Two-band tight-binding model for push–pull polyenes

Abstract

We propose a two-band model for the description of the electronic structure of push–pull polyenes in order to analyze in simple ways their potentially useful electronic and optical features. The polyene part is described by two (valence and conduction) bands, which are coupled with two tight-binding frontier orbitals representing the donor and acceptor end groups. In this model, the ground state consists of the one-electron states of the (π) valence band hybridized with the donor orbitals, while the charge-transfer excited state is described as an excitation from the highest occupied molecular orbital to the lowest unoccupied molecular orbital, the latter being a hybridized one-electron state between the (π*) conduction band and the acceptor orbital. It is shown, by the Green’s function method, that the electron localizations (the partial density of states) at the end groups are determined by three factors; (1) the unperturbed energy levels of the frontier orbitals, (2) the density of states of the unperturbed polyene bands, and (3) the coupling constants between the π (π*) band and the donor (acceptor) orbital. Based on the results, a simple description is provided for the characteristic nonlinear optical responses and the intramolecular adiabatic charge-transfer mechanism of push–pull polyenes. In order to estimate the magnitude of the coupling constants, we compare the analytical results from the model with numerical calculations based on an established semiempirical method. This kind of modeling provides guidance for the design of functional push–pull polyenes.