  We consider electrical transport through single molecules coupled to metal
electrodes via tunneling barriers. Approximating the molecule by the Anderson
impurity model as the simplest model which includes Coulomb charging effects,
we extend the ``orthodox'' theory to expand current and shot noise
systematically order by order in the tunnel couplings. In particular, we show
that a combined measurement of current and shot noise reveals detailed
information of the system even in the weak-coupling limit, such as the ratio of
the tunnel-coupling strengths of the molecule to the left and right electrode,
and the presence of the Coulomb charging energy. Our analysis holds for
single-level quantum dots as well.
