[Pw_forum] symmetry of the electron-phonon coupling coefficients
Alex Kutana
alex.kutana at gmail.com
Thu May 10 18:53:56 CEST 2012
Dear PW forum users and developers:
Could please somebody with the knowledge of inner workings of the
electron-phonon code help me with this issue:
I am looking at the symmetry of the electron-phonon coupling coefficients
with respect to displacement patterns.
In particular, if one displacement pattern is the negative of the other,
the coefficients should be identical but with opposite signs.
However, when I look at these coefficients in, an e.g. a CO molecule, there
is no such symmetry.
I have a C atom at the origin, and an O atom on the x axis at 1.133999556
0.0 0.0 A.
The first displacement pattern is
-1.000000000000000E+000,-0.000000000000000E+000
-0.000000000000000E+000,-0.000000000000000E+000
-0.000000000000000E+000,-0.000000000000000E+000
-0.000000000000000E+000,-0.000000000000000E+000
-0.000000000000000E+000,-0.000000000000000E+000
-0.000000000000000E+000,-0.000000000000000E+000
and the second one is
-0.000000000000000E+000,-0.000000000000000E+000
-0.000000000000000E+000,-0.000000000000000E+000
-0.000000000000000E+000,-0.000000000000000E+000
-1.000000000000000E+000,-0.000000000000000E+000
-0.000000000000000E+000,-0.000000000000000E+000
-0.000000000000000E+000,-0.000000000000000E+000
i.e. the second is the negative of the first.
However, the electron-phonon matrix elements for these patterns differ by
more than just a sign. Below is a list of matrix elements for transitions
among 9 electronic bands. As expected, the diagonal elements <i | dV | i>
are same and of opposite signs, but the off-diagonal elements are very
different. Is there an explanation of this that I was missing?
Thank you.
Alex Kutana
Naval Research Laboratory
displacement pattern #1:
0->0 0.286566684793000 -0.000000000000000 |g|^2= 0.082120464833251
1->0 -0.034559192981500 0.000031395207500 |g|^2= 0.001194338805192
2->0 -0.000000009558500 0.000000000406000 |g|^2= 0.000000000000000
3->0 0.000000003843000 -0.000000000408500 |g|^2= 0.000000000000000
4->0 0.209537778542500 0.001560705053000 |g|^2= 0.043908516436788
5->0 -0.000000245218500 0.000000483888500 |g|^2= 0.000000000000294
6->0 -0.000000151028000 -0.000000094130500 |g|^2= 0.000000000000032
7->0 0.015210336449500 0.009035433075000 |g|^2= 0.000312993385760
8->0 -0.018916187765500 0.000692293887500 |g|^2= 0.000358301430406
0->1 -0.065753284810500 -0.000059732881500 |g|^2= 0.004323498031388
1->1 -0.010470695547000 0.000000000000000 |g|^2= 0.000109635465238
2->1 0.000000003980500 0.000000000330000 |g|^2= 0.000000000000000
3->1 -0.000000001742000 0.000000000782000 |g|^2= 0.000000000000000
4->1 -0.116488042493500 -0.000973469004500 |g|^2= 0.013570411685870
5->1 0.000000058681500 -0.000000183316500 |g|^2= 0.000000000000037
6->1 0.000000093539000 0.000000028930500 |g|^2= 0.000000000000010
7->1 -0.007170125204000 -0.004268243132000 |g|^2= 0.000069628594875
8->1 0.006675139863000 -0.000242290788500 |g|^2= 0.000044616197017
0->2 -0.000000006649000 -0.000000000795500 |g|^2= 0.000000000000000
1->2 0.000000003757500 -0.000000000281000 |g|^2= 0.000000000000000
2->2 0.172144600342000 -0.000000000000000 |g|^2= 0.029633763426907
3->2 -0.000000007757000 0.000000000424000 |g|^2= 0.000000000000000
4->2 -0.000000007901500 -0.000000000563000 |g|^2= 0.000000000000000
5->2 0.030940253556500 -0.030452295289500 |g|^2= 0.001884641578539
6->2 -0.001917560140000 0.001237350092000 |g|^2= 0.000005208072141
7->2 -0.000005383433500 -0.000006566545000 |g|^2= 0.000000000072101
8->2 0.001206036691000 0.000501228329000 |g|^2= 0.000001705754338
0->3 0.000000002888000 -0.000000000118000 |g|^2= 0.000000000000000
1->3 -0.000000001701000 -0.000000000735000 |g|^2= 0.000000000000000
2->3 -0.000000007757000 -0.000000000424000 |g|^2= 0.000000000000000
3->3 0.172144582271500 -0.000000000000000 |g|^2= 0.029633757205429
4->3 0.000000004962500 0.000000000048500 |g|^2= 0.000000000000000
5->3 -0.002270121070500 0.000239348528500 |g|^2= 0.000005210737393
6->3 -0.043196420568000 -0.004313967793500 |g|^2= 0.001884541068011
7->3 -0.000000730034000 -0.000003790831000 |g|^2= 0.000000000014903
8->3 -0.000008416957500 0.000059829663500 |g|^2= 0.000000003650434
0->4 0.214778021593500 -0.001599735961000 |g|^2= 0.046132157714763
1->4 -0.124602739906000 0.001041282029500 |g|^2= 0.015526927060347
2->4 -0.000000007138000 0.000000000629000 |g|^2= 0.000000000000000
3->4 0.000000004680500 0.000000000120000 |g|^2= 0.000000000000000
4->4 -0.044695925543000 -0.000000000000000 |g|^2= 0.001997725760145
5->4 -0.000000242546000 0.000000487089500 |g|^2= 0.000000000000296
6->4 -0.000000143113500 -0.000000102335000 |g|^2= 0.000000000000031
7->4 -0.004399490592000 -0.002570431486500 |g|^2= 0.000025962635496
8->4 -0.042523842474500 0.001638507220500 |g|^2= 0.001810961884708
0->5 -0.000000167311000 -0.000000343222500 |g|^2= 0.000000000000146
1->5 0.000000058893000 0.000000158656000 |g|^2= 0.000000000000029
2->5 0.032613474298500 0.032099121156000 |g|^2= 0.002093992284806
3->5 -0.002392872109500 -0.000252279387500 |g|^2= 0.000005789481822
4->5 -0.000000180652000 -0.000000410655000 |g|^2= 0.000000000000201
5->5 -0.185897249768000 0.000000000000000 |g|^2= 0.034557787471306
6->5 -0.000000087123000 -0.000000071728500 |g|^2= 0.000000000000013
7->5 0.000000490662500 -0.000011219521500 |g|^2= 0.000000000126118
8->5 0.000649413466000 0.001510073388500 |g|^2= 0.000002702059488
0->6 -0.000000102127000 0.000000060209500 |g|^2= 0.000000000000014
1->6 0.000000074069000 -0.000000025468000 |g|^2= 0.000000000000006
2->6 -0.002021278101500 -0.001304265009000 |g|^2= 0.000005786672377
3->6 -0.045532542731000 0.004547271821500 |g|^2= 0.002093890128569
4->6 -0.000000144484000 0.000000080179500 |g|^2= 0.000000000000027
5->6 -0.000000087123000 0.000000071728500 |g|^2= 0.000000000000013
6->6 -0.185898399888000 -0.000000000000000 |g|^2= 0.034558215080919
7->6 0.000000984953000 0.000004942462000 |g|^2= 0.000000000025398
8->6 -0.000038006325000 -0.000142788293500 |g|^2= 0.000000021832978
0->7 0.015372187389000 -0.009132041345000 |g|^2= 0.000319698324249
1->7 -0.009727469332000 0.005790740403500 |g|^2= 0.000128156334026
2->7 -0.000004934450500 0.000006008964000 |g|^2= 0.000000000060456
3->7 -0.000000667739000 0.000003460446000 |g|^2= 0.000000000012421
4->7 -0.009877533487000 0.005769648051000 |g|^2= 0.000130854506419
5->7 0.000000496943500 0.000011202097500 |g|^2= 0.000000000125734
6->7 0.000000981650000 -0.000004929340500 |g|^2= 0.000000000025262
7->7 -0.000633793442000 0.000000000000000 |g|^2= 0.000000401694127
8->7 0.000030518449500 -0.000027055324500 |g|^2= 0.000000001663366
0->8 -0.013941745790500 -0.000533958928500 |g|^2= 0.000194657387824
1->8 0.004172651103000 0.000183619549500 |g|^2= 0.000017444733366
2->8 0.001106454865000 -0.000459738505500 |g|^2= 0.000001435601862
3->8 -0.000007736827500 -0.000054991042000 |g|^2= 0.000000003083873
4->8 -0.042832546265500 -0.001607772328500 |g|^2= 0.001837211951446
5->8 0.000648997548500 -0.001509835303000 |g|^2= 0.000002700800460
6->8 -0.000038017739500 0.000142907934000 |g|^2= 0.000000021868026
7->8 0.000025705638000 0.000024838755500 |g|^2= 0.000000001277744
8->8 -0.003734049495500 0.000000000000000 |g|^2= 0.000013943125635
displacement pattern #2:
0->0 -0.286565847377500 -0.000000000000000 |g|^2= 0.082119984883185
1->0 0.379851516091000 -0.000345068730000 |g|^2= 0.144287293349060
2->0 0.000000006163500 -0.000000002258000 |g|^2= 0.000000000000000
3->0 0.000000001618500 -0.000000001134500 |g|^2= 0.000000000000000
4->0 -0.133458411497500 -0.000994042731000 |g|^2= 0.017812135720387
5->0 0.000000190857000 -0.000000051579000 |g|^2= 0.000000000000039
6->0 -0.000000069523000 -0.000000017790500 |g|^2= 0.000000000000005
7->0 -0.019890115224000 -0.011817220800500 |g|^2= 0.000535263391072
8->0 -0.039430161288000 0.001065942700500 |g|^2= 0.001555873853038
0->1 0.462246877696500 0.000419919480500 |g|^2= 0.213672352272533
1->1 0.010494926539500 0.000000000000000 |g|^2= 0.000110143483070
2->1 -0.000000003602000 -0.000000000104000 |g|^2= 0.000000000000000
3->1 -0.000000004409500 0.000000001875500 |g|^2= 0.000000000000000
4->1 0.065269015154500 0.000545440362000 |g|^2= 0.004260341844427
5->1 -0.000000404569000 0.000000095724000 |g|^2= 0.000000000000173
6->1 0.000000304352500 -0.000000014508500 |g|^2= 0.000000000000093
7->1 0.018784573101500 0.011183159264000 |g|^2= 0.000477923237730
8->1 0.042649049483000 -0.001095308735500 |g|^2= 0.001820141123029
0->2 0.000000009800000 0.000000002671000 |g|^2= 0.000000000000000
1->2 -0.000000003294500 0.000000000339500 |g|^2= 0.000000000000000
2->2 -0.172141736923500 0.000000000000000 |g|^2= 0.029632777591039
3->2 0.000000095818500 -0.000000007298000 |g|^2= 0.000000000000009
4->2 0.000000001027500 0.000000000264500 |g|^2= 0.000000000000000
5->2 0.058175921580500 -0.057258304602500 |g|^2= 0.006662951297693
6->2 -0.003606567884000 0.002326495942500 |g|^2= 0.000018419915272
7->2 0.000017034603500 0.000020332543000 |g|^2= 0.000000000703590
8->2 -0.003455200640000 -0.001431532813500 |g|^2= 0.000013987697659
0->3 0.000000001244500 0.000000000964500 |g|^2= 0.000000000000000
1->3 -0.000000004262500 -0.000000001807000 |g|^2= 0.000000000000000
2->3 0.000000095818500 0.000000007298000 |g|^2= 0.000000000000009
3->3 -0.172141573131500 0.000000000000000 |g|^2= 0.029632721200188
4->3 0.000000002276500 -0.000000000110500 |g|^2= 0.000000000000000
5->3 -0.004267707540000 0.000449461611500 |g|^2= 0.000018415343387
6->3 -0.081224513696500 -0.008111670337000 |g|^2= 0.006663220820889
7->3 0.000001861979500 0.000010745158500 |g|^2= 0.000000000118925
8->3 0.000028586479000 -0.000167502870000 |g|^2= 0.000000028874398
0->4 -0.231003310734000 0.001720588928000 |g|^2= 0.053365489996328
1->4 0.047001759819500 -0.000392784013500 |g|^2= 0.002209319705411
2->4 0.000000001059500 -0.000000000150500 |g|^2= 0.000000000000000
3->4 0.000000002186000 0.000000000118000 |g|^2= 0.000000000000000
4->4 0.044659534793500 0.000000000000000 |g|^2= 0.001994474047972
5->4 0.000000150192500 0.000000032648000 |g|^2= 0.000000000000024
6->4 -0.000000156776000 -0.000000002718000 |g|^2= 0.000000000000025
7->4 -0.001310064441500 -0.000765519326000 |g|^2= 0.000002302288679
8->4 -0.020407897616500 0.000742934507000 |g|^2= 0.000417034236807
0->5 0.000000235769000 0.000000210453500 |g|^2= 0.000000000000100
1->5 -0.000000265807500 -0.000000046707500 |g|^2= 0.000000000000073
2->5 0.056219406513000 0.055332648710500 |g|^2= 0.006222323681994
3->5 -0.004124172441500 -0.000434330422000 |g|^2= 0.000017197441243
4->5 0.000000122701500 -0.000000029810500 |g|^2= 0.000000000000016
5->5 0.185880014452500 0.000000000000000 |g|^2= 0.034551379772862
6->5 0.000000140947000 0.000000125297000 |g|^2= 0.000000000000036
7->5 -0.000000941527500 0.000011971521000 |g|^2= 0.000000000144204
8->5 -0.000798785488000 -0.001869578039500 |g|^2= 0.000004133380302
0->6 0.000000026588500 0.000000024247000 |g|^2= 0.000000000000001
1->6 0.000000266009000 0.000000033201000 |g|^2= 0.000000000000072
2->6 -0.003485291586500 -0.002248257310000 |g|^2= 0.000017201918375
3->6 -0.078492855467500 0.007838873909000 |g|^2= 0.006222576303603
4->6 -0.000000139482000 -0.000000000856000 |g|^2= 0.000000000000019
5->6 0.000000140947000 -0.000000125297000 |g|^2= 0.000000000000036
6->6 0.185880943275000 -0.000000000000000 |g|^2= 0.034551725072804
7->6 -0.000001321611500 -0.000005771953000 |g|^2= 0.000000000035062
8->6 0.000048260043000 0.000176321833000 |g|^2= 0.000000033418421
0->7 -0.026071694374000 0.015489281608000 |g|^2= 0.000919651092263
1->7 0.001697741814000 -0.001010730029500 |g|^2= 0.000003903902460
2->7 0.000015106160500 -0.000018083799000 |g|^2= 0.000000000555220
3->7 0.000001672337500 -0.000009663610500 |g|^2= 0.000000000096182
4->7 0.002315940634500 -0.001352389584500 |g|^2= 0.000007192538611
5->7 -0.000000927570500 -0.000011708792000 |g|^2= 0.000000000137956
6->7 -0.000001291943000 0.000005661201000 |g|^2= 0.000000000033718
7->7 0.000818543483500 -0.000000000000000 |g|^2= 0.000000670013434
8->7 -0.000425351836000 0.000280356039500 |g|^2= 0.000000259523693
0->8 -0.026410868906000 -0.000617126400500 |g|^2= 0.000697914841364
1->8 0.008979264003000 0.000226470303000 |g|^2= 0.000080678470834
2->8 -0.003085839551500 0.001279050530500 |g|^2= 0.000011158375997
3->8 0.000025569678000 0.000149732451000 |g|^2= 0.000000023073615
4->8 -0.010002857794000 -0.000375228864000 |g|^2= 0.000100197960747
5->8 -0.000775808756500 0.001816292782500 |g|^2= 0.000003900798698
6->8 0.000046818670500 -0.000171407224000 |g|^2= 0.000000031572424
7->8 -0.000239755938500 -0.000163419629500 |g|^2= 0.000000084188885
8->8 0.003793073996500 0.000000000000000 |g|^2= 0.000014387410343
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