Charge cloud

Dispersion forces caimot be explained classically but a semiclassical description is possible. Consider the electronic charge cloud of an atom to be the time average of the motion of its electrons around the nucleus. 

The intensity of shading at any point represents the magnitude of 1, i.e. the probability of finding the electron at that point. This may also be called a spherical charge-cloud . In helium, with two electrons, the picture is the same, but the two electrons must have opposite spins. These two electrons in helium are in a definite energy level and occupy an orbital in this case an atomic orbital. 

Since nuclear masses are much greater than the electron mass we can treat the nucleus as if it were fixed in space. Taking the mass of the electron charge cloud as m, then k = mu>Q where angular frequency of the oscillator. 

On grouping functions of the same variable again, as in Eq. (8.12), we find A"(l,2) to describe something like the repulsion between overlap charge clouds . This has no classical parallel and the integral is simply called the exchange integral, for that is how it arose quantum mechanically. 

Both of the above approaches rely in most cases on classical ideas that picture the atoms and molecules in the system interacting via ordinary electrical and steric forces. These interactions between the species are expressed in terms of force fields, i.e., sets of mathematical equations that describe the attractions and repulsions between the atomic charges, the forces needed to stretch or compress the chemical bonds, repulsions between the atoms due to then-excluded volumes, etc. A variety of different force fields have been developed by different workers to represent the forces present in chemical systems, and although these differ in their details, they generally tend to include the same aspects of the molecular interactions. Some are directed more specifically at the forces important for, say, protein structure, while others focus more on features important in liquids. With time more and more sophisticated force fields are continually being introduced to include additional aspects of the interatomic interactions, e.g., polarizations of the atomic charge clouds and more subtle effects associated with quantum chemical effects. Naturally, inclusion of these additional features requires greater computational effort, so that a compromise between sophistication and practicality is required. 

This moment measures the extent and direction of the shift of an atom s electronic charge cloud with respect to the nucleus. The quantity M(fi) can effectively be regarded as an intra-atomic dipole moment. The intra-atomic dipole moment of each atom contributes to the... 

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.

To get the potential energy of two overlapping charge clouds, consider the interaction of small elements of each cloud and then form a double integral over each of them. Calling the clouds 1 and 2, and the volume elements within them dvi and dv2, each of which carries a charge equal to the charge density of each cloud times the element s volume, the potential is ... 

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