Let’s say we have a periodic crystal structure. We could, in theory, treat this system as if it were a large molecule. Therefore, we could use Hartree Fock theory or other methods to get the molecular orbitals of this system and also the energy levels.
My question is:
If we a have all of these molecular orbital energies, how can we get to the band diagram in k space? How are these two concepts related qualitatively and mathematically?
Comment: I know how to calculate band structures or molecular orbital energies. My question is not about how to calculate them but about how to switch between these two ‚representations’. Maybe one could list a step by step solution, this would be really helpful for the understanding of the topic.
Best Answer
It is basically means that you should write a Hamiltonian of the system with periodic potential, and solve the Schrodinger equation for the Hamiltonian. Then you get the wave functions corresponding to the system. However, if the interaction between molecules is not very strong you can say that you are going to use the wave functions of lone molecules.
Another thing about a band diagram, the point is that a limited crystal will have a certain number of energy levels, however if number of atoms is high they will form bands with very small distances between every level.
As for bands, you can solve the Schrodinger equation for an large number of delta-atoms (with a single level) separated by a distance, and you will see that a this level will split.