Bandgap oscillation in polyphenanthrenes

The electronic structures of carbon-based ladder polymers and polynuclear aromatic hydrocarbons (PAHs) with acene- and phenanthrene-edge structures are studied with an approximate molecular-orbital method, The difference between polyacene and polyphenanthrene can be derived from detailed orbital interaction analyses of anthracene and phenanthrene. The fragment molecular-orbital (FMO) method successfully characterizes the distinct electronic structures of the two small PAHs with different types of edges. We shed light on the electronic structures of ladder polymers with the phenanthrene-edge structure, PPh(n), in which n is the number of cis-polyene chains included. With an increase in width of the ladder polymers, the bandgap of PPh(n) approaches zero with a behavior that has a periodicity of 3. The PPh(n) series are classified into three subgroups: small-gap (metallic) PPh(3m + 1), large-gap PPh(Sm + 2), and medium-gap PPh(3m), where m = 0, 1, 2, .... The oscillating behavior in the bandgap of the three subgroups is analyzed from the viewpoint of interchain interactions in the frontier crystal orbitals.