[Pw_forum] EPC of Al at X

[Amit Kumar]

>>>>>>>>
 would you mind reading the answer that you get before
asking new questions, or more exactly, the same question?


 Dear Paolo,
 I read your every answer very carefully.
 My question was not the same.
 I agree that Methfessel-Paxton  or Gaussian broadening  might change  the
absolute
 value of Lambda little bit.
 However,
 last time I wanted to say that electron-phonon matrix elements are not
 converged using 32x32x32 k-point  grid.  I know  achieving convergency is
very
 slow and painful. But I was very surprised to see the value of averaged
'lambda' in the
 example 's out put directrory.  How come  it's so close to the
experimental value
 even for  very  low  el-ph broadening (0.01 Ryd).

 Please check it once.

  Electron-phonon coupling constant, lambda

 Broadening   0.0100 lambda       0.3845 dos_el   1.8818
 Broadening   0.0200 lambda       0.3744 dos_el   2.2498
 Broadening   0.0300 lambda       0.3447 dos_el   2.3960
 Broadening   0.0400 lambda       0.3446 dos_el   2.5079
 Broadening   0.0500 lambda       0.3515 dos_el   2.5896
 Broadening   0.0600 lambda       0.3555 dos_el   2.6381
 Broadening   0.0700 lambda       0.3551 dos_el   2.6616
 Broadening   0.0800 lambda       0.3516 dos_el   2.6709
 Broadening   0.0900 lambda       0.3463 dos_el   2.6737
 Broadening   0.1000 lambda       0.3405 dos_el   2.6743


 When individual matrix elements are not well converged (Please see my last
mail)
 then how come lambda value is so  good    even for   small broadening and
 small  nq value (4 4 4)????  Many things confuse me lot -----

 Which dos_el   or  Fermi energy or  double delta integral are
acceptable???

 Sometime with increasing  k-point grid we did not get better convergence
---
 it seems the value changes very slowly with increasing K-point.
 We can't take arbitrary large k-point  grid (millions of K-points) because
it  demands large
 disk space and very long computational time.


 Do you think the following numbers are converged???????

 . Gaussian Broadening:   0.010 Ry, ngauss=   0
     DOS =  1.881758 states/spin/Ry/Unit Cell at Ef=  8.327154 eV
     lambda( 1)=  0.0253   gamma=    0.92 GHz
     lambda( 2)=  0.0291   gamma=    1.05 GHz
     lambda( 3)=  0.0403   gamma=    6.35 GHz
     Gaussian Broadening:   0.020 Ry, ngauss=   0
     DOS =  2.249756 states/spin/Ry/Unit Cell at Ef=  8.324326 eV
     lambda( 1)=  0.0699   gamma=    3.02 GHz
     lambda( 2)=  0.0781   gamma=    3.37 GHz
     lambda( 3)=  0.1272   gamma=   24.01 GHz
     Gaussian Broadening:   0.030 Ry, ngauss=   0
     DOS =  2.396042 states/spin/Ry/Unit Cell at Ef=  8.311302 eV
     lambda( 1)=  0.0799   gamma=    3.67 GHz
     lambda( 2)=  0.0856   gamma=    3.93 GHz
     lambda( 3)=  0.1515   gamma=   30.44 GHz
     Gaussian Broadening:   0.040 Ry, ngauss=   0
     DOS =  2.507879 states/spin/Ry/Unit Cell at Ef=  8.299961 eV
     lambda( 1)=  0.0851   gamma=    4.10 GHz
     lambda( 2)=  0.0885   gamma=    4.26 GHz
     lambda( 3)=  0.1599   gamma=   33.63 GHz
     Gaussian Broadening:   0.050 Ry, ngauss=   0
     DOS =  2.589584 states/spin/Ry/Unit Cell at Ef=  8.291558 eV
     lambda( 1)=  0.0881   gamma=    4.38 GHz
     lambda( 2)=  0.0901   gamma=    4.48 GHz
     lambda( 3)=  0.1645   gamma=   35.73 GHz
     Gaussian Broadening:   0.060 Ry, ngauss=   0
     DOS =  2.638140 states/spin/Ry/Unit Cell at Ef=  8.285378 eV
     lambda( 1)=  0.0887   gamma=    4.49 GHz
     lambda( 2)=  0.0900   gamma=    4.56 GHz
     lambda( 3)=  0.1673   gamma=   37.02 GHz
     Gaussian Broadening:   0.070 Ry, ngauss=   0
     DOS =  2.661607 states/spin/Ry/Unit Cell at Ef=  8.280404 eV
     lambda( 1)=  0.0876   gamma=    4.47 GHz
     lambda( 2)=  0.0883   gamma=    4.51 GHz
     lambda( 3)=  0.1695   gamma=   37.82 GHz
     Gaussian Broadening:   0.080 Ry, ngauss=   0
     DOS =  2.670887 states/spin/Ry/Unit Cell at Ef=  8.275903 eV
     lambda( 1)=  0.0856   gamma=    4.39 GHz
     lambda( 2)=  0.0859   gamma=    4.40 GHz
     lambda( 3)=  0.1717   gamma=   38.47 GHz
     Gaussian Broadening:   0.090 Ry, ngauss=   0
     DOS =  2.673746 states/spin/Ry/Unit Cell at Ef=  8.271433 eV
     lambda( 1)=  0.0834   gamma=    4.28 GHz
     lambda( 2)=  0.0834   gamma=    4.28 GHz
     lambda( 3)=  0.1744   gamma=   39.10 GHz
     Gaussian Broadening:   0.100 Ry, ngauss=   0
     DOS =  2.674314 states/spin/Ry/Unit Cell at Ef=  8.266772 eV
     lambda( 1)=  0.0813   gamma=    4.17 GHz
     lambda( 2)=  0.0811   gamma=    4.16 GHz
     lambda( 3)=  0.1773   gamma=   39.76 GHz

     and so on ..........................

     It keeps on incresaing forever even with a very large K-point grid.

     Then how come averaged 'lamda' value is so closed to the experimental
value
     even with  small Gaussian broadennig and  small K-point grids (like 16
16 16) ???????

     Is it accidental??????

 Should  we take large value of nq like  nq1=32, nq2=32, nq3=32
 like large value of nk for better results?????????

 Sometime  even  in total energy calculatiion  we may get accidental
convergence.
 In MIT lecture notes, it's written that

 You do need to be careful though. It is possible to get "false" or
"accidental"
 convergence as well. That is, your energy at a 2x2x2 k-grid may be the same
as
 the energy at a 8x8x8 k-grid, but the energy at a 4x4x4 might be very
different
 from both of these. In this case, you aren't really converged at a 2x2x2
k-grid.


 Is it possible to calculate EPC for arbitrary q -point like
 0.13579         0.3474     0.83765  ???????????

 Looking forward to your valuable suggestions.


 With best regards,
 Amit

 P.S.  Dear Nicola, Thank you very much for  your  useful  reference.
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