Dear Matteo Barduzzi ,

What kind of hints do you want?

First of all, using a fixed occupation as you did in your calculation, you get a metallic system. This is not impossible (you did it!) but clearly signals that you should be better using a finite smearing. Indeed, in general it is suggested to start with a finite small smearing and then decide if it is better to work with fixed occupation. On the other hand, a fixed occupation simply means a standard Fermi distribution (i.e. a Theta function) at 0 temperature. The code fills in the states as they are available and needed.

The reason why you get that the LUMO is lowest than the HOMO lies in the fact that each k-point is essentially independent from the others. That means that for each k-point you simply need a certain number of states to place your electrons. The state that is probably moving around and determining the position of the HOMO and LUMO is the green one in between those energies.

The presence or the absence of an energy gap is not (directly) related on how you occupy your states, at least in the single particle picture of standard Density Functional Theory calculations.

Indeed, it is somewhat reassuring that the physics of the material (i.e. its metallicity) is not strongly affected by the way you fill in the energy levels up to a certain degree.

I hope this helps,

Roberto