Ab initio study of electron transport in dry poly(G)-poly(C) $A$-DNA strands

The bias-dependent transport properties of short poly(G)-poly(C) $A$-DNA strands attached to Au electrodes are investigated with first-principles electronic-transport methods. By using the nonequilibrium Green’s function approach combined with self-interaction-corrected density-functional theory, we calculate the fully self-consistent coherent $I\text{−}V$ curve of various double-strand polymeric DNA fragments. We show that electronic wave-function localization, induced either by the native electrical dipole and/or by the electrostatic disorder originating from the first few water solvation layers, drastically suppresses the magnitude of the elastic conductance of $A$-DNA oligonucleotides. We then argue that electron transport through DNA is the result of sequence-specific short-range tunneling across a few bases combined with general diffusive/inelastic processes.

Figure 1

(Color online) Geometric configuration of $A$-DNA both in its free form and when attached to the electrodes: [(a) and (b)] front and side view, respectively, of a 11 base-pair poly(G)-poly(C) $A$-DNA double helix. (c) Two-probe device setup used for transport calculations where the DNA molecule is attached to Au electrodes. Color code: $\text{yellow}=\text{Au}$, $\text{green}=\text{C}$, $\text{red}=\text{O}$, $\text{orange}=\text{P}$, $\text{blue-gray}=\text{N}$, $\text{cyan}=\text{H}$, and $\text{pale-green}=\text{S}$.

Figure 2

(Color online) Density of states projected onto different constituent parts of poly(G)-poly(C) $A$-DNA chains: (left panel) projected DOS for the infinite periodic DNA structure with 11 base pairs in the unit cell; (right panel) projected DOS for a finite 11 base-pair oligomer. The purple vertical line indicates the Fermi level.

Figure 3

(Color online) Projected DOS (top panels) and charge-density distribution (lower panels) for both infinite (left) and finite (right) DNA strands. The projected DOS are displayed over an energy window showing the first Guanine and Cytosine levels around the Fermi level. The arrows and the corresponding numbers mark the various energy levels, whose corresponding charge-density distributions are displayed in the lower panels. Note the delocalized nature of the HO and LU bands of the infinite chain in comparison with the localized states of the finite fragments.

Figure 4

(Color online) DNA electronic structure calculated at various levels of approximation and level alignment between the molecule and the Au electrodes. In the left panel we show the negative of the ionization potential (solid lines) and of the electron affinities (dashed lines) calculated from PBE0-$\Delta \text{SCF}$ and Hartree-Fock for pGpC DNA strands of different lengths. Also included for comparison are the highest occupied and lowest unoccupied eigenvalues from PBE calculations and the Au work function. In the middle panel we present the atom-projected DOS obtained, respectively, from LDA and ASIC calculations for the 11 base-pair DNA molecules attached to Au electrodes with the reference $\text{G}{3}^{\prime }\text{C}{3}^{\prime }\text{G}{5}^{\prime }\text{C}{5}^{\prime }$ geometry. Finally the right panel displays the zero-bias transmission coefficients as calculated with LDA and ASIC for the same system. The Au Fermi level is set to 0 eV.

Figure 5

(Color online) Zero-bias transport properties for an 11 base-pair pGpC in the reference $\text{G}{3}^{\prime }\text{C}{3}^{\prime }\text{G}{5}^{\prime }\text{C}{5}^{\prime }$ geometry. In the top left panel we present the projected density of states. The HOMO and LUMO are indicated by arrows and labeled by 1 and 2, respectively. In the bottom left panel the zero-bias transmission coefficient as a function of energy is presented. In the two right panels we show the charge-density distribution corresponding to the HOMO (top) and to the LUMO (bottom). Note that these are localized, respectively, near the $5^{\prime }$ end of the Guanine stack and near the $5^{\prime }$ end of the Cytosine stack.

Figure 6

(Color online) Zero-bias transport properties for three different bonding geometries of a pGpC 11 base-pairs DNA strand attached to gold. A schematic depicting the geometry of three different molecule-electrode linking configurations is show in the top panels. All the configurations are obtained from the reference $\left(\text{G}{3}^{\prime }\text{C}{3}^{\prime }\text{G}{5}^{\prime }\text{C}{5}^{\prime }\right)$ one, by removing two thiol linkers. The corresponding $T\left(E\right)$ for each geometry are presented in the lower panels. In all the figures the light brown line is the transmission for the reference $\text{G}{3}^{\prime }\text{C}{3}^{\prime }\text{G}{5}^{\prime }\text{C}{5}^{\prime }$ geometry.

Figure 7

(Color online) Projected density of states and charge-density plots for two different device setups comprising 6 base-pair pGpC DNA strands attached to Au electrodes. In the top (bottom) left panel we show the charge density corresponding to the HO orbital on the DNA molecule connected in the $\text{C}{3}^{\prime }\text{G}{3}^{\prime }$ $\left(\text{G}{5}^{\prime }\text{G}{3}^{\prime }\right)$ geometry. In the central top (bottom) panel the projected DOS for the $\text{C}{3}^{\prime }\text{G}{3}^{\prime }$ $\left(\text{G}{5}^{\prime }\text{G}{3}^{\prime }\right)$ setup is displayed. The HO and LU molecular states are indicated by arrows. Finally in the top (bottom) right panel we present the charge density corresponding to the LU orbital on the DNA molecule connected in the $\text{C}{3}^{\prime }\text{G}{3}^{\prime }$ $\left(\text{G}{5}^{\prime }\text{G}{3}^{\prime }\right)$ geometry.

Figure 8

(Color online) Finite-bias transport properties of the $\text{C}{3}^{\prime }\text{G}{3}^{\prime }$ molecule-electrode configuration. In the left panel we show the $I\text{−}V$ curve. Note that the current is displayed in logarithmic scale and that for $V<0$ we actually show the negative of the real current $\left(-I\right)$. In the central and right panels we present, respectively, the transmission coefficients as a function of energy at different bias voltages and the potential drop across the scattering region. In the $T\left(E\right)$ plots the vertical dashed lines mark the bias windows.

Figure 9

(Color online) Finite-bias transport properties of the $\text{G}{5}^{\prime }\text{G}{3}^{\prime }$ molecule-electrode configuration. In the left panel we show the $I\text{−}V$ curve. Note that the current is displayed in logarithmic scale and that for $V<0$ we actually show the negative of the real current $\left(-I\right)$. In the central and right panels we present, respectively, the transmission coefficients as a function of energy at different bias voltages and the potential drop across the scattering region. In the $T\left(E\right)$ plots the vertical dashed lines mark the bias windows.

Figure 10

(Color online) A 6 base-pair pGpC molecule in wet conditions. In (a) we show the scattering-region setup. This consists of a 6 base-pair pGpC $A$-DNA strand surrounded by a few layers of solvent including water molecules and ${\text{Na}}^{+}$ counterions. In (b) we show the planar average of the electrostatic potential across the system at zero bias. The green line shows the electrostatic potential in the absence of the solvent while the black line shows the potential averaged over 100 time snapshots of the system taken from the classical MD simulations. The gray lines show the electrostatic potential for the individual snapshots.

Figure 11

(Color online) Histograms showing the number of times, $N$, a certain molecular energy level is located within the energy interval given by the position and bin width of the corresponding histogram bar. The purple lines in panel (a) represent the HOMO and LUMO levels of the DNA strand in the absence of the solvent. The dashed lines represent the averages taken over the histograms. Panels (b)–(d) show the distribution of the highest (lowest) occupied (unoccupied) molecular levels localized on individual Guanine (Cytosine) bases. The Guanine bases labeled G1, G2, etc. are arranged from left to right with Guanine G1 at the $5^{\prime }$ end and G6 at the $3^{\prime }$ end.

Figure 12

(Color online) Projected DOS for different components of the DNA and solvent system. The bold dark lines show the PDOS averaged over the 100 MD snapshots. PDOS from all the individual snapshots are shown in gray.

Figure 13

(Color online) Zero-bias transmission coefficient and corresponding DOS for one representative time snapshot of the DNA and solvent system taken from classical MD simulations.