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<p>Hello everybody, </p>
<p>I know that the subject of calculating a bandstructure with hybrid potentials has been addressed already many times in the mailing list, but I couldn't found the answers to my questions. I'm using QE 7.0 and, among the existing methods mentioned elsewhere, I want to rely on the so called 'fake k-points' approach.</p>
<p>The procedure is globally clear to me: one first runs a SCF calculation on a regular grid, then runs a second SCF calculation with the hybrid potential of choice and an explicit list of k-points which includes the irreducible k-points with their associated weight plus those in the bandpath with a vanishing weight. The rest is basically just a matter of post-processing the output. </p>
<p>1/ What exactly is the first SCF calculation needed for? Is any of its output (density, wavefunctions, etc...) used by the subsequent hybrid calculation, or the only useful information is the list of irreducible k-points and their weights? In other words, if I get the correct list of k-points (grid, paths and weights) from an external source, can I just run directly the hybrid calculation with no preliminary step? </p>
<p>2/ I noticed that if I put the weight of the k-points in the bandpath exactly equal to 0, then their energies are not consistent with the rest of the calculation and their occupation is vanishing for all bands (see below the example). I have the impression that this is also the case if one uses the 'ADDITIONAL_K_POINTS' card. Instead, by putting a very low weight (0.0000001), I found no error. Why this? Is setting the weight = 0.0 really the right way to proceed?</p>
<p>Let me give an example of this to be clearer. I calculate the bandstructure of Si along a path passing through Gamma. Also the regular k-point mesh contains Gamma though. So, the Gamma point appears twice in the list of k-points specified in the hybrid calculation: once with a finite weight in the regular grid, and once with weight = 0.0 along the bandpath. Here below is the output of the hybrid calculation associated to the two occurrences. Notice that the energies are different although it is the same k-point in the same calculation, and the occupation is 0 in the second occurrence. </p>
<p>:: THE GRID OCCURRENCE WITH WEIGHT = 0.002 ::</p>
<p class="p1"><span class="s1">k = 0.0000 0.0000 0.0000 ( <span class="Apple-converted-space"> </span>749 PWs) <span class="Apple-converted-space"> </span>bands (ev):</span></p>
<p class="p2"><span class="Apple-converted-space" style="font-size: 10pt;"> </span><span style="font-size: 10pt;">-7.0330 </span><span class="Apple-converted-space" style="font-size: 10pt;"> </span><span style="font-size: 10pt;">5.0739 </span><span class="Apple-converted-space" style="font-size: 10pt;"> </span><span style="font-size: 10pt;">5.0739 </span><span class="Apple-converted-space" style="font-size: 10pt;"> </span><span style="font-size: 10pt;">5.0739 </span><span class="Apple-converted-space" style="font-size: 10pt;"> </span><span style="font-size: 10pt;">9.7109 </span><span class="Apple-converted-space" style="font-size: 10pt;"> </span><span style="font-size: 10pt;">9.7109 </span><span class="Apple-converted-space" style="font-size: 10pt;"> </span><span style="font-size: 10pt;">9.7109</span><span class="Apple-converted-space" style="font-size: 10pt;"> </span><span style="font-size: 10pt;">10.6652</span><span class="s1"></span><span class="s1"><span class="Apple-converted-space"> </span>14.8522<span class="Apple-converted-space"> </span>14.8522</span></p>
<p class="p2"><span class="Apple-converted-space" style="font-size: 10pt;"> </span><span style="font-size: 10pt;">occupation numbers</span><br /><span class="s1"></span></p>
<p class="p1"><span class="s1"><span class="Apple-converted-space"> </span>1.0000 <span class="Apple-converted-space"> </span>1.0000 <span class="Apple-converted-space"> </span>1.0000 <span class="Apple-converted-space"> </span>1.0000 <span class="Apple-converted-space"> </span>0.0000 <span class="Apple-converted-space"> </span>0.0000 <span class="Apple-converted-space"> </span>0.0000 <span class="Apple-converted-space"> </span>0.0000</span><span class="s1"><span class="Apple-converted-space"> </span>0.0000 <span class="Apple-converted-space"> </span>0.0000</span></p>
<p><br /></p>
<p>:: THE PATH OCCURRENCE WITH WEIGHT = 0.000 ::</p>
<p>k =<span class="s1"> 0.0000 0.0000 0.0000 ( <span class="Apple-converted-space"> </span>749 PWs) <span class="Apple-converted-space"> </span>bands (ev):</span></p>
<p class="p2"><span class="Apple-converted-space" style="font-size: 10pt;"> </span><span style="font-size: 10pt;">-4.6222 </span><span class="Apple-converted-space" style="font-size: 10pt;"> </span><span style="font-size: 10pt;">7.5761 </span><span class="Apple-converted-space" style="font-size: 10pt;"> </span><span style="font-size: 10pt;">7.5761 </span><span class="Apple-converted-space" style="font-size: 10pt;"> </span><span style="font-size: 10pt;">7.5761</span><span class="Apple-converted-space" style="font-size: 10pt;"> </span><span style="font-size: 10pt;">10.5198</span><span class="Apple-converted-space" style="font-size: 10pt;"> </span><span style="font-size: 10pt;">10.5198</span><span class="Apple-converted-space" style="font-size: 10pt;"> </span><span style="font-size: 10pt;">10.5198</span><span class="Apple-converted-space" style="font-size: 10pt;"> </span><span style="font-size: 10pt;">11.6019</span><span class="s1"></span><span class="s1"><span class="Apple-converted-space"> </span>15.2911<span class="Apple-converted-space"> </span>15.6844</span></p>
<p class="p2"><span class="Apple-converted-space" style="font-size: 10pt;"> </span><span style="font-size: 10pt;">occupation numbers</span><br /><span class="s1"></span></p>
<p class="p1"><span class="s1"><span class="Apple-converted-space"> </span>0.0000 <span class="Apple-converted-space"> </span>0.0000 <span class="Apple-converted-space"> </span>0.0000 <span class="Apple-converted-space"> </span>0.0000 <span class="Apple-converted-space"> </span>0.0000 <span class="Apple-converted-space"> </span>0.0000 <span class="Apple-converted-space"> </span>0.0000 <span class="Apple-converted-space"> </span>0.0000</span><span class="s1"><span class="Apple-converted-space"> </span>0.0000 <span class="Apple-converted-space"> </span>0.0000</span></p>
<p><br /></p>
<p>3/ In some hybrid calculations one has to set the variables nxq# > 1 to get accurate results. In this case, prescriptions are to add the k-points of the bandpath plus all the relevant k+q points. Where do I find them? How can I get them? How I can I get the very q-point grid used by the code? </p>
<p><br /></p>
<p>Many thanks for your answers, help, tricks and suggestions.</p>
<p>Cheers</p>
<p><br /></p>
<div id="signature">-- <br />
<div class="pre" style="margin: 0; padding: 0; font-family: monospace">Dr. Lorenzo Sponza<br />Chargé de Recherche au CNRS<br />Laboratoire d'étude de microstructures (LEM), CNRS-ONERA<br />29 Avenue de la division Leclerc, 92322 Châtillon<br />Tel: +33146734464</div>
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