WHAT IS ELECTRON DENSITY? - CHEMISTRY - 2025

The electron density is a measure of how likely it is to find the electron in a particular region of space; either around an atomic nucleus, or in the "neighborhoods" within molecular structures.

The higher the concentration of electrons at a given point, the higher the electron density, and therefore, it will be distinguished from its surroundings and will exhibit certain characteristics that explain chemical reactivity. An excellent graphical way to represent such a concept is through the electrostatic potential map.

Source: Manuel Almagro Rivas via Wikipedia

For example, the upper image shows the structure of the S-carnitine enantiomer with its corresponding electrostatic potential map. A scale composed of the colors of the rainbow can be observed: red to indicate the region with the highest electron density, and blue for that region that is poor in electrons.

As the molecule is traversed from left to right, we move away from the -CO ₂ ^{- group} towards the CH ₂ -CHOH-CH ₂ skeleton, where the colors are yellow and green, indicating a decrease in electron density; up to the group -N (CH ₃) ₃ ⁺, the most electron-poor region, colored blue.

Generally, the regions where the electron density is low (those colored yellow and green) are the least reactive in a molecule.

Concept

More than chemical, electron density is physical in nature, because electrons do not remain static, but travel from one side to another creating electric fields.

And the variation of these fields causes the differences in the electron densities in the van der Waals surfaces (all those surfaces of spheres).

The structure of S-carnitine is represented by a model of spheres and bars, but if it were by its van der Waals surface, the bars would disappear and only a caked set of spheres (with the same colors) would be observed.

Electrons are more likely to be around the more electronegative atoms; however, there may be more than one electronegative atom in the molecular structure, and therefore groups of atoms that also exert their own inductive effect.

This means that the electric field varies more than can be predicted by observing a molecule from a bird's eye view; that is, there may be more or less polarization of the negative charges or of the electron density.

This can also be explained in the following way: the distribution of the charges becomes more homogeneous.

Electrostatic potential map

For example, because the -OH group has an oxygen atom, it attracts the electronic density of its neighboring atoms; however, in S-carnitine it gives part of its electron density to the -CO ₂ ^{- group}, while at the same time it leaves the -N (CH ₃) ₃ ^{+ group} with a greater electronic deficiency.

Note that it can be very difficult to infer how inductive effects work on a complex molecule, such as a protein.

In order to have an at-hand overview of such differences in the electric fields in the structure, the computational calculation of the electrostatic potential maps is used.

These calculations consist of placing a positive point charge and moving it along the surface of the molecule; where there is less electron density, there will be electrostatic repulsion, and with greater repulsion, the more intense the blue color will be.

Where the electron density is higher, there will be a strong electrostatic attraction, represented by the color red.

The calculations take into account all the structural aspects, the dipole moments of the bonds, the inductive effects caused by all the highly electronegative atoms, etc. And as a result, you get those colorful and visually appealing surfaces.

Color comparison

Source: Wikimedia Commons

Above is the electrostatic potential map for a benzene molecule. Note that in the center of the ring there is a higher electron density, while its "tips" are bluish in color, due to the less electronegative hydrogen atoms. Likewise, this distribution of charges is due to the aromatic character of benzene.

In this map the colors green and yellow are also observed, indicating the approximations to the regions poor and rich in electrons.

These colors have their own scale, different from that of S-carnitine; and therefore, it is incorrect to compare the group -CO ₂ ^- and the center of the aromatic ring, both represented by the color red in their maps.

If they both kept the same color scale, the red color on the benzene map would be seen to turn a faint orange. Under this standardization, the electrostatic potential maps, and therefore the electron densities of various molecules, can be compared.

Otherwise, the map would only serve to know the charge distributions for an individual molecule.

Chemical reactivity

By observing a map of electrostatic potential, and therefore regions with high and low electron densities, it can be predicted (although not in all cases) where chemical reactions will occur in the molecular structure.

Regions with high electron density are capable of "providing" their electrons to surrounding species in need or in need of them; These negatively charged species, E ⁺, are known as electrophiles.

Therefore, electrophiles can react with the groups represented by the color red (the -CO ₂ ^{- group} and the center of the benzene ring).

While the regions with low electron density, react with negatively charged species, or with those that have free pairs of electrons to share; the latter are known as nucleophiles.

In the case of the -N (CH ₃) ₃ ^{+ group}, it will react in such a way that the nitrogen atom gains electrons (is reduced).

Electron density in the atom

In the atom, electrons move at enormous speeds and can be in several regions of space at the same time.

However, as the distance from the nucleus increases, the electrons acquire electronic potential energy and their probabilistic distribution decreases.

This means that the electronic clouds of an atom do not have a defined border, but a blurred one. Therefore, it is not easy to calculate the atomic radius; unless there are neighbors that establish a difference in the distances of their nuclei, half of which can be taken as the atomic radius (r = d / 2).

Atomic orbitals, and their radial and angular wave functions, demonstrate how electron density changes as a function of distance from the nucleus.

References

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