I read this (from this website, with my emphasis):
As the lattice constant is reduced, there is an overlap of the electron wavefunctions occupying adjacent atoms. This leads to a splitting of the energy levels consistent with the Pauli exclusion principle. The splitting results in an energy band containing $2N$ states in the $2s$ band and $6N$ states in the $2p$ band, where $N$ is the number of atoms in the crystal. A further reduction of the lattice constant causes the $2s$ and $2p$ energy bands to merge and split again into two bands containing $4N$ states each. At zero Kelvin, the lower band is completely filled with electrons and labeled as the valence band.
They had taken the example of a diamond in this case.
Update: JonCuster's comment (thanks!) makes it clear that the paragraph above talking about "$2N$ states in the $2s$ band and $6N$ states in the $2p$ band" is wrong, since once atomic subshells become a part of crystal subshells, they are now governed by Bloch functions and not electron wave functions. Yet, this site has also described the reorganization of these (non-existent) $2s$ and $2p$ bands into new bands in a certain detail. With regards to this additional detail (the highlighted sentence of the quoted paragraph), my question is: are they trying to simplify certain known details? Or are they effectively creating a wrong story entirely?
- Does this reorganization ("merge and split again") of energy bands occurs to lattices all elements, including metals?
- What exactly is the rule regarding this reorganization? (which has not been clearly mentioned there)
- And what do we name these new energy bands? I was told that the energy bands before reorganization are named the same as the subshell it was derived from. (A $2p$ energy band is derived by splitting the $2p$ subshells of $N$ identical atoms) Though, I am not sure how to name the new energy bands obtained after reorganization.
Regarding 2nd question, this is my thought: after a suitably large reduction of lattice constant, all the energy bands belonging to each shell of principal quantum number $n$ will reorganize with each other. For example, the $n=3$ shell had $18N$ electrons, initially organized as $2N, 6N, 10N$; but now will be reorganized as $6N$ in each new band according to me.
I hope I have clearly identified my question and provided reasonable attempts to identity the correct answers to it. Please comment for clarification. Thank you!