Isotropic charge distribution

Paramagnetic relaxation reagents (pa.r.r.), such as Gd, Mn ", Cu ", and Cr ", and other paramagnetic metal ions with isotropic charge-distribution, affect the nuclear relaxation rates, T, and T2, of species under investigation by n.m.r. spectroscopy through electron-nuclear spin-spin coupling. There are two classes of pa.r.r.s which are characterized by the predominant mechanism of relaxation enhancement. 

Increase of the positive charge at atom X enhances the acceptor ability for X. All HeX dications are covalently bonded according to the calculated pg and Hg values listed in Table 7. This holds also for X ions with isotropical charge distribution, i.e. species without holes in the valence sphere. The Laplace concentration of C ( S) is shown in Fig. 9a. Although isotropical, the charge concentration in the valence shell is so small that the C nucleus is insufficiently shielded and an oncoming He atom is attracted by C ( S). A weakly covalent bond is formed (D = 17.9 kcal/mol) which shows up in the Laplace concentration only by distortion in the valence shell concentration of (Fig. 9c). 

The integral over the nuclear charge distribution in (4.5) can be split into an isotropic and an anisotropic part by adding and subtracting = Yh which yields... 

The anisotropy of the spin-label hyperfine splitting is a consequence of the particular charge distribution symmetry within the molecule. The analysis of spectral anisotropy provides the immobilization extent of the spin label and is sensitive to the molecular conformation. Moreover, the spin-label molecules have their charge distribution distorted by the polarity of their environment. The isotropic hyperfine splitting constant (a0) provides a relative polarity indicator (Knowles et al., 1976 Campbell and Dwek, 1984). 

When the linear isotropic dielectric medium used in the standard model is replaced with a linear homogeneous medium with Green kernel Ge, and when the charge distribution is entirely supported inside the cavity, the reaction potential inside the cavity still has a simple integral representation ... 

Continuum solvation models consider the solvent as a homogeneous, isotropic, linear dielectric medium [104], The solute is considered to occupy a cavity in this medium. The ability of a bulk dielectric medium to be polarized and hence to exert an electric field back on the solute (this field is called the reaction field) is determined by the dielectric constant. The dielectric constant depends on the frequency of the applied field, and for equilibrium solvation we use the static dielectric constant that corresponds to a slowly changing field. In order to obtain accurate results, the solute charge distribution should be optimized in the presence of the field (the reaction field) exerted back on the solute by the dielectric medium. This is usually done by a quantum mechanical molecular orbital calculation called a self-consistent reaction field (SCRF) calculation, which is iterative since the reaction field depends on the distortion of the solute wave function and vice versa. While the assumption of linear homogeneous response is adequate for the solvent molecules at distant positions, it is a poor representation for the solute-solvent interaction in the first solvation shell. In this case, the solute sees the atomic-scale charge distribution of the solvent molecules and polarizes nonlinearly and system specifically on an atomic scale (see Figure 3.9). More generally, one could say that the breakdown of the linear response approximation is connected with the fact that the liquid medium is structured [105],... 

There are other parameterizations possible. Thole noted, in his original paper, that it would be more elegant to describe the interaction—between induced dipoles—in terms of two interacting charge distributions instead of his one-particle ansatz. Jensen et al. [35] took up this suggestion in order to arrive at traceless interaction tensors. He started from the interaction between two isotropic Gaussian charge distributions on a distance r ... 

Material Media and Their Reaction to External Fields. In a material medium, a charge distribution can induce some charge separations, or dipoles, which help to minimize the total energy. Similarly, an external magnetic field will induce some magnetic dipoles in the medium to counteract this field. To handle these effects, an electric polarization (or electrical dipole moment per unit volume) P and a magnetization (or magnetic dipole moment per unit volume) M are defined. If the medium is linear and isotropic, these two new vectors P and M are proportional to E and to H, respectively ... 

The distributed multipole model incorporates a nearly exact description of the molecular charge distribution into the evaluation of the electrostatic energy. Is the increase in accuracy gained by representing the effects of lone pair and 7i-electron density worth the extra complexity in the potential model Even if there is a significant enhancement, is it worth using such an elaborate model when only crude models, such as the isotropic atom-atom 6-exp potential, are available for the other contributions ... 

Only the anisotropy of the magnetic susceptibility influences the isotropic mean value, whereas the complete susceptibility tensor contributes to the chemical shift anisotropy [see Eq. (36)]. The influence of the susceptibility of a spherical symmetric charge distribution on the isotropic chemical shift of a nearby nucleus will be zero, but there is a contribution to the chemical shift tensor. Especially in solid state proton chemical shift investigations this effect is quite remarkable and can be observed when studying proton chemical shift anisotropies. 

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