Anisotropic distribution, of electron density

XB is a particularly directional interaction, more directional than HB. The angle between the covalent and non-covalent bonds around the halogen in D- X-Y is approximately 180° [48]. As discussed above, the origin of this directionality is in the anisotropic distribution of electron density around the halogen atom. Figure 5 shows the Cambridge Structure Database (CSD, ver-... 

For instance, both theoretical and experimental evidence indicates that Si bound to electron-withdrawing groups displays an anisotropic distribution of electron density, and four regions of positive electrostatic potential are present on the... 

In the simplest approximation, two sources can contribute to the total EFG. First, there could be an anisotropic (non-cubic) distribution of electron density in the valence shell of the Mossbauer nucleus, e.g. an asymmetric substitution pattern due to different ligands in a six-coordinate metal atom or an asymmetric (non-cubic) distribution of electrons in the molecular or atomic orbitals in the model of simple ligand field theory. This contribution is called the valence electron contribution to the EFG. The second contribution comes from the lattice, specifically charges or dipoles or distant ions or other components that surround the Mossbauer nucleus in a non-symmetric arrangement. This is the lattice contribution to the EFG. 

Fig. 3 Due to the anisotropic distribution of the electron density, halogen atoms show a negative electrostatic potential and a larger radius (rmax) in the equatorial region and a positive electrostatic potential and a smaller radius (rmjn) in the polar region. As a consequence of this, halogens behave as nucleophiles at the equator and as electrophiles at the pole...

The first attempt to clarify the physical basis of the Jahn-Teller theorem was due to Ruch, [3] in an introductory presentation to the 1957 annual meeting of the Bunsen-Gesellschaft in Kiel, which was organised by H. Hartmann. Ruch discussed the general connection between symmetry and chemical bonding, and also touched upon the Jahn-Teller effect in transition-metal complexes. He explained that degeneracy can always be related to the existence of a higher than twofold rotational axis and a wave function which is not totally symmetric under a rotation around this axis. Provided that the wave function is real the electron densities for such a wave function are bound to be anisotropic. The combination of an anisotropic distribution of the electron cloud and a symmetric nuclear frame leads to electrostatic distortion forces where the nuclear frame adapts itself to the anisotropic attraction force. 

In contrast to the situation in plasmas in steady state or in time-dependent plasmas, the electron density n z) in space-dependent plasmas always depends on the z coordinate, and this happens already if only conservative inelastic collisions are considered. As an immediate consequence, it no longer makes sense to separate the density from the isotropic and anisotropic distribution of the electrons. 

The analysis of the cluster atomic and electronic structure, distribution of electron and spin density, as well as the calculation of isotropic and anisotropic hyperfine coupling constants (IHC and AHC) was carried out. 

The anisotropic distribution of the electron density in halogen atoms of monovalent halogen derivatives accounts for their well-established amphoteric behavior and the different geometry of interactions formed with different entering groups. 

For anisotropic motions the expressions we have just discussed become more complicated. Note also that while these equations refer to positions and displacements of atoms (i.e. nuclei), the X-rays themselves are actually scattered by electrons. This is a potential problem, because the nature of chemical bonding means that the distribution of electrons is not a simple superposition of spherical atoms. And yet the assumption of exactly spherical atoms, also known as the independent atom model, is the basis of these equations. A more rigorous treatment relates the structure factors to electron density, i.e. the three-dimensional distribution of electrons in space represented by the function p x) with x representing space in three-dimensional coordinates x, y, z. Within this formalism the structure amplitude can then be expressed as... 

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