lines...

As defined in Equation 3.4, the spin part of i is a traceless symmetric tensor operator that can have nonvanishing matrix elements between states of spin multiplicity different by up to four, such as singlet and quintet or triplet and septet, etc., but in first order we now consider only its elements in the basis of the three sublevels of the T state. JZ is diagonalized in this subspace by rotation of the coordinate system into the principal system of axes x, y, and z in the molecular frame. In principle, the molecular magnetic axes defined in this fashion are different for every triplet state of the molecule. In the presence of symmetry, some or all of them are constrained to the molecular symmetry axes. 

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-... 

Lanthanide ions with anisotropic molecular magnetic susceptibility tensor Ay, for example, Er , Tm , or Yb , allow valuable structural information to be extracted from pseudocontact shifts (PCS, see also Section 3.6) and residual dipolar couplings (RDCs) arising from the partial alignment of the -labeled biomolecules in the induced magnetic field (Su et al., 2008b) ... 

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