Octacalcium phosphate (OCP), which is one of the bioactive calcium phosphates, can incorporate various organic molecules in its crystal lattice, forming the organic-inorganic hybrid derivatives. However, detailed atomic arrangements of OCP hybridized with organic molecules such as dicarboxylate are still unknown, although many years have passed since the first discovery of the materials systems. In the present study, some black-box optimization methods combined with first-principles calculations were used to theoretically identify the most stable atomic structure of the OCP with the incorporation of malonate ions as a typical case study. The results showed that the calculated interplanar spacing on the (100) plane of the most stable structure agrees well with experimental data, by taking account of implicit solvent of aqueous solution. An underlying mechanism that realizes the bridging feature of the incorporated malonate ions between the apatitic layers is also discussed. The present methodology can pave the way to accurately explore reliable atomic structures of such complicated organic-inorganic hybrid biomaterials with high structural degrees of freedom.
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