  Using benzene sandwiched between two Au leads as a model system, we
investigate from first principles the change in molecular conductance caused by
different atomic structures around the metal-molecule contact. Our motivation
is the variable situations that may arise in break junction experiments; our
approach is a combined density functional theory and Green function technique.
We focus on effects caused by (1) the presence of an additional Au atom at the
contact and (2) possible changes in the molecule-lead separation. The effects
of contact atomic relaxation and two different lead orientations are fully
considered. We find that the presence of an additional Au atom at each of the
two contacts will increase the equilibrium conductance by up to two orders of
magnitude regardless of either the lead orientation or different group-VI
anchoring atoms. This is due to a LUMO-like resonance peak near the Fermi
energy. In the non-equilibrium properties, the resonance peak manifests itself
in a large negative differential conductance. We find that the dependence of
the equilibrium conductance on the molecule-lead separation can be quite
subtle: either very weak or very strong depending on the separation regime.
