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2 (as measured by AFM, e.g., see ref 20) there are ∼5000 ± 1000 molecules in these junctions. This 20% error is much smaller than the variation in the current at low bias and low temperature (see black error bar on the bottom right of Figure 3). As for the isolated molecule junctions: the variation in currents is ∼5 (see red error bar in Figure 3), and hence we conclude that the number of bridging molecules in these junctions is small and very close to the single molecule limit. Due to the sudden and statistical nature of the method used to fabricate the latter junctions (instantaneous eruption to form a gap in the gold wire), it is reasonable to assume that any bridging molecules cannot be organized and that they behave independently. The larger variance in the in-wire currents is a result of two contributions, (i) The exact number of molecules in each junction is not known, (ii) A random distribution of the dihedral angle, θ, between adjacent phenyl rings in each molecule is also expected. It has been theoretically shown that by changing the value of θ for one phenyl ring from 0 to π/2, the electronic coupling through the molecule can be reduced by a factor of ∼8 (see for example Newton, M. D. Int. J. Quantum Chem. 2000, 77, 255). In contrast, an isolated molecule is expected to be coplanar at 10 K, as no local energetic minimum at θ≠0 is expected for this molecule (see ref 28). The results and errors in Figure 2 are based on five junctions of each type.
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24
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0034607434
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This value is low considering that the theoretical HOMO-LUMO gap of molecule 1 is ∼3.0 eV (see Seminario, J. M.; Zacarias, A. G.; Tour, J. M. J. Am. Chem. Soc. 2000, 122, 3015). However, vibrational coupling is not included in these estimations, and so the barrier could be very different once the molecule is "virtually" charged, see ref 24 for details. The change in barrier height should be in the order of the reorganization energy. While no specific calculation of this property for molecule 1 is currently available, we note that it has been suggested that the HOMO-LUMO gap in this molecule is decreased to ∼1.0 eV when charged by 1 electron (see Seminario, J. M.; Zacarias, A. G.; Tour, J. M. J. Am. Chem. Soc. 2000, 122, 3015). Image charge also affects the size of the gap. Recently it has been shown to decrease the gap of a related molecule from the theoretically expected value of ∼2.5 eV to experimentally measured value of ∼200 meV (see Kubatkin, S.; Danilov, A.; Hjort, M.; Cornil, J.; Breda, J.; Stuhr-Hansen, N.; Hedegard, P.; Bjornholm, T. Nature 2003, 425, 698).
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0034607434
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This value is low considering that the theoretical HOMO-LUMO gap of molecule 1 is ∼3.0 eV (see Seminario, J. M.; Zacarias, A. G.; Tour, J. M. J. Am. Chem. Soc. 2000, 122, 3015). However, vibrational coupling is not included in these estimations, and so the barrier could be very different once the molecule is "virtually" charged, see ref 24 for details. The change in barrier height should be in the order of the reorganization energy. While no specific calculation of this property for molecule 1 is currently available, we note that it has been suggested that the HOMO-LUMO gap in this molecule is decreased to ∼1.0 eV when charged by 1 electron (see Seminario, J. M.; Zacarias, A. G.; Tour, J. M. J. Am. Chem. Soc. 2000, 122, 3015). Image charge also affects the size of the gap. Recently it has been shown to decrease the gap of a related molecule from the theoretically expected value of ∼2.5 eV to experimentally measured value of ∼200 meV (see Kubatkin, S.; Danilov, A.; Hjort, M.; Cornil, J.; Breda, J.; Stuhr-Hansen, N.; Hedegard, P.; Bjornholm, T. Nature 2003, 425, 698).
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0142183388
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This value is low considering that the theoretical HOMO-LUMO gap of molecule 1 is ∼3.0 eV (see Seminario, J. M.; Zacarias, A. G.; Tour, J. M. J. Am. Chem. Soc. 2000, 122, 3015). However, vibrational coupling is not included in these estimations, and so the barrier could be very different once the molecule is "virtually" charged, see ref 24 for details. The change in barrier height should be in the order of the reorganization energy. While no specific calculation of this property for molecule 1 is currently available, we note that it has been suggested that the HOMO-LUMO gap in this molecule is decreased to ∼1.0 eV when charged by 1 electron (see Seminario, J. M.; Zacarias, A. G.; Tour, J. M. J. Am. Chem. Soc. 2000, 122, 3015). Image charge also affects the size of the gap. Recently it has been shown to decrease the gap of a related molecule from the theoretically expected value of ∼2.5 eV to experimentally measured value of ∼200 meV (see Kubatkin, S.; Danilov, A.; Hjort, M.; Cornil, J.; Breda, J.; Stuhr-Hansen, N.; Hedegard, P.; Bjornholm, T. Nature 2003, 425, 698).
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When the energy of the injected charge into a molecule is within few kT from a resonance level, there is no clear distinction between transmission in-resonance and in off-resonance. We artificially make such a distinction in order to simplify the discussion and to explain various heat dissipation mechanisms.
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