Dear Professor Cantele.<br><br><span id="view" class="stream _p _pl1 _pd1284685"><span class="mtxt">Thanks for your time,consideration </span></span>and detailed description.<br><br>Best regards.<br><br>Yavar<br><br><br><br>
<div class="gmail_quote">On Tue, Jul 17, 2012 at 1:35 PM, Giovanni Cantele <span dir="ltr"><<a href="mailto:giovanni.cantele@spin.cnr.it" target="_blank">giovanni.cantele@spin.cnr.it</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div style="word-wrap:break-word"><br><div><div><div class="h5"><div>On Jul 14, 2012, at 7:34 AM, yavar pour azar wrote:</div><br></div></div><blockquote type="cite"><div><div class="h5">Dear QE users,<br><br>I have a conceptual problem with k-point sampling in supercells.<br>
<br>Suppose
we have a simple cubic unit cell for the bulk, which it's electronic
structure, total energy and etc... is calculated by n*n*n BZ Sampling.<br>
for example I can see band width and band curvature along k axis, and i
will have max and min points for every band in different k_points such
gamma, X, L,......<br><br>Now, if we want to make a n*n*n supercell from
this unit cell, it is the known fact that just gamma point
calculations is enough.<br>
<br>Anyone can see following sentences in most QE tutorials; <br>"Increase
supercell in real space by a factor N along a ; EXACTLY same results
obtained by reducing divisions in k mesh (in the new smaller BZ) by
factor N"<br>
<br>This is the problem that I cant understand : when we substitute the
unit cell by n*n*n supercell ( k=0), the calculated bands with new
sampling has no curvature and extension along k axis, because we have
just a K point. Total Energy, probably is same as former unit cell (by
integer factor), but if we will lose information about other aspects of
electronic structure by this sampling?<br>
<h1>
</h1><p class="MsoNormal">I would appreciate it if anyone can help me to understand this, or refer me to a source.<br></p><p class="MsoNormal"><br></p>
PS: suppose supercell sustained no relaxation or similar changes, and
we have just the two different scales from one infinite, periodic
lattice.<br><br><br><br>Thanks in advance.<br><br>Yavar Taghipour Azar <br>
PhD student<br></div></div>Physics Group, AEOI, Tehran, Iran
_______________________________________________<br>Pw_forum mailing list<br><a href="mailto:Pw_forum@pwscf.org" target="_blank">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>
</blockquote></div><br><div>
<span style="text-indent:0px;letter-spacing:normal;font-variant:normal;text-align:-webkit-auto;font-style:normal;font-weight:normal;line-height:normal;border-collapse:separate;text-transform:none;font-size:medium;white-space:normal;font-family:Helvetica;word-spacing:0px"><span style="text-indent:0px;letter-spacing:normal;font-variant:normal;font-style:normal;font-weight:normal;line-height:normal;border-collapse:separate;text-transform:none;font-size:medium;white-space:normal;font-family:Helvetica;word-spacing:0px"><div style="word-wrap:break-word">
<span style="text-indent:0px;letter-spacing:normal;font-variant:normal;font-style:normal;font-weight:normal;line-height:normal;border-collapse:separate;text-transform:none;font-size:medium;white-space:normal;font-family:Helvetica;word-spacing:0px"><div style="word-wrap:break-word">
<span style="text-indent:0px;letter-spacing:normal;font-variant:normal;font-style:normal;font-weight:normal;line-height:normal;border-collapse:separate;text-transform:none;font-size:medium;white-space:normal;font-family:Helvetica;word-spacing:0px"><div style="word-wrap:break-word">
<span style="text-indent:0px;letter-spacing:normal;font-variant:normal;font-style:normal;font-weight:normal;line-height:normal;border-collapse:separate;text-transform:none;font-size:medium;white-space:normal;font-family:Helvetica;word-spacing:0px"><div>
<br>If you build your supercell correctly, of course no information will be lost. </div><div>Reverting to the example you did --namely, the same cubic structure simulated by using either a 1x1x1 unit cell with an NxNxN sampling</div>
<div>or an NxNxN supercell with a 1x1x1 sampling of the BZ-- you should consider that the band structure you plot in both cases is along a path</div><div>in the BZ that has NOTHING to do, in principle, with the sampling of the BZ itself.</div>
<div><br></div><div>The BZ sampling controls the convergence of the calculated properties (the ground-state charge density, for example) with respect to the BZ</div><div>integration.</div><div>The path along the BZ you use for band structure calculations is instead just a collection of k-points inside the BZ which you choose in order</div>
<div>to plot the band structure of a system. Of course, for the NxNxN supercell you expect to get a number of bands which is NxNxN times that</div><div>of the 1x1x1 calculation: this is the so called band structure folding. That means that your band structure, even though apparently</div>
<div>different, is just the same but described within a BZ which is NxNxN times smaller than for the 1x1x1 unit cell.</div><div>In conclusion, even for the NxNxN supercell, if you select a path in the BZ, you'll find the same electronic bands, gaps, curvature, even though</div>
<div>described within a different BZ.</div><div><br></div><div>Giovanni</div><div><br></div><div>--</div><div><div><br></div><div>**** PLEASE NOTICE THE NEW E-MAIL ADDRESS: <a href="mailto:giovanni.cantele@spin.cnr.it" target="_blank">giovanni.cantele@spin.cnr.it</a></div>
</div><div><br></div><div><div>Giovanni Cantele, PhD</div><div>CNR-SPIN</div><div>c/o Dipartimento di Scienze Fisiche</div><div>Universita' di Napoli "Federico II"</div><div>Complesso Universitario M. S. Angelo - Ed. 6</div>
<div>Via Cintia, I-80126, Napoli, Italy</div><div>Phone: +39 081 676910</div><div>Skype contact: giocan74</div><div><br></div><div>ResearcherID: <a href="http://www.researcherid.com/rid/A-1951-2009" target="_blank">http://www.researcherid.com/rid/A-1951-2009</a></div>
<div>Web page: <a href="http://people.na.infn.it/%7Ecantele" target="_blank">http://people.na.infn.it/~cantele</a></div><div> <a href="http://www.nanomat.unina.it" target="_blank">http://www.nanomat.unina.it</a></div>
</div></span></div></span></div></span></div></span></span>
</div>
<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>