We know every band in the band structure of solids is the result of overlaps of an orbital type. My question is that when there is not any overlap between a type of orbitals(which may be the lowerest energy subshells such as 1s), how the eigenstates corresponding to these orbitals appear in band structure? I don't know there is any real example of this situation. I just want to know what will be the result if we apply this assumption to for example DFT-based simulators.
I was not able to find any journal published examples, but this tutorial on electronic-structure calculations with a DFT solver shows how for the non-interacting low free energy electrons of silver, bands look like straight lines:
If there is no hamiltonian matrix element between such orbitals then the bandwidth vanishes.