Charge cloud model

A further point of interest regarding this problem has been raised by Bell et al. (1971). Calculations based on an electrostatic charge cloud model indicate that the variation in kH/kD is primarily determined by the tunnel correction. Different reactions will have different barrier widths, hence different tunneling probabilities, and, in the context of this hypothesis, different variations of isotope effects. The hypothesis still predicts, however, that for a given system kH/kD will have maximum value for the symmetrical transition state where the probability of tunneling is highest. 

This problem illustrates the application of the charge cloud model to the hydrogen atom. 

If, on the other hand, a vapor cloud s explosive potential is the starting point for, say, advanced design of blast-resistant structures, TNT blast may be a less than satisfactory model. In such cases, the blast wave s shape and positive-phase duration must be considered important parameters, so the use of a more realistic blast model may be required. A fuel-air charge blast model developed through the multienergy concept, as suggested by Van den Berg (1985), results in a more realistic representation of a vapor cloud explosion blast. 

Figure 3.3 Schematic model of a hydrogen molecule with two positive nuclei (separated by distance, r) embedded in a uniform charge cloud with spherical radius, R.

Interpretating Alkali Iodide Data. The alkali iodide data given above show that the idealized model of ionic crystals is inadequate since 8 9 constant and hp 9 0. To interpret the data one must consider the effects on the iodine 5p population by covalency, deformation of the charge cloud by electrostatic interaction, and deformation by overlap. 

In a non-atom-centered deformation model, due to Hellner and coworkers (Hellner 1977, Scheringer and Kotuglu 1983), the bonding density is described by charge clouds located between bonded atoms and in lone-pair regions. 

Like so many other molecular properties, shape is determined by the electronic structure of the bonded atoms. The approximate shape of a molecule can often be predicted by using what is called the valence-shell electron-pair repulsion (VSEPR) model. Electrons in bonds and in lone pairs can be thought of as "charge clouds" that repel one another and stay as far apart as possible, thus causing molecules to assume specific shapes. There are only two steps to remember in applying the VSEPR method ... 

The important quantity in the above equation which causes deviations from the ionic model is the constant, k, of the London energy which is proportional to the product of the polarizabilities of the interacting charge clouds. This energy increases down all Periodic Groups and is greatest in... 

It is important to realize that the Self-Avoiding MIDCO approach is not a fuzzy set version of a hard surface contact model. If various parts of a macromolecule are placed side by side, then the electronic density charge clouds mutually enhance each other due to their partial overlap, resulting in an actual shape change of these electron density clouds. The various MIDCOs G(K,a) experience significant swelling due to this overlap. The merger of the local parts of the MIDCO actually occurs at a point r that would fall on the outside of each individual MIDCO part without the presence of the other MIDCO part. 

In quantitative modeling of PESs the description of the molecular shape as a superposition of atomic components remains an attractive approach, but it is clear from the earlier discussion that it must be extended to accommodate two important factors. The atomic shape is not a rigid, but rather a soft, exponentially decaying electronic charge cloud. In addition, it should be anisotropic with the anisotropy depending not only on the atom itself, but also on its partner in the chemical bond. 

The success of the Debye-Hlickel limiting law is no mean achievement. One has only to think of the complex nature of the real system, of the presence of the solvent, which has been recognized only through a dielectric constant, of the simplicity of the Coulomb force law used, and, finally, of the fact that the ions are not point charges, to realize (Table 3.7) that the simple ionic cloud model has been brilliantly successful—almost unexpectedly so. It has grasped the essential truth about electrolytic... 

The situation here does have a fairly large shadow on it because of the use of the expression (3.120) in ic. It will be seen (Section 3.14) that, at concentrations as high as 1 N, there are some fundamental difficulties for the ionic-cloud model on which this ic expression of Eq. (3.120) was based (the ionic atmosphere can no longer be considered a continuum of smoothed-out charge). It is clear that when the necessary mathematics can be done, there will be an improvement on the VF expression, and one will hope to get it more correct than it now is. Because of this shadow, a comparison of Eq. (3.130) with experiment to test the validity of the model for removing solvent molecules to the ions sheathes should be done a little with tongue in cheek. 

This does not mean that the Debye-Htickel theory gives the right answer when there is ion-pair formation. The extent of ion-pair formation decides the value of the concentration to be used in the ionic-cloud model. By removing a fraction 0 of the total number of ions, only a fraction 1 - 0 of the ions remain for the Debye-Hiickel treatment, which interests itself only in the free charges. Thus, the Debye-Htickel expression for the activity coefficient [Eq. (3.120)] is valid for the free ions, with two important modifications (1) Instead of there being a concentration c of ions, there is only (1 - 0)c the remainder Oc is not reckoned with owing to association. (2) The distance of closest approach of free ions is q and not a. These modifications yield... 

Gedzelman and Arnold (1994) built on this isotopic approach, but with a more realistic two-dimensional, non-steady-state, cloud model. The model was mn for several idealized, classical stratiform and convective storm situations and the resulting isotope ratios of precipitation and water vapor estimated and compared to observations. The model reproduces many of the salient features of isotope meteorology when applied to snowstorms, stratiform rain, and convective precipitation. Also noticeable is the fact that isotope ratios are particularly low when the rain derives from a recirculation process in which air previously charged by vapor from falling rain subsequently rises. This provides a reasonable explanation for extraordinary low isotope ratios observed in some hurricanes and organized thunderstorms. 

Hence, a simple, essentially classical model provides a useful approximation to the relations between the electronic and nuclear distributions one may think of the electron distribution as a formal charge cloud, and the nuclear distribution as an... 

Current quantum-mechanical calculations are based on the independent-particle model, where one assumes that the molecular orbitals are either empty or occupied by at most two electrons. This model cannot give a completely correct description of a many-electron system mainly because it treats each of the particles as if it saw the others smeared out in a charge cloud. However, it accounts surprisingly well for many properties, especially those connected with the one-electron density. Consequently, it is worthwhile discussing it in detail. 

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