[Pw_forum] Separating Raman modes

[Stefano Baroni]

Dear Sophia & Alexandra:

I am not sure that group theory (which I am fond of) would help much  
here. For a disordered system modeled by a supercell, I see few other  
choices than estimating the Raman activity of each mode, and then sum  
the contributions from all the modes. The method by Mauri and  
coworkers (whose implementation status in QE is unknown to me) seems  
particularly suitable in this case. For those who do not know, the  
(non-resonant) Raman activity is given by the variation of the  
polarizability linearly induced by each vibrational mode (here is  
where selection rules ultimately come from). This "traditional" way of  
calculating the Raman activity is  not very practical for large  
supercells, because it requires several polarizability calculations  
for each phonon mode. An alternative would be 3rd order perturbation  
theory, which used to be implemented in QE. A bit awkward because of  
complications arising from the infamous q->0 limits that plague any  
polarizability calculations in infinite systems. The third (and most  
elegant) way is Mauri and collaborators'. The first derivative of the  
polarizability with respect to an atomic displacements is a third  
derivative of the energy, once with respect to a nuclear position,  
twice with respect to the strength of the electroc field. By changing  
the order of differentiation, this can be seen as the second  
dericative of the force acting on atoms with respect to an applied  
alectric field. This can be computed by 2nd order perturbation theory  
in the strength of the field.

An alternative is to rely on some polarizable-bond model for the  
polarizability and to estimate its derivative with respect to nuclear  
distortions using such a semi-empirical model.

Hope this helps.
Stefano

On Jun 23, 2009, at 10:31 AM, alexandra.carvalho at epfl.ch wrote:

> Dear Sophia,
>
> To select which modes are Raman active you must use the selection  
> rules.
> The following paper may be of help (see also the tables in it):
>
> Rosseau et al. Journal of Raman Spectroscopy 10, 253 (1981)
>
> If you are starting, I recommend having a look at the selection rules
> for molecules, for example in Tinkham, Group theory and Quantum
> mechanics (Dover, 1992,NY) pp248.
>
> Most likelly, you will be interested in the allowed transitions with  
> highest
> frequency.
>
> Hope this helps,
>
> Alexandra
>
>
> Quoting Jonathan <sophia.nishad at gmail.com>:
>
>> Dear users,
>>
>> I computed phonons only at the gamma point for a 64-atom binary
>> alloy. How do I separate the three main Raman modes.
>>
>> Would it be possible to get some help?
>> thanks,
>> --
>> Sophia
>> UCB, USA
>>
>
>
>
> -- 
>
> Alexandra Carvalho,
> Ceramics Laboratory
> Swiss Federal Institute of Technology of Lausanne (EPFL)
>
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---
Stefano Baroni - SISSA  &  DEMOCRITOS National Simulation Center -  
Trieste
[+39] 040 3787 406 (tel) -528 (fax) / stefanobaroni (skype)

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