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 polymer. We study HOMO and LUMO 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 β for exponential fits k(d), where d is the charge transfer distance, and the exponent η for power law fits k(N ) 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(d) or k(N ) becomes steeper and show the range covered by β and η. Finally, both for the time-independent and the time-dependent problem, we analyze the palindromicity and the degree of eigenspectrum dependence of the probabilities to find the carrier at a particular monomer.

We employ two Tight-Binding (TB) approaches to study the electronic structure and hole or electron transfer in B-DNA monomer polymers and dimer polymers made up of N monomers (base pairs): (I) at the base-pair level, using the on-site energies of base pairs and the hopping integrals between successive base pairs, i.e., a wire model and (II) at the single-base level, using the on-site energies of the bases and the hopping integrals between neighboring bases, i.e., an extended ladder model since we also include diagonal hoppings. We solve a system of M D ("matrix dimension") coupled equations [(I) M D = N , (II) M D = 2N ] for the time-independent problem, and a system of M D coupled 1 st order differential equations for the time-dependent problem. We study the HOMO and the LUMO eigenspectra, the occupation probabilities, the Density of States (DOS) and the HOMO-LUMO gap as well as the mean over time probabilities to find the carrier at each site [(I) base pair or (II) base)], the Fourier spectra, which reflect the frequency content of charge transfer (CT) and the pure mean transfer rates from a certain site to another. The two TB approaches give coherent, complementary aspects of electronic properties and charge transfer in B-DNA monomer polymers and dimer polymers.

Abstract. We call monomer a B-DNA base pair and study, analytically and numerically, electron or hole oscillations in monomers, dimers and trimers. We employ two Tight Binding (TB) approaches: (I) at the base-pair level, using the on-site energies of the base pairs and the hopping parameters between successive base pairs i.e. a wire model, and (II) at the single-base level, using the on-site energies of the bases and the hopping parameters between neighbouring bases, specifically between (a) two successive bases in the same strand, (b) complementary bases that define a base pair, and (c) diagonally located bases of successive base pairs, i.e. an extended ladder model since it also includes the diagonal hoppings (c). For monomers, with TB II, we predict periodic carrier oscillations with frequency f ≈ 50-550 THz. For dimers, with TB I, we predict periodic carrier oscillations with f ≈ 0.25-100 THz. For trimers made of identical monomers, with TB I, we predict periodic carrier oscillations with f ≈ 0.5-33 THz. In other cases, either with TB I or TB II, the oscillations may be not strictly periodic, but Fourier analysis shows similar frequency content. For dimers and trimers, TB I and TB II are successfully compared giving complementary aspects of the oscillations.

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