# [Pw_forum] phonon: definition of dynamical matrix and the printed out omega in phonon

MMS mm2422 at cornell.edu
Wed Oct 31 07:43:22 CET 2012

Dear all,

I have a question regarding the definition of the dynamical matrix. First
let me set the stage.

I am working on a X Ray Thermal Diffuse Scattering model and the literature
talks about two types of definitions for the dynamical matrix in the
reciprocal space:
(link:
http://www.oldenbourg-link.com/doi/abs/10.1524/zkri.2005.220.12_2005.1009)

The first one searches for a solution for the wave that takes explicit
account of the basis atoms. This substitution is made  during the
derivation of the eigenvalue equation from the Newton's law M u'' = F
involving the dynamical matrix. So the polarization vectors obtained are
orthogonal to each other.
*u* = Real {1/sqrt{mass} *u_0* exp[i *k* . (*Real Space Lattice
Vector* +*basis_atom
position*) \omega_k t]}

The second one searches for a solution for the wave that doesn't do this
and hence obtains a set of polarization vectors that are not orthogonal to
each other.
*u* = Real {1/sqrt{mass} *u_0* exp[i *k* . *Real Space Lattice Vector* - i
\omega_k t]}

Sigh!! I hope I made sense. Well the crux is both yield two different
dynamical matrices. I want to know which one Espresso uses?

Now one more clarification. In the final output of phonon frequencies the
output file reads

Omega = .... [THz]

Now does this refer to angular frequency ? or should I multiply by 2*pi to
get the angular frequency.

Thank you in advance.

Regards,
Meenakshi
Graduate Student
Mechanical Aerospace Engg
Cornell
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