The ABINIT Users Mailing List ( CLOSED )

[Fred Nastos <nastos@physics.utoronto.ca>]

just a brief comment...

On Friday 03 September 2004 10:54, Marek Veithen wrote:
>  At the opposite to the linear dielectric
> susceptibility chi^(1), that is necessarily positive,

I think you meant only the static limit chi^(1)(0), or the the
imaginary part, Im[chi^(1)] are necessarily positive. The real
part of the linear response may of course be negative at high
photon energy.

Regards,

Fred

> the chi^(2) can either be positive or 
> negative.
>    You should also note, that the sign of chi^(2) you compute with ABINIT
>    will depende on the orientation of your crystal axis.
>
> * Finally, the problem Wu Rongqin mentioned yesterday, has already been
>    reported by other people.
>    In order to compute a third-order energy derivative with respect to
> one or more
>    electric fields, I have to use a finite difference expression to
> compute the derivative
>    of a first-order wavefunction with respec to k. The way I implemented
> this
>    finite difference expression is quite stable in most circumstances.
> Nevertheless, there
>    are still some problems especially when you use a low number of
> k-points in your
>    calculation (f. ex. Wu Rongqin used ngkpt 2 2 2). In most cases, it
> is sufficient
>    to increase the number of k-points to circumvent this problem. In
> case of Wu's
>    input file, the problem should disappear if you use at least ngkpt 4 4
> 4.
>
>    In practical calculations on bulk crystals (at least those I did up
> to now),
>    this issue is not restrictive at all. In fact, in order to obtain
>    converged results, you have to use larger k-point grids than in a
> usual ground-state or
>    linear response calculations. In my calculations on ferroelectrics, I
> typically
>    used ngkpt 10 10 10 and for some semiconductors, I had to use ngkpt
> 16 16 16.
>    And for these large grids, there should be no problems at all.
>
> I hope, these few informations will help all those of you who are
> interested in doing
> non-linear response calculations. If you have still questions or
> suggestions,
> don't hesitate to contact me. Feedback is alway welcome.
>
> Marek
>
> Clovis Darrigan wrote:
> > Dear Wu and Abinitioners,
> >
> >     Actually for linear response, only the former can be obtained,
> >     right? because in the visible range, nonlinear as well as linear,
> >     is related to the properties of excitation states, which goes
> >     beyond lda, rhgit? But as for very low frequency, the perturbation
> >     only causes electronic polarization, right?
> >
> >
> > About non-linear optical properties : my thesis work was on their
> > calculation by sum over states method for linear, first non-linear and
> > second non-linear order (i.e. : alpha, beta, gamma, or khi(1), khi(2)
> > and khi(3)). Informations I need in input are only energie and
> > momentum transitions between all occupied and virtual bands. All
> > effects (SHG, THG, Kerr, Pockel, IDRI...) can be calculated with
> > respect to frequency(ies).
> >
> > Two years ago (during a postdoctoral position), I made an interface of
> > my program with the excellent ABINIT, and it gave me first interesting
> > results. But I was not able to finish properly this work because a
> > hierarchical superior don't give out MY work when I quit the
> > laboratory...
> >
> >     I tried but I got a negative nonlinear coefficient for ZnO, is
> >     this physical? I do not know why.
> >
> > For the first non-linear optical property, values can be negatives.
> >
> > I have a question about non-linear optical properties in v4.4. I read
> > it in the features but which effects will be available ?
> >
> > Sincerely,
> >
> >
> > Clovis Darrigan