# Do the bottom layers of the slab need to be fixed when we use DFPT or finite displacement methods to compute the phonon spectrum of a surface?

When using DFPT or the finite displacement (also known as the frozen phonon) method to compute surface phonon spectra, it is generally necessary to perform high-precision optimization on the slab structure.

My question is, when optimizing this slab structure, should the atoms in the bottom layers of the slab be fixed as usual?

• +1 and by the way, this was our 4000th question!!! Commented Apr 23 at 18:35
• I suppose if you keep the same atoms fixed during the DFPT calc too… otherwise they won’t be at potential minima (except by coincidence) and your structure will be unstable. Commented Apr 24 at 23:53

## 1 Answer

No you do not need to.

Fixing atoms during a finite displacement or a DFPT calculation is not a real thing. This is a huge approximation that will break the symmetry of the force constant matrix, leading to potentially incorrect results.

The most common case is the study of an adsorbate on a slab. Commonly you can see that only the modes of the slab are studied while the slab is kept “fixed”. This is simply assuming that there is no coupling between the modes of the slab and the adsorbate.

And… in practice it might work, depending what you want to compute. If you compute the Zero Point Energy it will probably work because it mainly depends on the high frequencies. If you want to compute the entropy of vibrations this will probably not work because it mainly depends on the low frequencies, which are the ones that will be changed by the coupling of the adsorbate and the slab.

If you just want to fix the bottom layers of a slab, I suspect you will be fine, but in theory this is an important approximation and you should compare to full calculation.

EDIT: Also, you should still relax the "fixed" atoms before running the phonon calculation, otherwise you will run into problems as stated in the comment of your question

• Yes, you are absolutely right that fixing all the atoms would break the symmetry of the force constant matrix. However, if we allow the bottom layers of the atoms to relax, we would end up with a slab that has two surfaces. Would there be any issues with the force constant matrix calculated in this way? Commented Apr 26 at 14:16
• That's pretty much the world we live in yes... The force constant matrix will be theoretically sound, within the framework you gave it. Now we can question wether or not the slab model is realistic but that's another issue. Depending on what you want to calculate I would say that you probably reached functional accuracy at that point anyway Commented Apr 26 at 14:59
• Thank you for your response. So as long as the number of layers is sufficiently large, the interactions between the upper surface atoms and lower surface atoms can be neglected, and thus the force constant matrix calculated in this way would be 'reliable'? Commented Apr 26 at 15:10
• There is no certainty, especially in computational chemistry, you will have to test for convergence etc… but I don’t think you should over complicate it, I suspect it will be fine Commented Apr 27 at 7:56