In general, a larger supercell will give better results for this type of calculation. However, there is clearly a time / computational resource limit to this. One way to test that your supercell is large enough is to make a plot of the magnitudes of the inter-atomic forces vs distance for all of your displacements.  Essentially, you are looking to see if the longer distance forces sufficiently fall off faster than ~1/r^2.  Another check is that if your system is known to be dynamically stable (i.e. have no soft modes so that all eigenvalues are positive) and soft modes do appear in your calculation, you'll need to go to a larger supercell.  If  you aren't sure or the systemis expected to be dynamically unstable (e.g. cubic HfO2) then you may need to do two calculations and compare if the phonon band structure changes significantly. For larger supercells, you can also break up the calculation into multiple steps for the finite displacement type calculation (for example if you have 5 atoms in the primitive cell and are doing displacements along the + and - of each cartesian axes, you would have 30 total degrees of freedom which depending upon the supercell size may be difficult to run within the wallclock of your machine. Instead, you can break it into 5 calculations and then extract the forces manually to feed into whatever code you use for the phonon dispersion).

On point 2, you have it backwards. Going to a larger supercell requires a smaller k-point grid not larger. This is due to the fact that increasing your cell size in real space decreases your cell size in reciprocal space. Therefore to have the equivalent sampling density, you can reduce the density of your grid.

Finally, keep in mind that VASP itself doesn't readily give you full phonon dispersion. This is fine, but it means you'll need to use a program like phonopy or a homemade code to calculate and diagonalize the dynamical matrix from your extracted forces.

In general, a larger supercell will give better results for this type of calculation. However, there is clearly a time / computational resource limit to this. One way to test that your supercell is large enough is to make a plot of the magnitudes of the inter-atomic forces vs distance for all of your displacements.  Essentially, you are looking to see if the longer distance forces sufficiently fall off faster than ~1/r^2.  Another check is that if your system is known to be dynamically stable (i.e. have no soft modes so that all eigenvalues are positive) and soft modes do appear in your calculation, you'll need to go to a larger supercell.  If  you aren't sure or the systemis expected to be dynamically unstable (e.g. cubic HfO2) then you may need to do two calculations and compare if the phonon band structure changes significantly. For larger supercells, you can also break up the calculation into multiple steps for the finite displacement type calculation (for example if you have 5 atoms in the primitive cell and are doing displacements along the + and - of each cartesian axes, you would have 30 total degrees of freedom which depending upon the supercell size may be difficult to run within the wallclock of your machine. Instead, you can break it into 5 calculations and then extract the forces manually to feed into whatever code you use for the phonon dispersion).

On point 2, you have it backwards. Going to a larger supercell requires a smaller k-point grid not larger. This is due to the fact that increasing your cell size in real space decreases your cell size in reciprocal space. Therefore to have the equivalent sampling density, you can reduce the density of your grid.

Finally, keep in mind that VASP itself doesn't readily give you full phonon dispersion. This is fine, but it means you'll need to use a program like phonopy or a homemade code to calculate and diagonalize the dynamical matrix from your extracted forces.

1) I agree with Andrew. There are rules of thumb to decide the size of the supercell, and in general the larger the better. If you are interested in a properties a good choice (if computationally available) is to start from 1x1x1, to 2x2x2, 3x3x3 and so on, until the properties converges.

2) K-points mesh has to be reduced if larger direct space cell is considered ( smaller k-space). But again you need to accurately covnerge the k-points. FDM requires well converged parameters.

Also you need to geometrically converge the cell below the usual threshold (10meV/A). I personally used 1meV/A, but it depends on the system.

3) I would suggest Atsushi Togo phonopy software to perform those calculations.

Thank both of you for your valuable suggestion! I also employ phonopy software for the FD calculation. Instead of VASP, I use Quantum Espresso for geometry optimization. I employed very strict convergence criterion (1d-6 Ry/Bohr=2.57d-5 eV/Angstrom) for geometry optimization.

Concerning the k-points mesh, I usually employed 4*3*3 for my unit cell(10A*13A*15A). If I make a 2*2*2 supercell, I think the minimum k-mesh I can use is 1*1*1.

Federico, when you use phonopy to calculate frequency of vibrational modes, do you use "--nac" parameter to consider LO-TO splitting? I have compared the results of with and without "--nac", I found there is no change in frequency and eigenvectors at all for gamma point. Is that normal?

There are always changes in frequency, especially for low-frequency modes,  in Quantum Espresso if LO-TO splitting is considered.

For the super cell I would use 222kmesh.anyway nac is important only for some system, depends which one you use. Also if you calculate the forces with VASP, you need to redo the geom opt. 

What do you mean "calculate the forces with vast"? I don't see "vast" in quantum espresso.

my experience tells me that 2*2*2 and 4*4*4 is better than 3*3*3 

if number of atoms in a supercell is more than 80, only gamma point is enough for calculation.

So you mean there is not large difference in energy or force between using gamma point and 2*2*2 .... if atom number exceeds 80.

1. In my experiences, for Si crystal, 64 sites are enough for phonon. My results showed convergence when I calculated 64 and 216 sites

2. Not only k-point, cutoff-energy does need converged calculations. Just starting from 1x1x1 untill the total energy converges. In the same way, also for cutoff-energy convergence check 

If you need , you can read my paper:

http://iopscience.iop.org/article/10.7567/JJAP.54.041301/meta

I meant VASP. If you change software you need to reoptimize. About the Gamma vs number of atoms, depends on the structure. If you have 80 atoms, but a small dimensionality in one direction, in that direction you might be interested in the dispersion.

Hi Sholihun Sholihun , do you have a last name or first name?

Sholihun is your full name?

just curious :-)

Hello everyone,

Phonon calculations (Phonon Band Structures, Phonon DOS, and thermal properties) in materials science using VASP and phonopy are explained on the Youtube Channel. Please find the link below:

https://bit.ly/2UtvbHE

https://www.youtube.com/watch?v=FX7WjL074g4

Best regards,

Rasoul Khaledialidusti

hello

What properties are we looking at when deciding the size of the supercell?

Federico Brivio