Conductance of molecular wires: Analytical modeling of connection to leads

The on-top and on-hollow connections of a molecule to leads are studied in the context of the single-molecule conductance measured by STM-related techniques. In the framework of the Landauer-Büttiker approach, the lead effects on the electrical properties of metal-molecular heterojunctions are expressed in terms of the spectral density (SD). The exact analytical expression of this quantity is obtained for n-dimensional (n = 1, 2, 3) semi-infinite tight-binding leads. It has been used to examine the SD energy dependence in three and one dimensions. In most realistic cases, SD is shown to be an asymmetric (with respect to the Fermi level) function of energy which is pronouncedly distinctive from the related local density of states (LDOS) on the metal surface. For different models of molecule-to-metal connection, the LDOS on an adsorbed atom, as well as the parent LDOS on a molecular tip-facing atom and respective transmission spectrum (TS) are discussed in detail. The LDOS and TS are exemplified by the p system of 4-aminothiophenol. The approach developed is applicable straightforwardly to a fully analytical description of electrical current through conjugated oligomers with arbitrary length and chemical structure of monomers.