Infrared absorption spectrum of brushite from first principles

Brushite, CaHPO₄·2H₂O, is a crystalline hydrated acidic form of calcium phosphate that occurs in both physiological and pathological biomineralization processes. Additionally, it is biocompatible in humans. Several groups have investigated the experimental Fourier transform infrared vibrational spectrum of brushite. These investigations have led to a long-standing debate concerning the correct assignment for a few of the observed frequencies, particularly, the water stretching and libration modes. Here, we perform a comprehensive first principles theoretical investigation of the vibrational spectrum of brushite with calculations based on dispersion-corrected density functional theory. We obtain both the vibrational frequencies, using the frozen phonon approach, and their corresponding peak intensities, based on the Born effective charge tensor. This allows for an unambiguous assignment of all vibrations, including water vibration and libration modes.