Because here protons are relatively localized with little overlap between each other, they were treated as distinguishable particles and no proton-proton correlation was included. We did not include electron-proton correlation (epc), either, because we have previously found that without an epc functional, CNEO-DFT and CNEO-MD are already sufficiently accurate for vibrational spectra calculations. We leave the investigation of epc effects for future studies. Both DFT and CNEO-DFT harmonic analyses were performed using a locally modified version of PySCF, which is available through our group Github. 67