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["Wu Rongqin" <g0203654@nus.edu.sg>]

Dear Dr. Mikami,

    Thank you very much for your directions. Now at present I am reading your 
publication:  Lattice dynamics and dielectric properties f TiO2 anatase: A 
first principle study ( PRB, 66,155213,2002 ). In it you gave the relation 
between epsilon_0 and epsilon_infinity by the mode oscillator strength and 
the omega. Your said that omega is the wave number of the mode m, however, 
this may be questionable as I summed over the optical modes to get epsilon_0 
by hand. Or in other words, omega should be the frequency of the mode m. 
would you please check it? Or maybe I am wrong.
    This does no harm to the significance of your paper, however, a 
clarification will be helpful to our novices.

    Regards

    Rongqin Wu 

-----Original Message-----
From: mmikami@rc.m-kagaku.co.jp [mailto:mmikami@rc.m-kagaku.co.jp] 
Sent: 2004年1月9日 17:47
To: forum@abinit.org
Subject: Re: [abinit-forum] Soft Phonon modes

Dear Rongqin Wu:

Please let me add just one more comment:
If you have the following book in your book-shelf/library,
it will be a good idea to check chapter 4 (in particular 4-A):
Walter A. Harrison, "Electronic Strcutre and the Properties of Solids"
(Dover, 1989) ISBN: 0-486-66021-4

There is an explanation regarding Prof. Ghosez's first remark ("to be 
rigorous...") :
Taking the limit of zero frequency In the frequency-dependent
polarizability formula (which is derived from Kubo-Greenwood formula)
--- and making use of Kramers-Kronig relations --- ,
we may identify the zero-frequency limit of the real part of the 
polarizability
with the susceptibility under the application of the static electric 
field E,
by noting the applied field E coresponds to a perturbing potential eEx.
(x: direction of the applied field E)  For the detail, please read the 
text.

Best wishes,
Masayoshi

On 2004.1.9, at 18:04 Asia/Tokyo, Philippe Ghosez wrote:

>> Dear Dr Ghosez,
>>
>>    I find that the dielectric tensor from abinis run is actually the 
>> dielectric tensor for zero frequency. However, in your publications 
>> you gave lot of tensor at infinite frequency. How to do such a 
>> calculation? Give me some hints, please
>>
>>    Rongqin Wu
>>
>
> Dear Rongqin Wu:
>
> In the computation of long range forces (as well as for the LO-TO 
> splitting), we use indeed \epsilon_\infty that corresponds to the 
> ELECTRONIC contribution to \epsilon.
>
> Abinit can compute both :
>
> - \epsilon_\infty : this corresponds to the dielectric constant as 
> measured at high frequency (high enough to avoid the ionic 
> contribution, ie optical range). It corresponds to the ELECTRONIC 
> contribution to epsilon, accessible directly with ABINIT, considering 
> the electric field perturbation. What could be confusing is that the 
> calculation is artificially done at zero frequency. The result 
> corresponds however to epsilon_infty because the ions are kept fixed. 
> Only the electronic contribution is considered and it is assumed it is 
> nearly independent of the frequency (to be rigorous the computed value 
> should be compared to an extrapolation at zero frequency of the 
> dielectric constant measured in the optical range).
>
> - epsilon_0 : this corresponds to the dielectric constant as measured 
> at low frequency. It corresponds to the electronic contribution 
> (epsilon_infty) + an ionic contribution computed from the knowledge of 
> the frequencies and IR oscillator strengths of the TO phonon modes at 
> Gamma.
>
> Best wishes,
>
> Philippe.
>
>
> ----------------------------------
> Philippe GHOSEZ
> Universite de Liege
> Institut de Physique, Bat. B5
> Allee du 6 aout, 17
> B- 4000 Sart Tilman
> BELGIUM
>
> Phone : ++(32) (0)4-366.36.11
> Fax   : ++(32) (0)4-366.29.90
> E-mail: Philippe.Ghosez@ulg.ac.be
>
> http://www.ulg.ac.be/phythema
> ----------------------------------
>