Phonon spectrum of Eu$_{2}$Sn$_{2}$O$_{7}$: ab initio calculation

Crystal structure and phonon spectrum of crystal Eu$_{2}$Sn$_{2}$O$_{7}$ were studied within the framework of density functional theory and MO LCAO approach. The calculations were performed by using hybrid functional that takes into account both local and nonlocal (in the Hartree–Fock formalism) exchange. The calculations were performed in the CRYSTAL17 program intended for simulating periodic structures in the MO LCAO approximation. The fundamental vibration frequencies of Eu$_{2}$Sn$_{2}$O$_{7}$ were calculated. The frequencies, intensities and types of the Raman and the IR-active modes have been calculated. An analysis of the displacement vectors obtained from the ab initio calculation, made it possible to estimate the degree of the ion participation in the vibrational mode. The elastic constants of the crystal have been calculated too.