Example: Gold electrodes

Download green_Au.run

In this example of green, the self-energies are calculated of gold electrodes, the material most often used in molecular electronics. In the example for the Benzenedithiol junction these self-energies will be used to calculate the DOS and transmission of a benzenedithiol junction. The geometry of the electrodes is shown in Fig. 1.

/scm-uploads/doc.2023/ADF/_images/green_contact.png

Figure 1: Geometry of the gold contact used in the calculation of the self-energy. The lead consists of two surface layers, left (red) and right (blue), and a bulk layer (green). Each principal layer in turn consists of three atomic layers. This should be sufficient to ensure that the Hamiltonian of the central (green) layer is a bulk Hamiltonian.

The final results are shown in the following figure:

/scm-uploads/doc.2023/ADF/_images/green_Au.png

From this figure it can be seen that around the Fermi energy (-0.2 Hartree), both the DOS and the transmission of gold are relatively constant. This feature makes gold an attractive material for electrodes, since one can expect that the transmission of a molecular junction will be dominated by the molecular properties.

#!/bin/sh

# In this example of green, the self-energies are calculated of gold electrodes,
# the material most often used in molecular electronics.
# In the example for the Benzenedithiol junction, green_BDT.run, these self-energies
# will be used to calculate the DOS and transmission of a benzenedithiol junction.

# Each principal layer contains 3x3x3=27 gold atoms.
# For the calculation of the self-energies three principal layers are needed,
# and therefore 81 gold atoms in total.
# To keep the runtimes manageable it is therefore important to choose the basis set
# as small as possible.
# For transport calculations, a DZ basis with a large frozen core is generally sufficient.
# Unfortunately, even with the largest frozen core (Au.4f),
# the basis set for Au still contains 19 electrons.
# A significant speedup can be obtained by limiting this to 11 electrons
# (only the outer *d* and *s* shells).
# Be advised that even with this reduction the total runtime of calculation can be long.

# To facilitate the calculation of the electrodes,
# first a gold atom fragment will be calculated with the smallest possible basis.
# The sample directory contains the required Au.5p and Au.5p.dirac files.
# Note that for gold relativistic effects are important.
# Therefore Scalar ZORA will be used throughout this example.

cp $AMSHOME/examples/adf/green_Al/Au.5p .
cp $AMSHOME/examples/adf/green_Al/Au.5p.dirac .

$AMSBIN/dirac < Au.5p.dirac
mv TAPE12 t12.rel

AMS_JOBNAME=Au $AMSBIN/ams <<eor
System
   Atoms
      Au 0.0 0.0 0.0
   End
end
Task SinglePoint
Engine ADF
  corepotentials t12.rel
  end
  create Au   file=Au.5p
  relativity
    level scalar
    formalism ZORA
  end
  xc
    lda SCF VWN
  end
EndEngine
eor

# A principal layer of gold consists of three atomic layers,
# which should be sufficient due to the small screening length.
# An atomic layer contains 3x3=9 atoms in a (111) FCC configuration.
# This allows one to use the top-, bride-, and hollow-site binding configurations for a molecule.
# For the following calculations it is necessary to first construct a fragment
# of a principal layer.

AMS_JOBNAME=layer $AMSBIN/ams <<eor
System
  atoms
     Au       -2.355588   -6.662612    0.000000
     Au       -2.355589   -4.164133   -1.442498
     Au       -2.355589   -4.164133    1.442498
     Au       -2.355589   -1.665653   -2.884996
     Au       -2.355589   -1.665653    0.000000
     Au       -2.355589   -1.665653    2.884996
     Au       -2.355589    0.832826   -1.442498
     Au       -2.355589    0.832826    1.442498
     Au       -2.355589    3.331306    0.000000
     Au        0.000000   -4.996959    0.000000
     Au        0.000000   -2.498480   -1.442498
     Au        0.000000   -2.498480    1.442498
     Au        0.000000    0.000000   -2.884996
     Au        0.000000    0.000000    0.000000
     Au        0.000000    0.000000    2.884996
     Au        0.000000    2.498480   -1.442498
     Au        0.000000    2.498480    1.442498
     Au        0.000000    4.996959    0.000000
     Au        2.355589   -3.331306    0.000000
     Au        2.355589   -0.832826   -1.442498
     Au        2.355589   -0.832826    1.442498
     Au        2.355589    1.665653   -2.884996
     Au        2.355589    1.665653    0.000000
     Au        2.355589    1.665653    2.884996
     Au        2.355589    4.164133   -1.442498
     Au        2.355589    4.164133    1.442498
     Au        2.355588    6.662612    0.000000
  end
end

Task SinglePoint

Engine ADF
  fragments
     Au  Au.results/adf.rkf
  end
  relativity
    level scalar
    formalism ZORA
  end
  symmetry NOSYM
  title Principal layer
  xc
    lda SCF VWN
  end
EndEngine
eor

# Three principal layers are stacked together to calculate the self-energies (see Fig. 1).
# The names of the fragments are significant, since one needs to refer to them by name in
# the calculation of the self-energies.

AMS_JOBNAME=bulk $AMSBIN/ams <<eor
System
  atoms
     Au       -9.422355  -11.659571    0.000000 adf.f=left
     Au       -9.422356   -9.161092   -1.442498 adf.f=left
     Au       -9.422356   -9.161092    1.442498 adf.f=left
     Au       -9.422356   -6.662612   -2.884996 adf.f=left
     Au       -9.422356   -6.662612    0.000000 adf.f=left
     Au       -9.422356   -6.662612    2.884996 adf.f=left
     Au       -9.422356   -4.164133   -1.442498 adf.f=left
     Au       -9.422356   -4.164133    1.442498 adf.f=left
     Au       -9.422356   -1.665653    0.000000 adf.f=left
     Au       -7.066767   -9.993918    0.000000 adf.f=left
     Au       -7.066767   -7.495439   -1.442498 adf.f=left
     Au       -7.066767   -7.495439    1.442498 adf.f=left
     Au       -7.066767   -4.996959   -2.884996 adf.f=left
     Au       -7.066767   -4.996959    0.000000 adf.f=left
     Au       -7.066767   -4.996959    2.884996 adf.f=left
     Au       -7.066767   -2.498479   -1.442498 adf.f=left
     Au       -7.066767   -2.498479    1.442498 adf.f=left
     Au       -7.066767    0.000000    0.000000 adf.f=left
     Au       -4.711178   -8.328265    0.000000 adf.f=left
     Au       -4.711178   -5.829785   -1.442498 adf.f=left
     Au       -4.711178   -5.829785    1.442498 adf.f=left
     Au       -4.711178   -3.331306   -2.884996 adf.f=left
     Au       -4.711178   -3.331306    0.000000 adf.f=left
     Au       -4.711178   -3.331306    2.884996 adf.f=left
     Au       -4.711178   -0.832826   -1.442498 adf.f=left
     Au       -4.711178   -0.832826    1.442498 adf.f=left
     Au       -4.711179    1.665653    0.000000 adf.f=left
     Au       -2.355588   -6.662612    0.000000 adf.f=center
     Au       -2.355589   -4.164133   -1.442498 adf.f=center
     Au       -2.355589   -4.164133    1.442498 adf.f=center
     Au       -2.355589   -1.665653   -2.884996 adf.f=center
     Au       -2.355589   -1.665653    0.000000 adf.f=center
     Au       -2.355589   -1.665653    2.884996 adf.f=center
     Au       -2.355589    0.832826   -1.442498 adf.f=center
     Au       -2.355589    0.832826    1.442498 adf.f=center
     Au       -2.355589    3.331306    0.000000 adf.f=center
     Au        0.000000   -4.996959    0.000000 adf.f=center
     Au        0.000000   -2.498480   -1.442498 adf.f=center
     Au        0.000000   -2.498480    1.442498 adf.f=center
     Au        0.000000    0.000000   -2.884996 adf.f=center
     Au        0.000000    0.000000    0.000000 adf.f=center
     Au        0.000000    0.000000    2.884996 adf.f=center
     Au        0.000000    2.498480   -1.442498 adf.f=center
     Au        0.000000    2.498480    1.442498 adf.f=center
     Au        0.000000    4.996959    0.000000 adf.f=center
     Au        2.355589   -3.331306    0.000000 adf.f=center
     Au        2.355589   -0.832826   -1.442498 adf.f=center
     Au        2.355589   -0.832826    1.442498 adf.f=center
     Au        2.355589    1.665653   -2.884996 adf.f=center
     Au        2.355589    1.665653    0.000000 adf.f=center
     Au        2.355589    1.665653    2.884996 adf.f=center
     Au        2.355589    4.164133   -1.442498 adf.f=center
     Au        2.355589    4.164133    1.442498 adf.f=center
     Au        2.355588    6.662612    0.000000 adf.f=center
     Au        4.711179   -1.665653    0.000000 adf.f=right
     Au        4.711178    0.832826   -1.442498 adf.f=right
     Au        4.711178    0.832826    1.442498 adf.f=right
     Au        4.711178    3.331306   -2.884996 adf.f=right
     Au        4.711178    3.331306    0.000000 adf.f=right
     Au        4.711178    3.331306    2.884996 adf.f=right
     Au        4.711178    5.829785   -1.442498 adf.f=right
     Au        4.711178    5.829785    1.442498 adf.f=right
     Au        4.711178    8.328265    0.000000 adf.f=right
     Au        7.066767    0.000000    0.000000 adf.f=right
     Au        7.066767    2.498479   -1.442498 adf.f=right
     Au        7.066767    2.498479    1.442498 adf.f=right
     Au        7.066767    4.996959   -2.884996 adf.f=right
     Au        7.066767    4.996959    0.000000 adf.f=right
     Au        7.066767    4.996959    2.884996 adf.f=right
     Au        7.066767    7.495439   -1.442498 adf.f=right
     Au        7.066767    7.495439    1.442498 adf.f=right
     Au        7.066767    9.993918    0.000000 adf.f=right
     Au        9.422356    1.665653    0.000000 adf.f=right
     Au        9.422356    4.164133   -1.442498 adf.f=right
     Au        9.422356    4.164133    1.442498 adf.f=right
     Au        9.422356    6.662612   -2.884996 adf.f=right
     Au        9.422356    6.662612    0.000000 adf.f=right
     Au        9.422356    6.662612    2.884996 adf.f=right
     Au        9.422356    9.161092   -1.442498 adf.f=right
     Au        9.422356    9.161092    1.442498 adf.f=right
     Au        9.422355   11.659571    0.000000 adf.f=right
  end
end

Task SinglePoint

Engine ADF
  fragments
     left    layer.results/adf.rkf
     center  layer.results/adf.rkf
     right   layer.results/adf.rkf
  end
  relativity
    level scalar
    formalism ZORA
  end
  symmetry NOSYM
  title Bulk gold
  xc
    lda SCF VWN
  end
EndEngine
eor

# Similar to the other examples, the self-energies of the left and right contacts
# is calculated for 1000 energy points between -0.5 and 0 Hartree.
# This results in two keyfiles of approximately 2.5 GB each.
# Since the self-energies are independent of whatever is placed between the contacts,
# they can be reused many times.

$AMSBIN/green << eor
SURFACE bulk.results/adf.rkf
    FRAGMENTS center right
END
EPS -0.5 0 1000
ETA 1e-6
eor
mv SURFACE left.kf

$AMSBIN/green << eor
SURFACE bulk.results/adf.rkf
    FRAGMENTS center left
END
EPS -0.5 0 1000
ETA 1e-6
eor
mv SURFACE right.kf

# In order to interpret transmissions calculated with these self-energies,
# it is necessary to know the location of the Fermi energy.
# An estimate for the Fermi energy can be obtained from the bulk SCF calculation
# by taking the average of the HOMO and LUMO energies, which in this case equals -0.195 Hartree.

# Usually the self-energies will be used to calculate the transmission of a molecular junction.
# However, it is instructive to use a principal layer of gold as the "molecule" and study
# the DOS and transmission of bulk gold.

$AMSBIN/green << eor
DOS bulk.results/adf.rkf
TRANS bulk.results/adf.rkf
EPS -0.5 0 1000
ETA 1e-6
LEFT left.kf
    FRAGMENT left
END
RIGHT right.kf
    FRAGMENT right
END
NOSAVE DOS_B, TRANS_B
eor

echo ""
echo "Contents of DOS_A:"
cat DOS_A
echo "END"
echo ""
echo "Contents of TRANS_A:"
cat TRANS_A
echo "END"