First, we benchmark the performance of the two composite NEO variants on one of the most prominent test cases for multicomponent methods, the energetic ordering of protonated water tetramers. The commonly used gold standard for electronic structure calculations CCSD(T) fails to predict the correct energetic ordering of the four isomers. This can only be restored adequately when anharmonic zero-point vibrations are included or multicomponent methods are employed directly. In our previous work we demonstrated that the correct ordering can be achieved qualitatively by employing CCSD(T) energies with a correction based on the LDF-NEO-RHF reference wave function. The now quantitative results from NEO-PNO-LMP2-F12 and NEO(MP2)-PNO-LCCSD(T)-F12 are shown in Fig. with corresponding values provided in Tab. S2.