Geometric and electronic structures of two-dimensionally polymerized triptycene: covalent honeycomb networks comprising triptycene and polyphenyl

Abstract

On the basis of the density functional theory with generalized gradient approximation, we investigated the geometric and electronic structures of two-dimensional covalent networks consisting of triptycene and phenyl groups, which are alternately arranged hexagonally. Calculated total energies of the networks are 48–63 meV per atom higher than that of an isolated benzene, indicating that the networks are energetically stable. All networks were semiconductors with a moderate band gap at the Γ point, the value of which is inversely proportional to the length of polyphenyl connecting triptycene. According to a kagome topology of π electrons distributed on sp2 hydrocarbons, the characteristic kagome energy bands consisting of a flat dispersion band and a Dirac cone emerge in valence and conduction states whose structure is sensitive to the mutual orientation of phenyl groups with respect to the polymer chain.