DFT+U periodicity (very confused results)
Posted: Thu Mar 31, 2016 8:51 am
Dear Adimin,
The system of my present VASP job is Li-intercalated β-MnO2 grain boundary. A collinear antiferromagnetic ordering is used in all our calculations. Valence electron configurations of the potentials were taken as 1s2 2s1 for Li, 3d6 4s1 for Mn, and 2s2 2p4 for O. But I find some very confused results.
I give “Structure A” a static calculation, the resulted energy is “-1617.4093eV”. Then I put “Structure A” just translate 0.5 along direction “a” to get “Structure B”. But the resulted energy is “-1614.0948” after a static calculation! To my knowledge, “Structure A” and “Structure B” are just the same due to Periodic boundary conditions, isn’t it?
Here are my relaxation inputs:
INCAR:
SYSTEM = MnO2
LWAVE=.FALSE.
LCHARG=.FALSE.
LASPH=.TRUE.
LREAL= Auto
ISTART=0
ICHARG=2
ALGO=Normal
PREC=Normal
#LPLANE = .TRUE.
NPAR = 6
#LSCALU = .FALSE.
#NSIM = 4
ISPIN=2
ENCUT=500
ISMEAR=0
SIGMA=0.2
LDAU=.TRUE.
LDAUTYPE=2
LDAUL= -1 2 -1
LDAUU= 0.0 6.1 0.0
LDAUJ= 0.0 1.0 0.0
LORBIT=10
NELM=300
MAGMOM=160*0 40*-1 40*1 1*0
KPOINTS:
AUTO GRID
0
M
2 1 1
0 0 0
The POSCAR file for "Structure A":
New structure
1.00000000000000
5.8893198967000000 0.0000000000000000 0.0000000000000000
0.0000000000000000 14.0908565521000000 0.0000000000000000
0.0000000000000000 0.0000000000000000 28.1817131042000000
O Mn Li
160 80 1
Direct
0.2499999850000023 0.2604309137599969 0.9993153614700034
0.7500000000000000 0.2604309137599969 0.9993153614700034
0.0000000000000000 0.7604308247600002 0.0006845765299985
0.5000000000000000 0.7604308247600002 0.0006845765299985
0.2499999850000023 0.9535387172199989 0.0317670078599974
0.7500000000000000 0.9535387172199989 0.0317670078599974
0.0000000000000000 0.5744181912600013 0.0326922833200030
0.5000000000000000 0.5744181912600013 0.0326922833200030
0.0000000000000000 0.1181449833100032 0.0408190930699988
0.5000000000000000 0.1181449833100032 0.0408190930699988
0.2499999850000023 0.4300077190800025 0.0583602348499994
0.7500000000000000 0.4300077190800025 0.0583602348499994
0.0000000000000000 0.2750738002499986 0.0769547092800025
0.5000000000000000 0.2750738002499986 0.0769547092800025
0.0000000000000000 0.8281392854100034 0.0824713827299988
0.5000000000000000 0.8281392854100034 0.0824713827299988
0.2499999850000023 0.6702044481399980 0.0958871600100011
0.7500000000000000 0.6702044481399980 0.0958871600100011
0.2499999850000023 0.1405752276699985 0.1174443782200001
0.7500000000000000 0.1405752276699985 0.1174443782200001
0.0000000000000000 0.9835755594300011 0.1176660121600008
0.5000000000000000 0.9835755594300011 0.1176660121600008
0.0000000000000000 0.5253804691500008 0.1296273580500014
0.5000000000000000 0.5253804691500008 0.1296273580500014
0.2499999850000023 0.3674343673899969 0.1408288305599967
0.7500000000000000 0.3674343673899969 0.1408288305599967
0.2499999850000023 0.8420608161950947 0.1606329583360910
0.7500000000000000 0.8419576349941530 0.1605784805773056
0.0002971055496690 0.6755195246260213 0.1731161805975153
0.4997028944503308 0.6755195246260213 0.1731161805975153
0.0006505469152588 0.2228384026803982 0.1827273190951359
0.4993494530847414 0.2228384026803982 0.1827273190951359
0.2499999850000023 0.0567571962727391 0.1897838676862794
0.7500000000000000 0.0575895704817379 0.1900331236710447
0.2499999850000023 0.5333032025208106 0.2109229664704642
0.7500000000000000 0.5345080075642623 0.2112907492968576
-0.0006375979311096 0.3755771804143354 0.2215603738685823
0.5006375979311104 0.3755771804143354 0.2215603738685823
-0.0006449500638147 0.9210834796620457 0.2307882159450288
0.5006449500638148 0.9210834796620457 0.2307882159450288
0.2499999850000023 0.7637251282672834 0.2385963064728941
0.7500000000000000 0.7630267008509802 0.2384581761160290
0.2499999850000023 0.2404468496006257 0.2623529424465632
0.7500000000000000 0.2362062497972112 0.2612751170217582
0.0024439850343002 0.0767166995824597 0.2668567154721664
0.4975560149656996 0.0767166995824597 0.2668567154721664
0.0008614027313266 0.6212415261444986 0.2788826594566275
0.4991385972686734 0.6212415261444986 0.2788826594566275
0.2499999850000023 0.4597567637593273 0.2886836727744723
0.7500000000000000 0.4620190046964892 0.2890293108191440
0.2499999850000023 0.9420308867353459 0.3098522501200190
0.7500000000000000 0.9420132621836951 0.3098854168004734
-0.0008512404902403 0.7757784128390164 0.3169074877027884
0.5008512404902401 0.7757784128390164 0.3169074877027884
-0.0120007479172201 0.3173569750939334 0.3325693485316588
0.5120007479172195 0.3173569750939334 0.3325693485316588
0.2499999850000023 0.1541879345581658 0.3379368137490409
0.7500000000000000 0.1437268142562705 0.3354093128287287
0.2499999850000023 0.6326832332071288 0.3595766382397638
0.7500000000000000 0.6315279577694289 0.3594197522689878
0.0015371559408095 0.4751923229431999 0.3703885155218432
0.4984628440591906 0.4751923229431999 0.3703885155218432
0.0045195278578886 0.0135521988048136 0.3843985854734830
0.4954804721421112 0.0135521988048136 0.3843985854734830
0.2499999850000023 0.8556894410653192 0.3817916758165630
0.7500000000000000 0.8595182822188527 0.3827875333635560
0.2499999850000023 0.3309474363045138 0.4092602568742005
0.7500000000000000 0.3427162216387513 0.4113952013895401
-0.0107311371496977 0.1770590615156627 0.4146196468539540
0.5107311371496979 0.1770590615156627 0.4146196468539540
-0.0007235647463764 0.7253265118554928 0.4231794258398183
0.5007235647463767 0.7253265118554928 0.4231794258398183
0.2499999850000023 0.5698794736869609 0.4423095165252708
0.7500000000000000 0.5688584430483821 0.4419577574804776
0.0005596655150598 0.8821136025423965 0.4594080168732146
0.4994403344849405 0.8821136025423965 0.4594080168732146
0.0029925330184703 0.4252692603299986 0.4700633316802076
0.4970074669815297 0.4252692603299986 0.4700633316802076
0.2499999850000023 0.0485745071718454 0.4684753548873323
0.7500000000000000 0.0470573140457040 0.4691513219628882
0.0001207273837843 0.2402746369224640 0.4991804763789167
0.4998792726162157 0.2402746369224640 0.4991804763789167
0.2499999850000023 0.7389487129825475 0.5008825702703713
0.7500000000000000 0.7388168342658420 0.5010282686150459
-0.0009409898642612 0.5486889040749999 0.5327471629372299
0.5009409898642612 0.5486889040749999 0.5327471629372299
0.2499999549999998 0.9257086960048311 0.5328647004274553
0.7499999400000021 0.9256884096239244 0.5328491795872844
0.2499999549999998 0.3830304341540672 0.5425025370865157
0.7499999400000021 0.3828153074656781 0.5421271456384813
0.0002450623039668 0.0700565214205394 0.5583883085417956
0.4997549376960332 0.0700565214205394 0.5583883085417956
0.2499999549999998 0.2244516310361494 0.5759660206034765
0.7499999400000021 0.2244407893671252 0.5759663325402654
0.2499999549999998 0.6714880917998274 0.5831662427237271
0.7499999400000021 0.6718877370769896 0.5835194765452297
0.0001168681418963 0.8308067569499871 0.5960971566501523
0.4998831318581032 0.8308067569499871 0.5960971566501523
-0.0001422219101575 0.3569873034009181 0.6182750599317623
0.5001422219101574 0.3569873034009181 0.6182750599317623
0.2499999549999998 0.5158306852305059 0.6180236575079782
0.7499999400000021 0.5159832717580731 0.6181816550317707
0.2499999549999998 0.9753430820891580 0.6297425345350216
0.7499999400000021 0.9752966899954144 0.6297433605799252
-0.0000111761964053 0.1333632691188763 0.6408525622000690
0.5000111761964056 0.1333632691188763 0.6408525622000690
0.0000894396663909 0.6579173337573946 0.6609025733280827
0.4999105603336093 0.6579173337573946 0.6609025733280827
0.2499999549999998 0.8250026629960682 0.6734695584508358
0.7499999400000021 0.8249755558566991 0.6734698762337797
0.2499999549999998 0.2768652009806421 0.6832008056017919
0.7499999400000021 0.2768658582137478 0.6832012083290943
0.0001120208297647 0.4419460398165975 0.6902560700044937
0.4998879791702355 0.4419460398165975 0.6902560700044937
0.0000038733377261 0.9670185125237015 0.7106870094138881
0.4999961266622742 0.9670185125237015 0.7106870094138881
0.2499999549999998 0.1242758159289821 0.7221543301972995
0.7499999400000021 0.1242593512482375 0.7221545005651921
0.2499999549999998 0.5771713730952310 0.7302691924461743
0.7499999400000021 0.5770740951510157 0.7302317785191008
-0.0000624819751946 0.7355601111227499 0.7387120463868266
0.5000624819751945 0.7355601111227499 0.7387120463868266
-0.0000009940682968 0.2651459138216287 0.7617478053216844
0.5000009940682969 0.2651459138216287 0.7617478053216844
0.2499999549999998 0.4229194841275341 0.7694491431107383
0.7499999400000021 0.4229172004771223 0.7694498664645296
0.2499999549999998 0.8767669274389217 0.7780156426712092
0.7499999400000021 0.8767860982033757 0.7780245411562264
-0.0000079398225850 0.0340563233738224 0.7893162434504482
0.5000079398225852 0.0340563233738224 0.7893162434504482
0.0000074429937248 0.5593209527705383 0.8095098625188276
0.4999925570062759 0.5593209527705383 0.8095098625188276
0.2499999549999998 0.7238728942349867 0.8172397893727178
0.7499999400000021 0.7238711063626166 0.8172419039135788
0.2499999549999998 0.1758593527734923 0.8268588152112514
0.7499999400000021 0.1758400622275137 0.8268375827300717
0.0000018587375673 0.3431600858225707 0.8396203642696094
0.4999981412624322 0.3431600858225707 0.8396203642696094
0.0000000000000000 0.8674342783900002 0.8591710054399968
0.5000000000000000 0.8674342783900002 0.8591710054399968
0.2499999549999998 0.0253805131499973 0.8703725379499971
0.7499999400000021 0.0253805131499973 0.8703725379499971
0.2499999549999998 0.4835755594300011 0.8823338318400005
0.7499999400000021 0.4835755594300011 0.8823338318400005
0.0000000000000000 0.6405751236699970 0.8825555247800025
0.5000000000000000 0.6405751236699970 0.8825555247800025
0.0000000000000000 0.1702044921400017 0.9041126909899972
0.5000000000000000 0.1702044921400017 0.9041126909899972
0.2499999549999998 0.3281393154099987 0.9175284682699996
0.7499999400000021 0.3281393154099987 0.9175284682699996
0.2499999549999998 0.7750737102499983 0.9230451497199965
0.7499999400000021 0.7750737102499983 0.9230451497199965
0.0000000000000000 0.9300076300799986 0.9416396241499996
0.5000000000000000 0.9300076300799986 0.9416396241499996
0.2499999549999998 0.6181448713100011 0.9591807759300011
0.7499999400000021 0.6181448713100011 0.9591807759300011
0.2499999549999998 0.0744182212599966 0.9673075916799974
0.7499999400000021 0.0744182212599966 0.9673075916799974
0.0000000000000000 0.4535387172199989 0.9682328621399989
0.5000000000000000 0.4535387172199989 0.9682328621399989
0.2499999549999998 0.5138390078300006 0.0015253939999980
0.7499999400000021 0.5138390078300006 0.0015253939999980
0.2499999850000023 0.1993901048399991 0.0566408064400008
0.7500000000000000 0.1993901048399991 0.0566408064400008
0.2499999850000023 0.9060885862599974 0.0988101646000032
0.7500000000000000 0.9060885862599974 0.0988101646000032
0.2499999850000023 0.5999232770899994 0.1520907401000002
0.7500000000000000 0.5999232770899994 0.1520907401000002
0.2499999850000023 0.3008428212059368 0.2004746674020850
0.7500000000000000 0.3004686864583284 0.2004145351132569
0.2499999850000023 -0.0022830969378047 0.2491242479237537
0.7500000000000000 -0.0016729204585980 0.2494171498791961
0.2499999850000023 0.6980877640575661 0.2987960628345260
0.7500000000000000 0.6978062403791558 0.2985975161943797
0.2499999850000023 0.3965984679588764 0.3493347498196309
0.7500000000000000 0.4068340477335063 0.3480838273628763
0.2499999850000023 0.0957195721128111 0.4007939683158623
0.7500000000000000 0.0857217699034751 0.4037296176301125
0.2499999850000023 0.8003996363836081 0.4438746991202605
0.7500000000000000 0.8005344734116436 0.4441029618302292
0.2499999549999998 0.4881036069631003 0.5003589753267451
0.7499999400000021 0.4876745192723155 0.4999236507442200
0.2499999549999998 0.7974985192511311 0.5572144187986685
0.7499999400000021 0.7978723646315707 0.5572557440732899
0.2499999549999998 0.0983776311690586 0.6006267809908650
0.7499999400000021 0.0983386391650913 0.6005923660910129
0.2499999549999998 0.3997851465675423 0.6539410578201373
0.7499999400000021 0.3997465986772131 0.6539951995682143
0.2499999549999998 0.6984042008077207 0.6996648995318631
0.7499999400000021 0.6983876302623856 0.6996499176211995
0.2499999549999998 0.0002279144413511 0.7500903477642973
0.7499999400000021 0.0002415967676132 0.7500885161408217
0.2499999549999998 0.3022636030825932 0.8009843602691160
0.7499999400000021 0.3022617839027095 0.8009846982522415
0.2499999549999998 0.5998386531500017 0.8466550186300026
0.7499999400000021 0.5998386531500017 0.8466550186300026
0.2499999549999998 0.9014906408599970 0.8997363362200019
0.7499999400000021 0.9014906408599970 0.8997363362200019
0.2499999549999998 0.2017832238700024 0.9432545935800007
0.7499999400000021 0.2017832238700024 0.9432545935800007
0.0000000000000000 0.0138390678299984 0.9984746060000020
0.5000000000000000 0.0138390678299984 0.9984746060000020
0.0000000000000000 0.7017831788700022 0.0567452724200024
0.5000000000000000 0.7017831788700022 0.0567452724200024
0.0000000000000000 0.4014907298600008 0.1002635147800035
0.5000000000000000 0.4014907298600008 0.1002635147800035
0.0000000000000000 0.0998387641500003 0.1533448773700030
0.5000000000000000 0.0998387641500003 0.1533448773700030
-0.0000669106130973 0.8010524584715649 0.1992452563700227
0.5000669106130974 0.8010524584715649 0.1992452563700227
0.0013891444162654 0.4984111888015441 0.2500021820896446
0.4986108555837344 0.4984111888015441 0.2500021820896446
0.0010167997681741 0.1942262581342066 0.2984093250020118
0.4989832002318258 0.1942262581342066 0.2984093250020118
0.0005237018682229 0.8981682083708146 0.3464282580393911
0.4994762981317774 0.8981682083708146 0.3464282580393911
0.0005503219952602 0.5998279662360126 0.4005252798476874
0.4994496780047398 0.5998279662360126 0.4005252798476874
0.0012909187222209 0.2999347938791176 0.4462512577860125
0.4987090812777793 0.2999347938791176 0.4462512577860125
0.0014831492999859 0.9857843675029612 0.5022166010267808
0.4985168507000141 0.9857843675029612 0.5022166010267808
0.0000598087550793 0.3018009119267794 0.5579178611649239
0.4999401912449204 0.3018009119267794 0.5579178611649239
-0.0001990915651206 0.5942209115296437 0.5999597389852391
0.5001990915651204 0.5942209115296437 0.5999597389852391
0.0000076878842180 0.9005072562125521 0.6522621768430167
0.4999923121157820 0.9005072562125521 0.6522621768430167
0.0000132958075497 0.1995361821516842 0.7016829122572804
0.4999867041924503 0.1995361821516842 0.7016829122572804
0.0000184649159010 0.5003509789083100 0.7502682255206382
0.4999815350840990 0.5003509789083100 0.7502682255206382
-0.0000113782044715 0.8011423397644464 0.7989555324884546
0.5000113782044709 0.8011423397644464 0.7989555324884546
0.0000000000000000 0.0999233000899977 0.8479091558999983
0.5000000000000000 0.0999233000899977 0.8479091558999983
0.0000000000000000 0.4060886152600034 0.9011896864000022
0.5000000000000000 0.4060886152600034 0.9011896864000022
0.0000000000000000 0.6993900008399976 0.9433590595600023
0.5000000000000000 0.6993900008399976 0.9433590595600023
0.7500000000000000 0.2446480898961925 0.3722180202783857
Thank you very much!
Jian Xu
The system of my present VASP job is Li-intercalated β-MnO2 grain boundary. A collinear antiferromagnetic ordering is used in all our calculations. Valence electron configurations of the potentials were taken as 1s2 2s1 for Li, 3d6 4s1 for Mn, and 2s2 2p4 for O. But I find some very confused results.
I give “Structure A” a static calculation, the resulted energy is “-1617.4093eV”. Then I put “Structure A” just translate 0.5 along direction “a” to get “Structure B”. But the resulted energy is “-1614.0948” after a static calculation! To my knowledge, “Structure A” and “Structure B” are just the same due to Periodic boundary conditions, isn’t it?
Here are my relaxation inputs:
INCAR:
SYSTEM = MnO2
LWAVE=.FALSE.
LCHARG=.FALSE.
LASPH=.TRUE.
LREAL= Auto
ISTART=0
ICHARG=2
ALGO=Normal
PREC=Normal
#LPLANE = .TRUE.
NPAR = 6
#LSCALU = .FALSE.
#NSIM = 4
ISPIN=2
ENCUT=500
ISMEAR=0
SIGMA=0.2
LDAU=.TRUE.
LDAUTYPE=2
LDAUL= -1 2 -1
LDAUU= 0.0 6.1 0.0
LDAUJ= 0.0 1.0 0.0
LORBIT=10
NELM=300
MAGMOM=160*0 40*-1 40*1 1*0
KPOINTS:
AUTO GRID
0
M
2 1 1
0 0 0
The POSCAR file for "Structure A":
New structure
1.00000000000000
5.8893198967000000 0.0000000000000000 0.0000000000000000
0.0000000000000000 14.0908565521000000 0.0000000000000000
0.0000000000000000 0.0000000000000000 28.1817131042000000
O Mn Li
160 80 1
Direct
0.2499999850000023 0.2604309137599969 0.9993153614700034
0.7500000000000000 0.2604309137599969 0.9993153614700034
0.0000000000000000 0.7604308247600002 0.0006845765299985
0.5000000000000000 0.7604308247600002 0.0006845765299985
0.2499999850000023 0.9535387172199989 0.0317670078599974
0.7500000000000000 0.9535387172199989 0.0317670078599974
0.0000000000000000 0.5744181912600013 0.0326922833200030
0.5000000000000000 0.5744181912600013 0.0326922833200030
0.0000000000000000 0.1181449833100032 0.0408190930699988
0.5000000000000000 0.1181449833100032 0.0408190930699988
0.2499999850000023 0.4300077190800025 0.0583602348499994
0.7500000000000000 0.4300077190800025 0.0583602348499994
0.0000000000000000 0.2750738002499986 0.0769547092800025
0.5000000000000000 0.2750738002499986 0.0769547092800025
0.0000000000000000 0.8281392854100034 0.0824713827299988
0.5000000000000000 0.8281392854100034 0.0824713827299988
0.2499999850000023 0.6702044481399980 0.0958871600100011
0.7500000000000000 0.6702044481399980 0.0958871600100011
0.2499999850000023 0.1405752276699985 0.1174443782200001
0.7500000000000000 0.1405752276699985 0.1174443782200001
0.0000000000000000 0.9835755594300011 0.1176660121600008
0.5000000000000000 0.9835755594300011 0.1176660121600008
0.0000000000000000 0.5253804691500008 0.1296273580500014
0.5000000000000000 0.5253804691500008 0.1296273580500014
0.2499999850000023 0.3674343673899969 0.1408288305599967
0.7500000000000000 0.3674343673899969 0.1408288305599967
0.2499999850000023 0.8420608161950947 0.1606329583360910
0.7500000000000000 0.8419576349941530 0.1605784805773056
0.0002971055496690 0.6755195246260213 0.1731161805975153
0.4997028944503308 0.6755195246260213 0.1731161805975153
0.0006505469152588 0.2228384026803982 0.1827273190951359
0.4993494530847414 0.2228384026803982 0.1827273190951359
0.2499999850000023 0.0567571962727391 0.1897838676862794
0.7500000000000000 0.0575895704817379 0.1900331236710447
0.2499999850000023 0.5333032025208106 0.2109229664704642
0.7500000000000000 0.5345080075642623 0.2112907492968576
-0.0006375979311096 0.3755771804143354 0.2215603738685823
0.5006375979311104 0.3755771804143354 0.2215603738685823
-0.0006449500638147 0.9210834796620457 0.2307882159450288
0.5006449500638148 0.9210834796620457 0.2307882159450288
0.2499999850000023 0.7637251282672834 0.2385963064728941
0.7500000000000000 0.7630267008509802 0.2384581761160290
0.2499999850000023 0.2404468496006257 0.2623529424465632
0.7500000000000000 0.2362062497972112 0.2612751170217582
0.0024439850343002 0.0767166995824597 0.2668567154721664
0.4975560149656996 0.0767166995824597 0.2668567154721664
0.0008614027313266 0.6212415261444986 0.2788826594566275
0.4991385972686734 0.6212415261444986 0.2788826594566275
0.2499999850000023 0.4597567637593273 0.2886836727744723
0.7500000000000000 0.4620190046964892 0.2890293108191440
0.2499999850000023 0.9420308867353459 0.3098522501200190
0.7500000000000000 0.9420132621836951 0.3098854168004734
-0.0008512404902403 0.7757784128390164 0.3169074877027884
0.5008512404902401 0.7757784128390164 0.3169074877027884
-0.0120007479172201 0.3173569750939334 0.3325693485316588
0.5120007479172195 0.3173569750939334 0.3325693485316588
0.2499999850000023 0.1541879345581658 0.3379368137490409
0.7500000000000000 0.1437268142562705 0.3354093128287287
0.2499999850000023 0.6326832332071288 0.3595766382397638
0.7500000000000000 0.6315279577694289 0.3594197522689878
0.0015371559408095 0.4751923229431999 0.3703885155218432
0.4984628440591906 0.4751923229431999 0.3703885155218432
0.0045195278578886 0.0135521988048136 0.3843985854734830
0.4954804721421112 0.0135521988048136 0.3843985854734830
0.2499999850000023 0.8556894410653192 0.3817916758165630
0.7500000000000000 0.8595182822188527 0.3827875333635560
0.2499999850000023 0.3309474363045138 0.4092602568742005
0.7500000000000000 0.3427162216387513 0.4113952013895401
-0.0107311371496977 0.1770590615156627 0.4146196468539540
0.5107311371496979 0.1770590615156627 0.4146196468539540
-0.0007235647463764 0.7253265118554928 0.4231794258398183
0.5007235647463767 0.7253265118554928 0.4231794258398183
0.2499999850000023 0.5698794736869609 0.4423095165252708
0.7500000000000000 0.5688584430483821 0.4419577574804776
0.0005596655150598 0.8821136025423965 0.4594080168732146
0.4994403344849405 0.8821136025423965 0.4594080168732146
0.0029925330184703 0.4252692603299986 0.4700633316802076
0.4970074669815297 0.4252692603299986 0.4700633316802076
0.2499999850000023 0.0485745071718454 0.4684753548873323
0.7500000000000000 0.0470573140457040 0.4691513219628882
0.0001207273837843 0.2402746369224640 0.4991804763789167
0.4998792726162157 0.2402746369224640 0.4991804763789167
0.2499999850000023 0.7389487129825475 0.5008825702703713
0.7500000000000000 0.7388168342658420 0.5010282686150459
-0.0009409898642612 0.5486889040749999 0.5327471629372299
0.5009409898642612 0.5486889040749999 0.5327471629372299
0.2499999549999998 0.9257086960048311 0.5328647004274553
0.7499999400000021 0.9256884096239244 0.5328491795872844
0.2499999549999998 0.3830304341540672 0.5425025370865157
0.7499999400000021 0.3828153074656781 0.5421271456384813
0.0002450623039668 0.0700565214205394 0.5583883085417956
0.4997549376960332 0.0700565214205394 0.5583883085417956
0.2499999549999998 0.2244516310361494 0.5759660206034765
0.7499999400000021 0.2244407893671252 0.5759663325402654
0.2499999549999998 0.6714880917998274 0.5831662427237271
0.7499999400000021 0.6718877370769896 0.5835194765452297
0.0001168681418963 0.8308067569499871 0.5960971566501523
0.4998831318581032 0.8308067569499871 0.5960971566501523
-0.0001422219101575 0.3569873034009181 0.6182750599317623
0.5001422219101574 0.3569873034009181 0.6182750599317623
0.2499999549999998 0.5158306852305059 0.6180236575079782
0.7499999400000021 0.5159832717580731 0.6181816550317707
0.2499999549999998 0.9753430820891580 0.6297425345350216
0.7499999400000021 0.9752966899954144 0.6297433605799252
-0.0000111761964053 0.1333632691188763 0.6408525622000690
0.5000111761964056 0.1333632691188763 0.6408525622000690
0.0000894396663909 0.6579173337573946 0.6609025733280827
0.4999105603336093 0.6579173337573946 0.6609025733280827
0.2499999549999998 0.8250026629960682 0.6734695584508358
0.7499999400000021 0.8249755558566991 0.6734698762337797
0.2499999549999998 0.2768652009806421 0.6832008056017919
0.7499999400000021 0.2768658582137478 0.6832012083290943
0.0001120208297647 0.4419460398165975 0.6902560700044937
0.4998879791702355 0.4419460398165975 0.6902560700044937
0.0000038733377261 0.9670185125237015 0.7106870094138881
0.4999961266622742 0.9670185125237015 0.7106870094138881
0.2499999549999998 0.1242758159289821 0.7221543301972995
0.7499999400000021 0.1242593512482375 0.7221545005651921
0.2499999549999998 0.5771713730952310 0.7302691924461743
0.7499999400000021 0.5770740951510157 0.7302317785191008
-0.0000624819751946 0.7355601111227499 0.7387120463868266
0.5000624819751945 0.7355601111227499 0.7387120463868266
-0.0000009940682968 0.2651459138216287 0.7617478053216844
0.5000009940682969 0.2651459138216287 0.7617478053216844
0.2499999549999998 0.4229194841275341 0.7694491431107383
0.7499999400000021 0.4229172004771223 0.7694498664645296
0.2499999549999998 0.8767669274389217 0.7780156426712092
0.7499999400000021 0.8767860982033757 0.7780245411562264
-0.0000079398225850 0.0340563233738224 0.7893162434504482
0.5000079398225852 0.0340563233738224 0.7893162434504482
0.0000074429937248 0.5593209527705383 0.8095098625188276
0.4999925570062759 0.5593209527705383 0.8095098625188276
0.2499999549999998 0.7238728942349867 0.8172397893727178
0.7499999400000021 0.7238711063626166 0.8172419039135788
0.2499999549999998 0.1758593527734923 0.8268588152112514
0.7499999400000021 0.1758400622275137 0.8268375827300717
0.0000018587375673 0.3431600858225707 0.8396203642696094
0.4999981412624322 0.3431600858225707 0.8396203642696094
0.0000000000000000 0.8674342783900002 0.8591710054399968
0.5000000000000000 0.8674342783900002 0.8591710054399968
0.2499999549999998 0.0253805131499973 0.8703725379499971
0.7499999400000021 0.0253805131499973 0.8703725379499971
0.2499999549999998 0.4835755594300011 0.8823338318400005
0.7499999400000021 0.4835755594300011 0.8823338318400005
0.0000000000000000 0.6405751236699970 0.8825555247800025
0.5000000000000000 0.6405751236699970 0.8825555247800025
0.0000000000000000 0.1702044921400017 0.9041126909899972
0.5000000000000000 0.1702044921400017 0.9041126909899972
0.2499999549999998 0.3281393154099987 0.9175284682699996
0.7499999400000021 0.3281393154099987 0.9175284682699996
0.2499999549999998 0.7750737102499983 0.9230451497199965
0.7499999400000021 0.7750737102499983 0.9230451497199965
0.0000000000000000 0.9300076300799986 0.9416396241499996
0.5000000000000000 0.9300076300799986 0.9416396241499996
0.2499999549999998 0.6181448713100011 0.9591807759300011
0.7499999400000021 0.6181448713100011 0.9591807759300011
0.2499999549999998 0.0744182212599966 0.9673075916799974
0.7499999400000021 0.0744182212599966 0.9673075916799974
0.0000000000000000 0.4535387172199989 0.9682328621399989
0.5000000000000000 0.4535387172199989 0.9682328621399989
0.2499999549999998 0.5138390078300006 0.0015253939999980
0.7499999400000021 0.5138390078300006 0.0015253939999980
0.2499999850000023 0.1993901048399991 0.0566408064400008
0.7500000000000000 0.1993901048399991 0.0566408064400008
0.2499999850000023 0.9060885862599974 0.0988101646000032
0.7500000000000000 0.9060885862599974 0.0988101646000032
0.2499999850000023 0.5999232770899994 0.1520907401000002
0.7500000000000000 0.5999232770899994 0.1520907401000002
0.2499999850000023 0.3008428212059368 0.2004746674020850
0.7500000000000000 0.3004686864583284 0.2004145351132569
0.2499999850000023 -0.0022830969378047 0.2491242479237537
0.7500000000000000 -0.0016729204585980 0.2494171498791961
0.2499999850000023 0.6980877640575661 0.2987960628345260
0.7500000000000000 0.6978062403791558 0.2985975161943797
0.2499999850000023 0.3965984679588764 0.3493347498196309
0.7500000000000000 0.4068340477335063 0.3480838273628763
0.2499999850000023 0.0957195721128111 0.4007939683158623
0.7500000000000000 0.0857217699034751 0.4037296176301125
0.2499999850000023 0.8003996363836081 0.4438746991202605
0.7500000000000000 0.8005344734116436 0.4441029618302292
0.2499999549999998 0.4881036069631003 0.5003589753267451
0.7499999400000021 0.4876745192723155 0.4999236507442200
0.2499999549999998 0.7974985192511311 0.5572144187986685
0.7499999400000021 0.7978723646315707 0.5572557440732899
0.2499999549999998 0.0983776311690586 0.6006267809908650
0.7499999400000021 0.0983386391650913 0.6005923660910129
0.2499999549999998 0.3997851465675423 0.6539410578201373
0.7499999400000021 0.3997465986772131 0.6539951995682143
0.2499999549999998 0.6984042008077207 0.6996648995318631
0.7499999400000021 0.6983876302623856 0.6996499176211995
0.2499999549999998 0.0002279144413511 0.7500903477642973
0.7499999400000021 0.0002415967676132 0.7500885161408217
0.2499999549999998 0.3022636030825932 0.8009843602691160
0.7499999400000021 0.3022617839027095 0.8009846982522415
0.2499999549999998 0.5998386531500017 0.8466550186300026
0.7499999400000021 0.5998386531500017 0.8466550186300026
0.2499999549999998 0.9014906408599970 0.8997363362200019
0.7499999400000021 0.9014906408599970 0.8997363362200019
0.2499999549999998 0.2017832238700024 0.9432545935800007
0.7499999400000021 0.2017832238700024 0.9432545935800007
0.0000000000000000 0.0138390678299984 0.9984746060000020
0.5000000000000000 0.0138390678299984 0.9984746060000020
0.0000000000000000 0.7017831788700022 0.0567452724200024
0.5000000000000000 0.7017831788700022 0.0567452724200024
0.0000000000000000 0.4014907298600008 0.1002635147800035
0.5000000000000000 0.4014907298600008 0.1002635147800035
0.0000000000000000 0.0998387641500003 0.1533448773700030
0.5000000000000000 0.0998387641500003 0.1533448773700030
-0.0000669106130973 0.8010524584715649 0.1992452563700227
0.5000669106130974 0.8010524584715649 0.1992452563700227
0.0013891444162654 0.4984111888015441 0.2500021820896446
0.4986108555837344 0.4984111888015441 0.2500021820896446
0.0010167997681741 0.1942262581342066 0.2984093250020118
0.4989832002318258 0.1942262581342066 0.2984093250020118
0.0005237018682229 0.8981682083708146 0.3464282580393911
0.4994762981317774 0.8981682083708146 0.3464282580393911
0.0005503219952602 0.5998279662360126 0.4005252798476874
0.4994496780047398 0.5998279662360126 0.4005252798476874
0.0012909187222209 0.2999347938791176 0.4462512577860125
0.4987090812777793 0.2999347938791176 0.4462512577860125
0.0014831492999859 0.9857843675029612 0.5022166010267808
0.4985168507000141 0.9857843675029612 0.5022166010267808
0.0000598087550793 0.3018009119267794 0.5579178611649239
0.4999401912449204 0.3018009119267794 0.5579178611649239
-0.0001990915651206 0.5942209115296437 0.5999597389852391
0.5001990915651204 0.5942209115296437 0.5999597389852391
0.0000076878842180 0.9005072562125521 0.6522621768430167
0.4999923121157820 0.9005072562125521 0.6522621768430167
0.0000132958075497 0.1995361821516842 0.7016829122572804
0.4999867041924503 0.1995361821516842 0.7016829122572804
0.0000184649159010 0.5003509789083100 0.7502682255206382
0.4999815350840990 0.5003509789083100 0.7502682255206382
-0.0000113782044715 0.8011423397644464 0.7989555324884546
0.5000113782044709 0.8011423397644464 0.7989555324884546
0.0000000000000000 0.0999233000899977 0.8479091558999983
0.5000000000000000 0.0999233000899977 0.8479091558999983
0.0000000000000000 0.4060886152600034 0.9011896864000022
0.5000000000000000 0.4060886152600034 0.9011896864000022
0.0000000000000000 0.6993900008399976 0.9433590595600023
0.5000000000000000 0.6993900008399976 0.9433590595600023
0.7500000000000000 0.2446480898961925 0.3722180202783857
Thank you very much!
Jian Xu