Molecular magnetic axes

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. 

The following were figures for Ax molecular magnetic anisotropy ... 

Breslow etal.133 investigated the microwave spectrum of cyclopropenone and determined data for bond lengths, bond angles, dipole moment (4.39 D from the molecular Stark effect), and magnetic susceptibility anisotropy (Ax) as seen in Table 5 in comparison with cyclopropene5 3 ... 

Terms of higher order in the field amplitudes or in the multipole expansion are indicated by. . . The other two tensors in (1) are the electric polarizability ax and the magnetizability The linear response tensors in (1) are molecular properties, amenable to ab initio computations, and the tensor elements are functions of the frequency m of the applied fields. Because of the time derivatives of the fields involved with the mixed electric-magnetic polarizabilities, chiroptical effects vanish as a> goes to zero (however, f has a nonzero static limit). Away from resonances, the OR parameter is given by [32]... 

Molecular shapes and 1H chemical shift patterns for chloro-ammine cobalt(III) compounds. Different environments for ammonia molecules in some complexes are defined by eq and ax subscripts, with the two types opposite different types of ligand leading to different magnetic environments and chemical shifts (8). 

In order to confirm the anisotropy due to the a-hydrogen, Salovey et al. [9] and Shimada et al. [10] studied the patterns of the ESR spectra from irradiated solution grown crystals of polyethylene. The crystal c-axis was oriented perpendicular to the plane of the sample while the a- and b-axes were randomly oriented in the plane as shown in Fig. 7.8. Six- and ten-line spectra were observed when the c-axis of the crystal was set to be parallel (Fig. 7.9(a)) and perpendicular (Fig. 7.9(b)) to the direction of the applied magnetic field, respectively. From these results, the anisotropic hyperfine splitting due to the a-hydrogen Ay = 0.75 mT, Ax = 1.72 mT and Az = 3.70 mT were determined and were related to the molecular orientation of the crystal. The x-, y- and z-axes coincide with the directions of the p-orbital, the (Ca )— Ha bond, and the main chain axis, respectively, as shown in Fig. 7.10. 

Experimental and a few theoretical values for the average magnetic susceptibility x. its components Xw (parallel) and Xi (perpendicular to the molecular symmetry axis), the anisotropy Ax = Xi 5Cii. the dia- and paramagnetic contributions x" and x are given in the table below. 

The magnetic properties of most free radicals can conveniently be represented by parameters describing their interaction with an external magnetic field and the intra-molecular hyperfine interactions, i.e. the parameters g and ax of the Spin-Hamiltonian... 

To appreciate the significance of these numerous orda parameters it is helpful to see how they are related to the anisotropic properties of a nematic. As an example we consider the anisotropy in the magnetic susceptibility. Ax, as we have for previous systems. The starting point is the magnetic polarisability expressed in a molecular frame s in a rigid fragment of the molecule. This tensor K ( ends, in genaal, on the conformation of the molecule, a fact which we have... 

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