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Graphite TS binding energy

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Task

In this example you will determine the interlayer binding energy of graphite in its experimental structure using the method of Tchatchenko and Scheffler to account for van der Waals interactions.

Semilocal DFT at the GGA level underestimates long-range dispersion interactions. In the case of graphite, PBE predicts the interlayer binding energy of ~1 meV/atom which is too small compared to the RPA reference of 0.048 eV/atom [1].

In this example, the interlayer binding energy of graphite in its experimental structure is determined using the Tkatchenko-Scheffler method, which performs well in description of the structure of graphite (see e.g. example graphite interlayer distance).


Input

POSCAR

  • Graphite:
graphite
1.0
1.22800000 -2.12695839  0.00000000
1.22800000  2.12695839  0.00000000
0.00000000  0.00000000  6.71
4
direct
   0.00000000  0.00000000  0.25000000
   0.00000000  0.00000000  0.75000000
   0.33333333  0.66666667  0.25000000
   0.66666667  0.33333333  0.75000000

  • Graphene:
graphite
1.0
1.22800000 -2.12695839  0.00000000
1.22800000  2.12695839  0.00000000
0.00000000  0.00000000  20.
2
direct
   0.00000000  0.00000000  0.25000000
   0.33333333  0.66666667  0.25000000

INCAR

IVDW = 20            
LVDW_EWALD =.TRUE. 
NSW = 1 
IBRION = 2
ISIF = 4
PREC = Accurate
EDIFFG = 1e-5
LWAVE = .FALSE.
LCHARG = .FALSE.
ISMEAR = -5
SIGMA = 0.01
EDIFF = 1e-6
ALGO = Fast
NPAR = 2


KPOINTS

  • Graphite:
Monkhorst Pack
0
gamma
16 16 8
0 0 0
  • Graphene:
Monkhorst Pack
0
gamma
16 16 1
0 0 0

There is no interaction of layers in z-direction for graphene so we need only 1 k point in this direction.

Running this example

To run this example, execute the run.sh bash-script:

#
# To run VASP this script calls $vasp_std
# (or posibly $vasp_gam and/or $vasp_ncl).
# These variables can be defined by sourcing vaspcmd
. vaspcmd 2> /dev/null

#
# When vaspcmd is not available and $vasp_std,
# $vasp_gam, and/or $vasp_ncl are not set as environment
# variables, you can specify them here
[ -z "`echo $vasp_std`" ] && vasp_std="mpirun -np 8 /path-to-your-vasp/vasp_std"
[ -z "`echo $vasp_gam`" ] && vasp_gam="mpirun -np 8 /path-to-your-vasp/vasp_gam"
[ -z "`echo $vasp_ncl`" ] && vasp_ncl="mpirun -np 8 /path-to-your-vasp/vasp_ncl"

#
# The real work starts here
#

rm results.dat

drct=$(pwd)

for i in graphene graphite
do
  cd $drct/$i
  $vasp_std
done

cd $drct

# obtain total energy for graphite 
en2=$(grep "free  ene" graphite/OUTCAR |tail -1|awk '{print $5}') 

# obtain total energy for graphene
en1=$(grep "free  ene" graphene/OUTCAR |tail -1|awk '{print $5}')

# compute interlayer binding energy (eV/atom)
deltaE=$(echo print $en2/4 - $en1/2 |python)

echo "Binding energy (eV/atom): " $deltaE >results.dat

Note that the calculation is performed in two steps (two separate single-point calculations) in which the energy for bulk graphite and for graphene are obtained. The binding energy is computed automatically and it is written in the file results.dat. (N.B.: for the latter python needs to be available.)

Even though the TS method predicts a reasonable geometry (see the Graphite interlayer distance example) it overestimates the energetics strongly: the computed binding energy of -0.083 eV/atom is too large compared to the RPA reference of 0.048 eV/atom. This overestimation is - at least in part - due to neglecting the many-body interactions (see example Graphite MBD binding energy).

Download

graphiteBinding_ts.tgz

References

  1. S. Lebègue, J. Harl, Tim Gould, J. G. Ángyán, G. Kresse, and J. F. Dobson, Phys. Rev. Lett. 105, 196401 (2010).

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