wannier90の収束の変更点

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#author("2023-11-02T20:51:26+00:00","","")
#author("2023-11-02T20:51:27+00:00","","")
[[wien2wannier]]

#contents


***shift [#k496231a]

k点のshiftを行うと結果が良くなる場合がある．
以下の例はスピン軌道結合のあるTiCである．
1000k.
projectionは
 ti:d;d
 c:p;p
irerationは10000回．

&attachref(./band1.png,15%);

左図がshiftをしたもの，右図はshiftを行わなかったものである．
shiftをしなかった場合にはL点付近で余分な振動が見られる．

Final state を以下に示す．
まずはshiftを行った場合は

  WF centre and spread    1  (  0.000000, -0.000000, -0.000000 )     0.92353716
  WF centre and spread    2  (  0.000000, -0.000000, -0.000000 )     0.92322019
  WF centre and spread    3  (  0.000000, -0.000000,  0.000000 )     0.92338969
  WF centre and spread    4  ( -0.000000, -0.000000,  0.000000 )     1.07755005
  WF centre and spread    5  (  0.000000,  0.000000,  0.000000 )     1.07715170
  WF centre and spread    6  (  0.000000, -0.000000, -0.000000 )     0.92341006
  WF centre and spread    7  (  0.000000, -0.000000, -0.000000 )     0.92322894
  WF centre and spread    8  (  0.000000, -0.000000,  0.000000 )     0.92322900
  WF centre and spread    9  ( -0.000000, -0.000000,  0.000000 )     1.07764170
  WF centre and spread   10  (  0.000000,  0.000000,  0.000000 )     1.07715824
  WF centre and spread   11  (  2.164001, -0.000000, -0.000000 )     1.43912871
  WF centre and spread   12  (  2.164001, -0.000000,  0.000000 )     1.40581154
  WF centre and spread   13  (  2.164001, -0.000000, -0.000000 )     1.40521304
  WF centre and spread   14  (  2.164001, -0.000000, -0.000000 )     1.43913189
  WF centre and spread   15  (  2.164001, -0.000000,  0.000000 )     1.40581161
  WF centre and spread   16  (  2.164001, -0.000000, -0.000000 )     1.40521481
  Sum of centres and spreads ( 12.984005, -0.000000, -0.000000 )    18.34982834

となり，ワニエ中心は元々の原子位置に一致している．SPRDも十分に小さい．

一方，shiftを行わなかった場合は

  WF centre and spread    1  ( -0.000400, -0.000227, -0.000420 )     0.99774068
  WF centre and spread    2  (  0.000177, -0.000185,  0.000106 )     0.95018138
  WF centre and spread    3  (  0.000007,  0.000207, -0.000240 )     0.95000238
  WF centre and spread    4  (  0.000153, -0.000464,  0.000211 )     1.01756440
  WF centre and spread    5  ( -0.000594,  0.000416, -0.000624 )     1.19223680
  WF centre and spread    6  ( -0.000012,  0.000078, -0.000140 )     0.94093937
  WF centre and spread    7  ( -0.000182, -0.000932, -0.000070 )     1.05415055
  WF centre and spread    8  ( -0.000112,  0.000006, -0.000172 )     0.96843276
  WF centre and spread    9  (  0.001281,  0.000054,  0.000239 )     1.08147756
  WF centre and spread   10  (  0.000147,  0.000228, -0.000056 )     1.25939411
  WF centre and spread   11  (  2.164172,  0.000072,  0.000231 )     1.47807846
  WF centre and spread   12  (  2.163706,  0.000190,  0.000260 )     1.44942112
  WF centre and spread   13  (  2.164715, -0.000774, -0.000678 )     1.45116021
  WF centre and spread   14  (  2.163862, -0.001004, -0.000282 )     1.45578648
  WF centre and spread   15  (  2.163199,  0.000562, -0.001137 )     1.53894880
  WF centre and spread   16  (  2.164908,  0.000129, -0.000090 )     1.50312616
  Sum of centres and spreads ( 12.985029, -0.001643, -0.002863 )    19.28864121

となった．ワニエ中心は微妙にずれ，SPRDもshiftを行った場合より大きくなっている．

なお，バンドをプロットする時には
 !!!! Kpoint grid does not include Gamma.  Interpolation may be incorrect. !!!!
と言われるが，上図を見ての通り，結果に問題はない．
***projectionの順番 [#q7acde94]

基底の並べ方にも依存するようである．

&attachref(./band2.png,15%);

左図は

 ti:d;d
 c:p;p

と並べたもの．右図は

 ti:d
 c:p
 ti:d
 c:p

の順に並べたものである．
右図ではWL上で余分な振動が見られる．
この場合のFinal Stateを以下に示す．

  WF centre and spread    1  ( -0.000108,  0.000030, -0.000145 )     0.94405689
  WF centre and spread    2  ( -0.481835,  0.345907, -0.549975 )     6.50740995
  WF centre and spread    3  ( -0.000023,  0.000001, -0.000173 )     0.96686799
  WF centre and spread    4  ( -0.004849,  0.001780, -0.004842 )     1.11306813
  WF centre and spread    5  ( -0.000195,  0.000171, -0.000133 )     1.02734642
  WF centre and spread    6  (  2.162524,  0.001317,  0.001365 )     1.42901568
  WF centre and spread    7  (  2.160812,  0.003399, -0.001837 )     1.44757049
  WF centre and spread    8  (  2.163350,  0.001242, -0.001401 )     1.43726764
  WF centre and spread    9  ( -0.000106,  0.000030, -0.000146 )     0.94361749
  WF centre and spread   10  ( -0.481111,  0.344923, -0.549083 )     6.50336825
  WF centre and spread   11  ( -0.000023,  0.000002, -0.000172 )     0.96771304
  WF centre and spread   12  ( -0.004880,  0.001789, -0.004854 )     1.11334713
  WF centre and spread   13  ( -0.000194,  0.000173, -0.000131 )     1.02728210
  WF centre and spread   14  (  2.162525,  0.001316,  0.001368 )     1.42940306
  WF centre and spread   15  (  2.160780,  0.003394, -0.001842 )     1.44774592
  WF centre and spread   16  (  2.163339,  0.001242, -0.001402 )     1.43674238
  Sum of centres and spreads ( 12.000007,  0.706717, -1.113403 )    29.74182255

WF2,9(ti:dxz)の中心がC原子の位置に近くまでずれており，これらのSPRDが異常に大きい．
- 1 -- [[ubaTaeCJ]] &new{2023-11-03 (金) 05:50:59};
- 1 -- [[ubaTaeCJ]] &new{2023-11-03 (金) 05:51:00};
- 1 -- [[ubaTaeCJ]] &new{2023-11-03 (金) 05:51:26};
- 1 -- [[ubaTaeCJ]] &new{2023-11-03 (金) 05:51:27};

#comment
wannier90の収束 の変更点

wannier90の収束の変更点
