  A systematic study of electron or hole transfer along DNA dimers, trimers and
polymers is presented with a tight-binding approach at the base-pair level,
using the relevant on-site energies of the base-pairs and the hopping
parameters between successive base-pairs. A system of $N$ coupled differential
equations is solved numerically with the eigenvalue method, allowing the
temporal and spatial evolution of electrons or holes along a $N$ base-pair DNA
segment to be determined. Useful physical quantities are defined and calculated
including the maximum transfer percentage $p$ and the pure maximum transfer
rate $\frac{p}{T}$ for cases where a period $T$ can be defined, as well as the
pure mean carrier transfer rate $k$ and the speed of charge transfer $u=kd$,
where $d = N \times$ 3.4 {\AA} is the charge transfer distance. The inverse
decay length $\beta$ used for the exponential fit $k = k_0 \exp(-\beta d)$ and
the exponent $\eta$ used for the power law fit $k = k_0' N^{-\eta}$ are
computed. The electron and hole transfer along polymers including
poly(dG)-poly(dC), poly(dA)-poly(dT), GCGCGC..., ATATAT... is studied, too.
$\beta$ falls in the range $\approx$ 0.2-2 {\AA}$^{-1}$, $k_0$ is usually
10$^{-2}$-10$^{-1}$ PHz although, generally, it falls in the wider range
10$^{-4}$-10 PHz. $\eta$ falls in the range $\approx$ 1.7-17, $k_0'$ is usually
$\approx 10^{-2}$-10$^{-1}$ PHz, although generally, it falls in the wider
range $\approx10^{-4}$-10$^3$ PHz. Finally, the results are compared with the
predictions of Wang et al. Phys. Rev. Lett. 93, (2004) 016401, as well as
experiments, including Murphy et al. Science 262, 1025 (1993); Arkin et al.
Science 273, 475 (1996); Giese et al. Angew. Chem. Int. Ed. 38, 996 (1999);
Giese et al. Nature 412, 318 (2001). This method allows to assess the extent at
which a specific DNA segment can serve as an efficient medium for charge
transfer.
