Abstract
The study of the charge transfer processes in biomacromolecules such as DNA is essential for the development of nanobioelectronics, design and construction of DNA-based nanowires, memory devices, logical elements, etc. Mathematical and computer modeling of charge transfer in biopolymer chains is an important part of these investigations. Some properties of charge transfer can be demonstrated by modeling of two-site chain. Based on the semi-classical Holstein model we consider a system of two sites and charged particle (electron or hole) in which the oscillations of the first site are not related to the charge motion, and the parameters of the second site correspond to a small-radius polaron. The system steady states depending on the electron energy H at the second site are studied numerically. The dynamics of the charge initially localized at the first site is modeled. Various modes depending on H are demonstrated: charge tunneling, resonant transfer, and lack of transfer.
Highlights
Mathematical modeling of charge transfer processes in biological systems is associated with the use of discrete models, in which the paths of charge transfer in macromolecules are considered
Some important properties of the dynamics of selfconsistent quantum-classical systems can be demonstrated by the example of a two-site model
As H > 0 increases to ≈ 1.55 (with this value of F(r) it touches the abscissa axis at the point r ≈ 0.45), the picture does not change – the system has one stationary mode, when the charge with the probability ≈ 1 is localized at the second site (Fig. 1, gray curve)
Summary
Mathematical modeling of charge transfer processes in biological systems is associated with the use of discrete models, in which the paths of charge transfer in macromolecules are considered. One of the first polaron models of charge propagation in a onedimensional chain was proposed by Holstein [4]. He considered a homogeneous chain of molecules (sites) as a chain of harmonic oscillators, under the assumption that the displacement of the site from the equilibrium position affects the charge energy at this site. In this work we consider a simple heterogeneous case when displacements of the first site do not interact with a charge. The model is based on the Holstein Hamiltonian for a discrete chain of sites [4], which in dimensionless variables [12] have the form. In the presence of dissipation in the classical subsystem, the evolution of the system will continue until it reaches one of its stationary states
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
