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14 The lattice structure of Au clusters was chosen fee with a lattice constant fixed to the experimental value 4.08 Å of bulk gold.
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For an analytical derivation of the method, in the content of carbon nanotubes, see: Nemec, N.; Tomanek, D.; Cuniberti, G. arXiv: 0711.1088v1.
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47349109142
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We describe the interaction between the extended molecule and the rest of semi-infinite electrodes via an efficient approximation for the self-energy, represented by a local leakage function, Σ(r, r′) ≈ iηδ(r - r′). To improve convergence with the number of Au contact atoms, we use chaotic cavities produced by adding a few adatoms to otherwise symmetric Au pyramids. The value of the level broadening η can then be varied by 1 order of magnitude (around ∼0.1 hartree in the present calculations) leaving the results for the transmission unchanged within a few percent.
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We describe the interaction between the "extended molecule" and the rest of semi-infinite electrodes via an efficient approximation for the self-energy, represented by a local leakage function, Σ(r, r′) ≈ iηδ(r - r′). To improve convergence with the number of Au contact atoms, we use chaotic cavities produced by adding a few adatoms to otherwise symmetric Au pyramids. The value of the level broadening η can then be varied by 1 order of magnitude (around ∼0.1 hartree in the present calculations) leaving the results for the transmission unchanged within a few percent.
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We mention that, in the case when nitrogen couples at atop or hollow position to a planar Au surface, we have N c ≈ 5, 8 not shown in Figure 2, Such contact geometries were considered by many authors. 19-21 Our calculation for atop coupling shows that leakage rates remain largely invariant, and ΓL ≃ ΓR ≃ Γ as one expects for strong coupling. We find a good quantitative agreement with refs 19 and 20. In our opinion, the quantitative mismatch with other authors21 can be attributed at least partly to the limited number of Au atoms included or a relative low amount of k-points accounted for in their calculation setup
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21 can be attributed at least partly to the limited number of Au atoms included or a relative low amount of k-points accounted for in their calculation setup.
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We have to point out that quite generally calculated conductance values should be considered with caution, because the approximative character of the LDA-type functionals (that usually are the only available choice for such calculations) implies modifications in position and width of the LUMO peak in the transmission spectrum. Nevertheless, the overall structure of molecular orbitals is very well described within density function theory (DFT) even when local functionals are employed, ensuring the qualitative validity of our results
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We have to point out that quite generally calculated conductance values should be considered with caution, because the approximative character of the LDA-type functionals (that usually are the only available choice for such calculations) implies modifications in position and width of the LUMO peak in the transmission spectrum. Nevertheless, the overall structure of molecular orbitals is very well described within density function theory (DFT) even when local functionals are employed, ensuring the qualitative validity of our results.
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We used the following parameters to construct cylindrical gates: a radius was chosen around ∼11 au with about ∼200 points forming a uniformly dense grid; to simulate screening effects due to solvent, a Gaussian distribution q(z) ≈ exp, z- z0)2/ 2δ2] of negative point charges was assumed as a function of their position around a center z0 of the redox-active core, which carries the positive charge here z-axis is along the gate, with σ ≃ dN-N/2 ≃ 3.33 au being one-half of the core size
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N-N/2 ≃ 3.33 au being one-half of the core size.
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0037104402
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See, for example: a
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We used Mulliken analysis to find population weights by projecting molecular orbitals (MO) of the extended molecule on the basis functions of all atoms inside the given functional group. The curves in Figure 5 were obtained by summing Lorentzians centered at the MO energies and weighted with the Mulliken population numbers. We have ascertained in test calculations that a moderate rearrangement of point counter-charges (e.g, up to 15% change of the cylindrical gate radius, see ref 24) leaves our results almost invariant: peaks shift typically by no more than 0.1 eV. Because the potential barrier seen by electron is around ∼3.0 eV, such small shifts could lead to minor changes (up to ∼1.5% only) in the tunneling exponent β 2n
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2n.
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R
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Köntopp, M.1
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2/h, where DFT-based transport calculations can be quantitatively very accurate.
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2/h, where DFT-based transport calculations can be quantitatively very accurate.
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