As to H 3 O - 2 , since both CCSD(T) and DFT optimized geometries are asymmetric, there is only the bound OH stretch mode instead of the proton transfer mode. Because of the incorrect physical picture, all their vibrational frequencies are significantly higher than the experimental reference values. It is also noteworthy that these DFT harmonic frequencies are extremely sensitive to the choice of the electronic functional, although it seems that ωB97X is still the best functional that matches the CCSD(T) result most. Based on the wrong physical picture, DFT-VPT2 gives even more unphysical results with all three functionals giving imaginary frequencies, indicating the failure of the perturbative treatment in such a double-well system. In contrast, CNEO-DFT gives much more reliable results with a quantum mechanical treatment on nuclei. Even though the result is still sensitive to the choice of the electronic functional, we found that ωB97X as the best functional that matches CCSD(T) most, manages to give the most accurate CNEO-DFT frequency compared to the experimental reference. All these results demonstrate that the quantum treatment on transferring proton is key to the qualitatively correct description of the proton transfer modes. Among the three functionals tested, since ωB97X is the best one that has the least error from the electronic part, we use it for AIMD simulations. To differentiate conventional paper, we call them conventional AIMD and CNEO-MD, respectively. Figure shows the IR predissociation spectra of the H 5 O + 2 • Ne complex and the simulated spectra for H 5 O + 2 using conventional AIMD and CNEO-MD. According to the experimental spectra, the proton transfer mode has strong absorption at 1047 cm -1 . However, there is an additional strong absorption at 928 cm -1 . The capture and assignment of the 928 cm -1 peak with theoretical simulations have been particularly challenging. MCTDH is the most reliable method that has successfully reproduced the Fermi resonance and characterized it as the resonance between the proton transfer mode and the combination band of the water wagging motion and O-O stretch motion. Conventional AIMD underestimates the proton transfer mode frequency, whereas CNEO-MD overestimates the mode frequency, which are consistent with the DFT harmonic results and CNEO-DFT harmonic results, respectively. Interestingly, for CNEO-MD, in addition to the main proton transfer mode absorption at about 1138 cm -1 , we additionally see a satellite peak at 1104 cm -1 . Through normal coordinate analysis on the CNEO-MD trajectory using Trajectory Analyzer and Visualizer, we find that both the main peak and the satellite peak have significant contributions from proton transfer motion and the wagging motion of water molecules (Supporting Information, Figure ).