  In many transition-metal oxides and dichalcogenides, the electronic and
lattice degrees of freedom are strongly coupled, giving rise to remarkable
phenomena, such as metal-insulator transition (MIT) and charge-density wave
(CDW) order. We study this interplay by tracing the instant electronic
structure under ab initio molecular dynamics. Applying this method to a 1T-TaS2
layer, we show that the CDW-triggered Mott gap undergoes a continuous reduction
as the lattice temperature raises, despite a nearly constant CDW amplitude.
Before the CDW order undergoes a sharp first-order transition around the room
temperature, the dynamical CDW fluctuation already shrinks the Mott gap size by
half. The gap size reduction is one order of magnitude larger than the lattice
temperature variation. Our calculation not only provides an important clue to
understand the thermodynamics behavior in 1T-TaS2, but also demonstrates a
general approach to quantify the lattice entropy effect in MIT.
