[QE-users] Incosistent energy contributions for 2D system

Thu Jul 25 19:11:31 CEST 2024

The "Hartree", "one-electron", "Ewald" contributions to the energy have 
something in common: the G=0 contribution to the energy separately 
diverges. Their sum however does not diverge for neutral cells. So one 
subtracts out the diverging terms and is left with a finite G=0 
contribution. This may however vary a lot between different structures, 
even if the sum of the three contributions is quite the same as in this 
case.

Paolo

On 25/07/2024 18:43, Lenz Fiedler wrote:
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> 
> Dear QE users,
> 
> I have a question regarding a 2D QE calculation.  Consider a very simple
> bilayer graphene system, which I calculate either with a "big" (23
> Angstrom in z-direction) or "small" (17 Angstrom in z-direction) cell
> (Input files are at the end of the message). The C atoms are in two
> planes in x-y-direction.
> 
> Now both calculations are the same except for their z-dimension. In the
> "small" case I make the cell a bit smaller in z-direction. I did careful
> calculations to determine by how much I can make it smaller without the
> total energy deviating too much from the original cell. The input I
> share here is still well within the range where the total energy error
> is very small. Of course, eventually one hits a point where there is a
> noticeable energy difference.
> 
> Now to my question: I have noticed that for both calculations, total
> energies are essentially the same, but what differs quite drastically,
> are the individual energy contributions. Namely I get:
> 
> "big":
> !    total energy              =     -48.18986746 Ry
>       estimated scf accuracy    <       0.00003985 Ry
>       smearing contrib. (-TS)   =      -0.00000000 Ry
>       internal energy E=F+TS    =     -48.18986746 Ry
> 
>       The total energy is F=E-TS. E is the sum of the following terms:
>       one-electron contribution =   -1245.11933758 Ry
>       hartree contribution      =     624.03689026 Ry
>       xc contribution           =     -17.17420972 Ry
>       ewald contribution        =     590.06678957 Ry
> 
> "small":
> !    total energy              =     -48.18985199 Ry
>       estimated scf accuracy    <       0.00007424 Ry
>       smearing contrib. (-TS)   =      -0.00000000 Ry
>       internal energy E=F+TS    =     -48.18985199 Ry
> 
>       The total energy is F=E-TS. E is the sum of the following terms:
>       one-electron contribution =    -759.11502918 Ry
>       hartree contribution      =     381.02359494 Ry
>       xc contribution           =     -17.17243795 Ry
>       ewald contribution        =     347.07402021 Ry
> 
> 
> As you can see, the total energies match up nicely, but all other terms
> except for the XC energy are different. Is this by design? Is there a
> numerical reason for it? I am trying to come up with a way to determine
> the minimal vacuum in z-direction I have to leave below and above my
> graphene planes, and had originally only checked the total energy. Now I
> am wondering if this is enough?
> 
> Kind regards
> Lenz Fiedler
> PhD student (Helmholtz-Zentrum Dresden-Rossendorf)
> 
> PS: I also disabled "assume_isolated = '2D'" - I still see the same
> behavior, albeit with different numbers for the energy contributions,
> the total energies are still the same.
> 
> Input files:
> 
> (PSP taken from http://www.pseudo-dojo.org/index.html):
> 
> 
> 
> "big":
> &CONTROL
>     calculation      = 'scf'
>     verbosity        = 'high'
>     restart_mode     = 'from_scratch'
>     outdir           = 'temp'
>     prefix           = 'C'
>     pseudo_dir       = './'
> /
> &SYSTEM
>     ibrav            = 0
>     nbnd             = 10
>     ecutwfc          = 80
>     ecutrho          = 320
>     nosym            = .true.
>     noinv            = .true.
>     occupations      = 'smearing'
>     degauss          = 0.0018874
>     smearing         = 'fermi-dirac'
>     ntyp             = 1
>     nat              = 4
>     assume_isolated  = '2D'
> /
> &ELECTRONS
>     conv_thr         = 7.599999999999999e-05
>     mixing_mode      = 'plain'
>     mixing_beta      = 0.1
> /
> &IONS
> /
> &CELL
> /
> 
> ATOMIC_SPECIES
> C 12.011 C_ncsr_0.5_pbe.upf
> 
> K_POINTS automatic
> 8 8 1 0 0 0
> 
> CELL_PARAMETERS angstrom
>   2.4622899999999999    0.0000000000000000    0.0000000000000000
>   1.2310682316596653    2.1324961988004443    0.0000000000000000
>   0.0000000000000000    0.0000000000000000   23.3000000000000007
> 
> ATOMIC_POSITIONS angstrom
> C 2.4622407526646328  0.0000426499239760  9.9535270000000011
> C 1.2310701657767995  0.7108036329841640  9.9532939999999996
> C 1.2310805438773487  2.1324748738384565 13.3464730000000014
> C 2.4620787720005488  1.4216712408542924 13.3467060000000011
> 
> 
> "small":
> same as big but with:
> 
> CELL_PARAMETERS angstrom
>   2.4622899999999999    0.0000000000000000    0.0000000000000000
>   1.2310682316596653    2.1324961988004443    0.0000000000000000
>   0.0000000000000000    0.0000000000000000   17.3040246000000018
> 
> ATOMIC_POSITIONS angstrom
> C 2.4622407526646328  0.0000426499239760  6.9555393000000016
> C 1.2310701657767995  0.7108036329841640  6.9553063000000002
> C 1.2310805438773487  2.1324748738384565 10.3484853000000019
> C 2.4620787720005488  1.4216712408542924 10.3487183000000016
> 
> -- 
> Lenz Fiedler, M. Sc.
> PhD Candidate | Machine Learning for Materials Design
> 
> Tel.: +49 3581 37523 55
> E-Mail: l.fiedler at hzdr.de
> https://www.casus.science
> 
> CASUS - Center for Advanced Systems Understanding
> Helmholtz-Zentrum Dresden-Rossendorf e.V. (HZDR)
> Conrad-Schiedt-Straße 20
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> 
> Vorstand: Prof. Dr. Sebastian M. Schmidt, Dr. Diana Stiller
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> 
> 
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Univ. Udine, via delle Scienze 206, 33100 Udine Italy, +39-0432-558216
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