  Starting from exact eigenstates for a symmetric ring, we derive a low-energy
effective generalized Anderson Hamiltonian which contains two spin doublets
with opposite momenta and a singlet for the neutral molecule. For benzene, the
singlet (doublets) represent the ground state of the neutral (singly charged)
molecule. We calculate the non-equilibrium conductance through a benzene
molecule, doped with one electron or a hole (i.e. in the Kondo regime), and
connected to two conducting leads at different positions. We solve the problem
using the Keldysh formalism and the non-crossing approximation (NCA). When the
leads are connected in the \emph{para} position (at 180 degrees), the model is
equivalent to the ordinary impurity Anderson model and its known properties are
recovered. For other positions, there is a partial destructive interference in
the cotunneling processes involving the two doublets and as a consequence, the
Kondo temperature and the height and width of the central peak (for bias
voltage $V_b$ near zero) of the differential conductance $G=dI/dV_b$ (where $I$
is the current) are reduced. In addition, two peaks at finite $V_b$ appear. We
study the position of these peaks, the temperature dependence of $G$ and the
spectral densities. Our formalism can also be applied to carbon nanotube
quantum dots with intervalley mixing.
