| With the ability to isolate individual molecules experimentally, a myriad of phenomena associated with their conductance have been observed. Theoretical approaches have determined that the contact geometry and Fermi level positioning wield tremendous influence in the behavior of the metal-molecule-metal system and that these factors require rigorous first-principles calculations in order to be determined. The first-principles theories, in turn, have their own 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 dissociations 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 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 enhanced xylyldithiol conductance with stretching and of the unexpected higher conductance of a four membered oligomer over its three membered counterpart. |
