[Pw_forum] Electron-phonon coupling

Malgorzata Wierzbowska wierzbom at tcd.ie
Sun Mar 30 11:37:39 CEST 2003


No, it is not not correct. Look to the definition of el-ph
in one of Savrasov's papers and you will see that that there is
double delta on Fermi surface. You can split the integration over
phonon vectors (q-points) and over electron momentum (k-points)
if you first  integrate over phonons and later over electrons.
Not the other way around. Just because there is delta_k+q delta_k .

You try to integrate delta_k * delta_q  or delta_k+q * delta_q
if I understand correctly your e-mail.
If you start from the integration over k first then at q=0 you meet
the problem of delta_k*delta_k+0 which is mathematically not defined.

Gosia


Eyvaz Isaev wrote:

>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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