# [Pw_forum] About the Frozen Phonon Method

Tue Aug 2 08:18:41 CEST 2011

```Dear Prof. Baroni

Thanks again

> Dear Prof. Baroni
>
> I wonder shouldn't the plot show the same frequency for a range of
> displacements?
>
>
> what range? why should it?
>
>
-- Because if we are in the neighberhood of a minimum "where a quadratic
could be fitted", any displacement in that range should result the same
frequency. By displacement, I mean the same pattern but different in
amplitude.

> And the same freq. for the range to be the harmonic frequency? or the zero
> displacement limit, is the harmonic frequency?
>
>
> yes, by definition
>
>  And when I test the displacements with the same amplitude, but different
> in sign (regarding the inward and outward atomic movements in the basis) I
> do not get the same results.
>
>
> why should you?
>
> Shouldn't the plot have symmetry vs. the vertical axis?
>
>
> why?
>

-- Consider for example a linear chain of atoms, with 2 atoms per basis. The
optical mode is the result of the outward movement of the atoms (The one in
+a/2 moves towards +x and the one in -a/2 moves towards -x). I expect that
if I displace the atoms in an inward movement with the same amplitude as the
outward, I should see the same frequency (The one in +a/2 moves towards -x
and the one in -a/2 moves towards +x) because the 2 patterns present the
same mode, right? That is what I've done in the case of Diamond. Is my
expectation wrong?

>
> please, try you best to answer my questions, and I will make my best to let
> you understand
>
> SB
>
>

> Thank You again
>
>
> On Mon, Aug 1, 2011 at 6:33 PM, Stefano Baroni <baroni at sissa.it> wrote:
>
>> Hi Mohaddesh. I do not understand why you say that the calculated
>> frequency (which, I assume you define as 2 * Delta E / u^2 ???) does not
>> converge as u->0. According to your plot, it does, and to a reasonable
>> value. The finite slope of your plot around u=0 seems to me nothing but a
>> manifestation of cubic anharmonicity ... What's wrong in this? SB
>>
>>
>>
>> Dear users,
>>
>> I have plotted the harmonic frequency (obtained within the frozen phonon
>> approach) of Diamond as a function of atomic displacements (small
>> displacements in the [1 1 1] direction, u(1)=±(u,u,u) and
>> u(2)=±(-u,-u,-u) are the displacements of two atoms in the basis). I expect
>> to see a range of displacements that tend to the similar frequency, but
>> there is no convergence in the plot. Also, the displacements with the same
>> amplitude but different in sign, do not tend to the same frequency, which is
>> not what I expect, too. The plot is attached.
>> I was wondering if anyone could help me to find the source of error. I
>> should expect the mentioned symmetry, right? Why there is no convergence?
>>
>>
>> Yours,
>> ---------------------------------------------------------
>>
>> Room No. 323, Department of Physics,
>> University of Tehran, North Karegar Ave.,
>> Tehran, P.O. Box: 14395-547- IRAN
>> Website:  http://physics.ut.ac.ir
>>
>> ---------------------------------------------------------
>>
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>>
>>  ---
>> Stefano Baroni - SISSA  &  DEMOCRITOS National Simulation Center -
>> Trieste
>> http://stefano.baroni.me [+39] 040 3787 406 (tel) -528 (fax) /
>> stefanobaroni (skype)
>>
>> La morale est une logique de l'action comme la logique est une morale de
>> la pensée - Jean Piaget
>>
>> Please, if possible, don't  send me MS Word or PowerPoint attachments
>> Why? See:  http://www.gnu.org/philosophy/no-word-attachments.html
>>
>>
>>
>>
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>
>
> --
> ---------------------------------------------------------
>
> Room No. 323, Department of Physics,
> University of Tehran, North Karegar Ave.,
> Tehran, P.O. Box: 14395-547- IRAN
> Tel. No.: +98 21 6111 8634  & Fax No.: +98 21 8800 4781
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>
>  ---
> Stefano Baroni - SISSA  &  DEMOCRITOS National Simulation Center - Trieste
> http://stefano.baroni.me [+39] 040 3787 406 (tel) -528 (fax) /
> stefanobaroni (skype)
>
> La morale est une logique de l'action comme la logique est une morale de la
> pensée - Jean Piaget
>
> Please, if possible, don't  send me MS Word or PowerPoint attachments
> Why? See:  http://www.gnu.org/philosophy/no-word-attachments.html
>
>
>
>
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>
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