Anyone who has gone near GCSE chemistry knows that an atom is made up of a nucleus (built out of protons and neutrons) surrounded by an electron cloud. Early quantum mechanics showed us that the electrons are only allowed to take certain quantized energy states, sharing, swapping and taking from other atoms to minimise the overall energy, forming compounds and ions.

But what are the subtleties of this process? How do we determine the 'shape' of these energy states, the so-called orbitals?