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]. 

An additional problem with triclinic systems is concerned with the process of fitting theory to experiment, for here it is necessary to reproduce all six independent components of the magnetic tensor simultaneously rather than, perhaps, just the three principal moments in more symmetric crystals. Coupled... 

This is a general scheme, which can allow for additional considerations and further approximations. First, the average with respect to picosecond dynamic processes is carried out, in practice, together with the average with respect to solvent coordinates to allow the QM evaluation of magnetic tensors corrected for solvent effects and for fast vibrational and solvent librational motions. The effective treatment of these aspects represents the heart of this contribution. 

Table 2.1 Isotropic parts of the magnetic tensors of TEMPO obtained by different QM methods are compared with the available experimental data...

The magnetic tensors for a molecule embedded in an anisotropic medium can be calculated on the basis of an effective Hamiltonian which, in addition to the Hamiltonian of the isolated molecule, contains a contribution describing the response function of the reaction potential [32]. The general aspects are presented in the contribution by Sadlej and Pecul. 

Order parameters are usually derived from the measured spectral splittings through relationships such as Equation (2.269-b) thus the availability of good estimates of the magnetic tensors is an essential requirement to obtain accurate order parameters. The theoretical results suggest that the magnetic tensors obtained from calculations in a solvent, introduced by the polarizable continuum model, should definitely be a better choice than the tensors derived, as customary, from solid-state data or from calculations for molecules in a vacuum. 

The 3x3 complex refractive index tensor N = n — ik is related to the dielectric tensor e and the magnetic tensor p by the Maxwell relation ... 

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... 

We assumed that the magnetic tensors appearing in the spin Hamiltonian and the diffusion tensor have the same principal axis system. The are the Wigner matrices of rank /. The nuclear spin operators are expanded over the set of (21 +1) matrices Af j, I being the nuclear angular moment, defined via... 

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) ... 

Fig. 2. Reference frames and sets of Euler angles required for the description of rotational diffusion and sample spinning in a general NMR experiment. The magnetic tensor system (top, left) is characterized by a diagonal chemical shift tensor <7. The sample system (centre, left) is defined by the axis z of sample spinning while the laboratory system is determined by the direction of the external magnetic field. For a transformation from the magnetic tensor system into the sample system, a full set of three Euler angles 3>, 0, and W is needed. For the transformation from the sample system into the laboratory system, only two Euler angles a and /3 are required as the external magnetic field is assumed to be of rotational symmetry.

The first one leads from the magnetic tensor system to the sample system, while the second one finally transforms into the laboratory system ... 

Wegener C, Savitsky A, Pfeiffer M, Mobius K, Steinhoff HJ (2001) High-field EPR-detected shifts of magnetic tensor components of spin label side chains reveal protein conformational changes the proton entrance channel of hacteriorhodopsin. Appl Magn Reson 21... 

Liq. cryst. system g-Tensor Hyperfine tensor Magnetic tensor orient. ... 

Euler angles relating magnetic tensor system and local molecular frame (see Fig. 12). 

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