The Chemical Bond

Hello everyone!

Now I'm going to give you a short introduction on what I want to do. I've already told you that I want to dedicate my work to solving the problem of the chemical bond. You may wonder: why?

I'll give you (in parts) a brief summary of what we know of the chemical bond.

So.

First let's define what a chemical bond is: A chemical bond it is say to be formed when two or more atoms are held together strong enough to form a molecule.

So, basically that is a chemical bond. There are various theories to describe it. But before the dawn of quantum mechanics the explanations were rather inaccurate. Since the proposal of the quantum theory and the birth of the Schrödinger equation theoretical chemists and physicists have developed several theories that unite the wave-particle duality of the electron and the interactions with the nuclei. The problem is that physics stumble with a great problem. This problem comes from classical mechanics. The many body problem. We can solve accurately for just two particles.

How many particles are in the simplest atom? The hydrogen atom has one proton, one electron and the nucleus. Too much bodies for the Schrödinger equation, so...now what?

Well before going into that I'm going to present a series of theories that have been proposed to explain the chemical bond.

One of the most remarkable ones, considered a classic in modern chemistry is the work of Linus Pauling, an american chemist, his work: The Nature of the Chemical Bond was a revolution in the theory of what the chemical bond was. He used quantum mechanics to explain the movement of the electrons and defined what are called orbitals. Those are solutions to the Schrödinger equation that define a spatial probability of where the electron may be found. So, every type of atom has its own set of atomic orbitals, they change depending on the energy level. There are multiple types of orbitals. In the next picture you can see a bunch of them!

And how did Pauling describe the chemical bond?

He proposed hybrid orbitals, atomic orbitals that combine each other in order to become hybrid and be able to form a bonding interaction. The bonding interaction forms by the overlap of two or more hybridized orbitals. A characteristic of these hybrid orbitals is that they are degenerate and localized, that is, they have the same energy, all of the atomic orbitals that combined to form the hybridized one. Also a very important thing is that the atom forms the necessary hybridized orbitals to form the bond. That is, if it needs 5 hybridized orbitals to form the bond, only 5 bonds will be created the other atomic orbitals that are left can be used to form new bonds. Pauling's theory is also known as the Valence Bond Theory.

But there is a problem with the VB theory, the idea that the hybridized orbitals that form bonds are degenerate and localized, that is pretty unlikely. There's another theory that helps us explain the chemical bond. The molecular orbital theory or MO for short. This theory is maybe the most used one in modern days, it describes the bond formation by the formation of molecular orbitals that form from the combination of atomic orbitals. The difference with the VB theory is that there molecular orbitals are delocalized over the molecule. Also atomic orbitals tend to combine better if they have similar energies or have the same size. Bigger atoms have bigger orbitals and thus, smaller atoms have smaller orbitals. Big + Big = good, Big + Small = not so good.

Also a very important concept in MO theory is symmetry, if the orbitals are not of the same symmetry the interaction between can be non existent or really really weak. That is the reason that for more complex molecules molecular symmetry and group theory is used in order to be able to classify the type of orbitals that will arise in that complex environment and thus predict the type of interactions that the molecule will have.

So, how is a molecular orbital described in terms of the wave functions?

A molecular orbital is the result of two atomic wave functions interacting with each other, they have two type of interactions, one is a bonding interactions and one an anti bonding interaction. A molecule is said to have bonds if the number of bonding interactions exceed the anti bonding interactions.

Both interactions between the orbitals are expressed by that plus/min sign. The Sa and the Sb correspond to the wave function of each atomic orbital. And N is a normalization constant.

So, I haven't said anything about the many body problem, guess I'll leave that for the next!

References:

Atkins, P. . (2014). Química Inorgánica. México: Reverté.
Cotton, F. . (1999). Advanced Inorganic Chemistry. USA: Wiley.