Electronic structure and bonding in calcium apatite crystals: Hydroxyapatite, fluorapatite, chlorapatite, and bromapatite

Abstract

We present a detailed analysis of the electronic structure, bonding, charge transfer, and optical properties of selected perfect-crystal calcium apatites [${\mathrm{Ca}}_{10}{({\mathrm{PO}}_{4})}_{6}{X}_{2}$ with $X={(\mathrm{OH})}^{\ensuremath{-}},{\mathrm{F}}^{\ensuremath{-}},{\mathrm{Cl}}^{\ensuremath{-}}$, or ${\mathrm{Br}}^{\ensuremath{-}}$]. The ab initio orthogonalized linear combinations of atomic orbitals-density-functional-theory-based computational method is used to obtain the band structure, total and partial density of states, bond order, Mulliken effective charge, dielectric constant, and energy-loss function for each system. Band results indicate that these materials are all wide band-gap insulators in the range of $\ensuremath{\sim}5.3\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. The bonding results show that the systems are dominated by two sets of structures: a ${\mathrm{PO}}_{4}$ sublattice and Ca channels populated by ion columns of $X$. The exact positions and orientations of the ions in the Ca channels are subject to debate on many levels. To contribute to the discussion, we analyze the position and orientation of the hydroxyl group from hydroxyapatite along the Ca channel using total-energy comparisons.