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

Dear Stephane,

On 07 Aug 2006, at 09:48, Stephane BECU wrote:

Abinit computes the electronic dielectric tensor via a linear response

calculation (2nd derivative of the energy) from DFPT. It also computes the

static dielectric tensor (at finite frequencies ie the ionic part of the

dielectric tensor) and the ELECTONIC NON-LINEAR susceptibilities via a

non-linear response calculation (3rd derivative of the energy) from DFPT.

What I am interested in are the STATIC NON-LINEAR susceptibilities (at

finite frequencies). In fact I think it is not available from DFPT with

abinit, but I think it could be possible to calculate them from a Berry

phase calculation. Am I right?

Stéphane

Thanks, this is much more detailed than you previous post. 

So, you are not interested by the frequency dependence in the optical

range, but in the one in the frequency range typical of nuclear motion, or even below.

Actually, you will have to consider  frequency behaviors typical

of nonlinear phenomena (rectification, second harmonic generation,

frequency mixing) :  if you apply an electric field at frequency omega,

the linear reponse change of polarization will have frequency omega,

by the non-linear change of polarization will have frequencies 0 (rectification) 

and 2*omega (frequency doubling).

Concerning ABINIT, supposing one approximates the electronic frequency dependence by the 

zero frequency response, one will need, in addition to the

electronic non-linear susceptibilities, and Raman tensor, that are already

computed in ABINIT, also at least the change of dynamical matrix at gamma,

with respect to an applied electric field. The latter is not coded using the 2n+1

theorem in ABINIT. However, you might have access to it either by a brute

force finite-difference calculation of polarization (Berry phase) change under a frozen phonon (2nd derivative) 

or by a coupled finite field and linear reponse calculation of dynamical matrix, as very recently

coded by Xinjie Wang (and coworkers David Vanderbilt and Don Hamann). Other information,

like anharmonic force constants, might be needed, but I have not worked out the formalism ...

In any case, the closest to your problem is the work that Marek Veithen did, about

electro-optic coefficients (Phys. Rev. Lett. 69, 187401 :1-4 (2004) ;

Phys. Rev. B 71, 125107:1-14 (2005), but there are several additional contributions in your problem.

Good luck,

Xavier