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.

[image]

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:

[image]

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"
