Ab initiocomputation of the transition temperature of the charge density wave transition inTiSe2

We present a density functional perturbation theory approach to estimate the transition temperature of the charge density wave transition of $\mathrm{TiS}{\mathrm{e}}_{2}$. The softening of the phonon mode at the $L$ point where in $\mathrm{TiS}{\mathrm{e}}_{2}$ a giant Kohn anomaly occurs, and the energy difference between the normal and distorted phase are analyzed. Both features are studied as functions of the electronic temperature, which corresponds to the Fermi-Dirac distribution smearing value in the calculation. The transition temperature is found to be 500 and 600 K by phonon and energy analysis, respectively, in reasonable agreement with the experimental value of 200 K.