Destructive Quantum Interference in Bicyclic Conjugated Hydrocarbons

We theoretically study coherent transport of charge carriers in molecular conductors based on bicyclic conjugated hydrocarbons. In the case of electrodes attached to the same cycle, within the framework of the Huckel model (the tight-binding model) without taking into account the electron-electron interaction, an analytical expression for the numerator of the transmission coefficient is derived, which zeroes determine energies of antiresonances. Analysis of this expression allowed us to formulate a relatively simple and clear rule for determining the presence/absence of destructive quantum interference near the Fermi energy, which, in essence, comes down to counting the number of atoms in the cycles and their mutual arrangement, as well as their arrangement relative to the electrodes. In particular, the proposed model correctly agrees with the results of numerical simulation and experiment for the azulene molecule, which did not fit into the previously proposed similar schematic rules.