Subject: Periodic frequency calculations

From: Aaron Deskins <ndeskins_at_purdue.edu>
Date: Tue, 14 Sep 2004 09:52:22 -0500

Hello fellow CCL'ers,
    
      I'm attempting some frequency (phonon) calculations with the VASP 
periodic DFT program. I'm hoping that those knowledgable with these type 
of calculations can help me out. After doing some reading, I think I 
have the basic theory down. First atom positions are perturbed from 
equilibrium to get the matrix, D(R), with elements of form 
d^2(V)/dr1dr2, or second partial derivatives of energy with respect to 
displacements 1 and 2. Next Bloch's theorem is applied to get the 
dynamical matrix: D(k) = Sum [ D(R)*exp[-i*dot(k,R)]. One can 
diagonalize the dynamical matrix to get the phonon spectrum. Does this 
sound right?
  
      In practice, VASP only calculates the spectrum at the gamma point, 
so in this case D(k) = D(R). In theory the code could be modified to 
include other k-points if needed. 
     
      What is the relationship between IR frequencies from experiment 
and the calculated phonon spectrum? Is there a special relationship 
between the IR frequencies and the gamma point?

      Any help, suggestions, comments, references, etc. are appreciated.

Aaron Deskins
Purdue University
Chemical Engineering