Dear Professor Stefano:<div>Thanks very much for your patient instruction.</div><div>I will read your mentioned paper carefully.</div><div>And now, I imagine that the phonon dispersion near Gamma point may look like:</div>
<div><div><br></div><div> ^ Frequency</div><div> |</div><div> |</div><div> <font class="Apple-style-span" color="#FF0000"><b>@@@@@</b> </font>|<font class="Apple-style-span" color="#FF0000"><b>@@@@@</b></font><b><font class="Apple-style-span" color="#FF0000"> </font></b><b><font class="Apple-style-span" color="#FF0000">LO</font></b></div>
<div> |</div><div> | </div><div><b> </b><font class="Apple-style-span" color="#000099"><b>$$$$$$$$$</b></font><b><font class="Apple-style-span" color="#FF0000">@</font><font class="Apple-style-span" color="#000099">$$$$$$$$$ TO</font></b></div>
<div> |</div><div> <-----------------------|-------------------------></div><div> Gamma wavevector near Gamma</div><div><br></div><div>When q->0, there is LO-TO splitting. </div>
<div>When q=0, q has no direction. Therefore,<span class="Apple-style-span" style="font-family: arial, sans-serif; font-size: 12.5px; border-collapse: collapse; "> optical modes can not be classified into longitude or transverse ones. As a result, at </span>q=0,<span class="Apple-style-span" style="font-family: arial, sans-serif; font-size: 12.5px; border-collapse: collapse; "> <font class="Apple-style-span" color="#000099"><b>$</b></font>=<b><font class="Apple-style-span" color="#FF0000">@.</font></b></span></div>
<div>However, there is not infinite crystal; and electric-static interaction always occurs for finite crystal.</div><div>Therefore, in experiment, LO-TO splitting exists at the q=0.</div><div><br></div><div><div class="gmail_quote">
On Fri, Apr 29, 2011 at 3:16 PM, Stefano de Gironcoli <span dir="ltr"><<a href="mailto:degironc@sissa.it">degironc@sissa.it</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
<div text="#000000" bgcolor="#ffffff">
the electristatic interaction at the origin of LO-TO splitting is
always present...<br>
<br>
for any q<>0 (even very small) it is included in the
calculation.<br>
<br>
in the limit of q->0 in non-metallic systems it gives origin to a
non analytic behavior that must be calculate separately.<br>
<br>
If you want to Fourier interpolate the phonon dispersions calculated
on a regular grid of q-points<br>
you are in trouble because non analyticity of the phonon dispersion
implyes long-range (1/R^3) interatomic force constants and so you
need to <br>
<br>
1) evaluate Z* and epsilon_infty in the limit of q->0 that
determine the non-analyticity<br>
2) remove from dynamical matrix in every q point in you grid an
electrostatic model that gives the correct non-analyticity for
q->0 and is smooth elsewhere<br>
3) Fourier interpolate the modified (hopefully short-range)
dynamical matrices <br>
4) add back the model in any q-point you want to study.<br>
<br>
This is what the sequence ph.x -> q2r.x -> matdyn.x does (in
example06 for instance) <br>
<br>
thete is some discussion of these issues in Review of Modern Physics
73, 515 (2001) and in Phys Rev 43, 7231 (1991)<br>
<br>
stefano <br><div class="im">
<br>
On 04/29/2011 05:05 AM, xirainbow wrote:
</div><blockquote type="cite"><div class="im">
<pre>Dear Eyvaz:
Thank you very much;)
</pre>
<blockquote type="cite">
<pre>Is there LO-TO splitting far away from Gamma point?
No.
</pre>
</blockquote>
<pre>Does LO-TO splitting must disappear at the boundary of Brillouin zone?
</pre>
</div><pre><fieldset></fieldset>
_______________________________________________
Pw_forum mailing list
<div class="im"><a href="mailto:Pw_forum@pwscf.org" target="_blank">Pw_forum@pwscf.org</a>
<a href="http://www.democritos.it/mailman/listinfo/pw_forum" target="_blank">http://www.democritos.it/mailman/listinfo/pw_forum</a>
</div></pre>
</blockquote>
<br>
</div>
<br>_______________________________________________<br>
Pw_forum mailing list<br>
<a href="mailto:Pw_forum@pwscf.org">Pw_forum@pwscf.org</a><br>
<a href="http://www.democritos.it/mailman/listinfo/pw_forum" target="_blank">http://www.democritos.it/mailman/listinfo/pw_forum</a><br>
<br></blockquote></div><br><br clear="all"><br>-- <br>____________________________________<br>Hui Wang<br>School of physics, Fudan University, Shanghai, China<br>
</div></div>