  The electronic conductance of a benzene molecule connected to gold electrodes
via thiol, thiolate, and amino anchoring groups is calculated using
nonequilibrium Green functions in combination with the fully selfconsistent GW
approximation. The calculated conductance of benzenedithiol and benzenediamine
is five times lower than predicted by standard density functional theory (DFT)
in very good agreement with experiments. In contrast, the widely studied
benzenedithiolate structure is found to have a significantly higher conductance
due to the unsaturated sulfur bonds. These findings suggest that more complex
gold/thiolate structures where the thiolate anchors are chemically passivated
by Au adatoms are responsible for the measured conductance. Analysis of the
energy level alignment obtained with DFT, Hartree-Fock and GW reveals the
importance of self-interaction corrections (exchange) on the molecule and
dynamical screening at the metal-molecule interface. The main effect of the GW
self-energy is to renormalize the level positions, however, its influence on
the shape of molecular resonances also affects the conductance.
Non-selfconsistent G0W0 calculations, starting from either DFT or Hartree-Fock,
yield conductance values within 50% of the selfconsistent GW results.
