[Pw_forum] absorption spectrum &dielectric constant of turboTDDFT

[dario rocca]

Dear SungHwan,
please refer to
http://arxiv.org/pdf/1402.0486.pdf
and
http://urania.sissa.it/xmlui/bitstream/handle/1963/5797/turboTDDFT-CPC.pdf?sequence=1
for more details.

In the output of the postprocessing chi_1_1 is the xx component of the
dynamical polarizability, chi_1_2 the xy component, etc.
Often chi is indicated as \alpha in the papers.
Specifically you would have

Component      energy of the perturbation      real part of
chi                          imaginary
                      (indicated either as E or \omega)
chi_1_1=          0.000000000000000E+00     0.955769346791472E+01
0.000000000000000E+00
.........

As you correctly say the absorption spectrum is related to the imaginary
part of the average of chi multiplied by E (the energy E is often
indicated as \omega).
This averaged quantity is contained in S(E). Specifically S(E) is the
strength function defined as
S(E)=2m/(\pi*e^2*\hbar) * E*Im[chi(E)], where chi has been averaged over
the 3 spatial directions.
This definition is convenient because S(E) satisfies the f-sum rule.
So if you extract S(E) and plot it you will have the absorption spectrum.
Let me know if it's still not clear
Best,
Dario




On Tue, Jul 19, 2016 at 4:01 PM, SungHwan Choi <sunghwanchoi91 at gmail.com>
wrote:

>     hi, I am a newbie for turboTDDFT. Now, I ran a simple example. It was assume.
> Now I have prefix.plot_chi.dat  file. then I don't know how to generate
> absorption spectrum from that file and dielectric constant values. As far
> as I understood, the absorption spectrum is related to imaginary part of
> average \chi value. but in the file there are 9 values
>          chi_1_1
>          chi_2_1
>          chi_3_1
>          chi_1_2
>          chi_2_2
>          chi_3_2
>          chi_1_3
>          chi_2_3
>          chi_3_3
> This is 3*3*3 tensor. how do I get an absorption spectrum and dieletric
> constant values? by the way S(E) means what?
>
> Sincerely
> Sunghwan Choi
>
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