<div dir="ltr">Dear Matthias and Marcella<div><br></div><div>thank you very much for your reply. </div><div>Now is much more clear.</div><div><br></div><div>However, I still have one doubt.</div><div><br></div><div>While in LSD we know the spin state of the system (i.e., S**2 and integrated spin mentioned above) at any step,</div><div>it seems to me that in SMEAR we lost such information: as Matthias said, .S**2 and integrated spin cannot be calculated for fractional occupation in SMEAR.</div><div><br></div><div>Using SMEAR, is it possible to define some average quantities defining the spin state of the system?<br></div><div>I do not know, for example,  the average occupation of the alpha and beta channels?</div><div>Or something else?</div><div><br></div><div>Thank you very very much for your replies and help</div><div><br></div><div>Best</div><div>Ivan </div><div><br></div><div><br><br>On Tuesday, August 18, 2020 at 5:54:48 PM UTC+3, Marcella Iannuzzi wrote:<blockquote class="gmail_quote" style="margin: 0;margin-left: 0.8ex;border-left: 1px #ccc solid;padding-left: 1ex;">Dear Ivan, <div><br></div><div>in addition to what Matthias already wrote, by default the multiplicity is not fixed with SMEAR + LSD. </div><div><br></div><div>Working with fractional orbital occupations requires the use of diagonalisation schemes, which are in general  more demanding in terms of computational costs if compared with the orbital transformation (OT) method. </div><div><br></div><div>Kind regards</div><div>Marcella</div><div><br><br></div><div class="gmail_quote"><div dir="auto">On Tuesday, August 18, 2020 at 4:42:07 PM UTC+2 Matthias Krack wrote:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">





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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1f497d">Dear Ivan<u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1f497d"><u></u> <u></u></span></p>
<p><u></u><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1f497d"><span>a)<span style="font:7.0pt "Times New Roman"">      
</span></span></span><u></u><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1f497d">SMEAR allows for fractional orbital occupations whereas LSD with RELAX_MULTIPLICITY is meant for systems with integer occupations, e.g. to allow for
 the spin flip needed to switch automatically from a singlet to a possibly lower lying triplet state. Thus, these schemes are not equivalent.<u></u><u></u></span></p>
<p><u></u><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1f497d"><span>b)<span style="font:7.0pt "Times New Roman"">     
</span></span></span><u></u><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1f497d">The expectation value of S**2 is only defined for calculations with integer orbital occupations Therefore this properties is not calculated/printed
 when SMEAR is active.<u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1f497d"><u></u> <u></u></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1f497d">HTH<u></u><u></u></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1f497d">Matthias<u></u><u></u></span></p></div></div><div lang="EN-US" link="blue" vlink="purple"><div>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1f497d"><u></u> <u></u></span></p>
<p class="MsoNormal"><b><span style="font-size:11.0pt;font-family:"Calibri",sans-serif">From:</span></b><span style="font-size:11.0pt;font-family:"Calibri",sans-serif"> <a rel="nofollow">c...@googlegroups.com</a> <<a rel="nofollow">c...@googlegroups.com</a>>
<b>On Behalf Of </b>Ivan Gladich<br>
<b>Sent:</b> Dienstag, 18. August 2020 15:56<br>
<b>To:</b> cp2k <<a rel="nofollow">c...@googlegroups.com</a>><br>
<b>Subject:</b> [CP2K:13797] SMEAR vs. LSD+RELAX_MULTIPLICITY/<wbr>MULTIPLICITY<u></u><u></u></span></p>
<p class="MsoNormal"><u></u> <u></u></p>
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<p class="MsoNormal"><a name="02c52b4a-4c82-4970-8fa5-63fad726406fn@googlegroups.com_m_-8592122066790477932__GoBack" rel="nofollow"></a><span style="font-size:13.5pt;font-family:"Arial",sans-serif;color:black">Dear CP2K users,</span><span style="font-size:13.5pt;color:black"><u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:13.5pt;font-family:"Arial",sans-serif;color:black"> </span><span style="font-size:13.5pt;color:black"><u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:13.5pt;font-family:"Arial",sans-serif;color:black">I would like some clarifications about SMEAR vs. LSD +RELAX_MULTIPLICTY in cp2k. I am trying to simulate a metallic nanoparticle
 (few tens of atoms) in water</span><span style="font-size:13.5pt;color:black"><u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:13.5pt;font-family:"Arial",sans-serif;color:black"> </span><span style="font-size:13.5pt;color:black"><u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:13.5pt;font-family:"Arial",sans-serif;color:black">I have two (maybe simple) questions:</span><span style="font-size:13.5pt;color:black"><u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:13.5pt;font-family:"Arial",sans-serif;color:black"> </span><span style="font-size:13.5pt;color:black"><u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:13.5pt;font-family:"Arial",sans-serif;color:black">a) From this post </span><span style="font-size:13.5pt;color:black"><u></u><u></u></span></p>
<p class="MsoNormal" style="margin-left:18.0pt"><span style="font-size:13.5pt;font-family:"Arial",sans-serif;color:black"><a href="https://groups.google.com/forum/#!topic/cp2k/GEKLwRQat_M" rel="nofollow" target="_blank" onmousedown="this.href='https://groups.google.com/forum/#!topic/cp2k/GEKLwRQat_M';return true;" onclick="this.href='https://groups.google.com/forum/#!topic/cp2k/GEKLwRQat_M';return true;"><span style="color:#954f72">https://groups.google.com/<wbr>forum/#!topic/cp2k/GEKLwRQat_M</span></a></span><span style="font-size:13.5pt;color:black"><u></u><u></u></span></p>
<p class="MsoNormal" style="margin-left:18.0pt"><span style="font-size:13.5pt;font-family:"Arial",sans-serif;color:black"> </span><span style="font-size:13.5pt;color:black"><u></u><u></u></span></p>
<p class="MsoNormal" style="margin-left:18.0pt"><span style="font-size:13.5pt;font-family:"Arial",sans-serif;color:black">my understanding is that the SMEAR option populates the alpha and beta channel according to a Fermi-Dirac </span><span style="font-size:13.5pt;color:black"><u></u><u></u></span></p>
<p class="MsoNormal" style="margin-left:18.0pt"><span style="font-size:13.5pt;font-family:"Arial",sans-serif;color:black"> </span><span style="font-size:13.5pt;color:black"><u></u><u></u></span></p>
<p class="MsoNormal" style="margin-left:18.0pt"><span style="font-size:13.5pt;font-family:"Arial",sans-serif;color:black">In LSD + MULTIPLICITY (or LSD + RELAX MULTIPLICITY)</span><span style="font-size:13.5pt;color:black"><u></u><u></u></span></p>
<p class="MsoNormal" style="margin-left:18.0pt"><span style="font-size:13.5pt;font-family:"Arial",sans-serif;color:black"><a href="https://groups.google.com/forum/#!searchin/cp2k/smearing$20spin%7Csort:date/cp2k/ugkJLz4PSSI/C-ProBR6BwAJ" rel="nofollow" target="_blank" onmousedown="this.href='https://groups.google.com/forum/#!searchin/cp2k/smearing$20spin%7Csort:date/cp2k/ugkJLz4PSSI/C-ProBR6BwAJ';return true;" onclick="this.href='https://groups.google.com/forum/#!searchin/cp2k/smearing$20spin%7Csort:date/cp2k/ugkJLz4PSSI/C-ProBR6BwAJ';return true;"><span style="color:#954f72">https://groups.google.com/<wbr>forum/#!searchin/cp2k/<wbr>smearing$20spin%7Csort:date/<wbr>cp2k/ugkJLz4PSSI/C-ProBR6BwAJ</span></a></span><span style="font-size:13.5pt;color:black"><u></u><u></u></span></p>
<p class="MsoNormal" style="margin-left:18.0pt"><span style="font-size:13.5pt;font-family:"Arial",sans-serif;color:black"> </span><span style="font-size:13.5pt;color:black"><u></u><u></u></span></p>
<p class="MsoNormal" style="margin-left:18.0pt"><span style="font-size:13.5pt;font-family:"Arial",sans-serif;color:black">my understating is that after energy levels are calculated, electrons are placed according to Aufbau principle,
 from the lowest to the highest in an unrestricted scheme. If MULTIPLICITY is set, the multiplicity is fixed, with RELAX_MULTIPLICITY no</span><span style="font-size:13.5pt;color:black"><u></u><u></u></span></p>
<p class="MsoNormal" style="margin-left:18.0pt"><span style="font-size:13.5pt;font-family:"Arial",sans-serif;color:black"> </span><span style="font-size:13.5pt;color:black"><u></u><u></u></span></p>
<p class="MsoNormal" style="margin-left:18.0pt"><span style="font-size:13.5pt;font-family:"Arial",sans-serif;color:black">Please correct me if my understanding is mistaken.</span><span style="font-size:13.5pt;color:black"><u></u><u></u></span></p>
<p class="MsoNormal" style="margin-left:18.0pt"><span style="font-size:13.5pt;font-family:"Arial",sans-serif;color:black"> </span><span style="font-size:13.5pt;color:black"><u></u><u></u></span></p>
<p class="MsoNormal" style="margin-left:18.0pt"><span style="font-size:13.5pt;font-family:"Arial",sans-serif;color:black">Question: are the two approaches (SMEAR vs. LSD +RELAX_MULTIPLICTY) equivalent? One approach is more appropriate
 than the other for particular systems? Is the computational cost the same?</span><span style="font-size:13.5pt;color:black"><u></u><u></u></span></p>
<p class="MsoNormal" style="margin-left:18.0pt"><span style="font-size:13.5pt;font-family:"Arial",sans-serif;color:black"> </span><span style="font-size:13.5pt;color:black"><u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:13.5pt;font-family:"Arial",sans-serif;color:black">b) If I use LSD +MULTIPLICTY in the output I get the</span><span style="font-size:13.5pt;color:black"><u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:13.5pt;font-family:"Arial",sans-serif;color:black"> </span><span style="font-size:13.5pt;color:black"><u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:13.5pt;font-family:"Arial",sans-serif;color:black">“Integrated absolute spin density” and  “Ideal and single determinant S**2”</span><span style="font-size:13.5pt;color:black"><u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:13.5pt;font-family:"Arial",sans-serif;color:black"> </span><span style="font-size:13.5pt;color:black"><u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:13.5pt;font-family:"Arial",sans-serif;color:black">That are </span><span style="font-size:13.5pt;font-family:"Arial",sans-serif;color:#222222">equations (2.271) and (2.272)<span> in
 “</span>Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory<span>,</span>Attila Bangha Szabo, Neil S. Ostlund</span><span><span style="font-size:10.0pt;font-family:"Arial",sans-serif;color:#222222"> “</span></span><span style="font-size:13.5pt;color:black"><u></u><u></u></span></p>
<p class="MsoNormal"><span><span style="font-size:10.0pt;font-family:"Arial",sans-serif;color:#222222"> </span></span><span style="font-size:13.5pt;color:black"><u></u><u></u></span></p>
<p class="MsoNormal"><span><span style="font-size:13.5pt;font-family:"Arial",sans-serif;color:#222222"><a href="https://groups.google.com/forum/#!topic/cp2k/flEEaseAd7c" rel="nofollow" target="_blank" onmousedown="this.href='https://groups.google.com/forum/#!topic/cp2k/flEEaseAd7c';return true;" onclick="this.href='https://groups.google.com/forum/#!topic/cp2k/flEEaseAd7c';return true;"><span style="color:#954f72">https://groups.google.com/<wbr>forum/#!topic/cp2k/flEEaseAd7c</span></a></span></span><span style="font-size:13.5pt;color:black"><u></u><u></u></span></p>
<p class="MsoNormal"><span><span style="font-size:10.0pt;font-family:"Arial",sans-serif;color:#222222"> </span></span><span style="font-size:13.5pt;color:black"><u></u><u></u></span></p>
<p class="MsoNormal"><span><span style="font-size:10.0pt;font-family:"Arial",sans-serif;color:#222222"> </span></span><span style="font-size:13.5pt;color:black"><u></u><u></u></span></p>
<p class="MsoNormal"><span><span style="font-size:13.5pt;font-family:"Arial",sans-serif;color:#222222">If I see the output of my calculation with SMEAR I do not see such or any other information
 about the spin state of my system. </span></span><span style="font-size:13.5pt;color:black"><u></u><u></u></span></p>
<p class="MsoNormal"><span><span style="font-size:13.5pt;font-family:"Arial",sans-serif;color:#222222"> </span></span><span style="font-size:13.5pt;color:black"><u></u><u></u></span></p>
<p class="MsoNormal"><span><span style="font-size:13.5pt;font-family:"Arial",sans-serif;color:#222222">Question: Is this expected? How I can easily get information about the spin state of my system
 when using SMEAR?</span></span><span style="font-size:13.5pt;color:black"><u></u><u></u></span></p>
<p class="MsoNormal"><span><span style="font-size:13.5pt;font-family:"Arial",sans-serif;color:#222222"> </span></span><span style="font-size:13.5pt;color:black"><u></u><u></u></span></p>
<p class="MsoNormal"><span><span style="font-size:13.5pt;font-family:"Arial",sans-serif;color:#222222">Thank you very much for any possible help</span></span><span style="font-size:13.5pt;color:black"><u></u><u></u></span></p>
<p class="MsoNormal"><span><span style="font-size:13.5pt;font-family:"Arial",sans-serif;color:#222222"> </span></span><span style="font-size:13.5pt;color:black"><u></u><u></u></span></p>
<p class="MsoNormal"><span><span style="font-size:13.5pt;font-family:"Arial",sans-serif;color:#222222">Best regards</span></span><span style="font-size:13.5pt;color:black"><u></u><u></u></span></p>
<p class="MsoNormal"><span><span style="font-size:13.5pt;font-family:"Arial",sans-serif;color:#222222">Ivan</span></span><span style="font-size:13.5pt;color:black"><u></u><u></u></span></p>
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