Hard tissues (e.g., bone, enamel, dentin) in vertebrates perform various and different functions, from sustaining the body to haematopoiesis. Such complex and hierarchal tissue is actually a material composite whose static and dynamic properties are controlled by the subtle physical and chemical interplay between its components, collagen (main organic part) and hydroxylapatite-like mineral. The knowledge needed to fully understand the properties of bony and dental tissues and to develop specific applicative biomaterials (e.g., fillers, prosthetics, scaffolds, implants, etc.) resides mostly at the atomic scale. Among the different methods to obtains such detailed information, atomistic computer simulations (in silico) have proven to be both corroborative and predictive tools in this subject. The authors have intensively worked on quantum mechanical simulations of bioapatite and the present work reports a detailed review addressed to the crystal-chemical, physical, spectroscopic, mechanical, and surface properties of the mineral phase of bone and dental tissues. The reviewed studies were conducted at different length and time scales, trying to understand the features of hydroxylapatite and biological apatite models alone and/or in interaction with simplified collagen-like models. The reported review shows the capability of the computational approach in dealing with complex biological physicochemical systems, providing accurate results that increase the overall knowledge of hard tissue science.

Apatite minerals draw the attention of many researchers not only in mineralogy, but also in biology, biochemistry, and medicine because hydroxylapatite [Ca₁₀(PO₄)₆(OH)₂] is the main component of the mineral phase of mammalian bones. However, in nature this mineral is mostly present with various stoichiometric defects. The carbonate ion is found commonly in its structure where it can occupy different crystallographic sites; however, its configurational energy and relative orientation in the apatite lattice is still debated. In this work, bulk structural features of hexagonal hydroxylapatite (space group P6₃) and type A carbonated apatite [Ca₁₀(PO₄)₆(CO₃), space group P1] have been modeled by density function method using the hybrid B3LYP functional and an all-electron polarized double-ζ quality Gaussian-type basis set using the CRYSTAL09 computer program. The effect on the structural parameters due to the adoption of the present all-electron basis set for the Ca ion compared to the pseuodpotential adopted in previous work has also been discussed. Different orientations of the carbonate ion in the apatite unit cell have been considered. The B3LYP functional and Gaussian-type basis set with polarization have been adopted. The geometry of the model (lattice parameters and internal coordinates) has been fully optimized and resulted in very good agreement with XRD data reported in literature that suggest a “close” configuration (type A1) of the carbonate ion, i.e., with a C-O bond perpendicular to the c-axis of the apatite cell.

In nature, hydroxylapatite [Ca₁₀(PO₄)₆(OH)₂] is mostly present with various stoichiometric defects. The most abundant is the carbonate ion that can occupy different crystallographic sites (namely A and B types), however, its effects on the apatite structure is still an object of debate. Type A carbonated apatite was quantum mechanically simulated in a previous study, here we extend the simulation to bulk structural and vibrational features of Na-bearing type B and mixed type A-B carbonated hydroxylapatite [Ca_10−xNa_x(PO₄)_6−x(CO₃)_x+y(OH)_2(1−y), space group P1]. The simulation has been performed by ab initio density functional methods. The geometry of the models (lattice parameters and internal coordinates) have been fully optimized exploring different positions of the sodium ion in the apatite unit cell. The results, in agreement with XRD data, suggest that in each crystallographic cell in the biological mineral there is at least one calcium ion substitution or vacancy per cell. The carbonate ion presence in the apatite structure is in good agreement with biological/chemical data. Furthermore, there is also a very good agreement with FTIR data reported in literature.