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.
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