[Wannier] Initial choice for projection

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>I went through (5,5) nanotube example (with no problem) and I have been
>playing with other parameter choices to learn more about wannier90.
>One of the things that I tried was using different initial projection. 
>For example, I tried

>Begin Projections
>Random
>C:pz:x=0,0,1
>End Projections

>It went through without a problem although the final results (band 
>structure, DOS) were somewhat different from the example.

50 random pz orbitals seems to be too far from the usual chemical bonding
picture of a CNT, where you would have
20 pz orbitals and 30 sp2 bonding orbitals.
Please check whether the elements of H matrix in WF basis are all real.
I vaguely remember that starting from not-so-good initial guess gave
imaginary H element. 


>HOWEVER, when I used the same random projection with 4 unit cells
>(80 carbons, num_bands = 320,num_wann  = 200) it didn't work and I got the 
>following message.

>The trial orbitals for disentanglement are not orthonormal
>Exiting.......
>Error in dis_main: orthonormal error 1

>I even tried the same projection like the one in example for 4 unit cells,
>but it didn't work neither with the same error message.

>My questions are:

>[1] Is there an option to orthogonalize the trial orbitals?

It's not an option. They are always orthonormalized in the way that is
described in Souza et al. PRB65, 035109 page 5.

>[2] Why the random projection works for 1 unit cell, but not for 4 unit
> cells?

I am afraid that you cannot really say that the random projection works for
1 unit cell if your final result is different from what's in the example.
If you are just mentioning about failure of orthonormalization. I don't
have a good answer. It's simply a mathematical operation not related to
physical picture of WFs.
Maybe your two initial WFs almost overlap and that could make the algorithm
unstable. But I really don't know... 

>[3] What is the best option for initial projection in carbon nanotube 
> system?

Starting from random pz orbitals is really a bad choice.
You have large vacuum region and most of initial pz WFs will fall in the
vacuum region. Then they'll have really small overlap with the final WFs
you want to obtain.
In addition, 60% of final WFs have symmetry totally different from the
initial pz orbitals.


Well, from my experience the best option would be to start from

s orbital at every bond center (30 orbitals) 
(or sp2 orbital at every other C atom - then you'd better specify x and z
directions for each orbital.
If the axis of CNT is parallel to z and the center of CNT is (x0,y0) then
for C atom at (cx,cy,cz):
c = cx, cy, cz :sp2 :x = 0,0,1 (or 0,0,-1 depending on the direction of the
C-C bond along z axis):z= cx-x0,cy-y0,0 )

and

pz orbital at every C atom (20 orbitals)
c = cx, cy, cz:pz :x=0,0,1:z=cx-c0,cy-y0,0  


         
Young-Su