[Wannier] Initial projection wannier centers (symmetry adapted wannier functions)

[Tobias Frank]

Dear wannier90 users,

I currently try to wannierize MoS2, which has a disconnected band manifold
of 11 bands (5 Mo d orbitals and 2*3 S p orbitals).

 *----------------------------------------------------------------------------*
 |   Site       Fractional Coordinate          Cartesian Coordinate (Ang)
  |
 +----------------------------------------------------------------------------+
 | Mo   1   0.33333   0.66667   0.50000   |   -0.00000   1.84059  12.50000
   |
 | S    1   0.66667   0.33333   0.56240   |    1.59400   0.92030  14.05992
   |
 | S    2   0.66667   0.33333   0.43760   |    1.59400   0.92030  10.94008
   |
 *----------------------------------------------------------------------------*

The goal is to get a symmetric tight-binding Hamiltonian (_hr.dat) out of
the calculation. The scheme I use is to project onto atomic orbitals
without any maximal localization iteration applied ("symmetry adapted
wannier functions") and guiding centers are turned on.

My initial (and final) state reads:
projections:Mo:d, S:p

 Initial State
  WF centre and spread    1  ( -0.000000,  1.840629, 12.500000 )
1.65212451
  WF centre and spread    2  ( -0.000000,  1.797275, 12.500000 )
1.88788741
  WF centre and spread    3  ( -0.000000,  1.883825, 12.500000 )
1.88514896
  WF centre and spread    4  ( -0.000000,  1.744405, 12.500000 )
1.79754077
  WF centre and spread    5  ( -0.000000,  1.936664, 12.500000 )
1.79758431
  WF centre and spread    6  (  1.594000,  0.920313, 14.121223 )
1.69614206
  WF centre and spread    7  (  1.594000,  0.932663, 14.015563 )
1.56344882
  WF centre and spread    8  (  1.594000,  0.908001, 14.015556 )
1.56201127
  WF centre and spread    9  (  1.594000,  0.920313, 10.878777 )
1.69614206
  WF centre and spread   10  (  1.594000,  0.932663, 10.984437 )
1.56344882
  WF centre and spread   11  (  1.594000,  0.908001, 10.984444 )
1.56201127
  Sum of centres and spreads (  9.564000, 14.724751,137.500000 )
 18.66349025

This yields a very good description of the band structure, but why are the
initial projections not exactly at the atomic sites, where I specified them
to be? This slight asymmetry reflects also in the tight-binding matrix
elements, where I would like to have symmetric ones. Could you give me a
hint how to get the wannier centers at the atomic positions?

I am aware about the publication of Sakuma ("Symmetry-adapted Wannier
functions in the maximal localization procedure"). I am using Quantum
Espresso, where it is not implemented. Is there any work on the way?

Thank you very much,
Tobias Frank
PhD student
Universität Regensburg
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