Semiempirieal Electronic Structure Calculation on Ga and Pb Apatites

A systematic study is made on the electronic structure of stoichiometric calcium and lead apatites, using the tight binding extended Hückel method (eHT). The aim is to investigate the applicability of the semiempirieal theory to study this family of compounds. A ₁₀(BO ₄) ₆X ₂ (A = Ca, Pb) apatites, differing by substitutions in the BO ₄ tetrahedral unit (B = P, As, and V) and X-channel ion (X = OH, Cl), are considered. The calculations show that eHT is suitable to describe basic properties especially concerning trends with atomic substitution and geometry changes. Band structure, Mulliken charge distribution, and bond orders are in good agreement with results of ab initio density functional theory (DFT) found in the literature. Large variations in the optical gap due to vanadium and lead substitutions are newly found. Changes in the anion X-channel affect the optical gap, which is in close agreement with DFT results. Analysis involving subnets are performed to determine the role of halogenic orbitals in the electronic structure of chloroapatites, showing evidence of covalent Cl bonding. It was also found that Pb-OH bonding in hydroxy-vanadinite Pb ₁₀(VO ₄)(OH) ₂, recently synthesized, is weaker than that of Ca-OH in vanadate Ca ₁₀(VO ₄) ₆(OH) ₂. Arsenium is found to be more weakely bound to the O-tetrahedron than phosphorous, although Ca-O bond is increased with the substitution. We investigate, in addition, the electronic structure of a model system Ca ₁₀(AsO ₄) ₆(OH) _2' obtained from direct As substitution in the vanadate Ca ₁₀(V0 ₄) ₆ (OH) ₂.