Example: Benzenedithiol junction: Wide-Band-Limit
*************************************************

"Download green_WBL.run"

In the wide-band limit (WBL) the coupling to the leads is assumed to
be independent of energy. Therefore one does not need to calculate any
self-energies. This also means that the eigenspace of the Green's
function is independent of energy. It can therefore be diagonalized in
advance, greatly speeding up the calculation of the DOS and the
transmission.

In the example $AMSHOME/examples/adf/green_Al/green_WBL/green_WBL.run
of *green*, the transmission of  benzenedithiol junction in the wide-
band limit (WBL) is calculated. In order to model the molecule-metal
interface, we do need to include a few gold layers in the calculation.
However, unlike  before, only a single atomic layer as the principal
layer is used.

Because a single atomic layer is an unnatural configuration for gold,
a minor amount of smearing is necessary to make the calculation
converge. The molecule is sandwiched in between the electrodes just
like before (see Fig. 2 in  the example for benzenedithiol). However,
this time each atomic layer of gold gets its own fragment. The reason
for this configuration is that if the WBL is used on the entire gold
contact the result is an an unphysical coupling to the leads; even the
gold atoms contacting the molecule would have a direct coupling to the
environment. A much better result can be obtained by only using the
WBL on the back-most atomic layer and letting the electrons propagate
naturally through the rest of the contact. Because the WBL is
computationally so inexpensive, we can easily calculate the DOS and
transmission for 10,000 points instead of 1000.

A comparison of the resulting transmission with the calculation with
self-energies is shown in the following figure:

[image]

The WBL shows good agreement with the non-WBL transmission around the
Fermi energy (-0.195 Hartree or -5.306 eV). Note that the quality of
the WBL depends on the choice of the coupling (ETA). For this
particular contact geometry we obtain good agreement for ETA = 0.02
Hartree, but a better value may be found for other electrodes.
Finally, the WBL can be incrementally improved by adding more gold
layers to the extended molecule. For many layers it converges to the
calculation with full self-energies.

   #!/bin/sh

   # In the wide-band limit (WBL) the coupling to the leads is assumed to be independent of energy.
   # Therefore one does not need to calculate any self-energies.
   # This also means that the eigenspace of the Green's function is independent of energy.
   # It can therefore be diagonalized in advance,
   # greatly speeding up the calculation of the DOS and the transmission.

   # In the example $AMSHOME/examples/adf/green_Al/green_WBL.run of green,
   # the transmission of  benzenedithiol junction, example green_BDT.run,
   # in the wide-band limit (WBL) is calculated.
   # In order to model the molecule-metal interface, we do need to include a few gold layers
   # in the calculation.
   # However, unlike in green_Au.run, only a single atomic layer as the principal layer is used.

   # In green_BDT.run 3 layers of gold atoms from 1 fragment.
   # In this example green_WBL.run each layer of gold atoms has its own fragment.
   # Because a single atomic layer is an unnatural configuration for gold,
   # a minor amount of smearing is necessary to make the calculation converge.
   # The molecule is sandwiched in between the electrodes just like before
   # (see the example for benzenedithiol, example green_BDT.run).
   # However, this time each atomic layer of gold gets its own fragment.
   # The reason for this configuration is that if the WBL is used on the
   # entire gold contact the result is an an unphysical coupling to the leads;
   # even the gold atoms contacting the molecule would have a direct coupling to the environment.
   # A much better result can be obtained by only using the WBL on the back-most atomic layer
   # and letting the electrons propagate naturally through the rest of the contact.
   # Because the WBL is computationally so inexpensive, we can easily calculate
   # the DOS and transmission for 10,000 points instead of 1000.

   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

   AMS_JOBNAME=layer $AMSBIN/ams <<eor
   System
     atoms
        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
     end
   end

   Task SinglePoint

   Engine ADF
     fragments
        Au  Au.t21
     end
     occupations Smearq=0.001
     relativity
       level scalar
       formalism ZORA
     end
     symmetry NOSYM
     title Principal layer
     xc
       lda SCF VWN
     end
   EndEngine
   eor

   AMS_JOBNAME=molecule $AMSBIN/ams <<eor
   System
     atoms
        C        -1.400000    0.000000    0.000000
        C        -0.700000    0.000000   -1.200000
        C        -0.700000    0.000000    1.200000
        C         0.700000    0.000000   -1.200000
        C         0.700000    0.000000    1.200000
        C         1.400000    0.000000    0.000000
        H        -1.200000    0.000000   -2.200000
        H        -1.200000    0.000000    2.200000
        H         1.200000    0.000000   -2.200000
        H         1.200000    0.000000    2.200000
        S        -3.200000    0.000000    0.000000
        S         3.200000    0.000000    0.000000
     end
   end

   Task SinglePoint

   Engine ADF
     basis
        type DZP
        core Large
        createOutput None
     end
     relativity
       level scalar
       formalism ZORA
     end
     symmetry NOSYM
     title Benzenedithiol
     xc
       lda SCF VWN
     end
   EndEngine
   eor

   AMS_JOBNAME=fock $AMSBIN/ams <<eor
   System
     atoms
        Au       -9.911177   -6.662612    0.000000 adf.f=left
        Au       -9.911178   -4.164133   -1.442498 adf.f=left
        Au       -9.911178   -4.164133    1.442498 adf.f=left
        Au       -9.911178   -1.665653   -2.884996 adf.f=left
        Au       -9.911178   -1.665653    0.000000 adf.f=left
        Au       -9.911178   -1.665653    2.884996 adf.f=left
        Au       -9.911178    0.832826   -1.442498 adf.f=left
        Au       -9.911178    0.832826    1.442498 adf.f=left
        Au       -9.911178    3.331306    0.000000 adf.f=left
        Au       -7.555589   -4.996959    0.000000 adf.f=left.2
        Au       -7.555589   -2.498480   -1.442498 adf.f=left.2
        Au       -7.555589   -2.498480    1.442498 adf.f=left.2
        Au       -7.555589    0.000000   -2.884996 adf.f=left.2
        Au       -7.555589    0.000000    0.000000 adf.f=left.2
        Au       -7.555589    0.000000    2.884996 adf.f=left.2
        Au       -7.555589    2.498480   -1.442498 adf.f=left.2
        Au       -7.555589    2.498480    1.442498 adf.f=left.2
        Au       -7.555589    4.996959    0.000000 adf.f=left.2
        Au       -5.200000   -3.331306    0.000000 adf.f=left.3
        Au       -5.200000   -0.832826   -1.442498 adf.f=left.3
        Au       -5.200000   -0.832826    1.442498 adf.f=left.3
        Au       -5.200000    1.665653   -2.884996 adf.f=left.3
        Au       -5.200000    1.665653    0.000000 adf.f=left.3
        Au       -5.200000    1.665653    2.884996 adf.f=left.3
        Au       -5.200000    4.164133   -1.442498 adf.f=left.3
        Au       -5.200000    4.164133    1.442498 adf.f=left.3
        Au       -5.200001    6.662612    0.000000 adf.f=left.3
        C        -1.400000    0.000000    0.000000 adf.f=molecule
        C        -0.700000    0.000000   -1.200000 adf.f=molecule
        C        -0.700000    0.000000    1.200000 adf.f=molecule
        C         0.700000    0.000000   -1.200000 adf.f=molecule
        C         0.700000    0.000000    1.200000 adf.f=molecule
        C         1.400000    0.000000    0.000000 adf.f=molecule
        H        -1.200000    0.000000   -2.200000 adf.f=molecule
        H        -1.200000    0.000000    2.200000 adf.f=molecule
        H         1.200000    0.000000   -2.200000 adf.f=molecule
        H         1.200000    0.000000    2.200000 adf.f=molecule
        S        -3.200000    0.000000    0.000000 adf.f=molecule
        S         3.200000    0.000000    0.000000 adf.f=molecule
        Au        5.200001   -6.662612    0.000000 adf.f=right.3
        Au        5.200000   -4.164133   -1.442498 adf.f=right.3
        Au        5.200000   -4.164133    1.442498 adf.f=right.3
        Au        5.200000   -1.665653   -2.884996 adf.f=right.3
        Au        5.200000   -1.665653    0.000000 adf.f=right.3
        Au        5.200000   -1.665653    2.884996 adf.f=right.3
        Au        5.200000    0.832826   -1.442498 adf.f=right.3
        Au        5.200000    0.832826    1.442498 adf.f=right.3
        Au        5.200000    3.331306    0.000000 adf.f=right.3
        Au        7.555589   -4.996959    0.000000 adf.f=right.2
        Au        7.555589   -2.498480   -1.442498 adf.f=right.2
        Au        7.555589   -2.498480    1.442498 adf.f=right.2
        Au        7.555589    0.000000   -2.884996 adf.f=right.2
        Au        7.555589    0.000000    0.000000 adf.f=right.2
        Au        7.555589    0.000000    2.884996 adf.f=right.2
        Au        7.555589    2.498480   -1.442498 adf.f=right.2
        Au        7.555589    2.498480    1.442498 adf.f=right.2
        Au        7.555589    4.996959    0.000000 adf.f=right.2
        Au        9.911178   -3.331306    0.000000 adf.f=right
        Au        9.911178   -0.832826   -1.442498 adf.f=right
        Au        9.911178   -0.832826    1.442498 adf.f=right
        Au        9.911178    1.665653   -2.884996 adf.f=right
        Au        9.911178    1.665653    0.000000 adf.f=right
        Au        9.911178    1.665653    2.884996 adf.f=right
        Au        9.911178    4.164133   -1.442498 adf.f=right
        Au        9.911178    4.164133    1.442498 adf.f=right
        Au        9.911177    6.662612    0.000000 adf.f=right
     end
   end

   Task SinglePoint

   Engine ADF
     fragments
        left        layer.t21
        left.2      layer.t21
        left.3      layer.t21
        molecule    molecule.t21
        right.3     layer.t21
        right.2     layer.t21
        right       layer.t21
     end
     relativity
       level scalar
       formalism ZORA
     end
     symmetry NOSYM
     title Benzenedithiol
     xc
       lda SCF VWN
     end
   EndEngine
   eor

   $AMSBIN/green << eor
   DOS fock.results/adf.rkf
   TRANS fock.results/adf.rkf
   EPS -0.5 0 10000
   ETA 1e-6
   LEFT
       FRAGMENT left
       ETA 2e-2
   END
   RIGHT
       FRAGMENT right
       ETA 2e-2
   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"
