The quantum chemical theory Atoms in Molecules


'A bond is a bond is a bond !' This definition gave Richard Bader after the defense of one of his PhD students, and I heard it again several times in discussions with him, what a chemical bond is.

Bader uses quantum mechanics to answer the question, what (and where) a bond is. He describes in his book 'Atoms in Molecules - A Quantum Theory' [Bader 1990] all the basic concepts in chemistry - atoms, molecules, chemical bonds, functional groups - using quantum mechanics.

To do this, he divides molecules in quantum mechanic subsystems, in atomic areas. The topology of the electron density is used to define where one atom ends and the next begins.

Each subsystem (or atom) is surrounded by a surface, through which the gradient vector field of the electron density has no flux.

Don't worry if you don't have a good quantum mechanic background. Here is a simple phenomenological picture what the formula means:

Take two atoms, for example two hydrogen atoms. You have around each of the atoms a sperical distribution of electron density which is highest at the position of the nuclei and falls down exponential with the distance from the nuclei.

The gradient vector field could be described by lines following the steepest decent. Like you staying on a hill and walk down in the direction of steepest decent.

The gradient vector field is zero at any point, where you have no decent. In the case of our two hydrogens this is exactly in the middle of them, describing a valley between two hills.

If you now take an oxygen instead of one of the hydrogen atoms, then the picture still hold true, just that the oxygen compared to the tiny hydrogen would be better described as a mountain next to our hill.

Using now 3 dimensions instead of two and the topology of the electron density, Bader describes 4 so called critical points.

So how are this critical points related to chemistry? Here is some explanation about the chemical meaning:

Connecting the critical points in space give again a space filling partitioning of space in atomic subunits. So in principle this model yields an exact quantum mechanic description where in a molecule bonds are. The topology works equally for coulomb bonds as for weak bonds.

There is only one disadvantage: You need the electron density first to identify the critical points in space. The model was originally intended to describe molecules in vacuum. But an example in the next chapter will show, that it may be used for solids too, even when the example shown is far, far away from the size of a protein.

Last slide Next slide Back to the first slide

Last Updated: 26 October 1996