  Coherent electronic transport through individual molecules is crucially
sensitive to quantum interference. Using exact diagonalization techniques, we
investigate the zero-bias and zero-temperature conductance through
$\pi$-conjugated annulene molecules (modeled by the Pariser-Parr-Pople and
Hubbard Hamiltonians) weakly coupled to two leads. We analyze the conductance
for different source-drain configurations, finding an important reduction for
certain transmission channels and for particular geometries as a consequence of
destructive quantum interference between states with definite momenta. When
translational symmetry is broken by an external perturbation we find an abrupt
increase of the conductance through those channels. Previous studies
concentrated on the effect at the Fermi energy, where this effect is very
small. By analysing the effect of symmetry breaking on the main transmission
channels we find a much larger response thus leading to the possibility of a
larger switching of the conductance through single molecules.
