| Charge transport through dGMP, HOMO pinning, charge excess and charging energy. a, Semi-log plots of electronic transmission with respect to Fermi energy at different bias. b, Energy difference between HOMO and electrochemical potential of the right electrode μ R in respect to bias. c, Charge excess Q obtained from Hirshfeld analysis versus bias. d, difference of HOMO energy level at finite and zero bias (circles), and charging energy E C obtained from equation (2) for C ES = 0.13 e/V (solid line). All calculations are performed in TranSIESTA.

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... transmission between the electrodes. For a fixed geometry of the nanopore and CNT electrodes, the coupling is nucleobase dependent, since the nucleobases have different sizes. For example, the dGMP HOMO level, with the help of the in-gap electric field gets to the vicinity of the Fermi level (E F ≡ µ R,L at V=0), ∆ = E F -E HOMO = 60 meV, (see Fig. 3a, top panel) and the transport through the molecular state dominates over coupling-induced broadening. However, for positive polarity, the dGMP HOMO follows the electrochemical potential µ R , i.e. keeps the energy distance to µ R almost constant ...

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... of the applied bias (see Fig. 3a), hence the molecular level will not contribute to transport as would be expected from the widely used zero-bias limit transport theory í µí±‡(í µí°¸, í µí±‰) ≈ í µí±‡(í µí°¸, 0). This effect, illustrated in Fig. 3a middle and lower panels, is shown in Fig. 3b for a range of applied biases. Consequently, HOMO is swept through the ...

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... of the applied bias (see Fig. 3a), hence the molecular level will not contribute to transport as would be expected from the widely used zero-bias limit transport theory í µí±‡(í µí°¸, í µí±‰) ≈ í µí±‡(í µí°¸, 0). This effect, illustrated in Fig. 3a middle and lower panels, is shown in Fig. 3b for a range of applied biases. Consequently, HOMO is swept through the "integration window" (marked yellow in Fig. 3a), with applied bias. This bias-polarity-triggered on-off switching of the HOMO-transport-channel results in strong rectification ...

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... of the applied bias (see Fig. 3a), hence the molecular level will not contribute to transport as would be expected from the widely used zero-bias limit transport theory í µí±‡(í µí°¸, í µí±‰) ≈ í µí±‡(í µí°¸, 0). This effect, illustrated in Fig. 3a middle and lower panels, is shown in Fig. 3b for a range of applied biases. Consequently, HOMO is swept through the "integration window" (marked yellow in Fig. 3a), with applied bias. This bias-polarity-triggered on-off switching of the HOMO-transport-channel results in strong rectification ...

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... level will not contribute to transport as would be expected from the widely used zero-bias limit transport theory í µí±‡(í µí°¸, í µí±‰) ≈ í µí±‡(í µí°¸, 0). This effect, illustrated in Fig. 3a middle and lower panels, is shown in Fig. 3b for a range of applied biases. Consequently, HOMO is swept through the "integration window" (marked yellow in Fig. 3a), with applied bias. This bias-polarity-triggered on-off switching of the HOMO-transport-channel results in strong rectification ...

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... explore the physics of the HOMO pinning to µ R , we employ again Hirshfeld's population analysis, calculating bias dependence of the charge excess Q on a nucleotide. We find that finite charge excess resides on the nucleotide for all bias levels (see Fig. 3c). This charge appears as a result of charge redistribution between the molecule and electrodes, while the system remains electroneutral. Note that the considered system is not in the weak coupling (quantum dot) regime and that the electronic wave function is spatially distributed both on the nucleotide and electrode atoms, resulting in ...

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... e is the elementary charge, q=Q(V)-Q(V=0), Q(V) is the charge excess at the nucleotide and C ES is the electrostatic capacitance across the system. In our model the charging energy is correlated with the shift of the E HOMO with field in respect to the zero-bias position. Fitting E C =E HOMO (V)-E HOMO (V=0) gives C ES = 0.13 e/V (Fig. 3d). This implies that charging shifts the energy level with respect to E F 42,43 . Even weak charging of ~0.1 e for dGMP at 1.6 V shifts HOMO by 800 meV (see Fig. 3c and d). We emphasize that HOMO shifting with E F by over 1 eV cannot be due to hydrogen bonding that has energy limited to about 300 meV, instead the dominant mechanism is ...

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... In our model the charging energy is correlated with the shift of the E HOMO with field in respect to the zero-bias position. Fitting E C =E HOMO (V)-E HOMO (V=0) gives C ES = 0.13 e/V (Fig. 3d). This implies that charging shifts the energy level with respect to E F 42,43 . Even weak charging of ~0.1 e for dGMP at 1.6 V shifts HOMO by 800 meV (see Fig. 3c and d). We emphasize that HOMO shifting with E F by over 1 eV cannot be due to hydrogen bonding that has energy limited to about 300 meV, instead the dominant mechanism is charging of the nucleotide. Consequently, the lowering of the energy level of the molecule with respect to E F keeps the energy difference to µ R constant and bias ...

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... 1 eV cannot be due to hydrogen bonding that has energy limited to about 300 meV, instead the dominant mechanism is charging of the nucleotide. Consequently, the lowering of the energy level of the molecule with respect to E F keeps the energy difference to µ R constant and bias independent, mimicking a "pinning" to the electrochemical potential (Fig. 3b). To explore the origin of molecular charging, we calculate the electrostatic potential energy profile across the gap with a molecule. We will show the relation between charging-induced HOMO pinning and bias-dependent changes in potential energy profile on the example of dAMP. The situation is more subtle for smaller nucleotides (dAMP, ...

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... In our notation (Fig. 1), for dGMP negligible current flows when the electrode facing the phosphosugar group is at a lower potential than its counterpart, while a much larger current flows under opposite bias. This rectification occurs even at small bias. For example, at 100mV, the current is fifty times larger for negative than for positive bias (Fig. ...

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... transmission between the electrodes. For a fixed geometry of the nanopore and CNT electrodes, the coupling is nucleobase dependent, since the nucleobases have different sizes. For example, the dGMP HOMO level, with the help of the in-gap electric field gets to the vicinity of the Fermi level (E F ≡ µ R,L at V=0), ∆ = E F -E HOMO = 60 meV, (see Fig. 3a, top panel) and the transport through the molecular state dominates over coupling-induced broadening. However, for positive polarity, the dGMP HOMO follows the electrochemical potential µ R , i.e. keeps the energy distance to µ R almost constant ...

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... of the applied bias (see Fig. 3a), hence the molecular level will not contribute to transport as would be expected from the widely used zero-bias limit transport theory í µí±‡(í µí°¸, í µí±‰) ≈ í µí±‡(í µí°¸, 0). This effect, illustrated in Fig. 3a middle and lower panels, is shown in Fig. 3b for a range of applied biases. Consequently, HOMO is swept through the ...

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... of the applied bias (see Fig. 3a), hence the molecular level will not contribute to transport as would be expected from the widely used zero-bias limit transport theory í µí±‡(í µí°¸, í µí±‰) ≈ í µí±‡(í µí°¸, 0). This effect, illustrated in Fig. 3a middle and lower panels, is shown in Fig. 3b for a range of applied biases. Consequently, HOMO is swept through the "integration window" (marked yellow in Fig. 3a), with applied bias. This bias-polarity-triggered on-off switching of the HOMO-transport-channel results in strong rectification ...

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... of the applied bias (see Fig. 3a), hence the molecular level will not contribute to transport as would be expected from the widely used zero-bias limit transport theory í µí±‡(í µí°¸, í µí±‰) ≈ í µí±‡(í µí°¸, 0). This effect, illustrated in Fig. 3a middle and lower panels, is shown in Fig. 3b for a range of applied biases. Consequently, HOMO is swept through the "integration window" (marked yellow in Fig. 3a), with applied bias. This bias-polarity-triggered on-off switching of the HOMO-transport-channel results in strong rectification ...

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... level will not contribute to transport as would be expected from the widely used zero-bias limit transport theory í µí±‡(í µí°¸, í µí±‰) ≈ í µí±‡(í µí°¸, 0). This effect, illustrated in Fig. 3a middle and lower panels, is shown in Fig. 3b for a range of applied biases. Consequently, HOMO is swept through the "integration window" (marked yellow in Fig. 3a), with applied bias. This bias-polarity-triggered on-off switching of the HOMO-transport-channel results in strong rectification ...

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... explore the physics of the HOMO pinning to µ R , we employ again Hirshfeld's population analysis, calculating bias dependence of the charge excess Q on a nucleotide. We find that finite charge excess resides on the nucleotide for all bias levels (see Fig. 3c). This charge appears as a result of charge redistribution between the molecule and electrodes, while the system remains electroneutral. Note that the considered system is not in the weak coupling (quantum dot) regime and that the electronic wave function is spatially distributed both on the nucleotide and electrode atoms, resulting in ...

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... e is the elementary charge, q=Q(V)-Q(V=0), Q(V) is the charge excess at the nucleotide and C ES is the electrostatic capacitance across the system. In our model the charging energy is correlated with the shift of the E HOMO with field in respect to the zero-bias position. Fitting E C =E HOMO (V)-E HOMO (V=0) gives C ES = 0.13 e/V (Fig. 3d). This implies that charging shifts the energy level with respect to E F 42,43 . Even weak charging of ~0.1 e for dGMP at 1.6 V shifts HOMO by 800 meV (see Fig. 3c and d). We emphasize that HOMO shifting with E F by over 1 eV cannot be due to hydrogen bonding that has energy limited to about 300 meV, instead the dominant mechanism is ...

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... In our model the charging energy is correlated with the shift of the E HOMO with field in respect to the zero-bias position. Fitting E C =E HOMO (V)-E HOMO (V=0) gives C ES = 0.13 e/V (Fig. 3d). This implies that charging shifts the energy level with respect to E F 42,43 . Even weak charging of ~0.1 e for dGMP at 1.6 V shifts HOMO by 800 meV (see Fig. 3c and d). We emphasize that HOMO shifting with E F by over 1 eV cannot be due to hydrogen bonding that has energy limited to about 300 meV, instead the dominant mechanism is charging of the nucleotide. Consequently, the lowering of the energy level of the molecule with respect to E F keeps the energy difference to µ R constant and bias ...

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... 1 eV cannot be due to hydrogen bonding that has energy limited to about 300 meV, instead the dominant mechanism is charging of the nucleotide. Consequently, the lowering of the energy level of the molecule with respect to E F keeps the energy difference to µ R constant and bias independent, mimicking a "pinning" to the electrochemical potential (Fig. 3b). To explore the origin of molecular charging, we calculate the electrostatic potential energy profile across the gap with a molecule. We will show the relation between charging-induced HOMO pinning and bias-dependent changes in potential energy profile on the example of dAMP. The situation is more subtle for smaller nucleotides (dAMP, ...

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... In our notation (Fig. 1), for dGMP negligible current flows when the electrode facing the phosphosugar group is at a lower potential than its counterpart, while a much larger current flows under opposite bias. This rectification occurs even at small bias. For example, at 100mV, the current is fifty times larger for negative than for positive bias (Fig. ...