![[PukiWiki]](image/pukiwiki.png "[PukiWiki]")
shift †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．
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 †基底の並べ方にも依存するようである．
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．
|
band1.png
band2.png
