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<p>There is the relation [1]: <br>
</p>
<p><span class="texhtml">λ = hc/E</span></p>
<p><span class="texhtml">Then with that:<br>
</span></p>
<p><span class="texhtml">λ = limit_{E→0} [hc/E] = </span><span
style="left: 369px; top: 1177.77px; font-size: 12.5721px;
font-family: serif; transform: scaleX(1.00646);"
role="presentation" dir="ltr"> </span><span class="texhtml"><span
style="left: 369px; top: 1177.77px; font-size: 12.5721px;
font-family: serif; transform: scaleX(1.00646);"
role="presentation" dir="ltr">∞</span></span><span
style="left: 369px; top: 1177.77px; font-size: 12.5721px;
font-family: serif; transform: scaleX(1.00646);"
role="presentation" dir="ltr"></span><span class="texhtml"></span></p>
<p>I seem to be missing what you defined epsilon_0 and epsilon_oo
as.</p>
<p>There is ε0 defined as the dielectric constant at low frequency
and ε<span class="texhtml"><span style="left: 369px; top:
1177.77px; font-size: 12.5721px; font-family: serif;
transform: scaleX(1.00646);" role="presentation" dir="ltr">∞</span></span>
the dielectric constant at high frequency like in equation (18) of
[2],</p>
<p>where ε0, ε(0), or εs might be also be known as the static
electric constant while ε<span class="texhtml"><span style="left:
369px; top: 1177.77px; font-size: 12.5721px; font-family:
serif; transform: scaleX(1.00646);" role="presentation"
dir="ltr">∞</span></span> the optical dielectric constant as
given in section "Debye relation" on page 12 in [3].</p>
<p>Or the epsilon_0 as defined as ε1(0), where ε1(ω) is the real
part and ε2(ω) is the imaginary part of the dielectric function
like in equation 1 of [4]:<br>
</p>
<p>ε(ω) = ε1(ω) + iε2(ω)<br>
</p>
<p><span style="left: 293.372px; top: 1142.64px; font-size:
18.1818px; font-family: sans-serif; transform: scaleX(1.03398);"
role="presentation" dir="ltr">where it may be that </span>ε1(0)
and ε1(<span class="texhtml"><span style="left: 369px; top:
1177.77px; font-size: 12.5721px; font-family: serif;
transform: scaleX(1.00646);" role="presentation" dir="ltr">∞</span></span>)
are given by equations 144 and 145 seen in [5].<br>
<span style="left: 293.372px; top: 1142.64px; font-size:
18.1818px; font-family: sans-serif; transform: scaleX(1.03398);"
role="presentation" dir="ltr"></span></p>
<p>Equation 5 in [4] has<br>
</p>
<p>ε1(ω) <span class="ILfuVd NA6bn"><span class="hgKElc">∝
Integral{</span></span><span class="ILfuVd NA6bn"><span
class="hgKElc">ε2(ω)}<br>
</span></span></p>
<p>where in equation 3 of [4]<br>
</p>
<p><span class="ILfuVd NA6bn"><span class="hgKElc">ε2(ω) </span></span><span
class="ILfuVd NA6bn"><span class="hgKElc">∝ </span></span><span
style="left: 590.775px; top: 412.364px; font-size: 18.1818px;
font-family: sans-serif;" role="presentation" dir="ltr">Integral{δ</span><span
style="left: 599.543px; top: 412.364px; font-size: 18.1818px;
font-family: sans-serif;" role="presentation" dir="ltr">(energy)}</span><br>
</p>
<p>I believe it was article [6] where equations such as 2.26 are
used by WIEN2k [7,8] that seems to correspond to equation 5 in
[4].<br>
</p>
<p>The energy you are referring to is ћω in equation 2.19 of [6] (or
equation 3 in [4]) unless I missed something and it is another
energy that is being talked about.<br>
</p>
[1]
<a class="moz-txt-link-freetext" href="https://en.wikipedia.org/wiki/Planck%E2%80%93Einstein_relation#Spectral_forms">https://en.wikipedia.org/wiki/Planck%E2%80%93Einstein_relation#Spectral_forms</a><br>
[2] <a class="moz-txt-link-freetext" href="http://www.lajpe.org/sep14/03_LAJPE_928_Sagadevan_Suresh.pdf">http://www.lajpe.org/sep14/03_LAJPE_928_Sagadevan_Suresh.pdf</a><br>
[3]
<a class="moz-txt-link-freetext" href="https://assets.testequity.com/te1/Documents/pdf/keysight/dielectric-measuring-basics-an.pdf">https://assets.testequity.com/te1/Documents/pdf/keysight/dielectric-measuring-basics-an.pdf</a><br>
[4] <a class="moz-txt-link-freetext" href="https://arxiv.org/abs/1909.11419v1">https://arxiv.org/abs/1909.11419v1</a><br>
[5]
<a class="moz-txt-link-freetext" href="https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.718.9681&rep=rep1&type=pdf">https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.718.9681&rep=rep1&type=pdf</a><br>
[6] <a class="moz-txt-link-freetext" href="https://arxiv.org/abs/cond-mat/0402523v1">https://arxiv.org/abs/cond-mat/0402523v1</a><br>
[7] <a class="moz-txt-link-freetext" href="http://www.wien2k.at/events/ws2006/Optics_Vienna_April_2006.pdf">http://www.wien2k.at/events/ws2006/Optics_Vienna_April_2006.pdf</a><br>
[8] <a class="moz-txt-link-freetext" href="http://www.wien2k.at/events/ws2008/talks/Ambrosch-Optics.pdf">http://www.wien2k.at/events/ws2008/talks/Ambrosch-Optics.pdf</a><br>
<br>
<div class="moz-cite-prefix">On 11/29/2021 11:30 PM, Fecher, Gerhard
wrote:<br>
</div>
<blockquote type="cite"
cite="mid:dc41b65f8590490d9f6efcb73da532f8@uni-mainz.de">
<pre class="moz-quote-pre" wrap="">What is the wavelength at zero energy ?
Ciao
Gerhard
DEEP THOUGHT in D. Adams; Hitchhikers Guide to the Galaxy:
"I think the problem, to be quite honest with you,
is that you have never actually known what the question is."
====================================
Dr. Gerhard H. Fecher
Institut of Physics
Johannes Gutenberg - University
55099 Mainz
________________________________________
Von: Wien [<a class="moz-txt-link-abbreviated" href="mailto:wien-bounces@zeus.theochem.tuwien.ac.at">wien-bounces@zeus.theochem.tuwien.ac.at</a>] im Auftrag von Atefe Marasi [<a class="moz-txt-link-abbreviated" href="mailto:13marasi@gmail.com">13marasi@gmail.com</a>]
Gesendet: Montag, 29. November 2021 23:25
An: <a class="moz-txt-link-abbreviated" href="mailto:wien@zeus.theochem.tuwien.ac.at">wien@zeus.theochem.tuwien.ac.at</a>
Betreff: Re: [Wien] How to find the exact value of infinte epsilon?
Dear Xavier
Thank you for your prompt reply.
</pre>
<blockquote type="cite">
<pre class="moz-quote-pre" wrap="">Infinite epsilon means that you extrapolate ...
</pre>
</blockquote>
<pre class="moz-quote-pre" wrap="">
Do you mean that infinite epsilon (epsilon_oo) is nothing more than epsilon zero (epsilon_0)?
</pre>
<blockquote type="cite">
<pre class="moz-quote-pre" wrap="">You must plot the real part...
</pre>
</blockquote>
<pre class="moz-quote-pre" wrap="">I have plotted the real part of epsilon in z direction(for BaTiO3), as would be seen from the following link:
<a class="moz-txt-link-freetext" href="https://imgurl.ir/uploads/p793339_infinite_epsilon.jpg">https://imgurl.ir/uploads/p793339_infinite_epsilon.jpg</a>
As expected, the above figure shows that the real part of the epsilon tends to unity at high frequency. From this plot, the epsilon_0 is about 6.5, but I am still not sure that whether infinite epsilon is really equal to epsilon_zero (epsilon_oo =? epsilon_0).
</pre>
<blockquote type="cite">
<pre class="moz-quote-pre" wrap="">You must be careful because if you have a band gap and a bad description of the gap value ...
</pre>
</blockquote>
<pre class="moz-quote-pre" wrap="">
Thank you for this hint. I will try to obtain a suitable band gap by TB-mBJ functional. However, at this step, I need to find out the difference between epsilon_oo and epsilon_0. In my opinion, which I am not sure about it, epsilon_00 would be evaluated at infinite energy, while epsilon_0 would be evaluated at zero energy, as deduced from their names.
Thank you for your nice cooperation.
Best Regards
Atefe Marasi
</pre>
</blockquote>
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