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dear Alex<br>
<br>
I don't think that the two matrix element should be equal and
opposite.<br>
suppose you apply both displacement together which means you
displace the molecule as a whole.<br>
<br>
the eigenvalue will not change, hence < i | dV | i > = 0<br>
but the new eigen-wavefunctions | i' > will be the translated
of the original ones, hence different from them.<br>
to first order |i'> = |i> + sum |j> <j|dv|i>/delta
e_IJ<br>
since |i'> =/= |i> no reason to believe that < j | d V |
i > = 0.<br>
<br>
stefano<br>
<br>
On 05/10/2012 06:53 PM, Alex Kutana wrote:
<blockquote
cite="mid:CACD3qTWiTOsDiKm=FGWOgVS_-QKMh6W145hUddcX3CyTPjn0iQ@mail.gmail.com"
type="cite">
<pre wrap="">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
</pre>
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</blockquote>
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