The analysis of the Electron Density of the compound Bi2S3 ( from my memoir of Magister)

The term "electron density" is used to express two different notions:

 The first notion is “the point specific electronic charge”. The term comes from the erroneous translation of "electronic density". Here, the dimension of the electronic density is therefore an electric charge divided by a volume. The system of units adopted is the atomic unit system (ua of charge (e) and ua of length (bohr)), which makes the unit equal to the number of electrons per unit of volume. This charge density is calculated from equation (V.2) and is illustrated by the contour representation.

 The second notion is “the density of electronic distribution” or “the density of probability of presence” ρ (r) which is the basis of the density functional theory. Here, the electron density is without unit and that of a single electron is calculated by the following formula:

This electronic density is illustrated by the relief representation (or 3 dimensions).

The total electronic density is obtained by summing the orbital densities. Let be an atom described by occupied orbitals ѱi each carrying neither electrons (ni = 1 or 2). The total charge density is therefore expressed as:

Although this density is mathematically a continuous function which extends in all space, it appears that this function is evanescent: beyond a certain distance, we can consider that the density is zero. The electronic cloud is therefore located around the atom without us knowing how to define its limit.

The topological analysis of the electron density at its critical points is a powerful tool for characterizing interatomic and intermolecular interactions. This method applies to crystalline materials (whether organic or mineral) and this in a completely consistent manner with the physicochemical concepts of structure and chemical bonding. It thus provides a quantitative and succinct basis for comparing different structures.

The topological distribution of the charge density in three dimensions and in contours as well as the representation plane (040) are illustrated in the following figures:

The calculation of the total charge density of valence allowed us to know the nature of the chemical bonds between the different atoms making up the Bismuth Sulfide molecule. The charge density is represented in a plane which contains the Bi-S bonds. The electronic distribution indicates that the Bi-S bond is an ionic bond with a weak covalent character. The covalent character is explained by a Bi atom linked to two S atoms; while the strong ionic character is explained by the density of the circles around the nuclei; which gives an S + 2 anion and a Bi-3 cation. This can be justified by the fact that the bond between a metal Bi and a non-metal S is an ionic bond. The difference in electronegativity makes the weak polar covalent bond towards the S atom.

Reference: https://aljazairi1970.blogspot.com/2020/03/my-memoir-of-magister-in-french.html