Smeared nuclear charge

The electrons in a molecule are in a very complex situation because they not only interact among themselves, but also with the nuclei. However, a simpler system has been elaborated theoretically for years a homogeneous gas model in a box °, or an electrically neutral system (the nuclear charge is smeared out uniformly). It does not represent the simplest system to study, but it turns out that theory is able to determine (exactly) some of its properties. For example, it has been deduced how E c depends on p, and even how it depends on Pa and pp. Since the gas... 

The nuclei see the electrons as a smeared-out cloud of negative charge which binds them in fixed relative positions (because of the mutual attraction between electrons and nuclei in the intemuclear region) and which defines the (somewhat fuzzy) surface [11] of the molecule (see Fig. 2.11). Because of the rapid motion of the electrons compared to the nuclei the permanent geometric parameters of the molecule are the nuclear coordinates. The energy (and the other properties) of a molecule is function of the electron coordinates (E = P(x, y, z of each electron) Section 5.2), but depends only parametrically on the nuclear coordinates, i.e. for each geometry 1,2,... there is a particular energy E Vfx, y,z...), E2 = 412 (x, y, z...) cf. xn, which is a function of x but depends only parametrically on the particular n. 

In the smeared charge multipole model, each atom i is represented by a smeared charge which consists of a nuclear... 

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