Atom motions anisotropy

The ability of probing surface anysotropic properties allows to define chemisorption sites based on purely geometrical considerations as well as to investigate the anisotropy of the damping factors (Debye Waller-like) i.e. of the amplitudes of the relative atomic motions in the directions perpendicular to the surface, or in the surface plane... 

The effects of anisotropy and anharmonicity in the atomic motions on the refinement of X-ray data for protein crystals are described in Chapt. XI. 

The spin-orbit interaction is also called spin-orbit effect or spin-orbit coupling, which is one cause of magnetocrystalline anisotropy. SOC, the intrinsic interaction between a particle spin and its motion, is responsible for various important phenomena, ranging from atomic fine structure to topological condensed matter physics. SOC plays a major role in many important condensed matter phenomena and applications, including spin and anomalous Hall effects, topological insulators, spintronics, spin quantum computation, and so on. 

A determination of the structure of l,4-dibromocycl[3,2,2]azine (lp) was complicated by the considerable anisotropy of thermal motion of the bromine atoms. It was concluded that the nitrogen configuration is probably planar, but, if not, the nitrogen atom is less than 0.07 A out of the mean plane of the molecule.55... 

Adding dynamical information to the static conformers can be achieved in several ways. In crystallography, B-factors (see below) are assigned to each atom representing the uncertainty in its coordinates caused primarily by thermal fluctuations. In exceptionally high-resolution structures even the anisotropy of these fluctuations can be depicted. In NMR, it is not possible to obtain information about the fluctuations of all atoms but only of selected motions of certain atom types (see below). Therefore, it is much more common to define order parameters reflecting the extent of the conformational space occupied by the bonds involved in the detected motions.8 The general form of the order parameters can be written as ... 

The next level of approximation accounts for the anisotropy of thermal motions in a harmonic approximation and describes atoms as ellipsoids in one of the three following forms, which are, in fact, equivalent to one another ... 

The anisotropic displacement parameters can be visualized as ellipsoids Figure 2.54) that delineate the volume where atoms are located most of the time, typically at the 50 % probability level. The magnitude of the anisotropy and the orientations of the ellipsoids may be used to validate the model of the crystal structure and the quality of refinement by comparing thermal motions of atoms with their bonding states. Because of this, when new structural data are published, the ellipsoid plot is usually required when the results are based on single crystal diffraction data. 

Anisotropy of molecular movement monosubstituted benzene rings, e.g. phenyl benzoate (44), show a very typical characteristic in the para position to the substituents the CH nuclei relax considerably more rapidly than in the ortho and meta positions. The reason for this is the anisotropy of the molecular motion the benzene rings rotate more easily around an axis which passes through the substituents and the para position, because this requires them to push aside the least number of neighbouring molecules. This rotation, which affects only the o-and m-CH units, is too rapid for an effective spin-lattice relaxation of the o- and m-C atoms. More efficient with respect to relaxation are the frequencies of ijiolecular rotations perpendicular to the preferred axis, and these affect the p-CH bond. If the phenyl rotation is impeded by bulky substituents, e.g. in 2,2, 6,6 -tetramethylbiphenyl (45), then the T, values of the CH atoms can be even less easily distinguished in the meta and para positions (3.0 and 2.7 s, respectively). 

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