[Wannier] Supercell size, b vectors or something else
Nicola Marzari
nicola.marzari at epfl.ch
Tue Aug 7 14:05:20 CEST 2012
Thanks Jeil for the careful analysis!
It seems that the first thing that goes wrong are the initial
projections - in going from 16 to 20 angstrom the spreads of the
4 "p_z" like-WFs are around ~16-17 A^2, instead of slightly more
than ~1 A^2, and a good symmetry is never recovered.
Now, the choice of example10 is to have a p_z projection
on every carbon (good) and a sp2 projection on every other
carbon (one in layer 1, one in layer 2). This sp2 choice is not
the most natural, since one really wants bond centered WFs, in addition
to p_z ones, and I wonder if some odd numerical instability is creeping
in.
So, first, could you try a different choice of projections, where you
put one p_z projection on every carbon, and one s-like projection
in the middle of each bond (make sure you identify correctly the mid
of each bond...).
Please report back, and we'll take it from there. If by any chance
the strategy above does not work, maybe you could try to also remove
one layer of carbon atoms, and the associated projections, and see what
you get (and you could try this also for your current case of sp2 and
p_z projections).
Best,
nicola
On 07/08/2012 05:20, Jeil Jung wrote:
> 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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--
----------------------------------------------------------------------
Prof Nicola Marzari, Chair of Theory and Simulation of Materials, EPFL
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