  If quantum interference patterns in the hearts of polycyclic aromatic
hydrocarbons (PAHs) could be isolated and manipulated, then a significant step
towards realizing the potential of single-molecule electronics would be
achieved. Here we demonstrate experimentally and theoretically that a simple,
parameter-free, analytic theory of interference patterns evaluated at the
mid-point of the HOMO-LUMO gap (referred to as M-functions) correctly predicts
conductance ratios of molecules with pyrene, naphthalene, anthracene,
anthanthrene or azulene hearts. M-functions provide new design strategies for
identifying molecules with phase-coherent logic functions and enhancing the
sensitivity of molecular-scale interferometers.
