[Pw_forum] 2nd and 3rd energy derivatives using DFPT?

[Lorenzo Paulatto]

On Wednesday, 20 April 2016 07:51:30 CEST Sabry Gad Al Hak Moustafa wrote:
> Thanks Stefano;
> 
> But, what do you mean by "some"? I am interested specifically in Fe at high
> pressure, so, can QE do 3rd derivative for that?
> 

Dear Sabry,
the generalized code to compute 3rd derivatives w.r.t any three harmonic 
perturbations exists but is currently still private; it is undergoing the 
finishing touches and testing before being released to public (Physical Review 
B 87 (21), 214303). It will still be limited to norm-conserving 
pseudopotentials, LDA and GGA functionals. It works best in conjunction with a 
robust library of NCPP, such as the ONCV ones.

The public release will arrive at the end of June, in conjunction with a 
summer school that I am organizing: <http://qethermo2016.sciencesconf.org/>.
There is no problem with using the code right now, on a collaboration basis, 
but the time I have to provide support is very limited.

With regard to the 4th derivative, it is possible to obtain it from finite 
differences on top of the 3rd order, or on top of a phonon calculation. Some 
simple but not friendly scripts to run these calculation exist, like those 
used by Nicola Bonini of KIng's College London (Phys. Rev. Lett. 99, 176802).

If you are interested in perturbative corrections to harmonic phonons there 
are other approaches that can be used, that avoid computing the 4th order, 
such as the Stochastic Self-consistent Harmonic Approximation plus the 3rd 
order (Physical Review B 91 (5), 054304). Note that the SSCHA code is not 
public at the moment, its main author is Ion Errea of the University of the 
Basque Country.

HTH
Lorenzo


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Dr. Lorenzo Paulatto
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