[Pw_forum] Electron-phonon coupling

Mon Mar 31 10:16:42 CEST 2003

Dear Ma

I am still developing the integration you want me to teach you.
I hope to finish it soon. About the pseudo for Nb, mine has a diffrent
valence configuration but anyway it works for phonons and electron-phonon
coupling. You can try it for some of your "bad" points.
Regards,
Gosia

ma Yanming wrote:

> 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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