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

Dear Corsin,

corsin.battaglia@freesurf.ch wrote:
> Dear abinit users
>
> I am still calculating phonons for the metallic compound NbTe2.
>
> In my initial unrelaxed calculation at the experimental crystal 
> structure, the phonon bandstructure exhibited imaginary frequencies 
> discussed several times on the ML. After relaxation of the structure 
> (maxfor=0.022 eV/A), these imaginary phonon modes disappeared.
>
> In an article by Ph. Ghosez et al, which I found at
> www.gl.ciw.edu/~cohen/meetings/ferro2000/proceedings/ghosez.pdf, phonon
> dispersion relations for ABO3 compounds are calculated at the 
> experimental lattice constants, although this corresponds to the effect 
> of an external pressure of 8.7 GPa. In Ph. Ghosez et al., PRB 60, 836 
> (1999) calculations for BaTiO3 are also carried out at the experimental 
> volume. The resulting LDA phonon dispersion relations exhibit imaginary 
> frequencies.
>
> My calculation at the experimental crystal structure of NbTe2 
> corresponds to a pressure of 4 GPa. In fact, my results are obtained for 
> an idealized hexagonal crystal structure, whereas the real laboratory 
> crystals exhibit a monoclinically distorted version of this idealized 
> structure. Instabilities in the phonon bandstructure are found at 
> q-vectors, coinciding approximately with the experimentally observed 
> modulation of the monoclinic structure. This has also been observed by 
> X. Gonze et al. in 
> www.gl.ciw.edu/~cohen/meetings/ferro2000/proceedings/gonze.pdf for 
> two-dimensional PbO layers.
>
> Under which conditions, one can work at unrelaxed structure parameters? 
> My current knowledge suggests that the interesting imaginary phonon 
> branches necessarily disappear for a LDA relaxed structure (harmonic 
> approximation valid). To which extend the interpolation performed by 
> anaddb is responsible for imaginary modes (in the case of PbO, 
> increasing the q-point grid results in a weaker instability, direct 
> calculation yields no instability)? Do the
> imaginary modes become stabilized (real valued), when anharmonic terms 
> are included in the calculation? Is it justified to make predictions 
> concerning possible phase transitions based on these instabilities?

Just to be sure that I understand correctly :
you are trying to predict an incommensurate phase transition,
where, experimentally, the average phase in monoclinic, while there
is another phase with higher symmetry.

This kind of situation was explored
by Razvan Caracas, who presented recently his PhD thesis under my supervision.
You should contact him : r.caracas@gl.ciw.edu ,
and get his thesis, as well as different recent papers.

To summarize the current understanding :
- on theoretical grounds, one should compute the phonon band structure
 from a theoretically stable phase (usually the low-symmetry one),
 and observe a small instability (if the stable phase at OKelvin
 is the incommensurate one)
- unfortunately, the required accuracy is quite difficult
 to reach, because these effects are very small, thus any numerical
 convergence is made quite difficult, and tiny effects from the
 choice of the XC functional, k-point sampling, or the interpolation 
technique might matters
- moreover, as you mention (if I understand correctly), even the prediction
 of the average phase might be difficult, because the LDA gives in effect
 lattice parameters that are in general too low, corresponding to a spurious
 pressure, and the wrong phase stabilize at that pressure
- our most successfull case was Pb_2MgTeO_6, in which there is definitely
 an instability in a whole region of non-zero q vectors,
 although different from experiment ...
- further studies of incommensirabilities in PbO, as well as in AuTe2
 are still inconclusive, due to the above-mentioned problems.

So, please contact Razvan, to get more information.

Best wishes,
Xavier