A large energy separation between the optical and acoustic modes implies that the ionic bonds between the atoms are very "rigid" and thus "hard" to vibrate. By decreasing this energy gap, the lattice becomes softer and softer, until one of the optical modes reaches Zero-energy. This leads to a phenomenon called polar instability, causing the entire lattice to undergo a structural change, forming a non-centrosymmetric lattice with a net electrical polarity.

More specifically speaking, while acoustic modes lead to a collective dragging of the entire lattice along certain crystalline directions, the optical modes cause more complicated vibrational patterns, such as breathing mode, stretch mode, wag mode etc. The latter, however, require sufficiently soft ionic bonds. Depending on this "softness", the resulting optical modes can either appear above the acoustic modes or overlap with them.

Dear Abhinav Nag ,

A phonon band gap between the acoustic and optical modes may affect the phonon scattering processes and thus the lattice thermal conductivity. A large band gap indicates a low scattering-process rate and large phonon lifetime which means that the lattice thermal conductivity is relativity high. A small bandgap indicates a high scattering-process rate and a short lifetime which means that the lattice thermal conductivity is relatively low.

Bests,

Nima