Second-order elastic constants of hexagonal hydroxylapatite (P63) from ab initio quantum mechanics: Comparison between DFT functionals and basis sets

Three very popular Hamiltonians in the density functional theory framework, PBE, PBEsol, and B3LYP, and different basis sets (Gaussian-type orbitals and plane waves) were employed to simulate the hydroxylapatite unit cell and its second-order elastic constants. Dispersive interactions were included in the quantum-mechanical treatment via the DFT-D2 and Tkatchenko-Scheffler schemes. The calculated bulk, shear, and Young's moduli were in the range of 82-117 GPa, 42-51 GPa, and 107-134 GPa, respectively. The axial moduli, Kaand Kb, were instead in the range of 277-322 GPa and 506-509 GPa. The theoretical data, especially those from plan waves simulations, are in good agreement with available results in literature and further extend the knowledge of the mechanical and vibrational properties of hydroxylapatite.