Based on the individually optimized geometries, we calculate the harmonic vibrational frequencies with DFT and CNEO-DFT. The results are shown in Table . For comparison, we additionally include DFT-VPT2 results and a prior literature results using the DVR analysis in two-dimensional (2D) and four-dimensional (4D) PESs. Note that because pure electronic DFT-B3LYP and DFT-ωB97X calculations break the C 2 symmetry of AHA -, leading to completely different normal modes that cannot correspond well to the experimental results, here we do not present their poor results. In AHA -, there are two modes that have significant contributions from the proton transfer mode. The reason is that the proton transfer mode ν ∥ and a hybridized carboxylate deformation mode δ(OCO) OOP have the same B symmetry within the C 2 point group and thus can linear combine to form two new modes, both of which involve a large displacement of the shared proton along the O-O direction. These two coupled modes are denoted as mode 1 and mode 2 in Table and Figure .