Structure and lattice dynamics of PrFe$_{3}$(BO$_{3}$)$_{4}$: Ab initio calculation

The crystal structure and phonon spectrum of PrFe$_{3}$(BO$_{3}$)$_{4}$ are ab initio calculated in the context of the density functional theory. The ion coordinates in the unit cell of a crystal and the lattice parameters are evaluated from the calculations. The types and frequencies of the fundamental vibrations, as well as the line intensities of the IR spectrum, are determined. The elastic constants of the crystal are calculated. A “seed” frequency of the vibration strongly interacting with the electron excitation on the praseodymium ion is obtained for low-frequency $A_2$ mode. The calculated results are in agreement with the known experimental data.