[Wannier] Spread convergence in a spin-oribit calculation

ppadmana at ph2.uni-koeln.de ppadmana at ph2.uni-koeln.de
Tue Mar 6 17:43:12 CET 2018


Hello Everyone,

I am attempting to perform a Wannierization of the valence bands of PbTe. I have performed a spin orbit calculation in QE (with lspinorb = true and noncolin = true). I did this using a 16x16x16 shifted grid for the scf calculation and an 8x8x8 full grid for the nscf calculation. Based on the results of a non-SO calculation, I know that the bands are primarily of Te-p and Pb-s character.

In the Wannierization step, I use the following input:

num_bands = 10
num_wann = 10
num_iter = 1000
conv_window = 10
conv_tol = 1e-5
spinors = true

bands_plot = true
begin kpoint_path
L 0.500 0.500 0.500 G 0.000 0.000 0.000
G 0.000 0.000 0.000 X 0.000 0.500 0.500
X 0.000 0.500 0.500 W 0.250 0.750 0.500
W 0.250 0.750 0.500 L 0.500 0.500 0.500
L 0.500 0.500 0.500 G 0.000 0.000 0.000
G 0.000 0.000 0.000 K 0.375 0.750 0.375
end kpoint_path

begin projections
c=-3.046778,3.731389,3.046598:pz
c=-2.754606,2.754517,2.755727:s
c=-3.731378,3.046842,3.046648:pz
c=-3.047456,3.047471,3.731244:pz
c=-3.145233,3.145233,6.290419:s
end projections

mp_grid = 8 8 8

begin kpoints
 **list of 512 points identical to nscf calculation**
end kpoints

begin atoms_frac
 Pb  0.000  0.000  0.000
 Te  0.500  0.500  0.500
end atoms_frac

begin unit_cell_cart
Ang
-3.145186   0.000000   3.145186
 0.000000   3.145186   3.145186
-3.145186   3.145186   0.000000
end unit_cell_cart

Unfortunately, even after 1000+ iterations, though my spreads are in the range of 4-5 Ang^2, they aren't converged, and I can only get to a DLTA of approximately 1E-5. If I look at the band structure, I see a difference between the Kramer’s degenerate states and wiggles at the high symmetry points. Moreover, unless I explicitly set the conv_tol to 1e-5 and convert_window to 10, it will basically iterate to the end and give me results that are even worse. It seems like gradient descent can’t find the global minima. Here’s a grep of the output and final state:

+--------------------------------------------------------------------+<-- CONV
 | Iter  Delta Spread     RMS Gradient      Spread (Ang^2)      Time  |<-- CONV
 +--------------------------------------------------------------------+<-- CONV
      0     0.886E+02     0.0000000000       88.5961756930       2.02  <-- CONV
      1    -0.193E+02     3.6519324709       69.2719457144       2.09  <-- CONV
      2    -0.119E+02     2.9217065446       57.4196136819       2.16  <-- CONV
      3    -0.789E+01     2.2523091155       49.5285805341       2.23  <-- CONV
      4    -0.405E+01     1.8769695123       45.4786941630       2.29  <-- CONV
      5    -0.117E+01     1.4810561663       44.3102929602       2.36  <-- CONV
      ...
    732    -0.954E-05     0.0812066914       41.5149635930      50.03  <-- CONV
    733    -0.485E-05     0.2124621933       41.5149587471      50.09  <-- CONV
    734    -0.587E-05     0.0551927135       41.5149528784      50.16  <-- CONV
    735    -0.479E-05     0.2156962496       41.5149480855      50.22  <-- CONV
    736    -0.461E-05     0.0560167032       41.5149434756      50.28  <-- CONV
    737    -0.365E-05     0.1892001198       41.5149398256      50.35  <— CONV

Final State
  WF centre and spread    1  ( -2.924839,  3.504327,  3.469653 )     4.69435114
  WF centre and spread    2  ( -2.925054,  3.503452,  3.470009 )     4.71351191
  WF centre and spread    3  ( -2.673238,  2.673025,  2.971221 )     3.59977954
  WF centre and spread    4  ( -2.672922,  2.673446,  2.971132 )     3.60028628
  WF centre and spread    5  ( -3.503953,  2.924918,  3.470236 )     4.70571734
  WF centre and spread    6  ( -3.505087,  2.924613,  3.471128 )     4.70069921
  WF centre and spread    7  ( -3.482302,  3.482023,  2.682537 )     3.93809935
  WF centre and spread    8  ( -3.481404,  3.482794,  2.682584 )     3.93941997
  WF centre and spread    9  ( -3.145268,  3.145207,  6.293045 )     3.82072386
  WF centre and spread   10  ( -3.145260,  3.145161,  6.293306 )     3.80235121
  Sum of centres and spreads (-31.459326, 31.458966, 37.774852 )    41.51493983

I should point out that when doing the non spin-orbit case, I didn't have a problem achieving convergence with spreads in the 2-3 Ang^2 range and DLTAs of 1E-11.

I tried various initial guesses for the projections, going so far as to using the centers from the non-SO MLWFs, but no luck. I would greatly appreciate any guidance. Thank you in advance.

Sincerely,

Prashant Padmanabhan
---
Post-doctoral Researcher
II. Physics Institute
University of Cologne
50823 Cologne
Germany


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