DFT Investigation of carbonate substituted hydroxyapatite by Infrared Spectra

Carbonate substitution in hydroxyapatite significantly alters its vibrational response, yet experimental infrared (IR) assignments remain ambiguous due to overlapping features from distinct defect configurations. We present a systematic first-principles study of the IR signatures of carbonate defects in hydroxyapatite using density functional theory molecular dynamics. A dataset of 33 structurally distinct carbonate-substituted models, including bulk and surface substitutions with various charge-compensation schemes, was constructed. IR spectra were obtained from finite-temperature dipole autocorrelation functions. Comparative analysis of peak positions, intensities, and line shapes reveals quantitative structure-spectra relationships that uniquely link specific carbonate environments to their vibrational fingerprints. Surface-associated carbonate defects produce a characteristic OH-stretching doublet near 3600 cm⁻¹. Substitution of phosphate by carbonate leads to diagnostic features in the 1100-1500 cm⁻¹ region whose positions and relative intensities depend on the number of substituted phosphate groups and proton/hydroxyl compensation. The local hydrogen-bonding environment is found to modulate ν(CO₃²⁻) band frequencies and shapes. These results provide a physically grounded reference for interpreting experimental IR spectra of carbonated apatites and demonstrate the utility of first-principles vibrational spectroscopy for resolving defect chemistry in complex inorganic solids.