A first principles study of the mechanical, electronic, and vibrational properties of lead oxide

The first principles study of the crystal structure, chemical bonds, elastic and mechanical properties, electron energy band structure and density, and normal long-wave vibrations of nine phases of lead monoxide, dioxide, and tetraoxide has been performed under normal and external pressure within the framework of density functional theory (DFT) with the Perdew–Becke–Ernzerhof (PBE) gradient exchange-correlation functional and its hybrid version with a 25% Hartree–Fock (HF) exchange contribution in the basis of localized atom orbitals. The behavior of physical parameters has been studied using the cold four- and threeparameter equations of state. The parameters of the crystal structures are in satisfactory agreement with experimental data, and elastic constants indicate their mechanical stability and anisotropy in the elastic properties. The elasticity, shear, and Young moduli, hardness, acoustic velocities, and Debye temperature of dioxide on the one hand and monoxide and tetraoxide on the other hand appreciably differ from each other. The difference between electron properties may be explained by the character of hybridization in the upper filled and lower empty energy bands as evident from the density of states. In monoxide, the indirect band gap width decreases with increasing pressure at a rate of 0.16 eV/GPa, and the direct band gap width increases at a rate of 0.13 eV/GPa. To identify crystalline phases, the frequencies and intensities of long-wave modes active in IR and Raman spectra have been calculated.