Small Polarons in Dry DNA

We report ab initio calculations for positively charged fragments of dry poly(dC)-poly(dG) DNA, with up to 4 C-G pairs. We find a strong hole-lattice coupling and clear evidence for the formation of small polarons. The largest geometry distortions occur in only one or two base pairs. They involve the stretching of weak bonds within each base pair, increasing the distance of positive hydrogens, and decreasing that of negative oxygens, to the region in which the hole localizes. We obtain an energy of $\sim 0.30\mathrm{e}\mathrm{V}$ for the polaron formation, nearly independent of the chain size. From it, we can estimate an activation energy for polaron hopping of $\sim 0.15\mathrm{e}\mathrm{V}$, consistent with the available experimental value.

Figure 1

Polaron binding energies $E_b^{(n)}$, calculated with the Holstein Hamiltonian of Eq. (1), as a function of the number $n$ of base pairs of the chain, and normalized to the case $n=1$. The curves correspond to different values of the parameter $B=A^2/Kt$. The black dots correspond to $B=64$, obtained from the values of $E_b$ and $t$ calculated from first principles.

Figure 2

Upper part: structure of a single DNA base pair with the guanine on the left. $d_1$, $d_2$, and $d_3$ are the interatomic distances that change the most after charging the system. Lower part: isosurface of constant electron density for the same system, colored from grey to dark grey (blue online) proportionally to the square of the hole wave function.

Figure 3

Upper panel: amount of hole charge on each guanine for the four-base-pair DNA fragment. Lower panels: corresponding changes in the distances $d_1$, $d_2$, and $d_3$.