Chemistry Reference
In-Depth Information
orbitals and energy levels has no theoretical basis. The KS orbitals are those
orbitals for the noninteracting problem that reproduce the correct ground-
state density. They should not be thought of as the true single-particle excita-
tions of the true system. However, as we have seen, the KS orbitals often
reproduce the single-particle excitations qualitatively, so it is not clear to
what extent their use in NEGF affects the conductance. Second, the geometry
of the conducting molecules was also suggested as a source of error. DFT first
relaxes the molecule to find its geometry, whereas in the experiments the mole-
cule may be subject to stresses that could rotate parts of it and/or squash parts
together. Calculations
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have shown that the geometry corrections are small.
Finally, the approximation that the nonequilibrium XC functional is the same
as for the static case has been suggested as a major source of error. In fact,
neither the HK theorem nor the RG theorem are strictly valid for current-
carrying systems in homogeneous electric fields. A dynamical correction to
the LDA functional for the static case has been derived using the Vignale-
Kohn functional TDCDFT, but these dynamical corrections were found to
yield only small improvements to ALDA.
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In a similar vein, the lack of the derivative discontinuity and the
existence of self-interaction errors (SIE) in the approximations to the XC
functional may be the source of this overestimation problem.
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In Hartree-
Fock calculations (and also in OEP calculations
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with EXX, exact exchange)
that have no SIE, the conductances are found to be much lower.
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Calcula-
tions have also been done on a simple model
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containing a KS potential with
a derivative discontinuity. The current-voltage (I-V) curves for this model sys-
tem are significantly different from those predicted by LDA. The discrepancy
was found to be most severe when the molecule was not coupled strongly to
the leads, but goes away when it is bonded covalently. Recent OEP calcula-
tions of the transmission along a chain consisting of H atoms verify these
features.
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Quantitative results can be found for molecular devices despite these
problems. By examining the bias at which a KS energy level gets moved
between the two chemical potentials of the leads (from Eq. [65] this gives a
peak in the conductance), one can predict
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positions of these peaks qualita-
tively, although the magnitude of the conductance may be incorrect by orders
of magnitude.
Because electron transport is a nonequilibrium process, we anticipate
that static DFT will not be able to accurately predict some features of electron
transport. A number of methods have been developed that allow one to use
TDDFT for these purposes. For example, Kurth et al.
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present a practical
scheme using TDDFT to calculate current. The basic idea is to ''pump'' the
system into a nonequilibrium initial state by some external bias and then allow
the KS orbitals to evolve in time via the TDKS equations. The RG theorem
then allows one to extract the longitudinal current using the continuity
equation. Using transparent boundary conditions that solve problems with
