Electronic Structure of Zinc-5,10,15,20-tetraethynylporphyrin: Evolution from the Molecule to a One-Dimensional Chain, a Two-Dimensional Covalent Organic Framework, and a Nanotube

Zinc-5,10,15,20-tetraethynylporphyrin (Zn-TEP) has been used as a building block to prepare one-dimensional (1D) chains, two-dimensional (2D) covalent organic frameworks, as well as nanotubes that represent molecular analogues of carbon nanotubes. It is of interest then to evaluate the electronic-structure evolution of Zn-TEP from the zero-dimensional (0D) molecule to the 1D chain, the 2D COF, and the nanotubes. Here, based on density functional theory calculations, we discuss the effects of dimensionality on the electronic structure of Zn-TEP by describing the fundamental relationship between the frontier molecular orbitals of Zn-TEP and the electronic bands in periodic lattices. Wavevector-independent flat bands appear in all the periodic systems due to the absence of wave function contribution on the meso carbons in the Zn-TEP frontier molecular orbitals. A zone-folding approach coming from a tight-binding model effectively captures the connection between the 2D COF and the nanotube when applying periodic boundary conditions along the circumferential direction around the nanotubes. Importantly, the Zn-TEP nanotube has a totally flat lowest conduction band, which provides an organic material platform to explore a variety of many-body phenomena.