[Wannier] initial projections

Tue Jul 14 08:29:45 CEST 2015

Dr.Giovanni,
Thanks again for your response. I have one more question. In case I have a
system of 15 carbon atoms. 5 of them are sp hybirdized. Another 5 atoms are
sp2 hybirdized and the last 5 are sp3 hybirdized. How can I define their
projections? My question may not be realistic, but I just want to have an
idea if it is possible and related to what you have explained to me. Thanks
in advance and looking forward to hearing from you or anyone who can
clarify it to me

Regards,
Zeina

On Wed, Jul 8, 2015 at 3:09 PM, Giovanni Cantele <
giovanni.cantele at spin.cnr.it> wrote:

> Sorry, I meant M1 and M2!
>
> Giovanni
>
> > On 08 Jul 2015, at 20:55, Zeina Al-Dolami <zaldolam at email.uark.edu>
> wrote:
> >
> > Dr. Giovanni,
> > Thanks so much for your nice explanation. I  just want to make sure of
> your answer to question 3. Did you mean M1 and M2 in answer 3 step 3?? What
> is M3? Thanks again and looking forward to hearing from you
> >
> > Zeina
> >
> > On Jul 7, 2015, at 4:13 AM, Giovanni Cantele <
> giovanni.cantele at spin.cnr.it> wrote:
> >
> >>
> >>> On 07 Jul 2015, at 09:45, Zeina Al-Dolami <zaldolam at email.uark.edu>
> wrote:
> >>>
> >>> Dear wannier90's owners and developers,
> >>> 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:
> >>>
> >>> 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?
> >>
> >> 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
> >> C     -3.151822438     -1.395018907     -0.615700000
> >> C     -2.303060204     -2.540325691     -0.615700000
> >> that are given in input. You find an s orbital at each middle bond.
> >>
> >>>
> >>> 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.
> >>> 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??
> >>
> >> 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.
> >>
> >>
> >>>
> >>> 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
> >>> How to get these numbers z=0.809016993454,0.587785253559,0.0? Is it
> same way as question 1?
> >>
> >> In this case, at variance with question 1, you are looking for a pz
> guess. The center is on the 1st carbon atom
> >> C     1.58342228     1.15042363     0.00000000
> >> 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.
> >> These are obtained (more difficult to say than to do it!) by:
> >> 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
> >> 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
> >> iii) compute V = (M2 x M3)/Norm[(M2 x M3)], where x = cross product (V
> is normal to both M2 and M3)
> >> 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
> >>
> >> The result is 0.809017, 0.587785, 0., that should answer your question
> >>
> >>
> >>>
> >>> 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.
> >>
> >> 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).
> >>
> >>>
> >>> 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
> >>
> >> Actually, apart from simple systems, choosing the proper initial guess
> might be a quite hard task.
> >>
> >> Giovanni
> >>
> >>>
> >>> --
> >>> Zeina Al-Dolami
> >>> PhD Candidate
> >>> Microelectronics and Photonics Graduate Program
> >>> University of Arkansas
> >>> Fayetteville, AR 72701
> >>> Office: PHYS 244
> >>> Email: zaldolam at email.uark.edu
> >>> _______________________________________________
> >>> Wannier mailing list
> >>> Wannier at quantum-espresso.org
> >>> http://mailman.qe-forge.org/cgi-bin/mailman/listinfo/wannier
> >>
> >> --
> >>
> >> Giovanni Cantele, PhD
> >> CNR-SPIN
> >> c/o Dipartimento di Fisica
> >> Universita' di Napoli "Federico II"
> >> Complesso Universitario M. S. Angelo - Ed. 6
> >> Via Cintia, I-80126, Napoli, Italy
> >> e-mail: giovanni.cantele at spin.cnr.it
> >> Phone: +39 081 676910
> >> Skype contact: giocan74
> >>
> >> ResearcherID: http://www.researcherid.com/rid/A-1951-2009
> >> Web page: http://people.na.infn.it/~cantele
> >>
> >> _______________________________________________
> >> Wannier mailing list
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> >> http://mailman.qe-forge.org/cgi-bin/mailman/listinfo/wannier
>
> --
>
> Giovanni Cantele, PhD
> CNR-SPIN
> c/o Dipartimento di Fisica
> Universita' di Napoli "Federico II"
> Complesso Universitario M. S. Angelo - Ed. 6
> Via Cintia, I-80126, Napoli, Italy
> e-mail: giovanni.cantele at spin.cnr.it
> Phone: +39 081 676910
> Skype contact: giocan74
>
> ResearcherID: http://www.researcherid.com/rid/A-1951-2009
> Web page: http://people.na.infn.it/~cantele
>
>
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>

-- 
Zeina Al-Dolami
PhD Candidate
Microelectronics and Photonics Graduate Program
University of Arkansas
Fayetteville, AR 72701
Office: PHYS 244
Email: zaldolam at email.uark.edu <cxm075 at email.uark.edu>
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