Absolute error / kcal mol -1 the loss in speed-up compared to the smaller cc-pVTZ-MP2FIT is only minor. The density fitting error of the proton-proton and electronproton contribution which depend both on the nuclear density fitting basis set was also discussed in prior mentioned works from the Hammes-Schi↵er group. In our work we constantly employ the 10s10p10d10f set as nuclear density fitting basis which leads to an absolute deviation of 4•10 8 kcal mol 1 for the largest protonated water cluster including 13 quantum protons. This is for all purposes a negligible error. This high accuracy of the nuclear density fitting can be exploited for the computation of the electron-proton correlation where the protonic part is treated with the density fitting approximation. This leads to an absolute deviation of 4•10 4 kcal mol 1 for the electron-proton correlation energy of the largest protonated water cluster. This is generally consistent with the error of the proton-proton correlation since the absolute contribution of the electron-proton correlation is four orders of magnitude higher than the proton-proton correlation. Although the employed nuclear density fitting basis set seems fairly large, the actual impact of the total computational timing is minor even for very large systems. This is demonstrated in the next section. Overall, the absolute error of the density fitting approximation within the NEO-MP2 method is governed by the fitting of the electron-electron correlation terms.