Lattice dynamics, force constants, and phonon dispersion in model ferroelastics Hg$_2$I$_2$

The dispersion dependences of the frequencies of acoustic and optical phonons have been calculated and plotted, and the density of states of the phonon spectrum of Hg$_2$I$_2$ crystals has been obtained. The influence of hydrostatic pressure on the frequency of acoustic and optical phonons and their dispersion has been theoretically analyzed. The slowest acoustic TA branch (soft mode) at the X point of the Brillouin-zone boundary exhibits strong softening with an increase in pressure.