Single-electron model for polaron on dimerized lattice

A new approach to modeling the electronic and dynamic properties of dimerized polyacetylene is proposed. Compared to the well-known and widely used approach, where dimerization is formed by the $\pi$-electrons of the valence band, in the proposed model the same effect is provided by an additional potential in the dynamic part of the Hamiltonian. In the usually used computational schemes, for a lattice of $N$ sites, $N$ $\pi$-electrons have to be used to describe dimerization, so the total number of equations for quantum and classical dynamics is approximately equal to $N^2/2$. The integration step is dictated by the “fast” quantum subsystem and should be small. Both of these reasons make modeling difficult at large times and scales. In the proposed approach, in contrast to the $N$-electronic model, for describing a polaron on a dimerized lattice, the one-electron approximation is sufficient when the electron occupies the lowest level of the conduction band. Thus, the number of basis functions decreases to $3N$, which allows to carry out calculations on large scales and times.