Posted by: Mark Foreman | September 26, 2013

S orbitals and a H-H bond

Dear Reader,

I was going to entertaintorment you with vogon poetry but why wife has told me to be good and spare you the poetry. But lets get on with writing about orbitials.

One of the joys of chemistry is the shapes and forms of the atomic and molecular orbitals. The thing is that an electron can not be located, the uncertainty principle means that you can not know both the location and the energy of an electron. The better defined one is the worse the uncertainty with which the other is known.

We know the energies of electrons in atoms and molecules well through photoelectron spectroscopy (PES) and other spectroscopic methods so the locations of the electrons are poorly known. But there is hope. We can draw a surface around the shape which has a given probability of containing the electron. In the same way as the improbability powered space ship in the Hitch Hikers Guide to the Galaxy did lots of wonderful things like turning missiles into vases of flowers (and whales) the shapes of the volumes of space which have a given probability of containing an electron can do wonderful things for our chemistry.

Now to get going we will consider the s orbitals of a hydrogen atom, OK a hydrogen atom might be small and weedy but we need to understand these little things before we move onto big things. We need to start with the 1s orbitial which has a simple radial wavefunction of

Ψ = e-kx

The electron density (electrons per cubic Å) is given by the square of the wavefunction (Ψ)

This gives us a sphere shaped orbital which is like a ball, it is very symmetric. Here are two views of the electron density in the 1s orbital. First here is the bird’s eye view of a slice through the centre of the orbitial.

Bird's eye view of the electron density in a 1s orbitial

Bird’s eye view of the electron density in a 1s orbitial

Then here is the 3D view of the electron density in the orbiital

3D view of the graph of electron density as a function of distance from the centre

3D view of the graph of electron density as a function of distance from the centre

We have another s orbitial with a higher energy (2s) which has a slightly more complex radial function which is

This means it has an inner part with the opposite sign wavefunction. We will get onto that soon, I also hope to write a spreadsheet which will give me a better ability to draw oribitials.

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