588
A. V. Luzanov
many interesting effects are revealed by very simple models such as the tight-binding
(TB) approximation (see review [10]). However, not all results of TB models can be
accepted with certainty even at the qualitative level. One of the issues that require to
be scrutinized more closely is an assumed increase of SMC with increasing size of
the chain-like molecules (usually SME is expected to be exponentially decaying with
length). It is found in the interesting papers [11–13] that for some structural types
TB predicts an increase of SMC with enlarging π -network, and these predictions
are in qualitative agreement with density functional theory (DFT) results. However,
note especially that generally DFT cannot be treated as fully reliable for SMC
because the typically used energy functionals frequently come to underestimating
HOMO-LUMO gaps [14–16]. As recognized in [17], “DFT tends to overestimate
conductances by up to several orders of magnitude”.
Thus, in investigating SMC for large systems we focus on the good-quality
semiempirical models which take into proper account of π -electron interaction
effects. Our previous studies [18, 19] also support use of relatively uncomplicated
π -models which, nonetheless, are beyond the crude TB topological approximation.
Therefore, the main goal of the paper is to elucidate, by using π -electron correlation models, whether it is indeed possible to predict an increase of single-molecule
conductance in long π -conjugated systems.
2 The Used Models
We will follow notations and definitions as in [18, 19]; for general notions and
terminology the reader refers to book [9]. In the ballistic regime, the T = 0 molecular
conductance at the Fermi energy is determined by matrix elements of the one-electron
Green’s function (GF), G, evaluated for a given electronic model. The position of
contacts (electrodes) predetermines which matrix elements of G must be computed.
Within π -electron schemes we deal with a standard basis set {|a} including the
2pπ atomic orbital of each carbon atom of the conjugated molecule in question
(1 ≤ a ≤ N , and N is a number of the atoms). For the given pair (a, b) where a and b
signify contacting carbon atoms, the corresponding molecular conductance g ab can
be estimated, within the conventional Landauer approach, by the relation
g ab /g 0 = a b |G ab |
2
.
(1)
Here g 0 is the quantum conductance unit, G ab = a|G |b is the GF matrix
element, and a and b are broadening parameters expressing approximately
coupling effects between electrodes and respective sites a and b of the molecule
in question.
A. V. Luzanov
many interesting effects are revealed by very simple models such as the tight-binding
(TB) approximation (see review [10]). However, not all results of TB models can be
accepted with certainty even at the qualitative level. One of the issues that require to
be scrutinized more closely is an assumed increase of SMC with increasing size of
the chain-like molecules (usually SME is expected to be exponentially decaying with
length). It is found in the interesting papers [11–13] that for some structural types
TB predicts an increase of SMC with enlarging π -network, and these predictions
are in qualitative agreement with density functional theory (DFT) results. However,
note especially that generally DFT cannot be treated as fully reliable for SMC
because the typically used energy functionals frequently come to underestimating
HOMO-LUMO gaps [14–16]. As recognized in [17], “DFT tends to overestimate
conductances by up to several orders of magnitude”.
Thus, in investigating SMC for large systems we focus on the good-quality
semiempirical models which take into proper account of π -electron interaction
effects. Our previous studies [18, 19] also support use of relatively uncomplicated
π -models which, nonetheless, are beyond the crude TB topological approximation.
Therefore, the main goal of the paper is to elucidate, by using π -electron correlation models, whether it is indeed possible to predict an increase of single-molecule
conductance in long π -conjugated systems.
2 The Used Models
We will follow notations and definitions as in [18, 19]; for general notions and
terminology the reader refers to book [9]. In the ballistic regime, the T = 0 molecular
conductance at the Fermi energy is determined by matrix elements of the one-electron
Green’s function (GF), G, evaluated for a given electronic model. The position of
contacts (electrodes) predetermines which matrix elements of G must be computed.
Within π -electron schemes we deal with a standard basis set {|a} including the
2pπ atomic orbital of each carbon atom of the conjugated molecule in question
(1 ≤ a ≤ N , and N is a number of the atoms). For the given pair (a, b) where a and b
signify contacting carbon atoms, the corresponding molecular conductance g ab can
be estimated, within the conventional Landauer approach, by the relation
g ab /g 0 = a b |G ab |
2
.
(1)
Here g 0 is the quantum conductance unit, G ab = a|G |b is the GF matrix
element, and a and b are broadening parameters expressing approximately
coupling effects between electrodes and respective sites a and b of the molecule
in question.