About vacuum padding for slab calculation

[Kaspar]

I am trying to do a test of how large my unit cell has to be in the direction normal to the surface for the surfaces not to "see" each other when the periodic calculations are performed. In my calculations I also have a molecule some distance from the surface, so what I actually want to avoid is that the molecule sees the surface from the periodic image.

I got some (to me) curious results, which make me doubt my procedure.
I varied the normal direction vector (vector_c) between 20 and 38 A. When it is 20 A, there is only 2.35 A between the molecule and the periodic image, but when I am comparing the total energy of the system for different sizes of the unit cell, I get basically the same for all sizes of unit cell. I had expected a difference!
Is it possible that 2.35 A distance to the periodic image is far enough that they do not "see" each other?

The following is the output of the attached script. The last point did not converge in the standard 99 iterations, which is why the energy is different from the trend.

20 vector_c, energy = -26623.0088858
22 vector_c, energy = -26622.5073079
24 vector_c, energy = -26622.5012136
26 vector_c, energy = -26622.5004979
28 vector_c, energy = -26622.5001226
30 vector_c, energy = -26622.499761
32 vector_c, energy = -26622.4996665
34 vector_c, energy = -26622.4994036
36 vector_c, energy = -26622.499307
38 vector_c, energy = -26618.9210823

Did I misunderstand something about this type of convergence test or about how the calculation is actually performed?

Thank you for any comments.

[Umberto Martinez]

Indeed energy will converge much faster with respect to vacuum regions with respect to a plane wave code, for example.
This is because in the LCAO methods the basis sets do not extend as much into vacuum.
This is also the reason ghost atoms are used in work function calculations, see:
http://quantumwise.com/publications/tutorials/item/499-computing-the-work-function-of-a-metal-surface-using-ghost-atoms
http://quantumwise.com/publications/tutorials/item/519-tuning-the-work-function-of-silver-by-deposition-of-ultrathin-oxide-layers

Two suggestions:
- increase k-point sampling, you will also converge big cells.
- see tutorials above to converge the effective potential (flat in the vacuum region) instead of energy. In order to apply Neumann boundary conditions you will have to change a bit your cell and make it orthogonal though.

[Anders Blom]

It's not only a matter of the basis sets, the electrostatic influence has a much longer range than that, and in tricky cases it can be hard to get rid fully of the long-range Coulomb terms.

Actually, at 20, you probably have some basis set overlap, which is why there is a significant difference to 22 and to the converged result (not relatively speaking of course, but it's still 0.5 eV).

At 22 however, you are indeed almost fully converged already. If your molecule is aligned such that there is no strong charge polarization in the transverse direction, then there is a very small residual electric field in this direction, as your convergence test in fact shows.