# Example: DOS and transmission: Aluminium¶

Download green_Al.run

#!/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:

$ADFBIN/adf <<eor TITLE Principal layer ATOMS Al -4.290000 0.000000 0.000000 Al -1.430000 0.000000 0.000000 Al 1.430000 0.000000 0.000000 Al 4.290000 0.000000 0.000000 END SYMMETRY NOSYM BASIS Type DZP Core Large CreateOutput None END SCF Converge 1.0e-8 END XC LDA SCF VWN END eor mv TAPE21 layer.t21 # The bulk contact geometry consists of three principal layers:$ADFBIN/adf <<eor
TITLE Bulk
ATOMS
Al      -15.730000    0.000000    0.000000 f=left
Al      -12.870000    0.000000    0.000000 f=left
Al      -10.010000    0.000000    0.000000 f=left
Al       -7.150000    0.000000    0.000000 f=left
Al       -4.290000    0.000000    0.000000 f=center
Al       -1.430000    0.000000    0.000000 f=center
Al        1.430000    0.000000    0.000000 f=center
Al        4.290000    0.000000    0.000000 f=center
Al        7.150000    0.000000    0.000000 f=right
Al       10.010000    0.000000    0.000000 f=right
Al       12.870000    0.000000    0.000000 f=right
Al       15.730000    0.000000    0.000000 f=right
END
SYMMETRY NOSYM
FRAGMENTS
left    layer.t21
center  layer.t21
right   layer.t21
END
XC
LDA SCF VWN
END
SCF
Converge 1.0e-10
AccelerationMethod LISTi
END
eor

mv TAPE21 bulk.t21

# 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.

$ADFBIN/green <<eor SURFACE bulk.t21 FRAGMENTS center right END EPS -0.4 0 1000 ETA 1e-6 eor mv SURFACE left.kf$ADFBIN/green <<eor
SURFACE bulk.t21
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.

DOS bulk.t21
TRANS bulk.t21
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"