Electronic structures of $A$- and $B$-type DNA crystals

The electronic band structures and total density of states based on a density-functional theory are performed on four deoxyribonucleic acid (DNA) molecules: namely, $A$- and $B$-type DNA where a single pitch is formed by 11 and 10 base pairs, respectively, of $\mathrm{Poly}\left(\mathrm{dA}\right)\bullet \mathrm{Poly}\left(\mathrm{dT}\right)$ and $\mathrm{Poly}\left(\mathrm{dG}\right)\bullet \mathrm{Poly}\left(\mathrm{dC}\right)$. $\mathrm{Poly}\left(\mathrm{dA}\right)\bullet \mathrm{Poly}\left(\mathrm{dT}\right)$ is a DNA where one single strand consists only of adenine (A) and the other single strand consists only of thymine (T), while $\mathrm{Poly}\left(\mathrm{dG}\right)\bullet \mathrm{Poly}\left(\mathrm{dC}\right)$ is a DNA where one single strand consists only of guanine (G) and the other of cytosine (C). $A$- and $B\text{−}\mathrm{Poly}\left(\mathrm{dA}\right)\bullet \mathrm{Poly}\left(\mathrm{dT}\right)$ and $A$- and $B\text{−}\mathrm{Poly}\left(\mathrm{dG}\right)\bullet \mathrm{Poly}\left(\mathrm{dC}\right)$ DNA. Compared in the same structure, the band gap of $\mathrm{Poly}\left(\mathrm{dA}\right)\bullet \mathrm{Poly}\left(\mathrm{dT}\right)$ is larger than that of $\mathrm{Poly}\left(\mathrm{dG}\right)\bullet \mathrm{Poly}\left(\mathrm{dC}\right)$. The highest occupied molecular orbitals (HOMO’s) of $\mathrm{Poly}\left(\mathrm{dA}\right)\bullet \mathrm{Poly}\left(\mathrm{dT}\right)$ and $\mathrm{Poly}\left(\mathrm{dG}\right)\bullet \mathrm{Poly}\left(\mathrm{dC}\right)$ are formed by adenine’s and guanine’s HOMO, respectively, regardless of the structure type. On the other hand, the lowest unoccupied molecular orbitals (LUMO’s) of DNA of both types are formed by the orbitals of Na and $\mathrm{P}{\mathrm{O}}_4$, though the LUMO’s of $B\text{−}\mathrm{Poly}\left(\mathrm{dA}\right)\bullet \mathrm{Poly}\left(\mathrm{dT}\right)$ and $B\text{−}\mathrm{Poly}\left(\mathrm{dG}\right)\bullet \mathrm{Poly}\left(\mathrm{dG}\right)$ are formed by thymine’s and cytosine’s LUMO when the DNA-DNA distance is more than $3\mathrm{nm}$. The minimum energy gap between the valence edge and the empty state of Na and $\mathrm{P}{\mathrm{O}}_4$ is $0.9\mathrm{eV}$ in $A\text{−}\mathrm{Poly}\left(\mathrm{dG}\right)\bullet \mathrm{Poly}\left(\mathrm{dC}\right)$. The narrow bandwidth of the valence and conduction bands show that the conduction arises not from band transport but a hopping mechanism in the presence of doping.

Figure 1

(Color) Side and top views of the crystal structure of (a) $A$-type DNA and (b) $B$-type DNA with $a=3\mathrm{nm}$. The green dot shows the Na atom.

Figure 2

(Color) Electronic band structures and total density of states of (a) $A\text{−}\mathrm{Poly}\left(\mathrm{dA}\right)\bullet \mathrm{Poly}\left(\mathrm{dT}\right)$ and (b) $A\text{−}\mathrm{Poly}\left(\mathrm{dG}\right)\bullet \mathrm{Poly}\left(\mathrm{dC}\right)$ with $a=3\mathrm{nm}$. The Fermi levels are set to $0\mathrm{eV}$.

Figure 3

(Color) Side views of the isosurface plot of (a) the HOMO and (b) the LUMO of $A\text{−}\mathrm{Poly}\left(\mathrm{dG}\right)\bullet \mathrm{Poly}\left(\mathrm{dC}\right)$ with $a=3\mathrm{nm}$ at the $\Gamma$ point. The blue and yellow isosurfaces show positive and negative isovalues, respectively. The isosurfaces have a value of 0.01.

Figure 4

(Color) Electronic band structures and total density of states of (a) $B\text{−}\mathrm{Poly}\left(\mathrm{dA}\right)\bullet \mathrm{Poly}\left(\mathrm{dT}\right)$ with $a=3\mathrm{nm}$, (b) $B\text{−}\mathrm{Poly}\left(\mathrm{dG}\right)\bullet \mathrm{Poly}\left(\mathrm{dC}\right)$ with $a=3\mathrm{nm}$, and (c) $B\text{−}\mathrm{Poly}\left(\mathrm{dG}\right)\bullet \mathrm{Poly}\left(\mathrm{dC}\right)$ with $a=2.5\mathrm{nm}$. The Fermi levels are set to $0\mathrm{eV}$.

Figure 5

(Color) Side views of the isosurface plot of (a) the HOMO and (b) the LUMO of $B\text{−}\mathrm{Poly}\left(\mathrm{dG}\right)\bullet \mathrm{Poly}\left(\mathrm{dC}\right)$ at the $\Gamma$ point with $a=3\mathrm{nm}$, and (c) the LUMO with $a=2.5\mathrm{nm}$. The blue and yellow isosurfaces show positive and negative isovalues, respectively. The isosurfaces have a value of 0.01.