<html><head><meta http-equiv="Content-Type" content="text/html charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" class="">the correct statement is not that “there is no way” to calculate band structure for a molecule, but that <div class="">a molecule has not a band structure. Band structure is a concept typical of solid state physics, and is related to</div><div class="">the occurrence, in crystals, of continuous energy intervals of allowed electronic levels separated by energy gaps</div><div class="">(where no electronic level can show up in an ideal crystal). The continuous distribution of levels in a band can be</div><div class="">described by assigning to each level a label, the k-vector, that represents the analogous of (but not the same as)</div><div class="">the momentum of the free electron when it moves in the free space instead of being subject to the periodic lattice</div><div class="">potential. The relation E(k) is just the energy dispersion and describes the band structure of the solid.</div><div class=""><br class=""></div><div class="">This is contrasted with discrete levels in molecules, where instead localised orbitals show up.</div><div class=""><br class=""></div><div class="">I want just to add that you can use plane waves to reproduce molecular orbitals, at the best level of approximation</div><div class="">allowed with the available exchange-correlation functionals. This means that if you calculate the molecular orbital of a molecule</div><div class="">within the GGA approximation, you get the same picture if you use plane wave packages, just as quantum-espresso, or other</div><div class="">packages based on localised basis sets. If using plane waves, you have just to take care of building appropriate super cells,</div><div class="">preventing the periodic replicas of the molecule form interacting with each other.</div><div class=""><br class=""></div><div class="">Giovanni</div><div class=""><br class=""><div><blockquote type="cite" class=""><div class="">On 29 Nov 2016, at 07:31, ashkan shekaari <<a href="mailto:shekaari@gmail.com" class="">shekaari@gmail.com</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><p dir="ltr" class="">Dear Giovanni,<br class="">
Thank you so much for your explanatory response. So, as I understood, there is no way to calculate band structure for a molecule and this is nonsensical. Is it true?</p>
<div class="gmail_extra"><br class=""><div class="gmail_quote">On Nov 29, 2016 1:46 AM, <<a href="mailto:meisam.a63@gmail.com" class="">meisam.a63@gmail.com</a>> wrote:<br type="attribution" class=""><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="auto" class=""><div class="">Just to add that plain wave is not a good approximation to reproduce molecular orbitals.<br class=""><br class=""><div class="">Mortaza A</div><div class=""><br class=""></div><div class="">PhD of Physics </div><div class="">Ulm University, Germany </div></div><div class=""><br class="">On 28 Nov 2016, at 21:43, Giovanni Cantele <<a href="mailto:giovanni.cantele@spin.cnr.it" target="_blank" class="">giovanni.cantele@spin.cnr.it</a>> wrote:<br class=""><br class=""></div><blockquote type="cite" class=""><div class="">if you try to ask the question: "what the k-point mesh is for?" you can easily understand<div class="">that a k-point mesh is for the Brillouin zone (BZ) sampling, that is, perform sums over k-points</div><div class="">that approximate, with a required level of accuracy, the integral over the whole BZ. This is</div><div class="">because in a crystal, the energy E(K) depends on the k vectors, and the same holds for the</div><div class="">wave functions. However, when you build for example a cubic supercell including vacuum to</div><div class="">simulate a molecule, you are actually dealing with a fictitious cubic crystal where the repeated</div><div class="">units are sufficiently far apart from each other to not interact.</div><div class=""><br class=""></div><div class="">Absence of interaction means flat (atomic-like) energy levels, that do not have dependence</div><div class="">on the k vector. That is, the E(K) dispersion that you get in the case of a molecule, provided</div><div class="">you include a sufficient vacuum space in your supercell, does not depend on k. If this is</div><div class="">the case, you can use only the gamma point (a larger grid means large but useless</div><div class="">computational time, because you are summing over eigenvalues at different k-points that </div><div class="">are all the same!) for self consistency and BZ path is not needed, because if you select any</div><div class="">path you should get flat, k-independent bands</div><div class=""><br class=""></div><div class="">Giovanni</div><div class=""><div class=""><br class=""></div><div class=""><br class=""><div class=""><blockquote type="cite" class=""><div class="">On 28 Nov 2016, at 18:12, ashkan shekaari <<a href="mailto:shekaari@gmail.com" target="_blank" class="">shekaari@gmail.com</a>> wrote:</div><br class="m_-5599770475287007092Apple-interchange-newline"><div class=""><div dir="ltr" class=""><div class=""><div class="">Dear experts,<br class=""><br class=""></div>Is it necessary using kpoint mesh when we are dealing with molecules?<br class=""><br class=""></div>In the case of a molecule in cubic vacuum, what path in BZ should be selected?<br clear="all" class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class="m_-5599770475287007092gmail_signature" data-smartmail="gmail_signature"><div dir="ltr" class=""><div class=""><div dir="ltr" class=""><div class=""><div dir="ltr" class=""><div class=""><div dir="ltr" class=""><div dir="ltr" class=""><div dir="ltr" class=""><div dir="ltr" class=""><div dir="ltr" class=""><div dir="ltr" class=""><div dir="ltr" class=""><div dir="ltr" class=""><div dir="ltr" class=""><div dir="ltr" class=""><div class=""><span class=""><span style="background-color:rgb(255,255,255)" class=""><b class="">--</b></span></span></div><div class=""><span class=""><span style="background-color:rgb(255,255,255)" class=""><i style="font-size:12.8px" class="">Regards,</i></span></span></div><div class=""><span class=""><span style="background-color:rgb(255,255,255)" class=""><i class="">Ashkan Shekaari</i></span></span></div><div class=""><span class=""><span style="background-color:rgb(255,255,255)" class=""><i class="">Plasma Physics Research Center</i></span></span></div><div class=""><span class=""><span style="background-color:rgb(255,255,255)" class=""><i style="font-size:12.8px" class=""><span style="font-size:12.8px" class="">Science and Research Branch</span></i></span></span></div><div class=""><span class=""><span style="background-color:rgb(255,255,255)" class=""><i class="">I A U, <span style="font-size:12.8px" class="">14778-93855 Tehran, Iran.</span></i></span></span></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div>
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-- <br class=""><br class="">Giovanni Cantele, PhD<br class="">CNR-SPIN<br class="">c/o Dipartimento di Fisica<br class="">Universita' di Napoli "Federico II"<br class="">Complesso Universitario M. S. Angelo - Ed. 6<br class="">Via Cintia, I-80126, Napoli, Italy<br class="">e-mail: <a href="mailto:giovanni.cantele@spin.cnr.it" class="">giovanni.cantele@spin.cnr.it</a><br class="">Phone: +39 081 676910<br class="">Skype contact: giocan74<br class=""><br class="">ResearcherID: <a href="http://www.researcherid.com/rid/A-1951-2009" class="">http://www.researcherid.com/rid/A-1951-2009</a><br class="">Web page: <a href="http://people.na.infn.it/~cantele" class="">http://people.na.infn.it/~cantele</a><br class="">
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