Back of the Envelope Selection Rule for Molecular Transmission: A Curly Arrow Approach

A new selection rule for transmission under small voltage for molecular electronic devices consisting of alternant hydrocarbons is established, based on curly arrow drawings of the displacement of electrons through the conjugated system of the molecule. If the displacement of electrons from one contact atom to the other can be drawn, transmission is possible. If not, then no transmission will take place. This simple, back of the envelope ansatz allows determination of quantum interferences for a wide range of experimentally studied molecules (linear polyenes, benzenoids, cross-conjugated molecules, ...) avoiding any calculation. This new selection rule bridges the conceptual gap between traditional reactivity theory and molecular electronics.