Throughout this work all NEO calculations are carried out with the PB4-F2 nuclear basis set together with the even tempered 10s10p10d10f fitting basis set with exponents ranging from 2 p 2 to 64 using Molpro. The cc-pVTZ electronic basis set for the benchmark calculations of our DF-NEO-MP2 and NEO-PNO-LMP2 implementations was employed together with the cc-pVXZ-JKFIT density fitting basis set at the X=T triple zeta and X=Q quadruple zeta level. The reference wave function was build by DF-NEO-RHF for the DF-NEO-MP2 method and LDF-NEO-RHF for the NEO-PNO-LMP2 method. Thereby, we set a threshold of 10 8 a.u. for the energy di↵erence within the electronic and nuclear SCF computations, the di↵erence in the density between iterations and the gradient of the respective nuclear and electronic subiterations. The overall energy di↵erence in the NEO-RHF iterations was set to a threshold of 10 7 Hartree for all systems besides the DNA strands where the threshold was set to 10 6 Hartree. All SCF computations employ the direct inversion in the iterative subspace starting after the first iteration with a maximum of 10 Fock matrices as basis to extrapolate. All results following the benchmark calculations are obtained for the wave function from DF-NEO-RHF with the settings mentioned before. However, in order to provide the most suitable basis set for the explicitly correlated methods the electronic basis set was changed to cc-pVTZ-F12 with the cc-pVQZ-JKFIT density fitting basis for the Fock and the exchange matrices as well as the complementary auxiliary basis set for the resolution of the identity and the cc-pVQZ-MP2FIT density fitting basis set. The presented F12B energies were obtained by employing the 3*A(LOC,FIX) ansatz with very tight domain settings and corrected by the complementary auxiliary basis set singles correction together with the scaling of the perturbative triples. The water tetramers and methanol-furan complexes were optimized with Gaussian16 employing the def2-TZVPP basis set with very tight SCF settings, tight optimization thresholds and a superfine grid utilizing B2PLYP-D3(BJ) and additionally for the methanol-furan complexes DSDPBEP86-D3(BJ) as well as B3LYP-D3(BJ). Energies and frequencies shown in this work were obtained with the same settings. In case of the proton-bound dimer of hydrogen sulfate and formate the structures were taken from Thomas et al.. According to their original work, the energies and frequencies were recomputed utilizing the aforementioned settings and the aug-cc-pVTZ basis set. All computations include the D3 dispersion correction with Becke-Johnson damping. The DNA model was constructed with Avogadro 1.2.0. 58 All nuclear densities shown are at a 0.01 contour level generated with the PyMOL 2.5.2 program. The DF-NEO-MP2 benchmark calculations were computed on a commercially available Intel ® Xeon ® Gold 6226R 2.90 GHz CPU with 8 threads and the NEO-PNO-LMP2 benchmark calculations utilized a commercially available Intel ® Xeon ® Gold 6342 2.80 GHz CPU with 8 threads.