The ABINIT Users Mailing List ( CLOSED )

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

Dear ZhangtingPKU,

On 04 Aug 2006, at 10:01, zhangtingPKU wrote:

> Dear all
>
> 	    I'm interested in the phonon-phonon interaction problem, like  
> the Umklapp process. To handle such a process like an optic phonon  
> spliting into two acoustic phonons with ab-initio method, we need  
> the 3rd order expansion of the potential:
>
>          U3= (1/6)sigma(B*R1*R2*R3)
>
>         And in particular, the 3rd order anharmonic coefficients  
> are the most important.

Right.

> I've read the paper "Density-functional approach to nonlinear- 
> response coefficients of solids" (PRB 39,13120, Year 1989), and I'm  
> interested in whether the ABINIT code can perform such a third- 
> order coefficients calculation.

Unfortunately, such a calculation using the 2n+1 theorem, is not  
implemented in the present version of ABINIT. Several other 3rd order  
coefficients can be computed
based on the 2n+1 theorem in ABINIT, but not the anharmonic phonon  
coefficients.

> This kind of task is not included in the tutorials, and I have made  
> some attempt but it failed. Can someone tell me how can I perform  
> this calculation? Thanks!
>         In attachment are my test files and the error message in  
> log file. I don't clearly know what's the meaning of the keywords  
> like "rf2phon" and "rf3phon". Does this mean the third phonon or  
> the 3rd order perturbation?

These input variables are not used in the present version of ABINIT.
The point is that, in the precursor of the DFPT part of ABINIT,  
called "RESPFN" (dating back 1990-1995), there was an implementation
of the computation of phonon-phonon interaction coefficients, for the  
Gamma point only (see the results
published in Phys. Rev. A 52, 1096 (1995), esp. page 1111 ). But,  
when the ground state ABINIT (v1) was merged
with RESPFN, some parts of RESPFN were left "temporarily" ... and  
never included again ...
So, some input variables are present, but not the computation.

If you are interested in the decay of a particular high-symmetry  
phonon, it should be possible to extract the
needed coefficients from coupled linear-response and finite- 
difference calculations :
compare the interatomic force constants for a geometry containing
this high-symmetry phonon in a frozen state to those derived from an  
unperturbed geometry calculation ...

Best wishes,
Xavier Gonze