<html><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; ">Soft modes at small (but finite) q can indeed be an indication of an elastic or a mechanical instability. At q=0, there should be exactly thre zero modes, though, irrespective of the occurrence of such an instability (I believe). Imaginary frequencies can also occur at q=0, but _in addition_ to the three zero modes mentioned above. cheers - SB<div><br><div><div>On Jun 19, 2008, at 7:10 PM, <a href="mailto:stewart@cnf.cornell.edu">stewart@cnf.cornell.edu</a> wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite"><div>Hi Stefano, <br><br>You raise a good point and perhaps I should have been more careful in my <br>previous statement. I agree that based on symmetry, the total forces on the <br>system should be zero and there should be a set of zero mode. Applying the <br>acoustic sum rule reinstates this fact. From my practical experience, I <br>recall having greater problems with negative frequencies at the Gamma point <br>for systems that had the lattice constant greater than the equilibrium value <br>(expanded system). This occurred for direct calculations at small q and <br>also based on interpolating the phonon dispersion from the q grid. Here you <br>get phonon softening which shifts the phonon dispersion curves down and <br>perhaps this leads to problems with calculating the phonon dispersion from <br>the given q grid near Gamma. I took this as an indication of the <br>instability of the expanded structure, but perhaps this is not the best way <br>to view it. <br><br>Best regards, <br><br>Derek <br><br><br>Stefano Baroni writes: <br><br><blockquote type="cite"><br></blockquote><blockquote type="cite">On Jun 19, 2008, at 4:17 PM, <a href="mailto:stewart@cnf.cornell.edu">stewart@cnf.cornell.edu</a> wrote: <br></blockquote><blockquote type="cite"><br></blockquote><blockquote type="cite"><blockquote type="cite">Fig 2 (D. A. Stewart, New. J. Phys. 10 043025 (2008)). Of course, the<br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">difference you get between ASR results and direct calculations will <br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">depend<br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">strongly on how well relaxed your structure is.<br></blockquote></blockquote><blockquote type="cite"><br></blockquote><blockquote type="cite">hmmm: this may well be the case, but if this is so, it must be for a <br></blockquote><blockquote type="cite">nontrivial reason (which, if true, would qualify the "of course" as <br></blockquote><blockquote type="cite">slightly misplaced). <br></blockquote><blockquote type="cite"><br></blockquote><blockquote type="cite">the total force acting on any isolated system is of course zero, even <br></blockquote><blockquote type="cite">though the system is not at equilibrium ("not well relaxed"). in <br></blockquote><blockquote type="cite">particular, this total force is invariant ("invariantly zero!") with <br></blockquote><blockquote type="cite">respect to a homogeneous translation of the system. therefore, the system <br></blockquote><blockquote type="cite">must have a zero mode (actually three of them: one for each cartesian <br></blockquote><blockquote type="cite">coordinate), irrespective on how well (or how bad) the internal degrees <br></blockquote><blockquote type="cite">of freedom have been optimized. <br></blockquote><blockquote type="cite"><br></blockquote><blockquote type="cite">is this wrong? <br></blockquote><blockquote type="cite"><br></blockquote><blockquote type="cite">SB <br></blockquote><blockquote type="cite"><br></blockquote><blockquote type="cite"><blockquote type="cite"><br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><a href="http://dx.doi.org/10.1088/1367-2630/10/4/043025">http://dx.doi.org/10.1088/1367-2630/10/4/043025</a> <br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">Best regards, <br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">Derek <br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">Paolo Giannozzi writes: <br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><a href="mailto:xwzhang@uestc.edu.cn">xwzhang@uestc.edu.cn</a> wrote: <br></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><br></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">are there any problem that the slope of the phonon around Gamma is<br></blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">incorrect, because ASR cure the problem of k=0, but what about other<br></blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">points near it?<br></blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><br></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">for phonons at k/=0, the error due to ASR violation seems to be<br></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">usually negligible. I never tried to make calculations with<br></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">very small q, though. <br></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><br></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">Paolo<br></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">-- <br></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">Paolo Giannozzi, Democritos and University of Udine, Italy<br></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">_______________________________________________<br></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">Pw_forum mailing list<br></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><a href="mailto:Pw_forum@pwscf.org">Pw_forum@pwscf.org</a><br></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><a href="http://www.democritos.it/mailman/listinfo/pw_forum">http://www.democritos.it/mailman/listinfo/pw_forum</a> <br></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><br></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">################################<br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">Derek Stewart, Ph. D.<br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">Scientific Computation Associate<br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><a href="http://www.people.cornell.edu/pages/das248/">http://www.people.cornell.edu/pages/das248/</a><br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">250 Duffield Hall<br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">Cornell Nanoscale Facility (CNF)<br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">Ithaca, NY 14853<br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">stewart (at) cnf.cornell.edu<br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">(607) 255-2856<br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">_______________________________________________<br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">Pw_forum mailing list<br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><a href="mailto:Pw_forum@pwscf.org">Pw_forum@pwscf.org</a><br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><a href="http://www.democritos.it/mailman/listinfo/pw_forum">http://www.democritos.it/mailman/listinfo/pw_forum</a><br></blockquote></blockquote><blockquote type="cite"><br></blockquote><blockquote type="cite">---<br></blockquote><blockquote type="cite">Stefano Baroni - SISSA & DEMOCRITOS National Simulation Center - <br></blockquote><blockquote type="cite">Trieste<br></blockquote><blockquote type="cite">[+39] 040 3787 406 (tel) -528 (fax) / stefanobaroni (skype) <br></blockquote><blockquote type="cite"><br></blockquote><blockquote type="cite">La morale est une logique de l'action comme la logique est une morale de <br></blockquote><blockquote type="cite">la pensée - Jean Piaget <br></blockquote><blockquote type="cite"><br></blockquote><blockquote type="cite">Please, if possible, don't send me MS Word or PowerPoint attachments<br></blockquote><blockquote type="cite">Why? See: <a href="http://www.gnu.org/philosophy/no-word-attachments.html">http://www.gnu.org/philosophy/no-word-attachments.html</a> <br></blockquote><blockquote type="cite"><br></blockquote><blockquote type="cite"><br></blockquote><blockquote type="cite"><br></blockquote><blockquote type="cite"><br></blockquote><br><br><br>################################<br>Derek Stewart, Ph. D.<br>Scientific Computation Associate<br>250 Duffield Hall<br>Cornell Nanoscale Facility (CNF)<br>Ithaca, NY 14853<br>stewart (at) cnf.cornell.edu<br>(607) 255-2856<br>_______________________________________________<br>Pw_forum mailing list<br><a href="mailto:Pw_forum@pwscf.org">Pw_forum@pwscf.org</a><br>http://www.democritos.it/mailman/listinfo/pw_forum<br></div></blockquote></div><br></div><br><br><div apple-content-edited="true"> <span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 14px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: 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: 0; "><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: 14px; 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: 14px; 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: 14px; 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; "><div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; ">---</span></font></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; ">Stefano Baroni - SISSA</span></font><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; "> </span></font><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; ">&</span></font><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; "> </span></font><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; ">DEMOCRITOS National Simulation Center - Trieste</span></font></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; "><a href="http://www.sissa.it/~baroni">http://www.sissa.it/~baroni</a> / [+39] 040 3787 406 (tel) -528 (fax) / stefanobaroni (skype)</span></font></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 12px/normal Helvetica; min-height: 14px; font-size: 12px; "><br style="font-size: 12px; "></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 12px/normal Helvetica; min-height: 14px; font-size: 12px; "><span class="Apple-style-span" style="font-size: 14px; "><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; ">La morale est une logique de l'action comme la logique est une morale de la pensée - Jean Piaget</span></font></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; "><br></span></font></div></span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; ">Please, if possible, don't</span></font><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; "> </span></font><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; ">send me MS Word or PowerPoint attachments</span></font></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; ">Why? See:</span></font><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; "> </span></font><font class="Apple-style-span" color="#0023E9" size="3"><span class="Apple-style-span" style="font-size: 12px; "><a href="http://www.gnu.org/philosophy/no-word-attachments.html">http://www.gnu.org/philosophy/no-word-attachments.html</a></span></font></div><div><font class="Apple-style-span" color="#0023E9" size="3"><span class="Apple-style-span" style="font-size: 12px; "><br class="webkit-block-placeholder"></span></font></div></div></div></span><br class="Apple-interchange-newline"></div></span><br class="Apple-interchange-newline"></div></span><br class="Apple-interchange-newline"></div></span><br class="Apple-interchange-newline"> </div><br></body></html>