Negative thermal expansion in TiF₃ from the first-principles prediction

Highlights: • Rhombohedral TiF₃ as a new NTE material is predicted from first-principles calculation. • The NTE mechanism is proposed based on the analysis of vibrational properties. • The rotation coupling of TiF₆ octahedra at low frequencies is most responsible for NTE. - Abstract: In negative thermal expansion (NTE) materials, rhombohedral TiF₃ as a new member is predicted from first-principles calculation. The NTE behavior of rhombohedral TiF₃ occurs at low temperatures. In our work, the NTE mechanism is elaborated in accordance with vibrational modes. It is confirmed that the rigid unit mode (RUM) of internal TiF₆ octahedra in low-frequency optical range is most responsible for the NTE properties