We call monomer a B-DNA base pair and examine, analytically and numerically, electron or hole oscillations in monomer and dimer polymers, i.e., periodic sequences with repetition unit made of one or two monomers. We employ a tight-binding (TB) approach at the base-pair level to readily determine the spatiotemporal evolution of a single extra carrier along a $N$ base-pair B-DNA segment. We study highest occupied molecular orbital and lowest unoccupied molecular orbital eigenspectra as well as the mean over time probabilities to find the carrier at a particular monomer. We use the pure mean transfer rate $k$ to evaluate the easiness of charge transfer. The inverse decay length $\beta$ for exponential fits $k\left(d\right)$, where $d$ is the charge transfer distance, and the exponent $\eta$ for power-law fits $k\left(N\right)$ are computed; generally power-law fits are better. We illustrate that increasing the number of different parameters involved in the TB description, the fall of $k\left(d\right)$ or $k\left(N\right)$ becomes steeper and show the range covered by $\beta$ and $\eta$. Finally, for both the time-independent and the time-dependent problems, we analyze the palindromicity and the degree of eigenspectrum dependence of the probabilities to find the carrier at a particular monomer.

• Received 10 April 2015
• Revised 13 July 2015
• Corrected 24 May 2016

DOI:https://doi.org/10.1103/PhysRevE.92.032725