[Pw_forum] How to determine the thickness in surface phonons calculation?

[Nicola Marzari]

Lijun Zhang wrote:
> 1.The highest mode should be about 3078 cm-1 (Th.Frauenheim Thin Solid 
> Films 272 (1996) 314-330), while I don't know what makes the optical 
> mode frequences so high, is it because of the thin vacuum layer?

The most likely reason for a 800 cm-1 discrepancy is that the system
you study is different from the one that was experimentally
characterized (provided your calculations are correct, of course).
Maybe the expt one has a different reconstruction, no hydrogen, etc...
Very difficult to say.

> 2.How to determine the thickness of the slab and the thickness of the 
> vacuum?

You increase them, separately, until the quantities you are interested
in do not change anymore. Certain quantities (e.g. the highest optical
frequency) converge fast - certain others (e.g. the zero-point motion
contribution, or the vibrational free energy, integrated on all the
phonons) are much slower to converge.

Making sure that you converge with respect to wfc cutoff, charge density
cutoff, k-point sampling (and smearing, in a metal), vacuum, slab
thickness, self-consistency threshold, and phonon self-consistency
threshold (these last two are *very* critical) is painful, slow, and
*necessary*.

Note that the acoustic frequencies at Gamma
are the most difficult to converge (if I remember well our 2005 PRB
Mounet and Marzari, to get them to 0 +/-1 cm-1 in bulk diamond we
needed to use a cutoff for ultrasoft C of 100 Ry (!), and a dual of 28,
i.e. a charge density cutoff of 2800 Ry). In practice, you never use
such a high cutoff (have a look at out paper for the right numbers), but
you enforce the acoustic sum rules (i.e. renormalize the interatomic
force constants so that if you rigidly translate all atoms, the energy
does not change). After imposing this physical symmetry, you'll find
that the convergence with respect to cutoff is much better behaved.

Of course, sometimes you might need accurate numbers for low frequency
mode that are close to zero but not zero (e.g. some torsional modes in
carbon nanotubes). Then, you just need to painstackingly verify
convergence.

> 3.I relaxed all the atom in the slab, should I fixed the middle 4 layers 
> (8 atoms)?

Depends, again, on what you want to calculate. It might be better
to not fix anything, fix a couple of layers in the middle, or a
couple of layers in the bottom. I usually do not fix anything, so
I have less parameters to worry about (which atoms to fix).

Best luck,

nicola


PS: of course, have a look at the literature to get some sense
of what is needed - the various phonon calculations in slabs
by Claudia Bungaro, for metals, or by Pavone, for semiconductors.


---------------------------------------------------------------------
Prof Nicola Marzari   Department of Materials Science and Engineering
13-5066   MIT   77 Massachusetts Avenue   Cambridge MA 02139-4307 USA
tel 617.4522758 fax 2586534 marzari at mit.edu http://quasiamore.mit.edu