[Pw_forum] Electron-phonon coupling
ma Yanming
yanming_ma at hotmail.com
Sun Mar 30 19:10:57 CEST 2003
Dear Gosia,
>Find some of my results and look to attached files with Eliashberg
function
>calculated for Nb with norm conserving PP (KB) and ultrasoft (US).
> You integrate only over k, leaving q-dependence (phonon).
>I integrate over both k and q points, but with frequncy resolution
As I know, PWSCF integrate only over K for a certain q point. Did you use
PWSCF for this Calculation?If so, can you teach me how can I calcualte E_P
Coupling in this way,i.e., integrate both q and k vectors.
> 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 made the Norm-Conserving PP by myself using FHI98 code. I got pretty good
EOS and phonon dispersion curve using this PP. The calculated phonon value
at Gamma point is around 0.10 THz. I think it is very reasonable.
>I am satisfied with the KB PP attached here (format for old version of
>PWscf). 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.
By the way, I am not familar with the PP format in the very old PWSCF
version.The Nb electronic configuration for valence electrons is 4d4 5s1.
But in your KB PP, it seems that there are 2 s electrons and 3 d electrons
in the valence electrons as you can see in your PP.
Wavefunction 5s
0 2.00 --------should be 0 1.00
...
Wavefunction 4d
2 3.00 --------should be 2 4.00
Concerning the US PP, did you use the parameters provided by David
Vanderbilt's group at http://www.physics.rutgers.edu/~dhv/uspp/index.html.
If you don't, it may help if you use these parameters. I did not try to use
US PP becasuse I am interested in High pressure research. It may have some
disadvantage using US PP for high pressure study.
Yours
Yanming Ma
>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.
> >> >>
> >> >> > My question is how to choose the q points properly in the first
BZ?
> >> >>
> >> >> choose a uniform grid (Monkhorst-Pack, for instance) and pick
> >> q-points
> >> >> in the irreducible BZ. Unless your \lambda(q) is strongly
anisotropic
> >> >> (this is the case of MgB_2, for instance: most of the contribution
to
> >> >> \lambda comes from a specific phonon branch), the convergence wrt
> >> >> the q-grid shouldn't be a big problem.
> >> >>
> >> >> > So My question is what is the criterion for the EP coupling
> >> >
> >> > convergency.
> >> >
> >> >>
> >> >> it is more or less the same criterion that is used to check for
> >> >> convergence in metals: you should try increasingly dense k-point
> >> >> grids and a range of gaussian broadenings for each grid. You should
> >> >> find a range of gaussian broadening and of k-point grids for which
> >> >> the value of \lambda(q) is reasonably constant. Unfortunately this
> >> >> usually happens with rather large grids.
> >> >>
> >> >> There is some ongoing work on a better algorithm for calculating
> >> >> electron-phonon coupling coefficients using tetrahedra.
> >> >>
> >> >> Paolo
> >> >> --
> >> >> Paolo Giannozzi e-mail: giannozz at nest.sns.it
> >> >> Scuola Normale Superiore Phone: +39/050509412
> >> >> Piazza dei Cavalieri 7 Fax: +39/050509417, 050563513
> >> >> I-56126 Pisa, Italy Office: Lab. NEST, Via della Faggiola 19
> >> >>
> >> >> _______________________________________________
> >> >> Pw_forum mailing list
> >> >> Pw_forum at pwscf.org
> >> >> http://www.democritos.it/mailman/listinfo/pw_forum
> >> >
> >> >
> >> >
> >> > _________________________________________________________________
> >> > 享用世界上最大的电子邮件系统― MSN Hotmail。 http://www.hotmail.com
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> >>
> >>
> >>
> >>
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> >
> >
> >
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> >
>
>
>
> 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
> c
> 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
> 0.44783107E-01 0.33709870E-01 0.24891743E-01 0.18015526E-01
> 0.12760914E-01 0.88380761E-02 0.59821813E-02 0.39525332E-02
> 0.25451067E-02 0.15944333E-02 0.97002682E-03 0.57199680E-03
> 0.32623901E-03 0.17957709E-03 0.95173253E-04 0.48443393E-04
> 0.23617994E-04 0.10997284E-04 0.48756322E-05 0.20506394E-05
> 0.81455411E-06 0.00000000E+00 0.00000000E+00 0.00000000E+00
> 0.00000000E+00
> Wavefunction 4d
> 2 3.00
> 0.12106738E-09 0.14603513E-09 0.17615200E-09 0.21247987E-09
> 0.25630097E-09 0.30915961E-09 0.37291960E-09 0.44982922E-09
> 0.54260040E-09 0.65450437E-09 0.78948699E-09 0.95230794E-09
> 0.11487085E-08 0.13856139E-08 0.16713779E-08 0.20160767E-08
> 0.24318649E-08 0.29334038E-08 0.35383781E-08 0.42681200E-08
> 0.51483611E-08 0.62101396E-08 0.74908952E-08 0.90357888E-08
> 0.10899295E-07 0.13147123E-07 0.15858534E-07 0.19129135E-07
> 0.23074251E-07 0.27832990E-07 0.33573150E-07 0.40497134E-07
> 0.48849088E-07 0.58923508E-07 0.71075625E-07 0.85733931E-07
> 0.10341529E-06 0.12474314E-06 0.15046953E-06 0.18150156E-06
> 0.21893342E-06 0.26408497E-06 0.31854823E-06 0.38424355E-06
> 0.46348729E-06 0.55907352E-06 0.67437248E-06 0.81344941E-06
> 0.98120788E-06 0.11835626E-05 0.14276481E-05 0.17220698E-05
> 0.20772079E-05 0.25055828E-05 0.30222964E-05 0.36455646E-05
> 0.43973590E-05 0.53041810E-05 0.63979957E-05 0.77173580E-05
> 0.93087704E-05 0.11228321E-04 0.13543659E-04 0.16336375E-04
> 0.19704875E-04 0.23767842E-04 0.28668411E-04 0.34579208E-04
> 0.41708412E-04 0.50307077E-04 0.60677953E-04 0.73186113E-04
> 0.88271766E-04 0.10646570E-03 0.12840788E-03 0.15486986E-03
> 0.18678177E-03 0.22526485E-03 0.27167055E-03 0.32762766E-03
> 0.39509901E-03 0.47644965E-03 0.57452886E-03 0.69276870E-03
> 0.83530246E-03 0.10071068E-02 0.12141723E-02 0.14637082E-02
> 0.17643870E-02 0.21266382E-02 0.25629982E-02 0.30885287E-02
> 0.37213151E-02 0.44830586E-02 0.53997790E-02 0.65026455E-02
> 0.78289556E-02 0.94232827E-02 0.11338816E-01 0.13638908E-01
> 0.16398856E-01 0.19707915E-01 0.23671547E-01 0.28413874E-01
> 0.34080275E-01 0.40840011E-01 0.48888685E-01 0.58450250E-01
> 0.69778129E-01 0.83154849E-01 0.98889373E-01 0.11731111E+00
> 0.13875933E+00 0.16356641E+00 0.19203341E+00 0.22439605E+00
> 0.26077988E+00 0.30114398E+00 0.34521490E+00 0.39241712E+00
> 0.44181325E+00 0.49207705E+00 0.54152887E+00 0.58826010E+00
> 0.63034947E+00 0.66613074E+00 0.69442746E+00 0.71466095E+00
> 0.72678932E+00 0.73112594E+00 0.72815165E+00 0.71841618E+00
> 0.70253756E+00 0.68123129E+00 0.65530135E+00 0.62558345E+00
> 0.59287831E+00 0.55791038E+00 0.52131883E+00 0.48366897E+00
> 0.44547075E+00 0.40719309E+00 0.36927281E+00 0.33211726E+00
> 0.29610235E+00 0.26156820E+00 0.22881436E+00 0.19809541E+00
> 0.16961747E+00 0.14353542E+00 0.11995106E+00 0.98911980E-01
> 0.80411652E-01 0.64390999E-01 0.50741867E-01 0.39312643E-01
> 0.29916004E-01 0.22338450E-01 0.16350958E-01 0.11719900E-01
> 0.82172747E-02 0.56294389E-02 0.37637187E-02 0.24526153E-02
> 0.15556211E-02 0.95894085E-03 0.57355942E-03 0.33227849E-03
> 0.18602211E-03 0.10042006E-03 0.52180064E-04 0.26039697E-04
> 0.12443422E-04 0.56732349E-05 0.00000000E+00 0.00000000E+00
> 0.00000000E+00 0.00000000E+00 0.00000000E+00 0.00000000E+00
> 0.00000000E+00 0.00000000E+00 0.00000000E+00 0.00000000E+00
> 0.00000000E+00 0.00000000E+00 0.00000000E+00 0.00000000E+00
> 0.00000000E+00
_________________________________________________________________
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