About small displacement method for phonons

[Hyla Brook]

Dear All,

I have trouble to understand the calculation of phonon using small displacement method. I found people said the limitation of this method was that it requires the wave vector k orthogonal to the supercell size(?). Does it mean the wave vector is not any you want? why? I got really confused. Any idea is highly appreciated. Thank you!

H.B

[DrDu]

Yes. You have to do a full electronic calculation for each choice of the k vector of the displacement. The super-cell has to fit the period of the k-vector.

[Hyla Brook]

Yes. You have to do a full electronic calculation for each choice of the k vector of the displacement. The super-cell has to fit the period of the k-vector.

Thank you for reply Dr. Du. But in the program (e.g. phon), the number of k point is variable. That means we can choose any k wave vector we want in the BZ.

The tutorial of this program says the limitation of this method is we need a large supercell to make Hellmann-Feynman force negligible outside the supercell. I think this is easy to understand because the element of the dynamical matrix is a summation involving the force constants, which in principle has infinite terms. I asked that question because that explanation was mentioned as equivalent as this one. I cannot even understand that well.

Could you explain it more?