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.
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