Theoretical study of two‐dimensionally fused zinc porphyrins: DFT calculations

Abstract

AbstractElectronic structures of D4h square‐fused zinc porphyrin sheets of two types (SA, SB), where SA is a directly meso‐meso‐, β‐β‐, and β‐β‐linked array and SB is a directly β‐fused array, were compared using density functional theory (DFT). The highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of oligomeric SAn are characteristically delocalized at the cyclooctatetraene‐like sites composed of β‐pyrrolic carbons and their nearest‐neighbor nitrogens. Those of oligomeric SBn remain solitary monomeric features, reflecting weakly interacting porphyrin units. These two‐dimensionally (2D) square‐fused sheets, especially for SAn, show effective reduction of both the HOMO–LUMO energy gaps (Eg) and the lowest Q‐like excitation energies because of LUMO's greater stabilization with increasing number of porphyrins than the corresponding one‐dimensionally (1D) linear‐fused tapes. To estimate the minimum value of Eg, the electronic band structures of the infinite‐fused SA∞ and SB∞ were examined in detail using modern periodic DFT. Results indicate a full metal for SA∞, with HOMO and LUMO bands crossing the Fermi level, and a semiconductor with Eg ≈ 0.5 eV for SB∞. Furthermore, the phonon modes and the electron–phonon coupling (EPC) constant of SA∞ were calculated throughout the Brillouin zone using density functional perturbation theory (DFPT), yielding a weak EPC constant, λ = 0.35. Within the standard phonon‐mediated BCS mechanism, the superconducting transition temperature, Tc is demonstrated using the McMillan formula, predicting ≈0.5 K. Results show that SA∞ will become a rare synthetic metal/superconductor without a metal‐insulator transition coming from Peierls lattice instability because it has no serious imaginary phonon modes. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009