Three-dimensional covalent networks of sp2 and sp3 C atoms: energetics and electronic properties of polymerized diphenylmethane and tetraphenylmethane

Abstract

Based on the density functional theory with the generalized gradient approximation, we investigate geometric and electronic structures of three-dimensional covalent organic frameworks of polymerized diphenylmethane and tetraphenylmethane in which phenyl and biphenyl are arranged in a tetrahedral manner connected via methane vertexes. These three-dimensional covalent networks are energetically stable with the total energy of 90 and 65 meV atom−1 for diphenylmethane and tetraphenylmethane polymers, respectively, with respect to that of diamond. Polymerization reactions of diphenylmethane and tetraphenylmethane are endothermic with the reaction energy of 1.62 and 0.68 eV, respectively. These polymers have the peculiar electronic band structures in their valence and conduction states, which consist of the combination of the doubly degenerate flat band and two dispersive states forming a Dirac cone at the W point. The wavefunction analyzes and the simple tight-binding calculations reveal that the peculiar electron states are ascribed to the delicate balance between inter- and intra-phenyl/biphenyl π electron transfers, indicating that these polymers could be regarded as the three-dimensional kagome or pyrocroa networks with the internal degree of freedom.