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["Shtogun, Yaroslav" <yshtogun@cas.usf.edu>]

Thank you so much for respond!

________________________________

From: Xavier Gonze [mailto:gonze@pcpm.ucl.ac.be]
Sent: Tue 3/14/2006 8:00 PM
To: forum@abinit.org
Subject: Re: [abinit-forum] Number of valence bands?




On 14 Mar 2006, at 17:50, yshtogun@cas.usf.edu wrote:

>  Dear All,
>   I tried to calculate band structure of carbon nanotubes in 
> external electric field (using barryopt 4). I meet problem with 
> number ob bands:
>
> initberry: ERROR -
>   In a finite electric field calculation, nband must be equal
>   to the number of valence bands.
>
>  Does somebody know why for electric field calculation nband must 
> be equal to the number of valence bands? Why does it work only for 
> valence bands? Is this restriction for electric field? Can I 
> calculate the band structure for all bands with electric field?

Dear Yaroslav,

If you look at the theory of the computations under electric field 
(see the references mentioned
in the tutorial on non-linear optics , section 3,
http://www.abinit.org/Infos_v4.6/Tutorial/lesson_nlo.html#3 )
you will see that the Kohn-Sham equation is modified by the presence 
of a d/dk operator, that
couple different k points, as well as different bands at different k 
points ! This is correctly
defined only for the Hilbert space spanned by an isolated group of 
bands. So, technically,
one cannot generalize easily the finite-electric field approach to 
the set of conduction bands,
that usually cannot be disentagled from all the higher-lying bands.

Well, there are two more fundamental problems, even with the valence 
bands :
- first the very well-known point that Kohn-Sham band structure 
should NOT be identified with
  the quasi-particle band structure (but everybody knows that usually 
one can rely on it, except for the gap)
- second the fact that the notion of band structure looses its 
meaning when
  a solid is placed in an electric field ! Indeed, an electric field 
corresponds to a linear potential
  in space, and there are no such things as Bloch states in an 
electric field - hence no band structure.
So, keep in mind that the quantity advertised as eigenenergies in the 
finite-field approach
implemented in ABINIT are formal, mathematical, quantities.

Of course, for sufficiently small fields, one might nevertheless 
examine long-lived resonances,
  and construct a  band structure relatively to a "not too large" 
region of space, where
  the electric field does not vary too much (see also the 
litterature, especially
  Nenciu's review paper).

But, nothing corresponding to this for the conduction states is 
implemented in ABINIT, and it is likely that
formal developments (to see how to get conduction band long-lived 
resonances energies from the finite-electric field
formalism) are needed before thinking to an implementation ...

Xavier

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