Trapping and hopping of bipolarons in DNA: Su-Schrieffer-Heeger model calculations

With the Su-Schrieffer-Heeger model involving the effects of solvent polarization and external electric field, we show that a bipolaron maybe more stable than two polarons when a dication is induced into a DNA stack. Under the high electric field, the dication can move quite a long distance through the DNA by a series of hopping process, partially losing its configuration instantaneously due to the nonadiabatic effects.

Figure 1

Energy levels for the random DNA stack with no external field nor e-e interaction concerned. (a) Neutral state, (b) polaron state induced by one hole doping, and (c) bipolaron state induced by two holes doping. The zero of energy is the on-site energy of the $T$ base. The $\pi \text{−}\pi \ast$ gap of DNA is $\sim 3.75\mathrm{eV}$ (see Ref. 3) and the polaron/bipolaron gap level is $0.35∕0.72\mathrm{eV}$ above the highest filled level.

Figure 2

Dication population (a) and the lattice distortion (b) for the random DNA stack under three conditions, without e-e interaction (solid lines), with nonscreened (dash lines), and with screened e-e interaction (dot lines). The inset in (a) shows the bipolaron self-trapping at a G/C-singlet site in a sequence containing no G/C multiplet. The inset in (b) shows the favorable screening to the formation of bipolaron.

Figure 3

$\Delta E^{\mathrm{cr}}$ of a bipolaron and two polarons as a function of the total site number $N$ at $f_s=0.8$. The inset shows the dependence of $\Delta E^{\mathrm{cr}}$ on $f_s$ at $N=28$.

Figure 4

The excess charges distribution as a function of time and site under electric field $\mathcal{E}=20{\mathcal{E}}_0$ at $f_s=0.8$. The inset shows the evolution of the occupation number of the bipolaron energy level. The occupation number of bipolaron level between 13.5 and 20 ps implies a strong mixed gap state due to the nonadiabatic effects under high electrical field.