Recently, our group developed a new framework of incorporating nuclear quantum effects in MD simulations through CMESs . In conventional PES-based MD simulations, nuclei are treated as point charges that are highly localized in space. This treatment loses the quantum delocalization picture for nuclei. In contrast, in CMES-MD, nuclei are treated quantum mechanically, but instead of directly evolving the quantum nuclei rigorously according to the time-dependent Schrödinger equation, we invoke an adiabatic assumption that every time the nuclei evolve to a quantum state with certain expectation positions and expectation momenta (X, P), the system always relaxes to the energy-minimized quantum state with the same (X, P). Under this assumption, it can be proved that the nuclear expectation positions and expectation momenta evolve classically according to the Newton's law of motion but with a caveat that nuclei evolve on the effective potential energy surface, i.e., the CMES, instead of the conventional PES.