# Band Theory - which orbitals overlap?

I have another question relating to band theory, wonder if anyone can help?

If I am correct, in band theory we have this idea of creating N different energy states for N atoms that are in a system (with a sigma and sigma* orbital being created for each orbital that the one atom had) The electrons from the N atoms populate these orbital from the lowest energy state, up. And with a large number of atoms (as you would expect in a normal system) you have so many energy states that this ends up with a wider number of states that we call a band. The 'band' that is full/almost full is the valence band and the band that is empty/almost empty is the conduction band.

As far as I know, for a metallic-type conductor we have the situation where the energy states of the valence band and the conduction band overlap so electrons can jump relatively freely (and hence allow for current flow to occur/conduct).

My question is: are the metallic and valence bands, sigma and sigma* bands? Or instead would they, for instance, be an s band and a p band? or a $$p_x$$ and a $$p_y$$ orbital? Or any of the above?

• The solutions to Schroedingers equations in a Crystal are Bloch functions that extend throughout the crystal. There is no one-to-one correspondence to atomic orbitals. Jul 10, 2020 at 13:49