[Wannier] Supercell size, b vectors or something else
Jeil Jung
jeil at physics.utexas.edu
Tue Aug 7 05:20:36 CEST 2012
Hi,
I started looking at wannier90 recently. First of all, many thanks to the developers for making available such a wonderful tool.
While going through the examples I found one problem I would like to comment on.
It must be related with handling finite differences from k-points for large supercells.
If one modifies example 10 for graphite to have a larger unit cell size in the z direction it automatically separates further the layers and the bands
become that of graphene.
By modifying accordingly the energy windows I can reproduce the bands for graphene reported in your accepted RMP paper.
The recipe of eliminating one of the carbon layers and separating the layers also gives essentially the same band structure of graphene.
The problem starts when the z-axis cell size becomes too large. When the inter-graphene layer distances are greater than about 8 angstroms
you start noticing that the center of the initial projections of the pz orbitans are slightly out of plane.
To illustrate my point I copy below the relevant regions of graphite.wout for two cases.
One is for graphite with Lz = 16 angstroms, this is 8 angstroms separation between layers
and another for Lz = 20 angstroms. You can notice that already for Lz=16 angstroms it starts to show
tiny out of plane displacements of the pz (or sigma) orbital projections from the planes that become notoriously larger when Lz=20 angstroms.
Lz = 16 angstroms (200 iterations)
------------------------------------------------------------------------------
Initial State
WF centre and spread 1 ( -0.352578, 0.610683, 12.000001 ) 0.60267243
WF centre and spread 2 ( -0.352578, -0.610683, 12.000000 ) 0.60267233
WF centre and spread 3 ( 0.705155, 0.000000, 12.000001 ) 0.60267249
WF centre and spread 4 ( 0.000000, 0.000000, 11.999996 ) 1.03588860
WF centre and spread 5 ( 0.357562, 1.840684, 4.000000 ) 0.60267395
WF centre and spread 6 ( 0.357559, 0.619314, 4.000000 ) 0.60267487
WF centre and spread 7 ( 1.415300, 1.230002, 4.000000 ) 0.60267488
WF centre and spread 8 ( 0.710140, 1.230000, 4.000015 ) 1.03634288
WF centre and spread 9 ( 0.000000, 0.000000, 4.000006 ) 1.03588731
WF centre and spread 10 ( -0.710140, -1.230000, 11.999980 ) 1.03634402
Sum of centres and spreads ( 2.130421, 3.690000, 79.999997 ) 7.76050374
0 0.776E+01 0.0000000000 7.7605037421 6.36 <-- CONV
O_D= 0.2585153 O_OD= 1.5936799 O_TOT= 7.7605037 <-- SPRD
Writing checkpoint file graphite.chk... done
Final State
WF centre and spread 1 ( -0.355069, 0.614998, 12.000030 ) 0.54986868
WF centre and spread 2 ( -0.355069, -0.614998, 12.000031 ) 0.54986863
WF centre and spread 3 ( 0.710139, 0.000000, 12.000031 ) 0.54986870
WF centre and spread 4 ( 0.000000, 0.000000, 11.999956 ) 1.03587760
WF centre and spread 5 ( 0.355069, 1.845001, 3.999973 ) 0.54986870
WF centre and spread 6 ( 0.355069, 0.614998, 3.999974 ) 0.54986865
WF centre and spread 7 ( 1.420283, 1.229999, 3.999973 ) 0.54986864
WF centre and spread 8 ( 0.710140, 1.229999, 4.000062 ) 1.03633230
WF centre and spread 9 ( 0.000000, 0.000000, 4.000038 ) 1.03587875
WF centre and spread 10 ( -0.710140, -1.229999, 11.999930 ) 1.03633257
Sum of centres and spreads ( 2.130422, 3.689998, 79.999997 ) 7.44363322
Spreads (Ang^2) Omega I = 5.908308580
================ Omega D = 0.020570360
Omega OD = 1.514754280
Final Spread (Ang^2) Omega Total = 7.443633219
------------------------------------------------------------------------------
Time for wannierise 3.627 (sec)
---------
Lz = 20 angstroms
------------------------------------------------------------------------------
Initial State
WF centre and spread 1 ( -0.349901, 0.598862, 14.995413 ) 0.62617014
WF centre and spread 2 ( -0.347302, -0.612222, 14.998605 ) 0.61406608
WF centre and spread 3 ( 0.695169, -0.009180, 14.993375 ) 0.64937494
WF centre and spread 4 ( 0.000002, -0.000002, 14.706700 ) 17.86025818
WF centre and spread 5 ( 0.358160, 1.838524, 5.001654 ) 0.61232466
WF centre and spread 6 ( 0.360228, 0.628444, 5.008041 ) 0.65266434
WF centre and spread 7 ( 1.411733, 1.231610, 5.001470 ) 0.60771954
WF centre and spread 8 ( 0.710141, 1.229999, 4.735334 ) 15.16970546
WF centre and spread 9 ( 0.000001, -0.000001, 4.752679 ) 14.71429866
WF centre and spread 10 ( -0.710141, -1.230001, 14.707123 ) 17.71804348
Sum of centres and spreads ( 2.128092, 3.676033, 98.900394 ) 69.22462547
0 0.692E+02 0.0000000000 69.2246254748 6.35 <-- CONV
O_D= 29.7816077 O_OD= 32.8026254 O_TOT= 69.2246255 <-- SPRD
Final State
WF centre and spread 1 ( -0.355898, 0.615907, 15.047911 ) 0.55389069
WF centre and spread 2 ( -0.356443, -0.615759, 15.029877 ) 0.55225267
WF centre and spread 3 ( 0.711527, 0.000548, 15.020749 ) 0.55177652
WF centre and spread 4 ( -0.000694, -0.000132, 14.966088 ) 1.24801183
WF centre and spread 5 ( 0.354420, 1.846537, 4.957860 ) 0.55345004
WF centre and spread 6 ( 0.354167, 0.613572, 4.967165 ) 0.55287958
WF centre and spread 7 ( 1.421761, 1.230258, 4.961887 ) 0.55318423
WF centre and spread 8 ( 0.710343, 1.230548, 5.043238 ) 1.16093772
WF centre and spread 9 ( -0.000472, -0.002028, 5.154334 ) 1.60886377
WF centre and spread 10 ( -0.708131, -1.229836, 14.867101 ) 1.50509444
Sum of centres and spreads ( 2.130578, 3.689615,100.016210 ) 8.84034150
Spreads (Ang^2) Omega I = 6.640392353
================ Omega D = 0.188848567
Omega OD = 2.011100578
Final Spread (Ang^2) Omega Total = 8.840341498
------------------------------------------------------------------------------
Time for wannierise 3.767 (sec)
Writing checkpoint file graphite.chk... done
Actually there is a previous email from a Chinese fellow last month showing results for graphene with interlayer separation of
10 Angstroms and you can notice this small effect in his results too.
This should be the reason for his antibonding pi bands looking different from the results in RMP paper outside the inner window.
My questions are:
1. Why are the initial projections of the wannier functions not centered exactly at the same z values like in normal graphite?
2. Why the localization procedure fails to bring them back in plane? I believe this question is related with 1.
3. How to foresee when this type of problems can happen in supercell calculations of slab geometries?
It certainly would be problematic if a DFT calculation can provide the inputs but for some reason wannier90.x cannot cope
with systems that have large vacuum spacing between the slabs.
From a more practical point of view, my question would be what to change in an example case of
graphite with Lz = 30 angstroms to prevent the centers from moving out of the plane? The input files would be essentially the same as
that provided with the codes but changing Lz = 30 and changing the energy windows. Another change was that I used norm conserving instead of ultrasoft.
I tried changing several other parameters, like increasing the density of in plane kx, ky, points to balance the weights
of the b vectors and their anisotropy but this did not have any effect. Switching on and off guiding_centres flag didn't do anything either.
Increasing the number of kz further increases the weight imbalance between the
b vectors but sometimes seemed to improve the final results but never completely and could not see any systematic behavior.
At times I needed to modify the 'search_shells' parameter to a larger number when very large Lz were used.
I haven't tried but I don't think that changing 'dist cutoff mode' nor the specification of the 'one dim axis' should be the solutions either.
The only clear thing I could conclude from trying different parameters was that when Lz becomes large enough, in this case larger than about 8 angstroms, the results start to go wrong.
However, from symmetry considerations I can't see why they should shift the wave functions centers.
Any insightful comment would be welcome.
Thanks,
Jeil
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