Time-dependent density functional calculations of fully π-conjugated zinc oligoporphyrins

Time-dependent density functional theory (TDDFT) calculations were performed on the excitation energies and oscillator strengths of fully π-conjugated zinc oligoporphyrins. The TDDFT calculated results for the Q bands of the triply meso-meso-, β-β-, and β-β-linked zinc oligoporphyrins can well reproduce the significantly increasing redshifted and intensified absorption maximum for the increasing number of porphyrins in the experimental data, which originates from the greater stabilized lowest unoccupied molecular orbital (LUMO) and the increasing contribution of the highest occupied molecular orbital $(\mathrm{HOMO}\mathrm{)\to }\mathrm{LUMO}$ excitation to the bands. In order to estimate the minimum value of the $\mathrm{HOMO}-\mathrm{LUMO}$ energy gap ${\mathrm{(E}}_g)$ of the infinite size oligoporphyrins, the DFT solid-state calculations for the one-dimensional tapelike and two-dimensional sheetlike π-conjugated zinc porphyrins were carried out using periodic boundary conditions. The results show that there is a metallic energy gap, $E_g\text{≈0.0\hspace{0.17em}}\mathrm{eV}$ for the tape, and a semiconducting one, $E_g\text{≈0.5\hspace{0.17em}}\mathrm{eV}$ for the sheet, which is caused by the difference in the local periodic structures at the minimum energy gap between them, namely the directly and indirectly connected zinc porphyrins for the former and the latter, respectively. Similarly, the corresponding infinite fused free-base porphyrins were also examined for comparison, which showed that a metallic behavior is also expected for them. The present fused porphyrin arrays may be used as conducting molecular wires or films.