It has been known in the multicomponent quantum chemistry community that, without electron-proton correlations, calculated proton densities tend to be overly localized. The inclusion of electron-proton correlations, particularly with functionals such as epc17-1, can lead to more delocalized proton densities, which better align with grid-based methods. The delocalization of proton densities received considerable attention because it was used to obtain proton vibrational frequencies before the development of NEO time-dependent density functional theory (NEO-TDDFT) and the invention of the CNEO framework. As such, many electron-proton correlation functionals, including the epc17, epc18, 54 and epc19 55 families were developed to yield more delocalized proton densities compared to calculations without electron-proton correlations. Calculations at the no-epc level produce the most localized proton densities, while the inclusion of the epc17-1 functional generates the most delocalized densities, with the epc17-2 functional falling in between. Based on past experience, one might expect that epc17-1, which provides the most delocalized densitiy, would yield the most accurate frequency for the PTM. However, this is not the case within the CNEO framework, where vibrational frequencies are obtained from the effective energy surface of CNEO rather than directly through the extent of proton densitiy delocalization. Although delocalization impacts the absolute zero-point energies, the accuracy of vibrational frequencies depends more on the relative energies, or more rigorously, the second-order derivatives of the energy surfaces. Therefore, although CNEO-DFT with epc17-1 produces a more delocalized density close to grid-based references while conventional DFT gives the most localized density, their performances in predicting vibrational frequencies can be equally bad.