We study the energy structure and the transfer of an extra electron or hole along periodic polymers made of N monomers, with a repetition unit made of P monomers, using a tight-binding wire model, where a site is a monomer (e.g., in DNA, a base pair), for P even, and deal with two categories of such polymers: made of the same monomer (GC…, GGCC…, etc.) and made of different monomers (GA…, GGAA…, etc.). We calculate the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) eigenspectra, density of states, and HOMO-LUMO gap and find some limiting properties these categories possess, as P increases. We further examine the properties of the mean over time probability to find the carrier at each monomer. We introduce the weighted mean frequency of each monomer and the total weighted mean frequency of the whole polymer, as a measure of the overall transfer frequency content. We study the pure mean transfer rates. These rates can be increased by many orders of magnitude with appropriate sequence choice. Generally, homopolymers display the most efficient charge transfer. Finally, we compare the pure mean transfer rates with experimental transfer rates obtained by time-resolved spectroscopy.

We report on the electronic structure, density of states and transmission properties of the periodic one-dimensional tight-binding (TB) lattice with a single orbital per site and nearest-neighbor hoppings, with a generic unit cell of u sites. The determination of the eigenvalues is equivalent to the diagonalization of a real tridiagonal symmetric u-Toeplitz matrix with (cyclic boundaries) or without (fixed boundaries) perturbed upper right and lower left corners. We solve the TB equations via the Transfer Matrix Method, producing analytical solutions and recursive relations for its eigenvalues, closely related to the Chebyshev polynomials. We examine the density of states and provide relevant analytical relations. We attach semi-infinite leads, determine and discuss the transmission coefficient at zero bias and investigate the peaks number and position, and the effect of the coupling strength and asymmetry as well as of the lead properties on the transmission profiles. We introduce a generic optimal coupling condition and demonstrate its physical meaning.