Example: DOS and transmission: Aluminium
****************************************

"Download green_Al.run"

As an example of a non-self-consistent Green's function calculation,
we will look at the density of states (DOS) and transmission of an
infinite 1D chain of Aluminum atoms.

The final resulting DOS and transmission are shown in the following
figure:

[image]

As would be expected for a 1D system, the DOS shows Van Hove
singularities at the band edges. Apart from oscillations due to the
finite size of the system in ADF, the transmission only reaches
integer values. Between approximately -0.35 and -0.15 Hartree, only
the sigma channel contributes to the transmission. Above -0.15 Hartree
also the two pi channels start to contribute.

   #!/bin/sh


   # As an example of a non-self-consistent Green's function calculation, we will
   # look at the density of states (DOS) and transmission of an infinite 1D chain
   # of Aluminum atoms.

   # First we need to perform a single-point calculation with ADF on a principal
   # layer, consisting, in this case, of four atoms. Since bulk Aluminum has an FCC
   # structure with a lattice constant of 4.05 Angstrom, the nearest neighbor
   # distance is approximately 2.83 Angstrom. green requires SYMMETRY NOSYM, so we
   # have the following input file for the principal layer:

   AMS_JOBNAME=layer $AMSBIN/ams <<eor
   System
     atoms
        Al       -4.290000    0.000000    0.000000
        Al       -1.430000    0.000000    0.000000
        Al        1.430000    0.000000    0.000000
        Al        4.290000    0.000000    0.000000
     end
   end

   Task SinglePoint

   Engine ADF
     basis
       core Large
       type DZP
     end
     scf
       converge 1.0e-8
     end
     symmetry NOSYM
     title Principal layer
     xc
       lda SCF VWN
     end
   EndEngine
   eor

   # The bulk contact geometry consists of three principal layers:

   AMS_JOBNAME=bulk $AMSBIN/ams <<eor
   System
     atoms
        Al      -15.730000    0.000000    0.000000 adf.f=left
        Al      -12.870000    0.000000    0.000000 adf.f=left
        Al      -10.010000    0.000000    0.000000 adf.f=left
        Al       -7.150000    0.000000    0.000000 adf.f=left
        Al       -4.290000    0.000000    0.000000 adf.f=center
        Al       -1.430000    0.000000    0.000000 adf.f=center
        Al        1.430000    0.000000    0.000000 adf.f=center
        Al        4.290000    0.000000    0.000000 adf.f=center
        Al        7.150000    0.000000    0.000000 adf.f=right
        Al       10.010000    0.000000    0.000000 adf.f=right
        Al       12.870000    0.000000    0.000000 adf.f=right
        Al       15.730000    0.000000    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
     scf
       accelerationmethod LISTi
       converge 1.0e-10
     end
     symmetry NOSYM
     title Bulk
     xc
       lda SCF VWN
     end
   EndEngine
   eor


   # Notice that we have increased the number of SCF iterations. The combination of
   # SYMMETRY NOSYM with a 1D chain of metal atoms generally leads to convergence
   # problems. This is the main reason why the principal layer consists of only
   # four atoms. Fortunately, for larger 3D contacts, the convergence is generally
   # better.

   # From the bulk TAPE21 file green can calculate the self-energies of the left
   # and right contacts. As discussed in the introduction, the self-energy of the
   # left contact needs the center and right fragments of the bulk calculation, and
   # the self-energy of the right contact needs the center and left fragments.
   # Since we need a self-energy matrix for every energy for which we want to
   # calculate the DOS and transmission, already here we have to specify the energy
   # range. We take 1000 points between -0.4 and 0 Hartree.

   $AMSBIN/green <<eor
   SURFACE bulk.results/adf.rkf
       FRAGMENTS center right
   END
   EPS -0.4 0 1000
   ETA 1e-6
   eor

   mv SURFACE left.kf

   $AMSBIN/green <<eor
   SURFACE bulk.results/adf.rkf
       FRAGMENTS center left
   END
   EPS -0.4 0 1000
   ETA 1e-6
   eor

   mv SURFACE right.kf

   # Since we want to calculate the DOS and transmission of bare aluminum, we can
   # reuse the bulk.t21 file for the extended molecule. We couple the left self-
   # energy to the 'left' fragment and the right self-energy to the 'right'
   # fragment in bulk.t21. Since we performed restricted ADF calculations, there is
   # no difference between spin-A and spin-B and we can omit spin-B from the
   # calculation.

   $AMSBIN/green <<eor
   DOS bulk.results/adf.rkf
   TRANS bulk.results/adf.rkf
   EPS -0.4 0 1000
   ETA 1e-6
   LEFT left.kf
       FRAGMENT left
   END
   RIGHT right.kf
       FRAGMENT right
   END
   NOSAVE DOS_B, TRANS_B
   eor

   # As would be expected for a 1D system, the DOS shows Van Hove singularities at
   # the band edges. Apart from oscillations due to the finite size of the system
   # in ADF, the transmission only reaches integer values. Between approximately
   # -0.35 and -0.15 Hartree, only the sigma channel contributes to the
   # transmission. Above -0.15 Hartree also the two pi channels start to
   # contribute.

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

