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Hydroxyapatite is a biomaterial that has great importance in the medical field and is commonly used as an implant to replace amputated bone in tissue and organ transplants and in drug delivery systems. Quantum chemistry is based on the density functional theory (DFT), which is an important tool for understanding structural arrangements and explaining the physicochemical properties of complexes. This work is mainly based on the synthesis of hydroxyapatite using the double-decomposition method. Fine hydroxyapatite powder was characterized by different techniques such as infrared spectroscopy, the X-ray diffraction method, scanning electron microscopy and density measurement. The crystalline microstructure of hydroxyapatite is hexagonal with lattice parameters a = b = 9.4260 Å and c = 6.8850 Å and space group P63/m. Hydroxyapatite has a porous surface particle morphology with a regular spherical shape. An agreement between the energies and the vibrational frequency of connection which are characteristic of the infrared spectrum. The geometry of the complex isolated using the DFT method was optimized in open air and in various solvents. Different functionals were chosen to determine the energies of excitation and the forces of the associated oscillator of the studied complex. Theoretical absorption spectra were obtained using the GaussView and Origin software programs.

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