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In DFT, we usually call the "equilibrium position" as the ion positions that corresponds to the global minimum of the (ground-state) Born-Oppenheimer potential energy surface (PES).

Let's consider a solid with only one atom in the unit cell. If I perform Born-Oppenheimer Molecular dynamics at 300 K, the atom will not stay at the "equilibrium position" and will vibrate.

My question is: Will the long-time average of instantaneous position of the atom in MD equal the above "equilibrium position"? (I know in the harmonic approximation of PES, this will hold)

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