and CCSD(T) mainly comes from the electronic error. Therefore, the good performance of DFT-PBE0 is accidentally caused by the error cancellation from the electronic part and the classical nuclear part. In this sense, the ωB97X functional is the best electronic functional for this system with similar performance to CCSD(T). For DFT-VPT2, although it is generally a reliable method for calculating anharmonicity, it fails badly for this system with the proton transfer mode frequency significantly overestimated by more than 300 cm -1 . In fact, it is known that the proton transfer modes in shared proton systems are especially challenging for VPT2 because the local higher order derivative information is not sufficient to capture the behavior of the whole surface. In contrast, even with a harmonic approximation, CNEO-DFT is able to give reasonably good descriptions for the proton transfer modes with slightly overestimated frequencies. The frequencies by CNEO-DFT are also sensitive on the choice of the electronic functional, but we find that ωB97X is the best-performing functional here, which overestimates the proton transfer mode frequency by ~80 cm -1 . Considering DFT-ωB97X gives the closest results to CCSD(T) with the least error from the electronic part, this result is inspiring because it indicates that CNEO-DFT performs well when the underlying electronic functional is reliable, which suggests the accurate description of the quantum proton by CNEO-DFT.