Electronic structure and carrier transfer in B-DNA monomer polymers and dimer polymers: Stationary and time-dependent aspects of wire model vs. extended ladder model

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 \textit{extended} ladder model since we also include diagonal hoppings. We solve a system of $MD$ ("matrix dimension") coupled equations [(I) $MD$ = $N$, (II) $MD$ = $2N$] for the time-independent problem, and a system of $MD$ coupled $1^\text{st}$ 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.