In molecular electronics, metallic contacts are made at two ends of the molecule, and electronic current is expected to be carried by electrons tunneling from the metal with energies in the band gap region. The branch point plays an important role in the analysis of the electron transport properties. The branch point energy, E bp , is an estimate for the lineup of the metal Fermi level (E F ) with the molecular levels, and β bp ) β(E bp ) provides the tunneling decay rate. We now use this information to obtain a simple estimate of the conductance of a molecule. According to Landauer theory, 51 when E F crosses a propagating molecular state (such as the highest occupied molecular orbital) in the real k region of the complex band structure, the low-voltage conductance of the molecule will be approximately equal to the quantum of conductance, G 0 ≈ 77 µS. However, E F will lie in the band gap, and the conductance, g, will be reduced from its value of G 0 by the approximate factor e -β bp L , where β bp is the β value of the most penetrating gap state at the Fermi level, E F , and L is the length of the molecule. Using these approxima- tions, the estimated conductance is given by g ≈ G 0 e -β bp L
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