[QE-users] ?= Recover phonons frequencies from the eigenmode

[Lorenzo Paulatto]

Possibly, here I'm on holiday and I can't really check, bu I think that it
is, safer to see this kind of derivative in cartesian coordinates than
think what it means to rotate on the basis of the displacements, there
could be a d u/d x factor

-- 
Lorenzo Paulatto
Written on a virtual keyboard with real fingers

On Sat, 14 Jul 2018, 11:25 JAY Antoine, <Antoine.JAY at isae-supaero.fr> wrote:

> Dear Lorenzo,
> I also forget to precise that as (R0+i*0.01U) I mean the norm of i*0.01*U
> which I defined in the 3Nat space as sqrt(sum_n(at_n_X^2+at_n_Y^2+at_nZ^2))
> Do you think this can be another source of error?
>
> Antoine Jay
>
>
> On Saturday, July 14, 2018 11:09 CEST, "JAY Antoine" <
> Antoine.JAY at isae-supaero.fr> wrote:
>
>
>
>
> Dear Lorenzo,
> As X I convert the atomic displacement to meters:
> (R0+i*0.01*U)*alat*au2meters
> where alat is the unit cell parameter (in a.u.)
> au2meters convert a.u to meters.
> R0/i*0.01U is in alat units (cubic cell)
>
> as Y I used the enery obtained in Ry ploted in Joules
> so d^2E/dXdX is in kg/s^2.
>
> I think that the difficulty of obtaining someting comparable is in the
> divison by the masses to obtain a result homogeneous to 1/s^2 (omega^2)
>
> In fact the dynamical matrix is filled by 1/sqrt(M_ati*M_atj)
> d^2E/dRatidRatj
>
> So the equivalent mass for the eigenmode obtained by diagonalising the
> matrix must be more complicated than just the reduce mass?
>
> If all my atoms are the same I just have to divide by one mass, but if
> not....
>
> Antoine
>
>
>
>
>
> On Saturday, July 14, 2018 10:51 CEST, Lorenzo Paulatto <paulatz at gmail.com>
> wrote:
>
>
> Hello Antoine,
> Your procedure does not look obviously wrong to me, but you did not say
> what X is.
>
> --
> Lorenzo Paulatto
> Written on a virtual keyboard with real fingers
>
> On Sat, 14 Jul 2018, 10:43 JAY Antoine, <Antoine.JAY at isae-supaero.fr>
> wrote:
>
>> Dear all,
>> I would like to (re)obtain the phonons frequencies that I first obtained
>> using DFPT but from finite difference.
>>
>> Lets be R0 the ground state atomic positions and U the normalised atomic
>> displacement of a normal mode obtained from DFPT.
>> I have calculated the total energy from DFT of 11 structures R0+i*0.01*U
>> with i variing from -5 to 5. The so obtained curve is fitted with a second
>> order polynom a0+a1*X+a2*X^2, so that I obtain the second order derivative
>> of the total energy with respect to the atomic displacements of the studied
>> mode: 2*a2. I then divided by the atomic mass (one type of mass) and I
>> should obtain the omega^2, but my resulting value is 3 or four times to big.
>>
>> I use a cubic supercell with one type of atom.
>>
>> Did someone already performed this kind of work?
>> How should I do with differents atomic masses?
>>
>> Thank you very much for your help,
>>
>> Antoine Jay
>>
>>
>>
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>
>
>
>
>
>
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