[Pw_forum] Electron-phonon coupling
Eyvaz Isaev
eyvaz_isaev at yahoo.com
Sun Mar 30 09:34:16 CEST 2003
Dear all,
Now I am trying to calculate the electron-phonon
coupling constant. According to the 7-th example the
code is able to calculate the EPC constant for an
arbitrary k-point in the BZ (\lambda_{nk}). I
followed this example and now I am calculating
\lambda_{nk} for a number of k-points in the 1/48 part
of the IBZ for FCC lattice (k-points are vertex of
small tetrahedra). Then I am going to integrate
\lambda_{nk} using the tetrahedron method.
So, I would like to ask you is this procedure correct?
If no, what should be done for this kind of
calculations?
Regards,
Eyvaz.
--- Malgorzata Wierzbowska <wierzbom at tcd.ie> wrote:
>
>
> Dear Ma Yanming,
>
> Find some of my results and look to attached files
> with Eliashberg function
> calculated for Nb with norm conserving PP (KB) and
> ultrasoft (US).
> Experimental total lambda is 1.04 or 1.22 (from refs
> in S.Y. Savrasov
> PRB, vol 54, p. 16487 (1996)), calculated by
> Savrasov 1.26.
>
> As you can see from attached files KB PP behaves
> correctly
> but US gives too big total lambda. The reason is
> because
> Eliashberg function, in case of US, doesn't fall
> down to zero for small
> frequencies. Small frequencies are for phonon
> vectors close to Gamma point.
> However for first sight we calculate different
> quantities we still can
> make common
> conclusions. You integrate only over k, leaving
> q-dependence (phonon).
> I integrate over both k and q points, but with
> frequncy resolution (I
> see the relations
> between q-points and frequencies.).
>
> The answer for the question whether you can just
> throw points is NO! It
> is not so easy,
> but we will get there. What I suggest is:
> If you could write a file with q-points you
> calculated and corresponding
> frequencies
> and corresponding calculated el-ph couplings. And if
> you could send me
> refs. to experimental
> values which you refer. Maybe we will see that one
> needs to work a bit
> more on generation of PP.
> Especially concentrating attention to get gamma
> point very close to zero.
>
> I am satisfied with the KB PP attached here (format
> for old version of
> PWscf). And I was still
> working on getting US PP better. But now I don't
> have enough computer
> power to continue
> because I lost an account in my previous place and
> here I work on a
> different project.
> Maybe you can generate better pseudos. If you decide
> to do this for US
> PP, there is a parameter
> called "rinner" in Vanderbilt's input. Phonons at
> gamma point are very
> sensitive on that.
>
> Good luck!
> Gosia
>
>
>
>
>
>
> ma Yanming wrote:
>
> > Dear Gosia
> >
> > Sorry for replying you so late. I'd already
> calculated the E_P
> > coupling for most of possible q vectors to try to
> analyze the results.
> > So It takes time. I use Norm-Conserving PPs. As
> what you said, for
> > some q vectors with small phonon frequencies, the
> calculated E_P
> > coupling is extremely large. I do not know why?
> >
> > I use 16 16 16 Monkshort-Pack K mesh to generate q
> points for BCC Nb.
> > At q point (0 -0.0625 0.1875) the E_P coupling is
> worst. For q points
> > as the following, the results are also bad
> > (0 -0.0625 0.4375)
> > (0 -0.125 0.5)
> > (0 -0.0625 0.3125)
> > (0 -0.125 0.375)
> > (0 -0.125 0.25)
> > (0 -0.1875 0.3125)
> > (-0.0625 -0.1875 0.25)
> > (-0.0625 -0.1875 0.375)
> > (-0.125 -0.1875 0.3125)
> > So Can I just pick out these unusual q vectors and
> then make average
> > over the left q points to get the E_P Coupling
> lambda. Or ...?
>
> >
> >> It would help to check from which
> >> region at frequency axis it comes.
> >
> >
> > I do not quite understand the above sentence.Can
> you give me more
> > explanation?
> > Thanks in advance.
>
> >
> > Best Wishes!
> >
> > Yanming Ma PhD
> > Steacie Institute for Molecular Sciences,
> > National Research Councils of Canada.
> > 100 Sussex
> > K1A 0R6
> >
> >
> >
> >
> >
> >> From: Malgorzata Wierzbowska <wierzbom at tcd.ie>
> >> Reply-To: pw_forum at pwscf.org
> >> To: pw_forum at pwscf.org
> >> Subject: Re: [Pw_forum] Electron-phonon coupling
> >> Date: Sat, 22 Mar 2003 13:03:41 +0000
> >>
> >>
> >> Which version of the program and what
> pseudopotentials do you use?
> >> If this is ultrasoft pseudopotetial then do as
> follows:
> >> Edit the file phonon.F (or phonon.f90) in phlib
> (or PH).
> >> Go to the end and you see the place when
> elph=.true..
> >> Write "call dvanqq" as it is below and recompile
> the program.
> >>
> >> if (elph) then
> >> call dvanqq
> >> if (.not.trans) call elphon
> >> call elphsum
> >> endif
> >>
> >> If pseudo is normconserving and you have too big
> el-ph couplings
> >> (with good phonon spectra) probably it happens at
> phonon vectors
> >> which have small frequencies.
> >> What exactly are the numbers? It would help to
> check from which
> >> region at frequency axis it comes.
> >> Which q-points are particularly bad?
> >>
> >> Gosia
> >>
> >>
> >>
> >> ma Yanming wrote:
> >>
> >> > Dear Paolo,
> >> >
> >> > Thanks for your reply.I do choose q points
> using Monkhorst-Pack K
> >> > mesh. But I am still upset. I already increased
> the K mesh to 48 48 48
> >> > when I calculated the EP coupling. To test the
> performance in several
> >> > high symmetry q if (elph) then points, I still
> got the results for
> >> > phonon linewidth far away from the experimental
> data, despite I
> >> > obtained the good results for phonon. :-(
> >> > Any comments?
> >> >
> >> > Best Wishes!
> >> >
> >> > Yanming Ma
> >> >
> >> >
> >> >> > I have been puzzled by the calculation of
> the electron-phonon (EP)
> >> >> > coupling coefficient lambda using PWSCF
> >> >>
> >> >> me too...
> >> >>
> >> >> The calculation of the electron-phonon
> coupling coefficients
> >> >> is presently done using a simple but
> not-so-smart algorithm:
> >> >> for each phonon q one calculates \lambda(q),
> performing a
> >> >> (slowly convergent) sum over k of electronic
> states.
>
=== message truncated ===>
> freq au freq. THz
> a2F(freq)
>
> 1 1.0198717373890380E-003
> 3.355202476562948 2.237529515947500
> 2 1.0596152121671143E-003
> 3.485951667970094 1.499468581009689
> 3 1.0993586869451901E-003
> 3.616700859377241 1.350706089637660
> 4 1.1391021617232664E-003
> 3.747450050784387 1.787859730300818
> 5 1.1788456365013427E-003
> 3.878199242191533 1.633521655247258
> 6 1.2185891112794187E-003
> 4.008948433598680 2.422545868169372
> 7 1.2583325860574948E-003
> 4.139697625005826 3.181579657060079
> 8 1.2980760608355710E-003
> 4.270446816412972 4.775643794216762
> 9 1.3378195356136473E-003
> 4.401196007820118 3.455151971299109
> 10 1.3775630103917234E-003
> 4.531945199227264 3.660159841903176
> 11 1.4173064851697994E-003
> 4.662694390634410 3.331080505617703
> 12 1.4570499599478756E-003
> 4.793443582041556 2.385202990990981
> 13 1.4967934347259517E-003
> 4.924192773448703 1.500343357387741
> 14 1.5365369095040275E-003
> 5.054941964855849 1.361790472536797
> 15 1.5762803842821040E-003
> 5.185691156262996 1.169814309637568
> 16 1.6160238590601801E-003
> 5.316440347670142 0.9833931057291112
> 17 1.6557673338382564E-003
> 5.447189539077288 0.9990683722507322
> 18 1.6955108086163322E-003
> 5.577938730484434 1.020410393873696
> 19 1.7352542833944085E-003
> 5.708687921891580 1.048469785644035
> 20 1.7749977581724847E-003
> 5.839437113298726 2.040019807863810
> 21 1.8147412329505608E-003
> 5.970186304705873 3.944271859907947
> 22 1.8544847077286368E-003
> 6.100935496113019 3.898784584719331
> 23 1.8942281825067131E-003
> 6.231684687520165 2.593718329665633
> 24 1.9339716572847889E-003
> 6.362433878927312 1.059836321559148
> 25 1.9737151320628655E-003
> 6.493183070334458 0.3946383516817085
> 26 2.0134586068409415E-003
> 6.623932261741603 0.2963668772225613
> 27 2.0532020816190180E-003
> 6.754681453148750 0.1797051121084532
> 28 2.0929455563970940E-003
> 6.885430644555897 8.5976271291996138E-002
> 29 2.1326890311751696E-003
> 7.016179835963042 6.8222080457730936E-002
> 30 2.1724325059532461E-003
> 7.146929027370189 0.0000000000000000E+000
>
> Total lambda 2.98
>
>
> >
> freq au freq. THz
> a2F(freq)
>
> 1 1.2438515240158456E-004
> 0.4092057423356754 2.8869733143880708E-002
> 2 1.7315545720475367E-004
> 0.5696516508351509 2.3385781074569358E-002
> 3 2.2192576200792278E-004
> 0.7300975593346266 3.1993707502021920E-002
> 4 2.7069606681109186E-004
> 0.8905434678341022 3.5713934152708573E-002
> 5 3.1946637161426099E-004
> 1.050989376333578 6.1944858809984709E-002
> 6 3.6823667641743008E-004
> 1.211435284833054 5.2590079578703453E-002
> 7 4.1700698122059920E-004
> 1.371881193332529 7.4231431621878619E-002
> 8 4.6577728602376833E-004
> 1.532327101832005 9.1897992378171267E-002
> 9 5.1454759082693746E-004
> 1.692773010331480 9.6819575939830322E-002
> 10 5.6331789563010650E-004
> 1.853218918830956 0.1076133627499602
> 11 6.1208820043327572E-004
> 2.013664827330432 0.1174886803214625
> 12 6.6085850523644476E-004
> 2.174110735829907 0.1334868819605516
> 13 7.0962881003961398E-004
> 2.334556644329383 0.1172762277885431
> 14 7.5839911484278293E-004
> 2.495002552828858 0.1601624697992450
> 15 8.0716941964595197E-004
> 2.655448461328334 0.1496093643983267
> 16 8.5593972444912119E-004
> 2.815894369827810 0.1926870865091957
> 17 9.0471002925229040E-004
> 2.976340278327286 0.2265583611652895
> 18 9.5348033405545944E-004
> 3.136786186826761 0.2342125536731038
> 19 1.0022506388586285E-003
> 3.297232095326236 0.2536025477932173
> 20 1.0510209436617977E-003
> 3.457678003825713 0.2969967638092281
> 21 1.0997912484649668E-003
> 3.618123912325188 0.3988061602289276
> 22 1.1485615532681359E-003
> 3.778569820824664 0.7690110504535764
> 23 1.1973318580713050E-003
> 3.939015729324139 0.8837328494542188
> 24 1.2461021628744742E-003
> 4.099461637823615 1.071354565294684
> 25 1.2948724676776433E-003
> 4.259907546323091 0.7903395888522454
> 26 1.3436427724808127E-003
> 4.420353454822566 0.5783290412553221
> 27 1.3924130772839816E-003
> 4.580799363322042 0.5451969602494918
> 28 1.4411833820871505E-003
> 4.741245271821517 0.6573407717215089
> 29 1.4899536868903196E-003
> 4.901691180320993 0.4927796721997354
> 30 1.5387239916934887E-003
> 5.062137088820468 0.4898505017287321
> 31 1.5874942964966579E-003
> 5.222582997319944 0.4815007364165790
> 32 1.6362646012998272E-003
> 5.383028905819420 0.4951156582318729
> 33 1.6850349061029959E-003
> 5.543474814318896 0.6488168419863590
> 34 1.7338052109061652E-003
> 5.703920722818371 0.9696502950376715
> 35 1.7825755157093339E-003
> 5.864366631317846 0.9959555280125480
> 36 1.8313458205125034E-003
> 6.024812539817323 1.016992835820577
> 37 1.8801161253156726E-003
> 6.185258448316798 0.4001474208086026
> 38 1.9288864301188418E-003
> 6.345704356816274 0.1898949853003984
> 39 1.9776567349220107E-003
> 6.506150265315750 9.8287516753835096E-002
> 40 2.0264270397251796E-003
> 6.666596173815225 0.0000000000000000E+000
>
> total lambda 1.178
>
>
>
> > PZ
> 'Nb' 5.0 2 2 3 .F. 0 .T. ! ** 41.0 Niobio
> transformed from BHS
> 2.410000 0.820000 3.741900 -2.741900
> 0.830000 1.690000 2.010000
> -0.721060000000000E+01 -0.373700000000000E+00
> -0.185600000000000E+00
> 0.776000000000000E-01 0.762000000000000E-01
> 0.198000000000000E-01
> 0.680000 1.030000 1.350000
> -0.660260000000000E+01 -0.864000000000000E+00
> -0.545200000000000E+00
> 0.161000000000000E-01 0.149000000000000E-01
> 0.212000000000000E-01
> 3.620000 4.740000 5.570000
> -0.238090000000000E+01 0.260200000000000E+00
> 0.288000000000000E-01
> -0.238000000000000E-01 -0.757000000000000E-01
> -0.479000000000000E-01
> 41.00 -4.00000 0.06250 189 3
> Wavefunction 5s
> 0 2.00
> 0.26558108E-04 0.28270959E-04 0.30094279E-04
> 0.32035194E-04
> 0.34101287E-04 0.36300632E-04 0.38641823E-04
> 0.41134008E-04
> 0.43786926E-04 0.46610943E-04 0.49617094E-04
> 0.52817125E-04
> 0.56223542E-04 0.59849655E-04 0.63709632E-04
> 0.67818559E-04
> 0.72192490E-04 0.76848517E-04 0.81804835E-04
> 0.87080810E-04
> 0.92697060E-04 0.98675532E-04 0.10503959E-03
> 0.11181409E-03
> 0.11902552E-03 0.12670206E-03 0.13487370E-03
> 0.14357238E-03
> 0.15283209E-03 0.16268902E-03 0.17318169E-03
> 0.18435110E-03
> 0.19624091E-03 0.20889758E-03 0.22237058E-03
> 0.23671257E-03
> 0.25197961E-03 0.26823136E-03 0.28553136E-03
> 0.30394722E-03
> 0.32355095E-03 0.34441917E-03 0.36663348E-03
> 0.39028073E-03
> 0.41545339E-03 0.44224990E-03 0.47077506E-03
> 0.50114045E-03
> 0.53346486E-03 0.56787476E-03 0.60450480E-03
> 0.64349837E-03
> 0.68500811E-03 0.72919658E-03 0.77623687E-03
> 0.82631328E-03
> 0.87962213E-03 0.93637243E-03 0.99678685E-03
> 0.10611025E-02
> 0.11295721E-02 0.12024646E-02 0.12800668E-02
> 0.13626842E-02
> 0.14506424E-02 0.15442884E-02 0.16439921E-02
> 0.17501479E-02
> 0.18631765E-02 0.19835265E-02 0.21116766E-02
> 0.22481379E-02
> 0.23934558E-02 0.25482131E-02 0.27130324E-02
> 0.28885793E-02
> 0.30755660E-02 0.32747545E-02 0.34869613E-02
> 0.37130613E-02
> 0.39539934E-02 0.42107658E-02 0.44844624E-02
> 0.47762501E-02
> 0.50873863E-02 0.54192285E-02 0.57732446E-02
> 0.61510242E-02
> 0.65542930E-02 0.69849276E-02 0.74449743E-02
> 0.79366695E-02
> 0.84624643E-02 0.90250533E-02 0.96274074E-02
> 0.10272813E-01
> 0.10964920E-01 0.11707793E-01 0.12505979E-01
> 0.13364582E-01
> 0.14289356E-01 0.15286815E-01 0.16364359E-01
> 0.17530436E-01
> 0.18794730E-01 0.20168383E-01 0.21664278E-01
> 0.23297367E-01
> 0.25085075E-01 0.27047797E-01 0.29209494E-01
> 0.31598425E-01
> 0.34248048E-01 0.37198109E-01 0.40495979E-01
> 0.44198285E-01
> 0.48372884E-01 0.53101244E-01 0.58481297E-01
> 0.64630783E-01
> 0.71691119E-01 0.79831726E-01 0.89254641E-01
> 0.10019903E+00
> 0.11294490E+00 0.12781473E+00 0.14517091E+00
> 0.16540587E+00
> 0.18892001E+00 0.21608170E+00 0.24716264E+00
> 0.28224441E+00
> 0.32109894E+00 0.36305988E+00 0.40692163E+00
> 0.45091914E+00
> 0.49283953E+00 0.53027893E+00 0.56099250E+00
> 0.58322637E+00
> 0.59591709E+00 0.59871013E+00 0.59183987E+00
> 0.57596317E+00
> 0.55202083E+00 0.52114959E+00 0.48462794E+00
> 0.44383131E+00
> 0.40018329E+00 0.35510151E+00 0.30994084E+00
> 0.26593959E+00
> 0.22417154E+00 0.18550756E+00 0.15058983E+00
> 0.11982118E+00
> 0.93370566E-01 0.71193969E-01 0.53068182E-01
> 0.38633497E-01
> 0.27440353E-01 0.18994996E-01 0.12799866E-01
> 0.83857028E-02
> 0.53338812E-02 0.32889959E-02 0.19627937E-02
> 0.11316214E-02
> 0.62882186E-03 0.33603430E-03 0.17237553E-03
> 0.84683462E-04
> 0.39729852E-04 0.17746346E-04 0.75224748E-05
> 0.30155030E-05
> 0.11389082E-05 0.40366301E-06 0.13369256E-06
> 0.41189222E-07
> 0.11748275E-07 0.30861089E-08 0.74291650E-09
> 0.16221986E-09
> 0.31184030E-10 0.00000000E+00 0.00000000E+00
> 0.00000000E+00
> 0.00000000E+00
> Wavefunction 5p
> 1 0.00
> 0.80423491E-08 0.91131754E-08 0.10326581E-07
> 0.11701549E-07
> 0.13259602E-07 0.15025108E-07 0.17025690E-07
> 0.19292649E-07
> 0.21861451E-07 0.24772288E-07 0.28070700E-07
> 0.31808294E-07
> 0.36043545E-07 0.40842718E-07 0.46280897E-07
> 0.52443165E-07
> 0.59425936E-07 0.67338458E-07 0.76304528E-07
> 0.86464423E-07
> 0.97977103E-07 0.11102269E-06 0.12580529E-06
> 0.14255618E-06
> 0.16153745E-06 0.18304606E-06 0.20741853E-06
> 0.23503618E-06
> 0.26633112E-06 0.30179296E-06 0.34197654E-06
> 0.38751055E-06
> 0.43910741E-06 0.49757438E-06 0.56382622E-06
> 0.63889950E-06
> 0.72396880E-06 0.82036511E-06 0.92959661E-06
> 0.10533724E-05
> 0.11936289E-05 0.13525608E-05 0.15326546E-05
> 0.17367282E-05
> 0.19679746E-05 0.22300118E-05 0.25269399E-05
> 0.28634049E-05
> 0.32446712E-05 0.36767046E-05 0.41662652E-05
> 0.47210133E-05
> 0.53496293E-05 0.60619498E-05 0.68691213E-05
> 0.77837749E-05
> 0.88202239E-05 0.99946882E-05 0.11325548E-04
> 0.12833632E-04
> 0.14542543E-04 0.16479030E-04 0.18673403E-04
> 0.21160012E-04
> 0.23977786E-04 0.27170839E-04 0.30789166E-04
> 0.34889427E-04
> 0.39535836E-04 0.44801168E-04 0.50767906E-04
> 0.57529536E-04
> 0.65192018E-04 0.73875454E-04 0.83715984E-04
> 0.94867930E-04
> 0.10750623E-03 0.12182922E-03 0.13806176E-03
> 0.15645879E-03
> 0.17730942E-03 0.20094148E-03 0.22772679E-03
> 0.25808712E-03
> 0.29250090E-03 0.33151098E-03 0.37573338E-03
> 0.42586727E-03
> 0.48270641E-03 0.54715211E-03 0.62022814E-03
> 0.70309766E-03
> 0.79708271E-03 0.90368648E-03 0.10246188E-02
> 0.11618257E-02
> 0.13175229E-02 0.14942348E-02 0.16948397E-02
> 0.19226214E-02
> 0.21813295E-02 0.24752495E-02 0.28092839E-02
> 0.31890472E-02
> 0.36209773E-02 0.41124651E-02 0.46720082E-02
> 0.53093911E-02
> 0.60358981E-02 0.68645666E-02 0.78104858E-02
> 0.88911540E-02
> 0.10126902E-01 0.11541398E-01 0.13162250E-01
> 0.15021723E-01
> 0.17157585E-01 0.19614118E-01 0.22443298E-01
> 0.25706184E-01
> 0.29474520E-01 0.33832571E-01 0.38879185E-01
> 0.44730046E-01
> 0.51520032E-01 0.59405487E-01 0.68566075E-01
> 0.79205661E-01
> 0.91551344E-01 0.10584939E+00 0.12235633E+00
> 0.14132302E+00
> 0.16296880E+00 0.18744332E+00 0.21477410E+00
> 0.24480202E+00
> 0.27711315E+00 0.31098503E+00 0.34537397E+00
> 0.37896943E+00
> 0.41032452E+00 0.43803812E+00 0.46093204E+00
> 0.47816152E+00
> 0.48923152E+00 0.49394180E+00 0.49231313E+00
> 0.48453536E+00
> 0.47094573E+00 0.45202351E+00 0.42838471E+00
> 0.40076901E+00
> 0.37001725E+00 0.33704027E+00 0.30278093E+00
> 0.26817164E+00
> 0.23409069E+00 0.20132254E+00 0.17052492E+00
> 0.14220639E+00
> 0.11671571E+00 0.94243430E-01 0.74834207E-01
> 0.58407430E-01
>
=== message truncated ===
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