For transmission of electrons through a π system, when the Landauer theory of molecular conductance is viewed from a molecular orbital (MO) perspective, there obtains a simple perturbation theoretic dependence, due to Yoshizawa and Tada, on a) the product of the orbital coefficients at the sites of electrode attachment, and b) the MO energies. The frontier orbitals consistently and simply indicate high or low transmission, even if other orbitals may contribute. This formalism, with its consequent reinforcement and/or interference of conductance, accounts for the (previously explained) difference in direct vs. cross conjugated transmission across an ethylene, as well as the comparative ON/OFF ratios in the experimentally investigated dimethyldihydropyrene and dithienylethene-type single-molecule switches. A strong dependence of the conductance on the site of attachment of the electrodes in a π system is an immediate extrapolation; the theory then predicts that for some specified sites the switching behavior will be inverted; i.e. the "open" molecular form of the switch will be more conductive. The phase and amplitude of the frontier molecular orbitals at the sites that are connected to electrodes play an essential role in determining transmission of electrons through a π system. When applied to two diarylethene switches, theory then predicts that for some specified sites the switching behavior will be inverted; that is, the "open" molecular form of the switch will be more conductive.
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