Formalism, analytical model, and a priori Green’s-function-based calculations of the current–voltage characteristics of molecular wires

Various Green’s-function-based formalisms which express the current I as a function of applied voltage V for an electrode–molecule–electrode assembly are compared and contrasted. The analytical solution for conduction through a Hückel (tight binding) chain molecule is examined and only one of these formalisms is shown to predict the known conductivity of a one-dimensional metallic wire. Also, from this solution we extract the counter-intuitive result that the imaginary component of the self-energy produces a shift in the voltage at which molecular resonances occur, and complete analytical descriptions are provided of the conductivity through one-atom and two-atom bridges. A method is presented by which a priori calculations could be performed, and this is examined using extended-Hückel calculations for two gold electrodes spanned by the dithioquinone dianion. A key feature of this is the use of known bulk-electrode properties to model the electrode surface rather than the variety of more approximate schemes which are in current use. These other schemes are shown to be qualitatively realistic but not sufficiently reliable for use in quantitative calculations. We show that in such calculations it is very important to obtain accurate estimates of both the molecule–electrode coupling strength and the location of the electrode’s Fermi energies with respect to the molecular state energies.