Periodic frequency calculations

[Aaron Deskins <ndeskins_at_purdue.edu>]

 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