is the CNEO-DFT energy surface. Note that CNEO-MD is essentially an AIMD method using the energies and gradients of CNEO-DFT computed on-the-fly at each MD step. Compared with conventional DFT-based AIMD, CNEO-MD only leads to a small increase in computational cost (<15 % with recent implementation) but much more accurate vibrational spectra with quantum nuclear delocalization effects incorporated. 3 COMPUTATIONAL DETAILS