Graphite MBD 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 MBD@rsSCS method of Tchatchenko et al. 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 contrast, the pairwise correction scheme of Tkatchenko and Scheffler, overestimates this quantity strongly (0.083 eV/atom, see the Graphite TS binding energy example). Here we show that this problem can be eliminated by if many-body effects in dispersion energy are taken into account using the MBD@rsSCS method of Tchatchenko et al. (see Many-body dispersion energy).

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 = 202           
LVDWEXPANSION =.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

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
#

# Here the work starts
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.)

The computed value of 0.050 eV/A is now fairly close to the RPA reference of 0.048 eV/atom ^[1].