Example: DOS and transmission: Aluminium¶

#!/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"