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 <i>P</i>6/<i>mmm</i> 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