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

[Lenz Fiedler]

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
02826 Görlitz

Vorstand: Prof. Dr. Sebastian M. Schmidt, Dr. Diana Stiller
Vereinsregister: VR 1693 beim Amtsgericht Dresden

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