Table 2. Analysis of the intrinsic errors of the density functionals with respect to CCSD(T) reference values, Δω_intrinsic, and estimates of the shifts due to NQE, Δω_NQE, in the bonded O–H vibrational frequencies of four different water clusters. The ω_DFT were calculated in Q-Chem with the def2-QZVPPD basis set and a (250 974) grid. Units are cm^–1.

Cluster bonded O–H errors	Δωintrinsic a = ωCCSD(T) – ωDFT			ΔωNQE b = ωexp – ωAIMD – Δωintrinsic
	revPBE-D3	B97M-rV	M06-L-D3	revPBE-D3	B97M-rV	M06-L-D3
Dimer	168	–5	29	–303	–202	–226
Trimer	191	–4	46	–252	–196	–236
Tetramer	240	–16	51	–270	–236	–205
Pentamer	252	–17	51	–374	–249	–310

	〈ΔΔωNQE〉clusters b			Predicted bonded O–H stretch in liquid
All clusters	–300	–220	–244	3104	3402	3331

^aNegative values correspond to blue shifts.

^bNegative values correspond to red shifts upon the treatment of nuclei dynamics quantum mechanically. The bonded OH frequencies have been averaged, and the values in the table are calculated using the raw data given in Tables S8 and S9.