Charge transfer along DNA dimers, trimers and polymers

The transfer of electrons and holes along DNA dimers, trimers and polymers is described at the base-pair level, using the relevant on-site energies of the base-pairs and the hopping parameters between successive base-pairs. The temporal and spatial evolution of carriers along a $N$ base-pair DNA segment is determined, solving a system of $N$ coupled differential equations. Useful physical quantities are calculated including the pure mean carrier transfer rate $k$, the inverse decay length $\beta$ used for exponential fit ($k = k_0 \textrm{exp}(-\beta d)$) of the transfer rate as a function of the charge transfer distance $d = N \times$ 3.4 {\AA} and the exponent $\eta$ used for a power law fit ($k = k_0' N^{-\eta}$) of the transfer rate as function of the number of monomers $N$. Among others, the electron and hole transfer along the polymers poly(dG)-poly(dC), poly(dA)-poly(dT), GCGCGC..., ATATAT... is studied. $\beta$ ($\eta$) falls in the range $\approx$ 0.2 - 2 {\AA}$^{-1}$ (1.7 - 17), $k_0$ ($k_0'$) is usually $\approx 10^{-2}$-10$^{-1}$ ($ 10^{-2}$-10$^{-1}$) PHz although, generally, it falls in the wider range $\approx 10^{-4}$-10 ($10^{-4}$-10$^3$) PHz. The results are compared with past predictions and experiments. Our approach illustrates to which extent a specific DNA segment can serve as an efficient medium for charge transfer.