Dear Wang, H:
>  Suppose a uniaxial crystal(no cubic): c>a=b. Suppose there is a
> double-degenerate polar E_u mode, in which all atoms move in the a-b plane.
> If the wavevector around Gamma point is in the a-b plane, the degenerate E
> mode will split into LO and TO mode.
> Am I right?
It is probable for some ionic crystals, but still depends.
Maybe the Equ. 98 (nonanalytic part of the dynamical matrix) in Rev. Mod. Phys. 
73, 515 (2001) by prof. S. Baroni etc. and the related parts in the book 
"Dynamical Theory of Crystal Lattices" by M. Born & K. Huang can give you much 
information if these things are important/interesting to you.
In addition, is the method "finite difference" you mentioned exactly the 
"frozen phonon" or "small displacement" method? If so, the treatment like that 
in PWSCF should be good to obtain a satisfied LO/TO splitting, although 
honestly I haven't done this in the "frozen phonon" method. Some people propose 
other methods, like using a prolonged supercell, which I think, could not fully 
describe the long-range dipolar interaction, because of its long-range 
character (as prof. Stefano de Gironcoli said ~1/R^3).  
Best Wishes!
Yours Sincerely
L. F. Huang
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L.F.Huang(???) DFT and phonon physics
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Add: Research Laboratory for Computational Materials Sciences,
Instutue of Solid State Physics,the Chinese Academy of Sciences,
P.O.Box 1129, Hefei 230031, P.R.China
Tel: 86-551-5591464-326(office)
Fax: 86-551-5591434
Our group: http://theory.issp.ac.cn
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