Complexities of the Molecular Conductance Problem
New conductance phenomena observed in isolated individual molecules require theoretical approaches that accurately represent contact geometry and Fermi-level positioning since these factors wield tremendous influence in the behavior of the metal–molecule–metal system. Although this argues that rigorous first-principles calculations must be performed, the various approaches each have significant drawbacks. The linearly independent plane wave basis ensures an accurate potential across the system, but this basis produces an intractably large rank Hamiltonian, and a local orbital basis must then be used. Density functional theory approaches allow the calculation of a Hamiltonian representing a hybrid of a metal and an unsaturated organic compound. However, bandgaps are underestimated, and bond lengths and dissociation energies are incorrectly calculated in this scheme. Using a combination of approaches, including complex bandstructure, density of states calculations, and a highly efficient scattering matrix method, insights about the nature of molecular conduction are drawn in this chapter. In addition, calculations over suites of Hamiltonians—for molecules in both a stretched configuration and at several positions within a vibrational mode—allow the determination of trends despite the known inaccuracies in the calculation. Results investigate the phenomena of conductance changes with stretching and of the unexpected higher conductance of a four-membered oligomer over its three-membered counterpart.