Could you provide an input file to get a better impression? Is this actually a film calculation or a periodic slab calculation with a large space in between the slabs? Is your film/slab setup symmetric or asymmetric? How thick is the slab, what kind of chemical element is involved. Depending on the quantity and the involved elements surface properties can either be converged with just a few layers or you may need several tens of atom layers.

In periodic slab calculations you also have the electrostatic interaction between the slabs that may require a very large vacuum region.

Dear Terry,

Could you please also paste the valenceDensity and coreStates sections for the last iteration of the largest setup from the out.xml file? It looks like you accumulate charge at the surfaces. Another thing that may become visible in this data is whether there are problems due to the very small MT radii you have to use due to the small bonding lengths. It may be that your observation has a physical origin and is not related to a problem of the calculation.

I think the bulk system of the surface you want to describe is an insulator. On the other hand the hydrogen atom only has a single s electron. The hydrogen layer on top of the bulk therefore may be similar to the situation in which you have an interface between an insulator and a metal. In such situations the metal can affect the electronic structure of the insulator. An example for this is a Schottky barrier. I think such effects can be rather extended. It may help a little to perform a structural optimization of the z positions of the different atoms, but this will not fundamentally cure the problem. I actually don't know how to deal with such situations in DFT calculations. Maybe there are tricks or there are extrapolation schemes. I think it may be a good idea to do some research on papers investigating metal-insulator or metal-semiconductor interfaces with DFT. Maybe one can find a good idea there.

EDIT: I just saw that you wrote that the geometry is already optimized. In this case the structural relaxation idea is nothing new.

With respect to the band gap I could imagine that a finite band gap actually is something artificial in the output here. Maybe with a finer k mesh it will just disappear. As mentioned I actually expect to see a conductive layer on the surface.

Just out of curiosity: Is this hydrogen termination actually observed for such surfaces in experiment? For example this could be the case if there are dangling bonds.

Maybe you are right, I only had a short look at your input. Only a band structure calculation could tell us whether it is an insulator or a metal. But in the end, as you just mentioned, this is not really relevant. The charge at the surface stays and leads to a very slow convergence with respect to the number of layers.