type clusters using DFT and CNEO-DFT. The X-H bond lengths in the optimized structures are listed in Table , where X stands for the heavy atom which is closer to the shared proton. The harmonic vibrational frequencies of the PTMs in these clusters are presented in Table , along with experimental references. DFT harmonic calculations consistently overestimate the vibrational frequencies of these modes, with a mean absolute error (MAE) of 452 cm -1 . In contrast, the MAE significantly reduces to 123 cm -1 when using the CNEO-DFT approach without electron-proton correlations. This finding is consistent with the previous results, showing that CNEO-DFT, even with a purely harmonic treatment, can accurately describe hydrogen-related vibrations as a result of the quantum delocalized Wavenumber / cm In ensi y / a.u.