[QE-developers] Problem of the momentum matrix element at the Gamma point

[L Y]

Dear Paolo,

Thank you for the quick response and pointing me in a direction!
I see that in "compute_ppsi.f90", the subroutines "gen_us_dj" and
"gen_us_dy" are called, inside of which the derivatives of the spherical
Bessel and spherical harmonics are calculated. I think the Gamma point is
special in the sense that it is the only point that can satisfy k+G=0, so I
thought perhaps the problem could be due to "dvkb" and "dvkb1" being
treated inaccurately at k+G=0. I checked that in "compute_ppsi.f90", for
k+G=0, the array "work(ig,:)=dvkb1(ig,:)+dvkb(ig,:)*gk(ipol,ig)" is zero.
The second term is obviously zero due to |k+G|=0, but I cannot see why
"dvkb1(ig,:)" is zero.
I think I am abit too inexperienced with the theory and code to find the
"bug", I only pieced together part of the puzzle by looking at Iurii's
thesis Sec 6.13. I dunno if anyone has time to look at this problem? I
think in my emerging physical discipline (attosecond strong-field physics
in solids), the correct calculation of the momentum matrix elements will be
needed alot in the future (to be used in the TDSE or time-dependent
density-matrix equations). But maybe this is not so urgent at the moment,
since only the Gamma point is an issue, so I can just circumvent this by
not choosing that point.

Best regards,
Lun Yue
Louisiana State University

Den lør. 16. maj 2020 kl. 01.44 skrev Paolo Giannozzi <p.giannozzi at gmail.com
>:

> The nonlocal contribution involves derivatives of j_l(kr). I vaguely
> remember that the limit k=0 is tricky, but I was convinced that it had been
> properly implemented many years ago
>
> Paolo
>
> On Sat, May 16, 2020 at 8:12 AM L Y <xifntx at gmail.com> wrote:
>
>> Dear Quantum ESPRESSO developers,
>>
>> My question was posted initially to the user mail list, and I already
>> obtained help from Dr. Iurii. It is abit technical, so I formulate it here
>> again to see if anyone has ideas or suggestions. I think it could be a bug.
>>
>> I calculated the the momentum matrix element between the valence and
>> conduction bands in MgO, along a k-path going through the Gamma point. At
>> the Gamma point, there is a clear discontinuity, see attachment
>> "p_with_nonlocal.png" (Gamma point at ik=31), while the band energies are
>> all continuous. I tried many different types of pseudopotentials (norm
>> conserving, ultrasoft, PAW) and functionals (LDA, PBE), all showing this
>> discontinuity, (although the SG15 ONCV pseudopotentials seem to be better).
>>
>> When I commented out the part in "compute_ppsi.f90" involving the
>> non-local pseudopotential, the discontinuity is gone, see attached
>> "p_without_nonlocal.png". This leads me to believe that there is
>> potentially a bug in the calculation of the commutator i [r, V_nl] for the
>> Gamma point. I was wondering whether anyone has ideas or suggestions on why
>> this occurs and where in the code I should look at to try to find the
>> potential "bug".
>>
>> Sorry for the long mail.
>> Best regards,
>> Lun Yue
>> Louisiana State University
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>> developers at lists.quantum-espresso.org
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>>
>
>
> --
> Paolo Giannozzi, Dip. Scienze Matematiche Informatiche e Fisiche,
> Univ. Udine, via delle Scienze 208, 33100 Udine, Italy
> Phone +39-0432-558216, fax +39-0432-558222
>
>
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