Spherically symmetric molecules, shifted

Atoms in molecules rarely possess spherically symmetric electron distributions due to the presence of chemical bonds or nonbonding rr-orbitals. The chemical shielding, therefore, depends on the orientation of the molecule with respect to the static magnetic field and the chemical shift is described by a second-rank tensor. The chemical-shift tensor is fully described by three principal values and three Euler angles that orient the principal axis system of the diagonalized chemical-shift tensor with respect to the molecular frame, fin, 522, and 633 (ppm) represent the three principal components of the shift tensor with the following rule 5ii 622 33. In... 

The polarizability of an atom or molecule describes the response of the electron cloud to an external field. The atomic or molecular energy shift KW due to an external electric field E is proportional to i for external fields that are weak compared to the internal electric fields between the nucleus and electron cloud. The electric dipole polarizability a is the constant of proportionality defined by KW = -0(i /2. The induced electric dipole moment is aE. Hyperpolarizabilities, coefficients of higher powers of , are less often required. Technically, the polarizability is a tensor quantity but for spherically symmetric charge distributions reduces to a single number. In any case, an average polarizability is usually adequate in calculations. Frequency-dependent or dynamic polarizabilities are needed for electric fields that vary in time, except for frequencies that are much lower than electron orbital frequencies, where static polarizabilities suffice. 

Chemical Shifts. The shielding effect of spherically symmetrical s electrons is discussed in Section 18.3.2.1. This diamagnetic upfield shift affects all nuclei since every molecule has s electrons. For electrons in /t-orbitals there is no spherical symmetry and the phenomenon of diamagnetic anisotropy is used to explain some otherwise... 

This form of the equation is valid for linear molecules and symmetric rotors (for which I corresponds to reorientation of the symmetry axis) and can be used for nondipolar solvents. A somewhat more complicated expression would hold in the absence of axial symmetry. Maroncelli et al. estimated the value tti for AP corresponding to a charge shift of a spherical ion in a continuum model of a polar solvent of dielectric constant s and showed that it increases with increasing solvent polarity and works well when tti is significantly larger than one. 

Chemical-shift anisotropy is very sensitive to molecular structure and dynamics. Each nucleus can be pictured as being surrounded by an ellipsoidal chemical-shift field, A, arising from the influences of neighboring spins, as described by Eq. (4). If the molecules in the sample have no preferred orientational order, these tensors will be randomly distributed, and the line-shape is predictable. If the shielding is equivalent in all directions = (5yy = zi, A is spherical), a symmetric peak, like shown that in Fig. 29a, will be observed at qjso, which is defined in Eq. (5). Axial symmetry = Gyy A is, more or less, football-shaped) results in a powder pattern like that shown in Fig. 29b. In this case, the tensor elements may be labeled CTy ) and (g x and Gj ). If there is no symmetry in the chemical-shift field (gxx is a flattened football), then the... 

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