[Wannier] initial projections

Wed Jul 8 20:55:00 CEST 2015

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 <cxm075 at email.uark.edu>
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-- 

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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