<html><head><meta http-equiv="Content-Type" content="text/html charset=windows-1252"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;"><br><div><div>On 23 Jan 2014, at 11:46, Mitul Mundra <<a href="mailto:mitulm@iitk.ac.in">mitulm@iitk.ac.in</a>> wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite"><div dir="ltr">Hello,<div><br></div><div>I am a beginner in using Quantum Espresso. I have a 64 atom Si supercell for which I am trying to plot band diagrams. I have gone through the tutorial "PWSCF: First Steps" available at <a href="http://www.fisica.uniud.it/~giannozz/QE-Tutorial/tutorial_pwscf_ex.pdf">http://www.fisica.uniud.it/~giannozz/QE-Tutorial/tutorial_pwscf_ex.pdf</a> .</div>
<div>The problem I am facing is that when I run a scf calculation using 4*4*4 k-points, my output file has energies of 128 bands for every k-point. For example,</div><div><div><b>k = 0.0000 0.0000 0.0000 ( 12797 PWs) bands (ev):</b></div>
<div><b><br></b></div><div><b> -5.6509 -4.5410 -4.5410 -4.5410 -4.5410 -4.5410 -4.5410 -3.5502</b></div><div><b> -3.5502 -3.5502 -3.5502 -3.5502 -3.5502 -3.5502 -3.5502 -3.5502</b></div><div><b> -3.5502 -3.5502 -3.5502 -3.2434 -3.2434 -3.2434 -3.2434 -1.3979</b></div>
<div><b> -1.3979 -1.3979 -1.3978 -1.3978 -1.3978 -1.2206 -1.2206 -1.2206</b></div><div><b> -1.2206 -1.2206 -1.2206 -1.2205 -1.2205 -1.2205 -1.2205 -1.2205</b></div><div><b> -1.2205 -0.5951 -0.5951 -0.5951 -0.5951 0.9797 0.9797 0.9797</b></div>
<div><b> 0.9797 0.9797 0.9797 0.9797 0.9797 0.9797 0.9797 0.9797</b></div><div><b> 0.9797 2.5385 2.5385 2.5385 2.5385 2.5385 2.5385 2.5385</b></div><div><b> 2.5385 2.5385 2.5385 2.5385 2.5385 2.6504 2.6504 2.6504</b></div>
<div><b> 2.6504 2.6504 2.6504 2.6504 2.6504 2.6504 2.6504 2.6504</b></div><div><b> 2.6504 3.0031 3.0031 3.0031 3.0031 3.0031 3.0031 3.5849</b></div><div><b> 3.5849 3.5849 3.5849 3.5849 3.5849 4.5713 4.5713 4.5713</b></div>
<div><b> 4.5713 4.5713 4.5713 4.5713 4.5713 4.5713 4.5713 4.5713</b></div><div><b> 4.5713 5.1567 5.1567 5.1567 5.1567 5.1568 5.1568 5.1568</b></div><div><b> 5.1568 5.1568 5.1568 5.1568 5.1568 5.2932 5.2932 5.2932</b></div>
<div><b> 5.2932 5.2932 5.2932 5.2932 5.2932 6.5240 6.5240 6.5240</b></div></div><div><br></div><div>On doing calculation = 'bands' and nbnd = 8, the output file contains energies of only 8 bands for every k-point which are the lowermost bands. </div>
<div><div><b>k = 0.0000 0.0000 0.0000 band energies (ev):</b></div><div><b><br></b></div><div><b> -5.6509 -4.5410 -4.5410 -4.5410 -4.5410 -4.5410 -4.5410 -3.5502</b></div></div><div>Then I run a bands.x executable to genrate bands.dat. On using plotband.x, I get the following.</div>
<div><br></div><div><div><b>/opt/apps/espresso-5.0.1/bin/plotband.x</b></div><div><b>Input file > bands.dat</b></div><div><b>Reading 8 bands at 10 k-points</b></div><div><b>Range: -5.6510 -3.5500eV Emin, Emax > -6, -3</b></div>
</div><div><b>high-symmetry point: 0.0000 0.0000 0.0000 x coordinate 0.0000<br></b></div><div><b>...</b></div><div><b>high-symmetry point: -0.5000-0.5000-0.5000 x coordinate 0.0000<br></b></div><div><div><b>output file (xmgr) > si.bands.xmgr</b></div>
<div><b>bands in xmgr format written to file si.bands.xmgr </b></div>
<div><b>output file (ps) > <a href="http://si.bands.ps/">si.bands.ps</a></b></div><div><b>Efermi > -3.987 </b></div><div><b>deltaE, reference E (for tics) 1.0, -3.987</b> </div></div><div><div><b>n= 2 3</b></div>
<div><b> 0.0000000E+00 0.0000000E+00</b></div><div><b> -5.651000 -5.581000 </b></div><div><b> NaN NaN </b> </div></div><div>....</div><div>....</div><div>....</div><div>and more NaNs and my <b><a href="http://si.bands.ps/">si.bands.ps</a></b> file contains no plot.</div>
<div><br></div><div>I would be extremely thankful if someone could tell me where am I wrong and what different can I do to obtain the band plot (4 valence bands and 4 conduction bands).</div><div><br></div><div>Thanks,</div>
<div>Mitul Mundra</div><div>Final Year Dual Degree Student</div><div>Department of Chemical Engineering</div><div>IIT Kanpur, India.</div><div><br></div></div>
_______________________________________________<br>Pw_forum mailing list<br><a href="mailto:Pw_forum@pwscf.org">Pw_forum@pwscf.org</a><br>http://pwscf.org/mailman/listinfo/pw_forum</blockquote></div><div><br></div><div><br></div><div><br></div>If you want to obtain the “textbook” band plot of silicon (4 valence bands and 4 conduction bands) you CANNOT use a 64-atom supercell, but<div>the 2-atom fcc unit cell of the silicon crystal.</div><div><br></div><div>Whatever lattice you are using, a 64-atom supercell contains 4*64 valence electrons, corresponding to 2*64=128 occupied (valence) bands!</div><div>That means that, even though you’re describing the silicon crystal just using a larger supercell (the textbook 2-atom fcc cell is the minimal choice</div><div>among a set of infinite equivalent choices of the unit cell), you get EXACTLY the same band structure but described within the Brillouin zone</div><div>of the lattice you are considering.</div><div><br></div><div>So, let’s suppose that you choose to replicate the Si fcc unit cell twice in each direction, thus using a 2x2x2 supercell, the Brillouin zone of this</div><div>crystal is 1/2 x 1/2 x 1/2 = 1/8 smaller that the Brillouin zone of the crystal as described with the minimal cell.</div><div>Because the electronic properties cannot depend on the choice of the unit cell, the silicon bands get folded into the smaller Brillouin zone.</div><div>Plotting this band structure is possible, but of course you obtain many more bands, which are more difficult to handle with than the simpler</div><div>Si band structure with only 4 valence bands. Therefore, the two band structures are DIFFERENT even though EQUIVALENT.</div><div><br></div><div>To get rid of this difficulty, if you really want to describe bulk Si with your unit cell, you could firstly calculate the density of states (DOS), Indeed,</div><div>being the DOS an integral over the Brillouin zone, the minimal and larger unit cell produce the SAME DOS with only a proportionality factor</div><div>of difference (in my example above, the 2x2x2 cell will produce the 8 times the DOS of the 1x1x1 unit cell). In this case comparing the two</div><div>results is more straightforward. </div><div><br></div><div>Giovanni</div><div><br></div><div><br></div><div><br><div apple-content-edited="true">
-- <br><br>Giovanni Cantele, PhD<br>CNR-SPIN<br>c/o Dipartimento di Fisica<br>Universita' di Napoli "Federico II"<br>Complesso Universitario M. S. Angelo - Ed. 6<br>Via Cintia, I-80126, Napoli, Italy<br>e-mail: <a href="mailto:giovanni.cantele@spin.cnr.it">giovanni.cantele@spin.cnr.it</a><br>Phone: +39 081 676910<br>Skype contact: giocan74<br><br>ResearcherID: <a href="http://www.researcherid.com/rid/A-1951-2009">http://www.researcherid.com/rid/A-1951-2009</a><br>Web page: <a href="http://people.na.infn.it/~cantele">http://people.na.infn.it/~cantele</a><br>
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