calculation of vibrational spectra, and here we adopted the PBE0 52,53 functional for both CNEO-DFT and DFT calculations as it was previously found that PBE0 is the best functional for free X-H stretches as benchmarked against the CCSD(T) method for a series of small organic molecules, where X is a heavy atom such as carbon, nitrogen and oxygen. However, because hydrogen bonds are not present in the small organic molecules that were benchmarked before, here for water cluster systems, we additionally benchmarked several commonly used functionals against CCSD(T) on the O-H stretch modes in H 4 O 2 .