Example: Benzenedithiol junction

Download green_BDT.run

In this example of green, the DOS and transmission of a benzenedithiol molecule between gold electrodes is calculated. The calculation uses the self-energies obtained in the example for the gold electrodes. Note that this is a relatively expensive calculation.

First a fragment of the isolated molecule is constructed:

$ADFBIN/adf << eor
TITLE Benzenedithiol
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
SYMMETRY NOSYM
RELATIVISTIC Scalar ZORA
BASIS
    type DZP
    core Large
    createOutput None
END
XC
    LDA SCF VWN
END
eor

mv TAPE21 molecule.t21

Next the molecule is sandwiched between the electrodes in the configuration of Fig. 2. For this the fragment of the principal layer obtained in the example for the gold electrodes is needed.

../_images/green_molecule.png

Figure 2: Geometry of the extended molecule used in the calculation of a benzenedithiol junction. The molecule is shown in green, while the left and right contact regions are shown in red and blue, respectively. Note that the red region corresponds to the blue surface layer in Figure 1 of the example for the gold electrodes and vice versa.

$ADFBIN/adf << eor
TITLE Benzenedithiol
ATOMS
    Au       -9.911177   -6.662612    0.000000 f=left
    Au       -9.911178   -4.164133   -1.442498 f=left
    Au       -9.911178   -4.164133    1.442498 f=left
    Au       -9.911178   -1.665653   -2.884996 f=left
    Au       -9.911178   -1.665653    0.000000 f=left
    Au       -9.911178   -1.665653    2.884996 f=left
    Au       -9.911178    0.832826   -1.442498 f=left
    Au       -9.911178    0.832826    1.442498 f=left
    Au       -9.911178    3.331306    0.000000 f=left
    Au       -7.555589   -4.996959    0.000000 f=left
    Au       -7.555589   -2.498480   -1.442498 f=left
    Au       -7.555589   -2.498480    1.442498 f=left
    Au       -7.555589    0.000000   -2.884996 f=left
    Au       -7.555589    0.000000    0.000000 f=left
    Au       -7.555589    0.000000    2.884996 f=left
    Au       -7.555589    2.498480   -1.442498 f=left
    Au       -7.555589    2.498480    1.442498 f=left
    Au       -7.555589    4.996959    0.000000 f=left
    Au       -5.200000   -3.331306    0.000000 f=left
    Au       -5.200000   -0.832826   -1.442498 f=left
    Au       -5.200000   -0.832826    1.442498 f=left
    Au       -5.200000    1.665653   -2.884996 f=left
    Au       -5.200000    1.665653    0.000000 f=left
    Au       -5.200000    1.665653    2.884996 f=left
    Au       -5.200000    4.164133   -1.442498 f=left
    Au       -5.200000    4.164133    1.442498 f=left
    Au       -5.200001    6.662612    0.000000 f=left
    C        -1.400000    0.000000    0.000000 f=molecule
    C        -0.700000    0.000000   -1.200000 f=molecule
    C        -0.700000    0.000000    1.200000 f=molecule
    C         0.700000    0.000000   -1.200000 f=molecule
    C         0.700000    0.000000    1.200000 f=molecule
    C         1.400000    0.000000    0.000000 f=molecule
    H        -1.200000    0.000000   -2.200000 f=molecule
    H        -1.200000    0.000000    2.200000 f=molecule
    H         1.200000    0.000000   -2.200000 f=molecule
    H         1.200000    0.000000    2.200000 f=molecule
    S        -3.200000    0.000000    0.000000 f=molecule
    S         3.200000    0.000000    0.000000 f=molecule
    Au        5.200001   -6.662612    0.000000 f=right
    Au        5.200000   -4.164133   -1.442498 f=right
    Au        5.200000   -4.164133    1.442498 f=right
    Au        5.200000   -1.665653   -2.884996 f=right
    Au        5.200000   -1.665653    0.000000 f=right
    Au        5.200000   -1.665653    2.884996 f=right
    Au        5.200000    0.832826   -1.442498 f=right
    Au        5.200000    0.832826    1.442498 f=right
    Au        5.200000    3.331306    0.000000 f=right
    Au        7.555589   -4.996959    0.000000 f=right
    Au        7.555589   -2.498480   -1.442498 f=right
    Au        7.555589   -2.498480    1.442498 f=right
    Au        7.555589    0.000000   -2.884996 f=right
    Au        7.555589    0.000000    0.000000 f=right
    Au        7.555589    0.000000    2.884996 f=right
    Au        7.555589    2.498480   -1.442498 f=right
    Au        7.555589    2.498480    1.442498 f=right
    Au        7.555589    4.996959    0.000000 f=right
    Au        9.911178   -3.331306    0.000000 f=right
    Au        9.911178   -0.832826   -1.442498 f=right
    Au        9.911178   -0.832826    1.442498 f=right
    Au        9.911178    1.665653   -2.884996 f=right
    Au        9.911178    1.665653    0.000000 f=right
    Au        9.911178    1.665653    2.884996 f=right
    Au        9.911178    4.164133   -1.442498 f=right
    Au        9.911178    4.164133    1.442498 f=right
    Au        9.911177    6.662612    0.000000 f=right
END
SYMMETRY NOSYM
RELATIVISTIC Scalar ZORA
FRAGMENTS
    left        layer.t21
    molecule    molecule.t21
    right       layer.t21
END
XC
    LDA SCF VWN
END
eor

mv TAPE21 fock.t21

The DOS and transmission can now be calculated:

$ADFBIN/green << eor
DOS fock.t21
TRANS fock.t21
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

The results are shown in the following figure:

../_images/green_BDT.png

The Fermi energy of the electrodes is -0.2 Hartree (see the example for the gold electrodes). This is just above the HOMO of the molecular junction. Consistent with literature, the HOMO and lower orbitals are combined into a broad peak just below the Fermi energy, while the LUMO is much sharper and situated about 2 eV above the Fermi energy.

The current can be calculated by integrating the transmission around the Fermi energy. At low temperatures this means that the differential conductance is equal to the transmission times the quantum of conductance.