Interestingly, similar observations had been made in the development of NEO-TDDFT for calculating proton vibrational excitations. As shown in Table .1.1 of Ref. 53, the vibrational excitation energies from NEO-TDDFT with no-epc and with the epc17-2 functional both match well with grid-based reference values, whereas those from the epc17-1 functional are far less accurate. Therefore, in both NEO-TDDFT and CNEO, it can be concluded that better proton densities are neither sufficient nor necessary conditions for obtaining accurate vibrational frequencies. The accurate descriptions of vibrational frequencies may be a delicate balance of electronic effects and quantum delocalization effects, and the future development of CNEO wave function theories, such as CNEO many-body perturbation theory and CNEO coupled cluster theory, may provide deeper insights into this topic.