Tuning Band Gap Energies in Pb3(C6X6) Extended Solid-State Structures

Abstract

A detailed plane-wave density functional theory investigation of the solid-state properties of the extended organometallic system Pb3C6X6 for X = O, S, Se, and Te has been performed. Initial geometry parameters for the Pb–X and C–X bond distances were obtained from optimized calculations on molecular fragment models. The Pb3C6X6 extended-solid molecular structures were constructed in the space group P6/mmm on the basis of the known structure for X = S. Ground-state geometries, band gap energies, densities of states, and charge densities were calculated with the PBE-generalized gradient exchange-correlation functional and the HSE06 hybrid exchange-correlation functional. The PBE band gap energies were found to be lower than the HSE06 values by >0.7 eV. The band energies at points of high symmetry along the first Brillouin zone in the crystal were larger than the overall band gap of the system. Pb3C6O6 was predicted to be a direct semiconductor (Γ point) with a PBE band gap of 0.28 eV and an HSE06 band gap of 1.06 eV. Pb3C6S6 and Pb3C6Se6 were predicted to have indirect band gaps. The PBE band gap for Pb3C6S6 was 0.98 eV, and the HSE06 band gap was 1.91 eV. The HSE06 value is in good agreement with the experimentally observed band gap of 1.7 eV. Pb3C6Se6 has a PBE band gap of 0.56 eV and a HSE06 band gap of 1.41 eV. Pb3C6Te6 was predicted to be metallic with both of the PBE and HSE06 functionals. A detailed analysis of the PBE band structure and partial density of states at two points before and after the metallic behavior reveals a change in orbital character indicative of band crossing in Pb3C6Te6. These results show that the band gap energies can be fine-tuned by changing the substituent X atom.