We employ two tight-binding (TB) approaches to systematically 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 onsite 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 onsite 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 $M$ (matrix dimension) coupled equations [(I) $M=N$, (II) $M=2N]$ for the time-independent problem, and a system of $M$ coupled first order differential equations for the time-dependent problem. We perform a comparative study of stationary and time-dependent aspects of the two TB variants, using realistic sets of parameters. The studied properties include HOMO and LUMO eigenspectra, occupation probabilities, density of states and HOMO-LUMO gaps as well as mean over time probabilities to find the carrier at each site [(I) base pair or (II) base], Fourier spectra, which reflect the frequency content of charge transfer, and 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.

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.

This review is devoted to tight-binding (TB) modeling of nucleic acid sequences like DNA and RNA. It addresses how various types of order (periodic, quasiperiodic, fractal) or disorder (diagonal, non-diagonal, random, methylation et cetera) affect charge transport. We include an introduction to TB and a discussion of its various submodels [wire, ladder, extended ladder, fishbone (wire), fishbone ladder] and of the process of renormalization. We proceed to a discussion of aperiodicity, quasicrystals and the mathematics of aperiodic substitutional sequences: primitive substitutions, Perron–Frobenius eigenvalue, induced substitutions, and Pisot property. We discuss the energy structure of nucleic acid wires, the coupling to the leads, the transmission coefficients and the current–voltage curves. We also summarize efforts aiming to examine the potentiality to utilize the charge transport characteristics of nucleic acids as a tool to probe several diseases or disorders.

Atomic carbon wires represent the ultimate one-atom-thick one-dimensional structure. We use a Tight-binding (TB) approach to determine the electronic structure of polyynic and cumulenic carbynes, in terms of their dispersion relations (for cyclic boundaries), eigenspectra (for fixed boundaries) and density of states (DOS). We further derive the transmission coefficient at zero-bias by attaching the carbynes to semi-infinite metallic leads, and demonstrate the effect of the coupling strength and asymmetry to the transparency of the system to incident carriers. Finally, we determine the current–voltage (I–V) characteristics of carbynes and study the effect of factors such as the weakening of the coupling of the system to one of the leads, the relative position of the Fermi levels of the carbyne and the leads, the leads' bandwidth and, finally, the difference in the energy structure between the leads. Our results confirm and reproduce some of the most recent experimental findings.

We study periodic, quasiperiodic (Thue-Morse, Fibonacci, period doubling, Rudin-Shapiro), fractal (Cantor, generalized Cantor), Kolakoski, and random binary sequences using a tight-binding wire model, where a site is a monomer (e.g., in DNA, a base pair). We use B-DNA as our prototype system. All sequences have purines, guanine (G) or adenine (A), on the same strand, i.e., our prototype binary alphabet is $\{\mathrm{G},\mathrm{A}\}$. Our aim is to examine the influence of sequence intricacy and magnitude of parameters on energy structure, localization, and charge transport. We study quantities such as autocorrelation function, eigenspectra, density of states, Lyapunov exponents, transmission coefficients, and current-voltage curves. We show that the degree of sequence intricacy and the presence of correlations decisively affect the aforementioned physical properties. Periodic segments have enhanced transport properties. Specifically, in homogeneous sequences transport efficiency is maximum. There are several deterministic aperiodic sequences that can support significant currents, depending on the Fermi level of the leads. Random sequences is the less efficient category.