  We show that the inclusion of screened exchange via hybrid functionals
provides a unified description of the electronic and vibrational properties of
TiSe2. In contrast to local approximations in density functional theory, the
explicit inclusion of exact, non-local exchange captures the effects of the
electron-electron interaction needed to both separate the Ti-d states from the
Se-p states and stabilize the charge-density-wave (CDW) (or low-T) phase
through the formation of a p-d hybridized state. We further show that this
leads to an enhanced electron-phonon coupling that can drive the transition
even if a small gap opens in the high-T phase. Finally, we demonstrate that the
hybrid functionals can generate a CDW phase where the electronic bands, the
geometry, and the phonon frequencies are in agreement with experiments.
