[Pw_forum] Dielectric constant with Lyddane-Sachs-Teller relation

[TuanAnh Pham]

Dear Pwscf users,

I have a question about calculation of the static dielectric constant.
In the phonon code the high frequency dielectric constant is given and in
order to
find \epsilon_0 we need to add the ionic contribution. The ionic
contribution can be
defined as in this link of Quantum-espresso:
http://www.quantum-espresso.org/wiki/index.php/Dielectric_constant
as well as in several papers (Gonze et al, PRB 55, 10355 (1997)):

\epsilon_0 - \epsilon_{\infty} =
4*pi*\sum_{m}{\frac{S_m}{\omega^2_m}}            [1]

in which omega_m is the phonon frequency and S_m is the mode-oscillator
strength.
On another hand, \epsilon_0 can also be calculated by Lyddane-Sachs-Teller
(LST)
relation using LO-TO splitting provided in the code:

\frac{\epsilon_0}{\epsilon_{\infty}} =
\prod{\frac{\omega^2_LO}{\omega^2_TO}}  [2]

Could you please let me know what is the different between these two methods
?
Is that correct that the LST relation only works for the system with
sufficient symmetry?

Thank you very much and best regards,
Tuan Anh.
-- 
Tuan Anh Pham
Graduate Student
University of California, Davis
Phone: 530-752-0957
Homepage: http://angstrom.ucdavis.edu/
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