comparing g on coarse and fine q-meshes

[MaxS]

Dear developers,

I am trying to obtain the el-ph matrix elements g in Wannier-Bloch representation on the fine q-mesh, which are stored in epmatwef. Since in EPW these quantities are only hold in memory during the run, I write the variable epmatwef for each q-vector of the fine grid to disc.

For comparison, I set nkf=nk=(6,6,1) and nqf=nq=(3,3,1) and let EPW calculate the matrix elements g for graphene. My idea was that since the fine and coarse meshes are identical, the g in empatwe and epmatwef should be comparable. I might be wrong, because I once read somewhere that the el-ph matrix elements are not uniquely defined.

However, when I compare the matrix elements in epmatwe and epmatwef for q=(0,0,0), they do actually differ substantially. The biggest values from both variables differ by approx. one order of magnitude. Can somebody tell the reason?

The g from both variables for q=(0,0,0)/iq=1 and R_e=(0,0,0)/irk=22 are listed down below.

epmatwe
iq, irk, ibnd, jbnd, imode, epmatwe
1 22 1 1 1 0.39440079+0.00000000i
1 22 1 1 2 -0.22770743-0.00000000i
1 22 1 1 3 0.00000383-0.00000000i
1 22 1 1 4 -0.39440099-0.00000000i
1 22 1 1 5 0.22770747+0.00000000i
1 22 1 1 6 0.00000363-0.00000000i
1 22 1 2 1 -0.03630683-0.00000022i
1 22 1 2 2 -0.02096193-0.00000003i
1 22 1 2 3 0.00000049+0.00000000i
1 22 1 2 4 0.06649935+0.00000017i
1 22 1 2 5 0.03839345-0.00000004i
1 22 1 2 6 0.00000183-0.00000000i
1 22 1 3 1 0.00000024-0.00000004i
1 22 1 3 2 0.04192376+0.00000011i
1 22 1 3 3 0.00000049-0.00000001i
1 22 1 3 4 -0.00000010-0.00000005i
1 22 1 3 5 -0.07678709+0.00000000i
1 22 1 3 6 0.00000168+0.00000011i
1 22 1 4 1 0.00000033+0.00000029i
1 22 1 4 2 -0.00000003+0.00000018i
1 22 1 4 3 -0.08629688+0.00000019i
1 22 1 4 4 -0.00000082-0.00000074i
1 22 1 4 5 0.00000075+0.00000043i
1 22 1 4 6 -0.16686706-0.00000003i
1 22 1 5 1 0.00000149-0.00000000i
1 22 1 5 2 0.00000043-0.00000001i
1 22 1 5 3 0.03581494-0.00000003i
1 22 1 5 4 -0.00000114+0.00000021i
1 22 1 5 5 -0.00000043+0.00000001i
1 22 1 5 6 0.01963768+0.00000008i
1 22 2 1 1 -0.03630683+0.00000022i
1 22 2 1 2 -0.02096193+0.00000003i
1 22 2 1 3 0.00000049-0.00000000i
1 22 2 1 4 0.06649935-0.00000017i
1 22 2 1 5 0.03839345+0.00000004i
1 22 2 1 6 0.00000183+0.00000000i
1 22 2 2 1 -0.00000006-0.00000000i
1 22 2 2 2 0.45541501+0.00000000i
1 22 2 2 3 0.00000387-0.00000000i
1 22 2 2 4 0.00000008+0.00000000i
1 22 2 2 5 -0.45541494+0.00000000i
1 22 2 2 6 0.00000354-0.00000000i
1 22 2 3 1 0.03630698-0.00000008i
1 22 2 3 2 -0.02096166-0.00000012i
1 22 2 3 3 0.00000050+0.00000003i
1 22 2 3 4 -0.06649936-0.00000002i
1 22 2 3 5 0.03839358+0.00000013i
1 22 2 3 6 0.00000180-0.00000006i
1 22 2 4 1 0.00000028-0.00000011i
1 22 2 4 2 0.00000050-0.00000047i
1 22 2 4 3 -0.08629716-0.00000011i
1 22 2 4 4 0.00000040+0.00000017i
1 22 2 4 5 -0.00000162+0.00000067i
1 22 2 4 6 -0.16686706-0.00000003i
1 22 2 5 1 0.00000103+0.00000014i
1 22 2 5 2 0.00000094+0.00000009i
1 22 2 5 3 0.03581486+0.00000004i
1 22 2 5 4 -0.00000106+0.00000005i
1 22 2 5 5 -0.00000050-0.00000049i
1 22 2 5 6 0.01963776+0.00000012i
1 22 3 1 1 0.00000024+0.00000004i
1 22 3 1 2 0.04192376-0.00000011i
1 22 3 1 3 0.00000049+0.00000001i
1 22 3 1 4 -0.00000010+0.00000005i
1 22 3 1 5 -0.07678709-0.00000000i
1 22 3 1 6 0.00000168-0.00000011i
1 22 3 2 1 0.03630698+0.00000008i
1 22 3 2 2 -0.02096166+0.00000012i
1 22 3 2 3 0.00000050-0.00000003i
1 22 3 2 4 -0.06649936+0.00000002i
1 22 3 2 5 0.03839358-0.00000013i
1 22 3 2 6 0.00000180+0.00000006i
1 22 3 3 1 -0.39440145-0.00000000i
1 22 3 3 2 -0.22770790-0.00000000i
1 22 3 3 3 0.00000338-0.00000000i
1 22 3 3 4 0.39440135-0.00000000i
1 22 3 3 5 0.22770787-0.00000000i
1 22 3 3 6 0.00000314-0.00000000i
1 22 3 4 1 -0.00000051-0.00000018i
1 22 3 4 2 -0.00000045+0.00000046i
1 22 3 4 3 -0.08629722-0.00000010i
1 22 3 4 4 0.00000128+0.00000009i
1 22 3 4 5 0.00000068-0.00000022i
1 22 3 4 6 -0.16686713+0.00000002i
1 22 3 5 1 -0.00000173+0.00000006i
1 22 3 5 2 -0.00000084-0.00000036i
1 22 3 5 3 -0.16686723-0.00000003i
1 22 3 5 4 0.00000100-0.00000009i
1 22 3 5 5 0.00000056+0.00000035i
1 22 3 5 6 -0.08629725-0.00000006i
1 22 4 1 1 0.00000033-0.00000029i
1 22 4 1 2 -0.00000003-0.00000018i
1 22 4 1 3 -0.08629688-0.00000019i
1 22 4 1 4 -0.00000082+0.00000074i
1 22 4 1 5 0.00000075-0.00000043i
1 22 4 1 6 -0.16686706+0.00000003i
1 22 4 2 1 0.00000028+0.00000011i
1 22 4 2 2 0.00000050+0.00000047i
1 22 4 2 3 -0.08629716+0.00000011i
1 22 4 2 4 0.00000040-0.00000017i
1 22 4 2 5 -0.00000162-0.00000067i
1 22 4 2 6 -0.16686706+0.00000003i
1 22 4 3 1 -0.00000051+0.00000018i
1 22 4 3 2 -0.00000045-0.00000046i
1 22 4 3 3 -0.08629722+0.00000010i
1 22 4 3 4 0.00000128-0.00000009i
1 22 4 3 5 0.00000068+0.00000022i
1 22 4 3 6 -0.16686713-0.00000002i
1 22 4 4 1 -0.00000012+0.00000000i
1 22 4 4 2 0.00000006+0.00000000i
1 22 4 4 3 -0.00000342-0.00000000i
1 22 4 4 4 0.00000010-0.00000000i
1 22 4 4 5 0.00000006-0.00000000i
1 22 4 4 6 -0.00000613-0.00000000i
1 22 4 5 1 -0.16119768-0.00000002i
1 22 4 5 2 -0.09306744-0.00000006i
1 22 4 5 3 -0.00000112+0.00000000i
1 22 4 5 4 0.16119756+0.00000000i
1 22 4 5 5 0.09306734+0.00000004i
1 22 4 5 6 0.00000006-0.00000028i
1 22 5 1 1 0.00000149+0.00000000i
1 22 5 1 2 0.00000043+0.00000001i
1 22 5 1 3 0.03581494+0.00000003i
1 22 5 1 4 -0.00000114-0.00000021i
1 22 5 1 5 -0.00000043-0.00000001i
1 22 5 1 6 0.01963768-0.00000008i
1 22 5 2 1 0.00000103-0.00000014i
1 22 5 2 2 0.00000094-0.00000009i
1 22 5 2 3 0.03581486-0.00000004i
1 22 5 2 4 -0.00000106-0.00000005i
1 22 5 2 5 -0.00000050+0.00000049i
1 22 5 2 6 0.01963776-0.00000012i
1 22 5 3 1 -0.00000173-0.00000006i
1 22 5 3 2 -0.00000084+0.00000036i
1 22 5 3 3 -0.16686723+0.00000003i
1 22 5 3 4 0.00000100+0.00000009i
1 22 5 3 5 0.00000056-0.00000035i
1 22 5 3 6 -0.08629725+0.00000006i
1 22 5 4 1 -0.16119768+0.00000002i
1 22 5 4 2 -0.09306744+0.00000006i
1 22 5 4 3 -0.00000112-0.00000000i
1 22 5 4 4 0.16119756-0.00000000i
1 22 5 4 5 0.09306734-0.00000004i
1 22 5 4 6 0.00000006+0.00000028i
1 22 5 5 1 -0.00000005-0.00000000i
1 22 5 5 2 -0.00000004-0.00000000i
1 22 5 5 3 -0.00000701-0.00000000i
1 22 5 5 4 0.00000009+0.00000000i
1 22 5 5 5 -0.00000001+0.00000000i
1 22 5 5 6 -0.00000592+0.00000000i

epmatwef for iq=1
irk, ibnd, jbnd, imode, epmatwe
22 1 1 1 0.00000005-0.00000000i
22 1 1 2 0.00000000+0.00000000i
22 1 1 3 -0.00000000-0.00000000i
22 1 1 4 -0.00000000+0.00000000i
22 1 1 5 -0.00575747-0.00000000i
22 1 1 6 0.00218496+0.00000000i
22 1 2 1 0.00000002+0.00000000i
22 1 2 2 -0.00023267+0.00000000i
22 1 2 3 0.00003776+0.00000000i
22 1 2 4 0.00000001-0.00000000i
22 1 2 5 0.00012857+0.00000000i
22 1 2 6 -0.00079224-0.00000000i
22 1 3 1 0.00000001+0.00000000i
22 1 3 2 0.00014903-0.00000000i
22 1 3 3 0.00018262-0.00000000i
22 1 3 4 0.00000001+0.00000000i
22 1 3 5 0.00062181+0.00000000i
22 1 3 6 0.00050747+0.00000000i
22 1 4 1 -0.00171164+0.00000000i
22 1 4 2 -0.00000000-0.00000000i
22 1 4 3 -0.00000001-0.00000001i
22 1 4 4 -0.00054474-0.00000000i
22 1 4 5 -0.00000001-0.00000001i
22 1 4 6 0.00000000+0.00000000i
22 1 5 1 0.00037492+0.00000000i
22 1 5 2 -0.00000000-0.00000000i
22 1 5 3 0.00000000+0.00000000i
22 1 5 4 -0.00010937+0.00000000i
22 1 5 5 -0.00000001+0.00000000i
22 1 5 6 0.00000002-0.00000000i
22 2 1 1 0.00000002-0.00000000i
22 2 1 2 -0.00023267-0.00000000i
22 2 1 3 0.00003776-0.00000000i
22 2 1 4 0.00000001+0.00000000i
22 2 1 5 0.00012857-0.00000000i
22 2 1 6 -0.00079224+0.00000000i
22 2 2 1 0.00000005-0.00000000i
22 2 2 2 -0.00000000+0.00000000i
22 2 2 3 -0.00000000+0.00000000i
22 2 2 4 -0.00000000+0.00000000i
22 2 2 5 0.00477097+0.00000000i
22 2 2 6 0.00389363+0.00000000i
22 2 3 1 0.00000002-0.00000000i
22 2 3 2 0.00008363+0.00000000i
22 2 3 3 -0.00022038-0.00000000i
22 2 3 4 0.00000001-0.00000000i
22 2 3 5 -0.00075038-0.00000000i
22 2 3 6 0.00028477-0.00000000i
22 2 4 1 -0.00171164-0.00000000i
22 2 4 2 0.00000000-0.00000000i
22 2 4 3 0.00000001-0.00000000i
22 2 4 4 -0.00054473+0.00000000i
22 2 4 5 0.00000001-0.00000000i
22 2 4 6 0.00000001-0.00000001i
22 2 5 1 0.00037492+0.00000000i
22 2 5 2 -0.00000000+0.00000000i
22 2 5 3 -0.00000000+0.00000000i
22 2 5 4 -0.00010937+0.00000000i
22 2 5 5 -0.00000000+0.00000000i
22 2 5 6 0.00000002+0.00000000i
22 3 1 1 0.00000001-0.00000000i
22 3 1 2 0.00014903+0.00000000i
22 3 1 3 0.00018262+0.00000000i
22 3 1 4 0.00000001-0.00000000i
22 3 1 5 0.00062181-0.00000000i
22 3 1 6 0.00050747-0.00000000i
22 3 2 1 0.00000002+0.00000000i
22 3 2 2 0.00008363-0.00000000i
22 3 2 3 -0.00022038+0.00000000i
22 3 2 4 0.00000001+0.00000000i
22 3 2 5 -0.00075038+0.00000000i
22 3 2 6 0.00028477+0.00000000i
22 3 3 1 0.00000004-0.00000000i
22 3 3 2 0.00000000+0.00000000i
22 3 3 3 -0.00000000-0.00000000i
22 3 3 4 -0.00000000+0.00000000i
22 3 3 5 0.00098650+0.00000000i
22 3 3 6 -0.00607860-0.00000000i
22 3 4 1 -0.00171165-0.00000000i
22 3 4 2 -0.00000001-0.00000000i
22 3 4 3 0.00000000-0.00000000i
22 3 4 4 -0.00054473+0.00000000i
22 3 4 5 0.00000000+0.00000000i
22 3 4 6 -0.00000001+0.00000000i
22 3 5 1 -0.00171165-0.00000000i
22 3 5 2 0.00000000+0.00000000i
22 3 5 3 -0.00000000-0.00000000i
22 3 5 4 0.00054473-0.00000000i
22 3 5 5 0.00000000-0.00000000i
22 3 5 6 -0.00000002-0.00000000i
22 4 1 1 -0.00171164-0.00000000i
22 4 1 2 -0.00000000+0.00000000i
22 4 1 3 -0.00000001+0.00000001i
22 4 1 4 -0.00054474+0.00000000i
22 4 1 5 -0.00000001+0.00000001i
22 4 1 6 0.00000000-0.00000000i
22 4 2 1 -0.00171164+0.00000000i
22 4 2 2 0.00000000+0.00000000i
22 4 2 3 0.00000001+0.00000000i
22 4 2 4 -0.00054473-0.00000000i
22 4 2 5 0.00000001+0.00000000i
22 4 2 6 0.00000001+0.00000001i
22 4 3 1 -0.00171165+0.00000000i
22 4 3 2 -0.00000001+0.00000000i
22 4 3 3 0.00000000+0.00000000i
22 4 3 4 -0.00054473-0.00000000i
22 4 3 5 0.00000000-0.00000000i
22 4 3 6 -0.00000001-0.00000000i
22 4 4 1 -0.00000006-0.00000000i
22 4 4 2 -0.00000000+0.00000000i
22 4 4 3 -0.00000000-0.00000000i
22 4 4 4 -0.00000002-0.00000000i
22 4 4 5 0.00000000+0.00000000i
22 4 4 6 -0.00000000+0.00000000i
22 4 5 1 -0.00000001-0.00000000i
22 4 5 2 0.00000000+0.00000000i
22 4 5 3 -0.00000000+0.00000000i
22 4 5 4 0.00000001-0.00000000i
22 4 5 5 0.00040320-0.00000000i
22 4 5 6 -0.00248441-0.00000000i
22 5 1 1 0.00037492-0.00000000i
22 5 1 2 -0.00000000+0.00000000i
22 5 1 3 0.00000000-0.00000000i
22 5 1 4 -0.00010937-0.00000000i
22 5 1 5 -0.00000001-0.00000000i
22 5 1 6 0.00000002+0.00000000i
22 5 2 1 0.00037492-0.00000000i
22 5 2 2 -0.00000000-0.00000000i
22 5 2 3 -0.00000000-0.00000000i
22 5 2 4 -0.00010937-0.00000000i
22 5 2 5 -0.00000000-0.00000000i
22 5 2 6 0.00000002-0.00000000i
22 5 3 1 -0.00171165+0.00000000i
22 5 3 2 0.00000000-0.00000000i
22 5 3 3 -0.00000000+0.00000000i
22 5 3 4 0.00054473+0.00000000i
22 5 3 5 0.00000000+0.00000000i
22 5 3 6 -0.00000002+0.00000000i
22 5 4 1 -0.00000001+0.00000000i
22 5 4 2 0.00000000-0.00000000i
22 5 4 3 -0.00000000-0.00000000i
22 5 4 4 0.00000001+0.00000000i
22 5 4 5 0.00040320+0.00000000i
22 5 4 6 -0.00248441+0.00000000i
22 5 5 1 -0.00000009-0.00000000i
22 5 5 2 -0.00000000-0.00000000i
22 5 5 3 0.00000000+0.00000000i
22 5 5 4 0.00000001+0.00000000i
22 5 5 5 0.00000000-0.00000000i
22 5 5 6 -0.00000000-0.00000000i

[sponce]

Dear MaxS,

Those are intermediate quantities where part is in Bloch and part is in real-space representation.

First what I would do is to make sure that the coarse Bloch-Bloch quantity and the fine Bloch-Bloch quantities are the same if you use the same grid. This should be the case if your Wannier functions are good enough.

So first, can you test that the epb and the epmatf are the same ?

If this is the case, then you can start comparing intermediate quantities.

Best wishes,
Samuel

[MaxS]

Dear Samuel, thank you for your suggestion.

I assume that by "epb" you mean the variable epmatq. In the following epmatq and epmatf are listed for k=(0,0,0) and q=(0,0,0). They are actually totally different. The wannier functions look pretty good. They are real and well localized.

I noticed that the phononic eigen frequencies coming from ph.x of the acoustic modes at the gamma point are negative:
freq ( 1) = -1.581620 [THz] = -52.757172 [cm-1]
freq ( 2) = -0.729948 [THz] = -24.348428 [cm-1]
freq ( 3) = -0.729948 [THz] = -24.348428 [cm-1]
freq ( 4) = 27.597090 [THz] = 920.539848 [cm-1]
freq ( 5) = 45.661251 [THz] = 1523.095383 [cm-1]
freq ( 6) = 45.661251 [THz] = 1523.095383 [cm-1]

But the interpolated eigen frequencies are much closer to zero:
lambda___( 1 )= 0.000000 gamma___= 0.000000 meV omega= 0.0273 cm-1
lambda___( 2 )= 0.000000 gamma___= 0.000000 meV omega= 0.0615 cm-1
lambda___( 3 )= 0.000000 gamma___= 0.000000 meV omega= 0.0726 cm-1
lambda___( 4 )= 0.000000 gamma___= 0.000000 meV omega= 922.0503 cm-1
lambda___( 5 )= 0.000000 gamma___= 0.000000 meV omega= 1523.2899 cm-1
lambda___( 6 )= 0.000000 gamma___= 0.000000 meV omega= 1523.2899 cm-1

Why is that and could this be the source for the differences in epmatq and epmatf?

Thank you again and best regards,
Maxim

epmatq
# iq, ik, ibnd, jbnd, imode, epmatq
1 1 1 1 1 -0.00000007-0.00000000i
1 1 1 1 2 -0.00000008+0.00000000i
1 1 1 1 3 -0.00000002-0.00000000i
1 1 1 1 4 0.00000008-0.00000000i
1 1 1 1 5 0.00000012-0.00000000i
1 1 1 1 6 0.00000002-0.00000000i
1 1 1 2 1 0.00000013+0.00000012i
1 1 1 2 2 0.00000003-0.00000004i
1 1 1 2 3 -0.03832134+0.21879751i
1 1 1 2 4 -0.00000012+0.00000002i
1 1 1 2 5 -0.00000008+0.00000006i
1 1 1 2 6 -0.03832129+0.21879761i
1 1 1 3 1 0.26840808-0.03899343i
1 1 1 3 2 0.15499010-0.02250160i
1 1 1 3 3 -0.00000007+0.00000003i
1 1 1 3 4 -0.26840835+0.03899331i
1 1 1 3 5 -0.15499005+0.02250157i
1 1 1 3 6 0.00000010+0.00000002i
1 1 1 4 1 0.03844085-0.15182391i
1 1 1 4 2 -0.06659688+0.26292187i
1 1 1 4 3 0.00000004+0.00000003i
1 1 1 4 4 -0.03844101+0.15182398i
1 1 1 4 5 0.06659692-0.26292206i
1 1 1 4 6 -0.00000003+0.00000001i
1 1 1 5 1 0.00000005+0.00000002i
1 1 1 5 2 -0.00000006-0.00000009i
1 1 1 5 3 0.00000011-0.00000012i
1 1 1 5 4 0.00000002-0.00000000i
1 1 1 5 5 -0.00000000-0.00000003i
1 1 1 5 6 -0.00000003-0.00000003i
1 1 2 1 1 0.00000013-0.00000012i
1 1 2 1 2 0.00000003+0.00000004i
1 1 2 1 3 -0.03832134-0.21879751i
1 1 2 1 4 -0.00000012-0.00000002i
1 1 2 1 5 -0.00000008-0.00000006i
1 1 2 1 6 -0.03832129-0.21879761i
1 1 2 2 1 -0.00000154+0.00000000i
1 1 2 2 2 -0.00000086-0.00000000i
1 1 2 2 3 -0.00000075-0.00000000i
1 1 2 2 4 0.00000091+0.00000000i
1 1 2 2 5 0.00000015-0.00000000i
1 1 2 2 6 0.00000000-0.00000000i
1 1 2 3 1 -0.00000004-0.00000024i
1 1 2 3 2 -0.00000023-0.00000010i
1 1 2 3 3 0.00000126+0.00000093i
1 1 2 3 4 0.00000006+0.00000110i
1 1 2 3 5 0.00000031+0.00000032i
1 1 2 3 6 0.00000042+0.00000039i
1 1 2 4 1 -0.00000052-0.00000014i
1 1 2 4 2 0.00000010+0.00000085i
1 1 2 4 3 -0.00000006+0.00000079i
1 1 2 4 4 0.00000041+0.00000118i
1 1 2 4 5 -0.00000103-0.00000088i
1 1 2 4 6 0.00000009+0.00000061i
1 1 2 5 1 -0.00000007+0.00000002i
1 1 2 5 2 -0.00000025-0.00000012i
1 1 2 5 3 -0.16095974+0.05764946i
1 1 2 5 4 0.00000035-0.00000017i
1 1 2 5 5 0.00000036+0.00000020i
1 1 2 5 6 -0.16095965+0.05764920i
1 1 3 1 1 0.26840808+0.03899343i
1 1 3 1 2 0.15499010+0.02250160i
1 1 3 1 3 -0.00000007-0.00000003i
1 1 3 1 4 -0.26840835-0.03899331i
1 1 3 1 5 -0.15499005-0.02250157i
1 1 3 1 6 0.00000010-0.00000002i
1 1 3 2 1 -0.00000004+0.00000024i
1 1 3 2 2 -0.00000023+0.00000010i
1 1 3 2 3 0.00000126-0.00000093i
1 1 3 2 4 0.00000006-0.00000110i
1 1 3 2 5 0.00000031-0.00000032i
1 1 3 2 6 0.00000042-0.00000039i
1 1 3 3 1 -0.51041416+0.00000000i
1 1 3 3 2 -0.29460297+0.00000000i
1 1 3 3 3 -0.00000040-0.00000000i
1 1 3 3 4 0.51041508-0.00000000i
1 1 3 3 5 0.29460312-0.00000000i
1 1 3 3 6 0.00000051-0.00000000i
1 1 3 4 1 0.11266816-0.27220642i
1 1 3 4 2 -0.19511527+0.47164916i
1 1 3 4 3 -0.00000057-0.00000035i
1 1 3 4 4 -0.11266801+0.27220605i
1 1 3 4 5 0.19511544-0.47164897i
1 1 3 4 6 0.00000030+0.00000017i
1 1 3 5 1 0.00108769+0.04140882i
1 1 3 5 2 0.00063047+0.02391100i
1 1 3 5 3 0.00000019-0.00000026i
1 1 3 5 4 -0.00108799-0.04140905i
1 1 3 5 5 -0.00063050-0.02391064i
1 1 3 5 6 0.00000017-0.00000057i
1 1 4 1 1 0.03844085+0.15182391i
1 1 4 1 2 -0.06659688-0.26292187i
1 1 4 1 3 0.00000004-0.00000003i
1 1 4 1 4 -0.03844101-0.15182398i
1 1 4 1 5 0.06659692+0.26292206i
1 1 4 1 6 -0.00000003-0.00000001i
1 1 4 2 1 -0.00000052+0.00000014i
1 1 4 2 2 0.00000010-0.00000085i
1 1 4 2 3 -0.00000006-0.00000079i
1 1 4 2 4 0.00000041-0.00000118i
1 1 4 2 5 -0.00000103+0.00000088i
1 1 4 2 6 0.00000009-0.00000061i
1 1 4 3 1 0.11266816+0.27220642i
1 1 4 3 2 -0.19511527-0.47164916i
1 1 4 3 3 -0.00000057+0.00000035i
1 1 4 3 4 -0.11266801-0.27220605i
1 1 4 3 5 0.19511544+0.47164897i
1 1 4 3 6 0.00000030-0.00000017i
1 1 4 4 1 0.51041497+0.00000000i
1 1 4 4 2 0.29460139-0.00000000i
1 1 4 4 3 -0.00000013+0.00000000i
1 1 4 4 4 -0.51041452-0.00000000i
1 1 4 4 5 -0.29460151-0.00000000i
1 1 4 4 6 -0.00000011+0.00000000i
1 1 4 5 1 -0.02185454+0.00972058i
1 1 4 5 2 0.03784623-0.01683808i
1 1 4 5 3 -0.00000021-0.00000013i
1 1 4 5 4 0.02185478-0.00972091i
1 1 4 5 5 -0.03784596+0.01683809i
1 1 4 5 6 -0.00000019-0.00000034i
1 1 5 1 1 0.00000005-0.00000002i
1 1 5 1 2 -0.00000006+0.00000009i
1 1 5 1 3 0.00000011+0.00000012i
1 1 5 1 4 0.00000002+0.00000000i
1 1 5 1 5 -0.00000000+0.00000003i
1 1 5 1 6 -0.00000003+0.00000003i
1 1 5 2 1 -0.00000007-0.00000002i
1 1 5 2 2 -0.00000025+0.00000012i
1 1 5 2 3 -0.16095974-0.05764946i
1 1 5 2 4 0.00000035+0.00000017i
1 1 5 2 5 0.00000036-0.00000020i
1 1 5 2 6 -0.16095965-0.05764920i
1 1 5 3 1 0.00108769-0.04140882i
1 1 5 3 2 0.00063047-0.02391100i
1 1 5 3 3 0.00000019+0.00000026i
1 1 5 3 4 -0.00108799+0.04140905i
1 1 5 3 5 -0.00063050+0.02391064i
1 1 5 3 6 0.00000017+0.00000057i
1 1 5 4 1 -0.02185454-0.00972058i
1 1 5 4 2 0.03784623+0.01683808i
1 1 5 4 3 -0.00000021+0.00000013i
1 1 5 4 4 0.02185478+0.00972091i
1 1 5 4 5 -0.03784596-0.01683809i
1 1 5 4 6 -0.00000019+0.00000034i
1 1 5 5 1 0.00000003+0.00000000i
1 1 5 5 2 -0.00000008-0.00000000i
1 1 5 5 3 -0.00000003+0.00000000i
1 1 5 5 4 0.00000004+0.00000000i
1 1 5 5 5 -0.00000005+0.00000000i
1 1 5 5 6 0.00000000+0.00000000i

epmatf
# ibnd, jbnd, imode, epmatf
1 1 1 0.00000000+0.00000000i
1 1 2 -0.00000000+0.00000000i
1 1 3 -0.00000000-0.00000000i
1 1 4 0.00000000+0.00000000i
1 1 5 -0.00000000-0.00000000i
1 1 6 -0.00000000+0.00000000i
1 2 1 -0.00292375+0.00068807i
1 2 2 0.00000000-0.00000000i
1 2 3 -0.00000000+0.00000000i
1 2 4 -0.00000000+0.00000000i
1 2 5 0.00000000-0.00000000i
1 2 6 0.00000000+0.00000000i
1 3 1 -0.00000000-0.00000000i
1 3 2 -0.00000000+0.00000000i
1 3 3 0.00000000-0.00000000i
1 3 4 -0.00000000+0.00000000i
1 3 5 0.00029724-0.00057681i
1 3 6 -0.00191805+0.00371962i
1 4 1 -0.00000000-0.00000000i
1 4 2 -0.00000000-0.00000000i
1 4 3 0.00000000-0.00000000i
1 4 4 0.00000000+0.00000000i
1 4 5 0.00102261-0.00405816i
1 4 6 0.00015872-0.00062917i
1 5 1 0.00000000-0.00000000i
1 5 2 -0.00000000+0.00000000i
1 5 3 -0.00000000-0.00000000i
1 5 4 -0.00071478+0.00016821i
1 5 5 0.00000000-0.00000000i
1 5 6 -0.00000000-0.00000000i
2 1 1 -0.00292375-0.00068807i
2 1 2 0.00000000+0.00000000i
2 1 3 -0.00000000-0.00000000i
2 1 4 -0.00000000-0.00000000i
2 1 5 0.00000000+0.00000000i
2 1 6 0.00000000-0.00000000i
2 2 1 -0.00000001-0.00000000i
2 2 2 0.00000001+0.00000000i
2 2 3 0.00000000-0.00000000i
2 2 4 0.00000001+0.00000000i
2 2 5 0.00000001-0.00000000i
2 2 6 -0.00000002-0.00000000i
2 3 1 -0.00000000+0.00000001i
2 3 2 0.00000000-0.00000000i
2 3 3 -0.00000000+0.00000000i
2 3 4 0.00000000-0.00000001i
2 3 5 -0.00000000-0.00000000i
2 3 6 0.00000001-0.00000001i
2 4 1 -0.00000001-0.00000000i
2 4 2 0.00000000+0.00000001i
2 4 3 -0.00000001+0.00000000i
2 4 4 0.00000000+0.00000000i
2 4 5 -0.00000002+0.00000000i
2 4 6 -0.00000000-0.00000000i
2 5 1 0.00000000+0.00000001i
2 5 2 0.00000001-0.00000001i
2 5 3 -0.00000000-0.00000001i
2 5 4 0.00000000-0.00000001i
2 5 5 -0.00000000+0.00000000i
2 5 6 -0.00000001+0.00000001i
3 1 1 -0.00000000+0.00000000i
3 1 2 -0.00000000-0.00000000i
3 1 3 0.00000000+0.00000000i
3 1 4 -0.00000000-0.00000000i
3 1 5 0.00029724+0.00057681i
3 1 6 -0.00191805-0.00371962i
3 2 1 -0.00000000-0.00000001i
3 2 2 0.00000000+0.00000000i
3 2 3 -0.00000000-0.00000000i
3 2 4 0.00000000+0.00000001i
3 2 5 -0.00000000+0.00000000i
3 2 6 0.00000001+0.00000001i
3 3 1 0.00000000-0.00000000i
3 3 2 -0.00000001-0.00000000i
3 3 3 0.00000000+0.00000000i
3 3 4 0.00000001+0.00000000i
3 3 5 0.00138758+0.00000000i
3 3 6 -0.00784724-0.00000000i
3 4 1 -0.00000000-0.00000000i
3 4 2 -0.00000000-0.00000000i
3 4 3 0.00000000-0.00000000i
3 4 4 0.00000000+0.00000001i
3 4 5 -0.00764198+0.00178303i
3 4 6 -0.00135115+0.00031592i
3 5 1 -0.00000001+0.00000000i
3 5 2 0.00000001-0.00000001i
3 5 3 0.00000001-0.00000000i
3 5 4 0.00000000+0.00000000i
3 5 5 -0.00000000+0.00000000i
3 5 6 -0.00000000+0.00000000i
4 1 1 -0.00000000+0.00000000i
4 1 2 -0.00000000+0.00000000i
4 1 3 0.00000000+0.00000000i
4 1 4 0.00000000-0.00000000i
4 1 5 0.00102261+0.00405816i
4 1 6 0.00015872+0.00062917i
4 2 1 -0.00000001+0.00000000i
4 2 2 0.00000000-0.00000001i
4 2 3 -0.00000001-0.00000000i
4 2 4 0.00000000-0.00000000i
4 2 5 -0.00000002-0.00000000i
4 2 6 -0.00000000+0.00000000i
4 3 1 -0.00000000+0.00000000i
4 3 2 -0.00000000+0.00000000i
4 3 3 0.00000000+0.00000000i
4 3 4 0.00000000-0.00000001i
4 3 5 -0.00764198-0.00178303i
4 3 6 -0.00135115-0.00031592i
4 4 1 -0.00000000-0.00000000i
4 4 2 -0.00000000-0.00000000i
4 4 3 0.00000000-0.00000000i
4 4 4 0.00000000+0.00000000i
4 4 5 -0.00138760-0.00000000i
4 4 6 0.00784723+0.00000000i
4 5 1 0.00000001+0.00000000i
4 5 2 -0.00000000+0.00000000i
4 5 3 0.00000000+0.00000000i
4 5 4 -0.00000000-0.00000000i
4 5 5 0.00000001-0.00000000i
4 5 6 -0.00000000+0.00000000i
5 1 1 0.00000000+0.00000000i
5 1 2 -0.00000000-0.00000000i
5 1 3 -0.00000000+0.00000000i
5 1 4 -0.00071478-0.00016821i
5 1 5 0.00000000+0.00000000i
5 1 6 -0.00000000+0.00000000i
5 2 1 0.00000000-0.00000001i
5 2 2 0.00000001+0.00000001i
5 2 3 -0.00000000+0.00000001i
5 2 4 0.00000000+0.00000001i
5 2 5 -0.00000000-0.00000000i
5 2 6 -0.00000001-0.00000001i
5 3 1 -0.00000001-0.00000000i
5 3 2 0.00000001+0.00000001i
5 3 3 0.00000001+0.00000000i
5 3 4 0.00000000-0.00000000i
5 3 5 -0.00000000-0.00000000i
5 3 6 -0.00000000-0.00000000i
5 4 1 0.00000001-0.00000000i
5 4 2 -0.00000000-0.00000000i
5 4 3 0.00000000-0.00000000i
5 4 4 -0.00000000+0.00000000i
5 4 5 0.00000001+0.00000000i
5 4 6 -0.00000000-0.00000000i
5 5 1 0.00000001+0.00000000i
5 5 2 0.00000000-0.00000000i
5 5 3 0.00000001-0.00000000i
5 5 4 -0.00000002+0.00000000i
5 5 5 -0.00000000+0.00000000i
5 5 6 -0.00000001-0.00000000i

[sponce]

Hello,

Ok. I've done many of those comparison. It was always fine but its difficult to compare the correct things. Note that if some state are degenerate, they need to be averaged over (degenerate eigenvalues and degenerate phonon modes). The phonon mode being negative is not an issue. We use an acoustic sum rule internally but its fine.

I suggest you to do the following:
1) print the electron and phonon bandstructure along high symmetry path using EPW.
For this use the band_plot variable: http://epw.org.uk/Documentation/Inputs#band_plot

Are the electron and phonon BS exactly the same as the one you get from QE (pw.x) and matdyn.x ?

2) Use the prtgkk EPW variable http://epw.org.uk/Documentation/Inputs#prtgkk
This will print the matrix elements but will also do the correct averaging. Check that you get the same as your epmatf results.
Also not that you might have to remove the phonon frequency in the denominator for direct comparison

3) Do the same kind of averaging on the epmatq

Best wishes,
Samuel

[carla.verdi]

Hi,

If I remember correctly you cannot compare directly the matrix elements stored in the 'epmatq'. Yes those are the matrix elements on the coarse k,q grid, however
i) they don't contain the prefactor 1/sqrt(2\omega_q\nu) that you have if you use 'prtgkk' to output the matrix elements on the fine grids (whereas if you go inside the code and just print the epmatf that's ok)
ii) more importantly, the epmatq are actually g(k,q)*u^-1(q,\nu) (u is the phonon eigenvector). If you want the actual g, you'd need to print them before the last zgemv call in the subr rotate_epmat.

Best,
Carla

[MaxS]

Dear Samuel and Carla,

many thanks for your suggestions and information. I will plot the band structures along the high symmetry lines as a basic check.
I was not aware of the prtgkk flag, that might be helpful indeed.

I've also noticed that the phononic eigenvectors u are multiplied with the el-ph matrix elements somewhere in the code (g(k,q)*u^-1(q,\nu)) but I was not sure whether this applies only to epmatq or also to epmatf. Thank you for that hint, Carla!

Best regards,
Maxim Skripnik
Department of Physics
University of Konstanz
Germany

[MaxS]

ii) more importantly, the epmatq are actually g(k,q)*u^-1(q,\nu) (u is the phonon eigenvector). If you want the actual g, you'd need to print them before the last zgemv call in the subr rotate_epmat.

Do you mean I have to print eptmp after

Code: Select all

        CALL zgemv ('t', nmodes, nmodes, cone, cz1, nmodes,  &
                   epmatq_opt(ibnd, jbnd, ik, :), 1, czero, eptmp, 1 )

but before

Code: Select all

        CALL zgemv ('t', nmodes, nmodes, cone, cz2, nmodes, &
                   eptmp, 1, czero, epmatq(ibnd, jbnd, ik, :, iq), 1 )

in rotate_epmat in order to get g(k,q) instead of g(k,q)*u^-1(q,\nu)?

Isn't g(k,q) in eigenmode rep. acutally calculated in the subroutine elphon_shuffle with the following line, even before rotate_epmat is called?

Code: Select all

CALL zgemv ('n', nmodes, nmodes, cone, CONJG( u ), nmodes, &
            el_ph_mat (ibnd,jbnd,ik,:), 1, czero, epmatq (ibnd,jbnd,ik,:,iq), 1 )

If not, what does epmatq = conjug(u) * el_ph_mat mean?

edit: Ok, I've printed the variable u and it does not contain the eigenvectors of the dynamical matrix from prefix.dyn files, which I originally thought. Now the above calculations make more sense to me ...