Calcium orthophosphates (CaPs) are the hard constituents of bones and teeth, and thus of ultimate importance to humankind, while amorphous CaPs (ACPs) may play crucial roles in CaP biomineralization.Among the various ACPs with Ca/P atomic ratios between 1.0~1.5, an established structural model exists for basic ACP (Ca/P=1.5), while those of other ACPs remain unclear. Herein, the structure of amorphous calcium hydrogen phosphate (ACHP; Ca/P=1.0) obtained via aqueous routes at near-neutral pH values, without stabilizers, was studied by experiments (mainly, TEM with ED, XRD, IR and NMR spectroscopies, as well as EXAFS) and computer simulation. Our results globally show that ACHP has a distinct short-range structure, and we propose calcium hydrogen phosphate clusters (CHPCs) as its basic unit. This model is consistent with both computer simulations, and the experimental results, where CHPCs are arranged together with water molecules to build up ACHP. We demonstrate that Posner's clusters, which are conventionally accepted to be the building unit of basic ACPs, do not represent the short-range structure of ACHP, as Posner's clusters and CHPCs are structurally distinct. This finding is important not only for the determination of the structures of diverse ACPs with varying Ca/P atomic ratios, but also for fundamental understanding of a major mineral class that is central to biomineralization in vertebrates, and, thus, humans, in particular.

A new force field has been derived for the aqueous calcium phosphate system that aims to reproduce the key thermodynamic properties of the system, including free energies of hydration of the ions and the solubility of the solid mineral phases. Interactions of three phosphate anions (PO, HPO, and HPO) with water were calibrated through comparison with the results obtained from ab initio molecular dynamics using both GGA and hybrid density functional theory with dispersion corrections. In the solid state, the force field has been evaluated by benchmarking against experiment and other existing models and is shown to reproduce the structural and mechanical properties well, despite the primary focus being on thermodynamics. To validate the force field, the thermodynamics of ion pairing for calcium phosphate species in water has been computed and shown to be in excellent agreement with experimental data.

Classical molecular dynamics simulations and free energy methods have been used to obtain a better understanding of the molecular processes occurring prior to the first nucleation event for calcium phosphate biominerals. The association constants for the formation of negatively charged complexes containing calcium and phosphate ions in aqueous solution have been computed, and these results suggest that the previously proposed calcium phosphate building unit, [Ca­(HPO4)3]4–, should only be present in small amounts under normal experimental conditions. However, the presence of an activation barrier for the removal of an HPO4 2– ion from this complex indicates that this species could be kinetically trapped. Aggregation pathways involving CaHPO4, [Ca­(HPO4)2]2–, and [Ca­(HPO4)3]4– complexes have been explored with the finding that dimerization is favorable up to a Ca/HPO4 ratio of 1:2.

Biominerals are crucial materials that play a vital role in many forms of life. Understanding the various steps through which ions in aqueous environment associate to form increasingly structured particles that eventually transform into the final crystalline or amorphous poly(a)morph in the presence of biologically active molecules is therefore of great significance. In this context, computer modeling is now able to provide an accurate atomistic picture of the dynamics and thermodynamics of possible association events in solution, as well as to make predictions as to particle stability and possible alternative nucleation pathways, as a complement to experiment. This review provides a general overview of the most significant computational methods and of their achievements in this field, with a focus on calcium carbonate as the most abundant biomineral.

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