[Pw_forum] EPC of Aluminium 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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