Model calculations on the band structures of one-dimensional mixed donor-acceptor systems

The band structures of one-dimensional donor-acceptor (D-A) stacks have been studied by means of the crystal-orbital (CO) formalism based on the tight-binding approximation. The model polymers of the present study are composed of quinhydrone moieties (10 and 11) where the donor and acceptor groups show either a parallel or a perpendicular orientation. These idealized systems have been adopted as models for D-A polymers in the recently synthesized class of D-A phanes. The strength of the D-A interaction has been modified due to alterations of the D-A distances within the unit cells and due to modifications in the effective electronegativity of the active groups (hydroxyl and carbonyl). The computational framework is a semiempirical intermediate neglect of differential overlap (INDO) CO formalism with a variable model Hamiltonian that allowed the simulation of the different types of D-A interactions (weak versus strong D-A pairs). An insulator-metal transition is predicted in the 0° arrangement of 10 for short D-A distances and larger differences in the electronegativities of both fragments. The 90° conformation shows an avoided crossing between the highest filled and the lowest unfilled $\epsilon \mathrm{}\left(k\right)\mathrm{}$ curves. This leads to a finite band gap for all studied interaction conditions. The band structures, the charge transfer in the D-A stacks, and the excited-state properties of 10 and 11 are analyzed as a function of the D-A geometry (distance, mutual orientation) and as a function of the strength of the D-A pairs. Semiquantitative solid-state models are compared with the INDO CO data, synthetic strategies for the design of D-A phanes with small (vanishing) band gaps are formulated, and various solid-state effects encountered in related low-dimensional D-A systems are briefly discussed.