<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=""><br class=""><div><blockquote type="cite" class=""><div class="">On 07 Jul 2015, at 09:45, Zeina Al-Dolami <<a href="mailto:zaldolam@email.uark.edu" class="">zaldolam@email.uark.edu</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><div dir="ltr" class="">Dear wannier90's owners and developers,<div class="">I have been trying to understand the examples well before going further. One of the relevant topic that I am having hard time understanding is the initial projections and the best way to define them for a system. I have read the user guide and tutorials to gain more insight. Also, I have found nice details and explanations related to the projections of carbon nano tubes and graphene systems based on the examples provided within wannier90. However, I am totally confused about the way that these projections are found. My questions might be related to the chemistry, but I need your help to start and then go from there. My questions are:</div><div class=""><br class=""></div><div class="">1. Prof.Nicola has mentioned that s-like projections are in the middle of each bond that has to be identified correctly. How to identify them? To clarify, example13 has this projection c= -2.7274, -1.9677, -0.6157 :s . How to find these numbers for the center of projections? Is there mathematical formula or chemistry reasons? How are they found preciously for any system? </div></div></div></blockquote><div><br class=""></div><div>This example refers to a carbon nanotube, where the initial guess consists in one pz orbital (with the z axis properly oriented) per each C atom, and one s orbital at each bond. This reflects the chemistry of C-based nanostructures (C nanotubes, graphene), where the sp2 hybridisation occurs. The numbers you mention are the coordinates of the middle point between the atoms</div><div>C -3.151822438 -1.395018907 -0.615700000<br class="">C -2.303060204 -2.540325691 -0.615700000<br class="">that are given in input. You find an s orbital at each middle bond.</div><br class=""><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class=""><br class=""></div><div class="">2. One of the pz projections of the same example is c= 3.3780, -0.7128, -0.6157 :pz :z= 3.3780, -0.7128, 0.0000 :x=0,0,1. The center of CNT is 0,0,0.</div><div class="">In the forum, there is an emphasis that the direction of the CNT along z-axis, so z and x are identified to be along z direction. In case CNT is along x, should we have z=0.0,-0.7128, -0.6157 :x=1,0,0 or I am confused by the statement in the forum??</div></div></div></blockquote><div><br class=""></div>The carbon nanotube axis, of the mentioned example, is parallel to the z axis. However, for each C atom, the corresponding pz orbital is not parallel to the z axis but orthogonal to the nanotube surface, as the chemistry of a C nanotube tells you. In other words, for each C atom, you must calculate the direction normal to the nanotube and tell wannier90 to use as an initial guess a pz orbital along that direction. Should you have graphene, this problem would not occur, in that case all pz orbital would be parallel to each other.</div><div><br class=""></div><div><br class=""><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class=""><br class=""></div><div class="">3.In example15, one of the pz projections is c=18,1.15042363,0.0:pz:z=0.809016993454,0.587785253559,0.0:x=0,0,1 </div><div class="">How to get these numbers z=0.809016993454,0.587785253559,0.0? Is it same way as question 1? </div></div></div></blockquote><div><br class=""></div><div>In this case, at variance with question 1, you are looking for a pz guess. The center is on the 1st carbon atom</div><div>C 1.58342228 1.15042363 0.00000000</div><div>so the coordinates that follow “c=“ are the same as those of this C atom. What follows, as specified before, is the direction of the axis along with to put the pz orbital.</div><div>These are obtained (more difficult to say than to do it!) by:</div><div>i) identifying the three first neighbours (manually, for example visualizing the structure with XCrysDen or automatically, by writing some simple script once you understand the algorithm) of the C atom , say P1, P2, P3</div><div>ii) compute M1 = (P1 - P2)/Norm[P1 - P2] and M2 = (P1 - P3)/Norm[P1 - P3], these are the versors connecting P1 and P2 and P1 and P3, respectively</div><div>iii) compute V = (M2 x M3)/Norm[(M2 x M3)], where x = cross product (V is normal to both M2 and M3)</div><div>iv) because the ideal nanotube surface is such that at each point the normal is always perpendicular to the nanotube axis, get rid of the V component parallel to the nanotube axis, so V’ = V - (V . z) z, where . = dot product and z is the versor of the nanotube axis</div><div><br class=""></div><div>The result is 0.809017, 0.587785, 0., that should answer your question</div><div><br class=""></div><br class=""><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class=""><br class=""></div><div class="">4. How or why do we choose a specific number of projections? I am assuming it depends on the MLWF and bands that we are interested in but not sure.</div></div></div></blockquote><div><br class=""></div>Yes it depends, generally you should recognise the chemistry of your system and the character (in terms of atomic orbitals or their combinations) of the bands you are interested in (you might what to reproduce only a subset of your band structure, for example group of bands close to the Fermi level).</div><div><br class=""><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class=""><br class=""></div><div class="">You can tell from my questions that I am totally confused. Any feedback and comments from anyone are greatly appreciated. Apologies for such long email and questions. Looking forward to hearing from you. Many thanks in advance </div></div></div></blockquote><div><br class=""></div><div>Actually, apart from simple systems, choosing the proper initial guess might be a quite hard task.</div><div><br class=""></div><div>Giovanni</div><br class=""><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class=""><br class=""></div><div class="">-- <br class=""><div class="gmail_signature"><div dir="ltr" class=""><span class=""><font color="#888888" class="">Zeina Al-Dolami<br class="">PhD Candidate<br class="">Microelectronics and Photonics Graduate Program <br class="">University of Arkansas<br class="">Fayetteville, AR 72701<br class="">Office: PHYS 244<br class="">Email: <a href="mailto:zaldolam@email.uark.edu" target="_blank" class="">zaldolam@email.uark.edu</a><a href="mailto:cxm075@email.uark.edu" target="_blank" class=""></a></font></span></div></div>
</div></div>
_______________________________________________<br class="">Wannier mailing list<br class=""><a href="mailto:Wannier@quantum-espresso.org" class="">Wannier@quantum-espresso.org</a><br class="">http://mailman.qe-forge.org/cgi-bin/mailman/listinfo/wannier<br class=""></div></blockquote></div><br class=""><div apple-content-edited="true" class="">
-- <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="">
</div>
<br class=""></body></html>