Chemistry Reference
In-Depth Information
Figure 16
Schematic representation of a benzene-1,4-di-thiol molecule between two
gold contacts. The molecule plus gold pyramids (55 atoms each) constitute the
extended
molecule
as used in the DFT calculations for the Landauer approach.
Electron Transport
Electron transport through single molecules may become a key compo-
nent of future nanotechnology.
359
Present theoretical formulations rely on
ground-state density functionals to describe the stationary nonequilibrium
current-carrying state,
360
but suggestions have been made to consider this as
a time-dependent problem
361-364
and use TD(C)DFT for a full description of
the situation. Imagine the scenario of Figure 16 where a conducting molecule
is sandwiched between two contacts that are connected to semi-infinite leads.
The Landauer formula for the current is
ð
1
1
p
I
¼
dET
ð
E
Þ½
f
L
ð
E
Þ
f
R
ð
E
Þ
½
65
1
where
T
is
the Fermi distribution function for the left/right lead. The transmission proba-
bility of the system can be written using nonequilibrium Green's functions
(NEGF). Ground-state DFT is used to find the KS orbitals and energies of
the extended molecule and also used to find the self-energies of the leads.
These orbitals and energies are then fed into the NEGF model to determine
T
ð
E
Þ
is the transmission probability for a given energy and
f
L
=
R
ð
E
Þ
and hence the current.
The NEGF scheme has had a number of successes, most notably for
atomic-scale point contacts and metallic wires. Generally, it does well for
systems where the conductance is high, but it was found that the conductance
is overestimated by 1-3 orders of magnitude for molecular wires.
Various explanations for this overestimation and the problems with DFT
combined with NEGF in general have been suggested. First, the use of the KS
ð
E
Þ
