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[Xavier Gonze <gonze@pcpm.ucl.ac.be>]

Dear Narayani,

Narayani Choudhury wrote:
> Dear Prof. Gonze,
>
> I have used ABINIT (v403)  for
>
> (i) long wavelength  linear response studies using ddk and homogeneous
> electric field perturbation for a ferroeelectric perovskite based
> supercell with few unstable modes to study their LO-TO splittings. The
> mode effective charges are large and I have the LO and TO  frequencies,
> but do not know their correlation and therefore LO-TO splittings through
> this approach
>
> (iii) To understand the correlation, I computed the LO-TO splittings from
> the IR oscillator strengths (as described in Rignanese et. al., PRB63,
> 104305 (2001).
>
> there are differences in the LO-TO splittings obtained between approach
> (i) and (iii) due to the mixing of the eigenvectors.

Yes.

> Rignanese et al. have used a one-to-one correlation in zircon for the
> LO-TO splitting using  electric field perturbations; instead can I use the
> IR oscillator strength calc and use the closest LO freq obtained from the
> electric field perturbation?  Which of these 2 approaches gives the more
> accurate "LO" frequency? Rignanese et al. say that the IR oscillator
> strength approach is a first order approximation.. are the numbers here
> less precise than using the E-field pert approach?

The (i) approach gives the correct LO frequencies (as well as the TO, that are
not affected by the electric field). Approach (iii) is approximate only ...

Referring to section VIII B of PRB55,10355 (1997), in order to obtain
the TO mode frequencies, one only considers the first term
in the right-hand side of Eq.(59), and diagonalize it.
When the full Eq.(59) is used, and diagonalized, some of the modes, depending 
on
the direction, are modified, while others do not feel anything due to Eq.(61).
With the full diagonalisation, usually, the modes that are changed are mixed 
together.
However, when the symmetry constraints are large enough, one might use the
Eq.(62) and get exactly the same results as with Eq.(59). This is not always 
the case.
If the symmetry constraints are not large enough, with Eq.(62) one obtains 
approximate values.

Let us now comment about the the identification of similarity between the LO 
modes
and the TO modes.
What you can do, in all cases, is to compute the matrix of overlap between the
eigenvectors of the first term in the right-hand side of Eq.(59) and those
of the full Eq.(59). This must be done by hand (one should write
a small script, using output of ANADDB).
For example, such overlap was computed in the Tables III and V
of Ghosez, Gonze and Michenaud, Ferroelectrics 194, 39-54 (1997)
and Table III of Ghosez, Gonze and Michenaud, Europhysics Letters 33, 713 
(1996).

Two final comments :
(1) do not forget that for different q directions, different
TO modes are affected by the electric field, and generate different LO modes.
(2) please, switch to v4.2 or v4.3 : v4.0 is obsolete ...

Xavier