Thanks for the response, I'm under the impression that the band gap exists in a region whereby bands don't overlap or in other words where the density of states is 0. So to some degree what you're saying must be an extension of this principle?
Considering the fermi level for a chain of F+ I would presume it would lie slightly below its placement for the F chain, at the level of the degenerate pi orbitals. But what does this imply about its conductivity? It still overlaps the pz sigma character band (that is now unoccupied) so doesn't this make it a metal?
To extend this concept a bit further, wouldn't F2+ (ignoring infinite charge) also lie in the same place as F+ because there would still exist one fully occupied pi degenerate orbital? I believe that S would also share a similar chain band structure as F+ as well but without the infinite charge to make the theory a little less fictitious. Thanks,