Electronic Structure of Wet DNA

The electronic properties of a $Z$-DNA crystal synthesized in the laboratory are investigated by means of density-functional theory Car-Parrinello calculations. The electronic structure has a gap of only 1.28 eV. This separates a manifold of 12 occupied states which came from the $\pi$ guanine orbitals from the lowest empty states in which the electron is transferred to the $\mathrm{N}{\mathrm{a}}^{\mathrm{+}}$ from $\mathrm{P}{\mathrm{O}}_{\mathrm{4}}^{\mathrm{-}}$ groups and water molecules. We have evaluated the anisotropic optical conductivity. At low frequency the conductivity is dominated by the $\pi \to \mathrm{N}{\mathrm{a}}^{\mathrm{+}}$ transitions. Our calculation demonstrates that the cost of introducing electron holes in wet DNA strands could be lower than previously anticipated.

Figure 1

View of the three-dimensional structure of the Gua:Cyt dodecamer [11] (a) along, (b) orthogonal to the $\mathbf{c}(z)$ axis. Water molecules, counterions, and hydrogens have been removed for clarity. The sugar-phosphate backbone is represented as ribbons.

Figure 2

(a) H bond pattern of water droplets present in the minor grooves; (b) Comparison of the H bond pattern obtained by ab initio (white and red molecules) and molecular mechanics (orange molecules); and (c) Histogram of the dipole moment distribution of the water molecules; the dipole of water in the bulk [21] and gas [22] phase are represented in green and red, respectively.

Figure 3

(a) Electronic charge density ${\rho }_e(z)$ along the $z$ axis integrated over the $x$ and $y$ directions. The integrals are performed only in regions surrounding the Gua basis. These regions are defined as the union of all the cubes of side 2.1 Å which have a guanosine atom at their center. In red we show the ${\rho }_e(z)$ of the top state. The black line give the total ${\rho }_e(z)$ of the manifold. (b) Schematic level diagram around the Fermi level. The Fermi level positioned in the middle of the gap has been chosen as the zero of energy.

Figure 4

(a) Side and top view of the electronic density isosurface associated with the manifold of the 12 top states of the valence band. (b) Top and side view of the electronic density isosurface associated with the manifold of the 12 low states of the conduction band. The isosurfaces represented have a value of ${10}^{-2}$ electrons ${\AA }^{-3}$.

Figure 5

Optical conductivity (${\Omega }^{-1}\mathrm{c}{\mathrm{m}}^{\mathrm{-}\mathrm{1}}$) versus frequency (eV). (a) ${\sigma }_{\mathrm{a}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{g}\mathrm{e}}(\omega )$, (b) ${\sigma }_{\parallel }(\omega )$, and (c) ${\sigma }_{\perp }(\omega )$. The orange histograms are the contribution to the total conductivity (gray) due to excitations ending on the $\mathrm{N}{\mathrm{a}}^{\mathrm{+}}$ electron transfer virtual states. The continuous black line in the right-hand figures is the average conductivity.