Conduction of a molecular junction

In most models of molecular conduction the system is divided into three subregions associated with the two leads and the molecule(s) that bridge them. This division is not unique and different choices can be made according to the chosen calculation strategy. In particular, it is often advantageous to combine the molecular bridge, the molecule-metal bond, and small sections of the leads themselves into a supermolecule that connects between the remaining (still infinite) parts of the leads. In accordance, the Hamiltonian of the overall junction is written as 

Alternatively, one often uses for the bridge a local representation, where the basis n comprises functions that are localized on different bridge segments. 

In most practical applications different basis sets are used, for example, atomic orbitals associated or other wavefunctions localized in the different subsystems. 

The model (17.19) remains the same, except that Hs is written in this non-diagonal representation as 

By the nature of our problem, the molecular subsystem S is a finite system, and we will assume that it can be adequately described by a finite basis n), n = 1,2,. ..,2V. The leads are obviously infinite, at least in the direction of current flow, and consequently the eigenvalue spectra 77/ and /-, constitute continuous sets that are characterized by density of states functions and pr( ), respectively. Below we also use the index k to denote states belonging to either the L or the R leads. 

From the results of Section 9.5.3 and Appendix 9C we can obtain an expression for the conduction of this model system. Indeed, using Eq. (9.139) and noting that the electron flux acquires an additional factor of 2 because of contributions from the two spin populations, we get the unidirectional transmitted flux per unit energy in the form 

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Reed MA, Zhou C, Muller CJ, Burgin TP, Tour JM (1997) Conductance of a molecular junction. Science 278(5336) 252-254... 

The conductance of a molecular junction was measured in 1997.26 As shown in Figure 5.2, two Au wires were covered with SAMs of benzene-1,4-dithiol in THF. The wires were bent until they broke, and the broken ends were brought together in picometer increments... 

Fig. 17.10 A schematic display of molecular conduction. The full line represents the overall conductance of a molecular junction, as expected from Eqs (17.38), (17.25), and (17.30). The thin dotted lines trace individual resonances.

The electric conductance of a molecular junction is calculated by recasting the Keldysh formalism in Liouville space. Dyson equations for non-equilibrium many-body Green functions (NEGF) are derived directly in real (physical) time. The various NEGFs appear naturally in the theory as time-ordered products of superoperators, while the Keldysh forward/backward time loop is avoided. 

The probability matrix plays an important role in many processes in chemical physics. For chemical reactions, the probability of reaction is often limited by tunnelling tlnough a barrier, or by the fonnation of metastable states (resonances) in an intennediate well. Equivalently, the conductivity of a molecular wire is related to the probability of transmission of conduction electrons tlttough the junction region between the wire and the electrodes to which the wire is attached. 

Fig. 17.11 The current (right axis) and conductance (left axis) of a molecular junction plotted against the applied voltage. Each plot shows several sweeps of the potential. The different plots correspond to different junctions prepared by the mechanically controlled break junction technique using gold contacts with the molecule shown, (from H. B. Weber, J. Reichert, F. Weigend, R. Ochs, D. Beckmann, M. Mayor, R. Ahlrichs, and H.v. Lohneysen, Chem. Phys. 281, 113 (2002).)...

G]J (the intrinsic conductance of an isolated molecule could be much higher). The maximum overall conductance of a molecular wire and its junctions to arbitrary metal electrodes is (1/2) Gl (assuming two carriers of opposite spin). 

In a recent development novel nano-cluster based devices enabled to switch the conductivity of a non-junction by changing the oxidation state of a bridging molecule. Some redox-active molecules contain a molecular center where reduction or oxidation can be achieved more or less reversibly supporting quite large currents. A fundamental prerequisite is the overlapping of the electron energy bands of the molecule with those of... 

An expression for the current across a molecular junction is developed by analogy with the description of unimolecular solution phase electron transfer. The conduction is written 1201... 

Tao et al. [32] pioneered a technique based on the formation of single molecular junctions between the tip of an STM and a metal substrate. The method was adapted by other groups, modified and applied to a large number of molecular conductance studies at (electrified) solid/liquid interfaces [33, 113-119]. For details we refer to Sect. 2.3. 

In the following we will present results of a single-junction conductance study with 44-BP under electrochemical potential control, enabling the precise tuning of the molecular orientation, relative to the substrate, upon application of an adjustable gate voltage [290] in a well-controlled environment [86, 302]. 

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