<html><head></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><br><div><div>On Jul 14, 2012, at 7:34 AM, yavar pour azar wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite">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>Physics Group, AEOI, Tehran, Iran
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<span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: -webkit-auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; font-size: medium; "><span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; font-size: medium; "><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-size: medium; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; "><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-size: medium; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; "><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-size: medium; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; "><div><br class="Apple-interchange-newline">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">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">http://www.researcherid.com/rid/A-1951-2009</a></div><div>Web page: <a href="http://people.na.infn.it/~cantele">http://people.na.infn.it/~cantele</a></div><div> <a href="http://www.nanomat.unina.it">http://www.nanomat.unina.it</a></div></div></span></div></span></div></span></div></span></span>
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